Title: On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay Auctions
Abstract: In first-price and all-pay auctions under the standard symmetric independent private-values model, we show that the unique Bayesian Coarse Correlated Equilibrium with symmetric, differentiable and strictly increasing bidding strategies is the unique strict Bayesian Nash Equilibrium. Interestingly, this result does not require assumptions on the prior distribution. The proof is based on a dual bound of the infinite-dimensional linear program. Numerical experiments without restrictions on bidding strategies show that for first-price auctions and discretisations up to 21 of the type and bid space, increasing discretisation sizes actually increase the concentration of Bayesian Coarse Correlated Equilibrium over the Bayesian Nash Equilibrium, so long as the prior c.d.f. is concave. Such a concentration is also observed for all-pay auctions, independent of the prior distribution. Overall, our results imply that the equilibria of these important class of auctions are indeed learnable.


Title: Inductive Synthesis of Finite-State Controllers for POMDPs
Abstract: We present a novel learning framework to obtain finite-state controllers (FSCs) for partially observable Markov decision processes and illustrate its applicability for indefinite-horizon specifications. Our framework builds on oracle-guided inductive synthesis to explore a design space compactly representing available FSCs. The inductive synthesis approach consists of two stages: The outer stage determines the design space, i.e., the set of FSC candidates, while the inner stage efficiently explores the design space. This framework is easily generalisable and shows promising results when compared to existing approaches. Experiments indicate that our technique is (i) competitive to state-of-the-art belief-based approaches for indefinite-horizon properties, (ii) yields smaller FSCs than existing methods for several models, and (iii) naturally treats multi-objective specifications.


Title: Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
Abstract: We show the existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation for homogeneous kernels satisfying $C_1 \left(x^{-a}y^{b}+x^{b}y^{-a}\right)\leq K\left(x,y\right)\leq C_2\left(x^{-a}y^{b}+x^{b}y^{-a}\right)$ with $a>0$ and $b<1$. This covers especially the case of Smoluchowski's classical kernel $K(x,y)=(x^{1/3} + y^{1/3})(x^{-1/3} + y^{-1/3})$. For the proof of existence we first consider some regularized kernel $K_{\epsilon}$ for which we construct a sequence of solutions $h_{\epsilon}$. In a second step we pass to the limit $\epsilon\to 0$ to obtain a solution for the original kernel $K$. The main difficulty is to establish a uniform lower bound on $h_{\epsilon}$. The basic idea for this is to consider the time-dependent problem and choosing a special test function that solves the dual problem.


Title: Inequalities about the area bounded by three cevian lines of a triangle
Abstract: In the paper we prove generalization of Schl\"omilch's and Zetel's theorems about concurrent lines in a triangle. This generalization is obtained as a corollary of sharp geometric inequality about the ratio of triangular areas which is proved using discrete variant of H\"older's inequality. Also a new sharp refinement of J.F. Rigby's inequality, which itself generalized M\"obius theorem about the areas of triangles formed by cevians of a triangle, is proved.


Title: b-articulation points and b-bridges in strongly biconnected directed graphs
Abstract: A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. This class of directed graphs was first introduced by Wu and Grumbach. Let $G=(V,E)$ be a strongly biconnected directed graph. An edge $e\in E$ is a b-bridge if the subgraph $G\setminus \left\lbrace e\right\rbrace =(V,E\setminus \left\lbrace e\right\rbrace) $ is not strongly biconnected. A vertex $w\in V$ is a b-articulation point if $G\setminus \left\lbrace w\right\rbrace$ is not strongly biconnected, where $G\setminus \left\lbrace w\right\rbrace$ is the subgraph obtained from $G$ by removing $w$. In this paper we study b-articulation points and b-bridges.


Title: Gradient Methods Never Overfit On Separable Data
Abstract: A line of recent works established that when training linear predictors over separable data, using gradient methods and exponentially-tailed losses, the predictors asymptotically converge in direction to the max-margin predictor. As a consequence, the predictors asymptotically do not overfit. However, this does not address the question of whether overfitting might occur non-asymptotically, after some bounded number of iterations. In this paper, we formally show that standard gradient methods (in particular, gradient flow, gradient descent and stochastic gradient descent) never overfit on separable data: If we run these methods for $T$ iterations on a dataset of size $m$, both the empirical risk and the generalization error decrease at an essentially optimal rate of $\tilde{\mathcal{O}}(1/\gamma^2 T)$ up till $T\approx m$, at which point the generalization error remains fixed at an essentially optimal level of $\tilde{\mathcal{O}}(1/\gamma^2 m)$ regardless of how large $T$ is. Along the way, we present non-asymptotic bounds on the number of margin violations over the dataset, and prove their tightness.


Title: SCALA: Sparsification-based Contrastive Learning for Anomaly Detection on Attributed Networks
Abstract: Anomaly detection on attributed networks aims to find the nodes whose behaviors are significantly different from other majority nodes. Generally, network data contains information about relationships between entities, and the anomaly is usually embodied in these relationships. Therefore, how to comprehensively model complex interaction patterns in networks is still a major focus. It can be observed that anomalies in networks violate the homophily assumption. However, most existing studies only considered this phenomenon obliquely rather than explicitly. Besides, the node representation of normal entities can be perturbed easily by the noise relationships introduced by anomalous nodes. To address the above issues, we present a novel contrastive learning framework for anomaly detection on attributed networks, \textbf{SCALA}, aiming to improve the embedding quality of the network and provide a new measurement of qualifying the anomaly score for each node by introducing sparsification into the conventional method. Extensive experiments are conducted on five benchmark real-world datasets and the results show that SCALA consistently outperforms all baseline methods significantly.


Title: Asymptotic behavior of positive solutions of some nonlinear elliptic equations on cylinders
Abstract: We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such as the Yamabe equation, Hardy-H\'enon equation etc.


Title: Twisted Yang-Baxter sets, cohomology theory, and application to knots
Abstract: In this article, we introduce a notion of twisted set-theoretic Yang-Baxter solution, which is a triplet $(X,f,R)$, where $(X,R)$ is a Yang-Baxter set and $f:X \to X$ is an automorphism of $(X,R)$. We present a cohomology theory for it, and use cocycles of twisted biquandles in amalgamation with Alexander numbering to construct state-sum invariant of knots and knotted surfaces. Additionally, we introduce a twisted version of cohomology theory for Yang-Baxter sets and give applications to knot theory.


Title: Bounds on the minimum distance of locally recoverable codes
Abstract: We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length $n=n_q(k,d,r)$ of a linear $[n,k,d]_q$-code with locality $r$. For $k\le 7$ we exactly determine all values of $n_2(k,d,2)$ and for $k\le 6$ we exactly determine all values of $n_2(k,d,1)$. For the ternary field we also state a few numerical results. As a general result we prove that $n_q(k,d,r)$ equals the Griesmer bound if the minimum Hamming distance $d$ is sufficiently large and all other parameters are fixed.


Title: Best Practices for Scientific Computing
Abstract: Scientists spend an increasing amount of time building and using software. However, most scientists are never taught how to do this efficiently. As a result, many are unaware of tools and practices that would allow them to write more reliable and maintainable code with less effort. We describe a set of best practices for scientific software development that have solid foundations in research and experience, and that improve scientists' productivity and the reliability of their software.


Title: GEqO: ML-Accelerated Semantic Equivalence Detection
Abstract: Large scale analytics engines have become a core dependency for modern data-driven enterprises to derive business insights and drive actions. These engines support a large number of analytic jobs processing huge volumes of data on a daily basis, and workloads are often inundated with overlapping computations across multiple jobs. Reusing common computation is crucial for efficient cluster resource utilization and reducing job execution time. Detecting common computation is the first and key step for reducing this computational redundancy. However, detecting equivalence on large-scale analytics engines requires efficient and scalable solutions that are fully automated. In addition, to maximize computation reuse, equivalence needs to be detected at the semantic level instead of just the syntactic level (i.e., the ability to detect semantic equivalence of seemingly different-looking queries). Unfortunately, existing solutions fall short of satisfying these requirements. In this paper, we take a major step towards filling this gap by proposing GEqO, a portable and lightweight machine-learning-based framework for efficiently identifying semantically equivalent computations at scale. GEqO introduces two machine-learning-based filters that quickly prune out nonequivalent subexpressions and employs a semi-supervised learning feedback loop to iteratively improve its model with an intelligent sampling mechanism. Further, with its novel database-agnostic featurization method, GEqO can transfer the learning from one workload and database to another. Our extensive empirical evaluation shows that, on TPC-DS-like queries, GEqO yields significant performance gains-up to 200x faster than automated verifiers-and finds up to 2x more equivalences than optimizer and signature-based equivalence detection approaches.


Title: Function approximation by deep networks
Abstract: We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same compositional structure, while a shallow network cannot exploit this knowledge. Thus, the blessing of compositionality mitigates the curse of dimensionality. On the other hand, a theorem called good propagation of errors allows to `lift' theorems about shallow networks to those about deep networks with an appropriate choice of norms, smoothness, etc. We illustrate this in three contexts where each channel in the deep network calculates a spherical polynomial, a non-smooth ReLU network, or another zonal function network related closely with the ReLU network.


Title: Pre-foliations of co-degree one on $\mathbb{P}^{2}_{\mathbb{C}}$ with a flat Legendre transform
Abstract: A holomorphic pre-foliation $\mathscr{F}=\ell\boxtimes\mathcal{F}$ of co-degree $1$ and degree $d$ on $\mathbb{P}^{2}_{\mathbb{C}}$ is the data of a line $\ell$ of $\mathbb{P}^{2}_{\mathbb{C}}$ and a holomorphic foliation $\mathcal{F}$ on $\mathbb{P }^{2}_{\mathbb{C}}$ of degree $d-1.$ We study pre-foliations of co-degree $1$ on $\mathbb{P}^{2}_{\mathbb{ C}}$ with a flat Legendre transform (dual web). After having established some general results on the flatness of the dual $d$-web of a homogeneous pre-foliation of co-degree $1$ and degree $d$, we describe some explicit examples and we show that up to automorphism of $\mathbb{P}^{2}_{\mathbb{C}}$ there are two families and six examples of homogeneous pre-foliations of co-degree $1$ and degree $3$ on $\mathbb {P}^{2}_{\mathbb{C}}$ with a flat dual web. This allows us to prove an analogue for pre-foliations of co-degree $1$ and degree~$3$ of a result, obtained in collaboration with D. Mar\'{\i}n, on foliations of degree $3$ with non-degenerate singularities and a flat Legendre transform. We also show that the dual web of a reduced convex pre-foliation of co-degree $1$ on $\mathbb{P}^{2}_{\mathbb{C}}$ is flat. This is an analogue of a result on foliations of $\mathbb{P}^{2}_{\mathbb{C}}$ due to D. Mar\'{\i}n and J. V. Pereira.


Title: A minimum semi-degree sufficient condition for one-to-many disjoint path covers in semicomplete digraphs
Abstract: Let $D$ be a digraph. We define the minimum semi-degree of $D$ as $\delta^{0}(D) := \min \{\delta^{+}(D), \delta^{-}(D)\}$. Let $k$ be a positive integer, and let $S = \{s\}$ and $T = \{t_{1}, \dots ,t_{k}\}$ be any two disjoint subsets of $V(D)$. A set of $k$ internally disjoint paths joining source set $S$ and sink set $T$ that cover all vertices $D$ are called a one-to-many $k$-disjoint directed path cover ($k$-DDPC for short) of $D$. A digraph $D$ is semicomplete if for every pair $x,y$ of vertices of it, there is at least one arc between $x$ and $y$. In this paper, we prove that every semicomplete digraph $D$ of sufficiently large order $n$ with $\delta^{0}(D) \geq \lceil (n+k-1)/2\rceil$ has a one-to-many $k$-DDPC joining any disjoint source set $S$ and sink set $T$, where $S = \{s\}, T = \{t_{1}, \dots, t_{k}\}$.


Title: Infinite transition solutions for an Allen-Cahn equation
Abstract: We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen--Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.


Title: A Markov Process Approach to Ensemble Control of Smart Buildings
Abstract: This paper describes a step-by-step procedure that converts a physical model of a building into a Markov Process that characterizes energy consumption of this and other similar buildings. Relative to existing thermo-physics-based building models, the proposed procedure reduces model complexity and depends on fewer parameters, while also maintaining accuracy and feasibility sufficient for system-level analyses. Furthermore, the proposed Markov Process approach makes it possible to leverage real-time data streams available from intelligent data acquisition systems, which are readily available in smart buildings, and merge it with physics-based and statistical models. Construction of the Markov Process naturally leads to a Markov Decision Process formulation, which describes optimal probabilistic control of a collection of similar buildings. The approach is illustrated using validated building data from Belgium.


Title: Dynamical processes on metric networks
Abstract: The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and changes, coupled oscillators, and random walks. In parallel to these developments, there have been many studies of wave propagation and other spatially extended processes on networks. These latter studies consider metric networks, in which the edges are associated with real intervals. Metric networks give a mathematical framework to describe dynamical processes that include both temporal and spatial evolution of some quantity of interest -- such as the concentration of a diffusing substance or the amplitude of a wave -- by using edge-specific intervals that quantify distance information between nodes. Dynamical processes on metric networks often take the form of partial differential equations (PDEs). In this paper, we present a collection of techniques and paradigmatic linear PDEs that are useful to investigate the interplay between structure and dynamics in metric networks. We start by considering a time-independent Schr\"odinger equation. We then use both finite-difference and spectral approaches to study the Poisson, heat, and wave equations as paradigmatic examples of elliptic, parabolic, and hyperbolic PDE problems on metric networks. Our spectral approach is able to account for degenerate eigenmodes. In our numerical experiments, we consider metric networks with up to about $10^4$ nodes and about $10^4$ edges. A key contribution of our paper is to increase the accessibility of studying PDEs on metric networks. Software that implements our numerical approaches is available at https://gitlab.com/ComputationalScience/metric-networks.


Title: Domination Polynomial of the Rook Graph
Abstract: A placement of chess pieces on a chessboard is called dominating, if each free square of the chessboard is under attack by at least one piece. In this contribution we compute the number of dominating arrangements of $k$ rooks on an $n\times m$ chessboard. To this end we derive an expression for the corresponding generating function, the domination polynomial of the $n\times m$ rook graph.


Title: Estimates for Character Sums with Various Convolutions
Abstract: We provide estimates for sums of the form \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\chi(a+b+c)\right|\] and \[\left|\sum_{a\in A}\sum_{b\in B}\sum_{c\in C}\sum_{d\in D}\chi(a+b+cd)\right|\] when $A,B,C,D\subset \mathbb F_p$, the field with $p$ elements and $\chi$ is a non-trivial multiplicative character modulo $p$.


Title: Cuckoo Trie: Exploiting Memory-Level Parallelism for Efficient DRAM Indexing
Abstract: We present the Cuckoo Trie, a fast, memory-efficient ordered index structure. The Cuckoo Trie is designed to have memory-level parallelism -- which a modern out-of-order processor can exploit to execute DRAM accesses in parallel -- without sacrificing memory efficiency. The Cuckoo Trie thus breaks a fundamental performance barrier faced by current indexes, whose bottleneck is a series of dependent pointer-chasing DRAM accesses -- e.g., traversing a search tree path -- which the processor cannot parallelize. Our evaluation shows that the Cuckoo Trie outperforms state-of-the-art-indexes by up to 20%--360% on a variety of datasets and workloads, typically with a smaller or comparable memory footprint.


Title: Existence and concentration of solutions for a class of biharmonic equations
Abstract: Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial solutions are related to a suitable truncated equation.


Title: Purposeful and Operation-based Cognitive System for AGI
Abstract: This paper proposes a new cognitive model, acting as the main component of an AGI agent. The model is introduced in its mature state, and as an extension of previous models, DENN, and especially AKREM, by including operational models (frames/classes) and will. In addition, it is mainly based on the duality principle in every known intelligent aspect, such as exhibiting both top-down and bottom-up model learning, generalization verse specialization, and more. Furthermore, a holistic approach is advocated for AGI designing and cognition under constraints or efficiency is proposed, in the form of reusability and simplicity. Finally, reaching this mature state is described via a cognitive evolution from infancy to adulthood, utilizing a consolidation principle. The final product of this cognitive model is a dynamic operational memory of models and instances.


Title: Nonterminal complexity of some families of infinite regular languages
Abstract: Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different families of regular languages. In this paper we study nonterminal complexity of some families of infinite regular languages.


Title: Obvious Manipulability of Voting Rules
Abstract: The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion. We also show that several voting rules including k-approval fail to satisfy this property. We characterize conditions under which voting rules are obviously manipulable. One of our insights is that certain rules are obviously manipulable when the number of alternatives is relatively large compared to the number of voters. In contrast to the Gibbard-Satterthwaite theorem, many of the rules we examined are not obviously manipulable. This reflects the relatively easier satisfiability of the notion and the zero information assumption of not obvious manipulability, as opposed to the perfect information assumption of strategyproofness. We also present algorithmic results for computing obvious manipulations and report on experiments.


Title: Diametral notions for elements of the unit ball of a Banach space
Abstract: We introduce extensions of $\Delta$-points and Daugavet points in which slices are replaced by relative weakly open subsets (super $\Delta$-points and super Daugavet points) or by convex combinations of slices (ccs $\Delta$-points and ccs Daugavet points). We first give a general overview on these new concepts and provide some isometric consequences on the spaces. As examples: if a Banach space contains a super $\Delta$-point, then it does not admit an unconditional FDD with suppression constant smaller than two; if a real Banach space contains a ccs $\Delta$-point, then it does not admit a one-unconditional basis; if a Banach space contains a ccs Daugavet point, then every convex combination of slices of its unit ball has diameter two. We next characterize the notions in some classes of Banach spaces showing, for instance, that all the notions coincide in $L_1$-predual spaces and that all the notions but ccs Daugavet points coincide in $L_1$-spaces. We next remark on some examples which have previously appeared in the literature and provide some new intriguing examples: examples of super $\Delta$-points which are as closed as desired to strongly exposed points (hence failing to be Daugavet points in an extreme way); an example of a super $\Delta$-point which is strongly regular (hence failing to be a ccs $\Delta$-point in the strongest way); a super Daugavet point which fails to be a ccs $\Delta$-point. The extensions of the diametral notions to point in the open unit ball and the consequences on the spaces are also studied. Last, we investigate the Kuratowski measure of relative weakly open subsets and of convex combinations of slices in the presence of super $\Delta$-points or ccs $\Delta$-points, as well as for spaces enjoying diameter 2 properties. We conclude the paper with a section on open problems.


Title: Zero-shot Active Learning Using Self Supervised Learning
Abstract: Deep learning algorithms are often said to be data hungry. The performance of such algorithms generally improve as more and more annotated data is fed into the model. While collecting unlabelled data is easier (as they can be scraped easily from the internet), annotating them is a tedious and expensive task. Given a fixed budget available for data annotation, Active Learning helps selecting the best subset of data for annotation, such that the deep learning model when trained over that subset will have maximum generalization performance under this budget. In this work, we aim to propose a new Active Learning approach which is model agnostic as well as one doesn't require an iterative process. We aim to leverage self-supervised learnt features for the task of Active Learning. The benefit of self-supervised learning, is that one can get useful feature representation of the input data, without having any annotation.


Title: Semistability of pairs for projective toric varieties
Abstract: Let $X \to \mathbb P^N$ be a smooth linearly normal projective variety. It was proved by Paul that the $K$-energy of $(X,\omega_{FS}|_{X})$ restricted to the Bergman metrics is bounded from below if and only if the pair of (rescaled) Chow/Hurwitz forms of $X$ is semistable. In this paper, we provide a necessary and sufficient condition for a given smooth toric variety $X_P$ to be semistable of pairs with respect to $\mathcal O_{X_P}(i)$ for a positive integer $i$. Applying this result to a smooth polarized toric variety $(X_P, L_P)$, we prove that $(X_P, L_P)$ is asymptotically semistable of pairs if and only if it is K-semistable for toric degenerations.


Title: A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds
Abstract: We present a comprehensive survey and benchmark of both traditional and learning-based methods for surface reconstruction from point clouds. This task is particularly challenging for real-world acquisitions due to factors like noise, outliers, non-uniform sampling, and missing data. Traditional approaches often simplify the problem by imposing handcrafted priors on either the input point clouds or the resulting surface, a process that can necessitate tedious hyperparameter tuning. Conversely, deep learning models have the capability to directly learn the properties of input point clouds and desired surfaces from data. We study the influence of these handcrafted and learned priors on the precision and robustness of surface reconstruction techniques. We evaluate various time-tested and contemporary methods in a standardized manner. When both trained and evaluated on point clouds with identical characteristics, the learning-based models consistently produce superior surfaces compared to their traditional counterparts$\unicode{x2013}$even in scenarios involving novel shape categories. However, traditional methods demonstrate greater resilience to the diverse array of point cloud anomalies commonly found in real-world 3D acquisitions. For the benefit of the research community, we make our code and datasets available, inviting further enhancements to learning-based surface reconstruction. This can be accessed at https://github.com/raphaelsulzer/dsr-benchmark .


Title: On groups with BFC-covered word values
Abstract: For a group G and a positive integer n write B_n(G) = {x \in G : |x^G | \le n}. If s is a positive integer and w is a group word, say that G satisfies the (n,s)-covering condition with respect to the word w if there exists a subset S of G such that |S| \le s and all w-values of G are contained in B_n(G)S. In a natural way, this condition emerged in the study of probabilistically nilpotent groups of class two. In this paper we obtain the following results. Let w be a multilinear commutator word on k variables and let G be a group satisfying the (n,s)-covering condition with respect to the word w. Then G has a soluble subgroup T such that the index [G : T] and the derived length of T are both (k,n,s)-bounded. Let G be a group satisfying the (n,s)-covering condition with respect to the word \gamma_k. Then (1) \gamma_{2k-1}(G) has a subgroup $T$ such that the index [\gamma_{2k-1}(G) : T] and |T'| are both (k,n,s)-bounded; and (2) G has a nilpotent subgroup U such that the index [G : U] and the nilpotency class of U are both (k,n,s)-bounded.


Title: Unsupervised Body Part Regression via Spatially Self-ordering Convolutional Neural Networks
Abstract: Automatic body part recognition for CT slices can benefit various medical image applications. Recent deep learning methods demonstrate promising performance, with the requirement of large amounts of labeled images for training. The intrinsic structural or superior-inferior slice ordering information in CT volumes is not fully exploited. In this paper, we propose a convolutional neural network (CNN) based Unsupervised Body part Regression (UBR) algorithm to address this problem. A novel unsupervised learning method and two inter-sample CNN loss functions are presented. Distinct from previous work, UBR builds a coordinate system for the human body and outputs a continuous score for each axial slice, representing the normalized position of the body part in the slice. The training process of UBR resembles a self-organization process: slice scores are learned from inter-slice relationships. The training samples are unlabeled CT volumes that are abundant, thus no extra annotation effort is needed. UBR is simple, fast, and accurate. Quantitative and qualitative experiments validate its effectiveness. In addition, we show two applications of UBR in network initialization and anomaly detection.


Title: Augmenting Supervised Learning by Meta-learning Unsupervised Local Rules
Abstract: The brain performs unsupervised learning and (perhaps) simultaneous supervised learning. This raises the question as to whether a hybrid of supervised and unsupervised methods will produce better learning. Inspired by the rich space of Hebbian learning rules, we set out to directly learn the unsupervised learning rule on local information that best augments a supervised signal. We present the Hebbian-augmented training algorithm (HAT) for combining gradient-based learning with an unsupervised rule on pre-synpatic activity, post-synaptic activities, and current weights. We test HAT's effect on a simple problem (Fashion-MNIST) and find consistently higher performance than supervised learning alone. This finding provides empirical evidence that unsupervised learning on synaptic activities provides a strong signal that can be used to augment gradient-based methods. We further find that the meta-learned update rule is a time-varying function; thus, it is difficult to pinpoint an interpretable Hebbian update rule that aids in training. We do find that the meta-learner eventually degenerates into a non-Hebbian rule that preserves important weights so as not to disturb the learner's convergence.


Title: Damped Arrow-Hurwicz algorithm for sphere packing
Abstract: We consider algorithms that, from an arbitrarily sampling of $N$ spheres (possibly overlapping), find a close packed configuration without overlapping. These problems can be formulated as minimization problems with non-convex constraints. For such packing problems, we observe that the classical iterative Arrow-Hurwicz algorithm does not converge. We derive a novel algorithm from a multi-step variant of the Arrow-Hurwicz scheme with damping. We compare this algorithm with classical algorithms belonging to the class of linearly constrained Lagrangian methods and show that it performs better. We provide an analysis of the convergence of these algorithms in the simple case of two spheres in one spatial dimension. Finally, we investigate the behaviour of our algorithm when the number of spheres is large.


Title: Duality for convex infinite optimization on linear spaces
Abstract: This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called sup-dual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.


Title: Theory of Solutions for An Inextensible Cantilever
Abstract: Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin-Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.


Title: Existence of Classic Solution of the Boussinesq Equation
Abstract: We generalize intermediate value Theorem to metric space,and make use of it to discuss existence of classic solution of the Boussinesq equation.


Title: Chaos expansion of 2D parabolic Anderson model
Abstract: We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the annealed density function of the polymer in a white noise environment.


Title: Sensing Aided Covert Communications: Turning Interference into Allies
Abstract: In this paper, we investigate the realization of covert communication in a general radar-communication cooperation system, which includes integrated sensing and communications as a special example. We explore the possibility of utilizing the sensing ability of radar to track and jam the aerial adversary target attempting to detect the transmission. Based on the echoes from the target, the extended Kalman filtering technique is employed to predict its trajectory as well as the corresponding channels. Depending on the maneuvering altitude of adversary target, two channel state information (CSI) models are considered, with the aim of maximizing the covert transmission rate by jointly designing the radar waveform and communication transmit beamforming vector based on the constructed channels. For perfect CSI under the free-space propagation model, by decoupling the joint design, we propose an efficient algorithm to guarantee that the target cannot detect the transmission. For imperfect CSI due to the multi-path components, a robust joint transmission scheme is proposed based on the property of the Kullback-Leibler divergence. The convergence behaviour, tracking MSE, false alarm and missed detection probabilities, and covert transmission rate are evaluated. Simulation results show that the proposed algorithms achieve accurate tracking. For both channel models, the proposed sensing-assisted covert transmission design is able to guarantee the covertness, and significantly outperforms the conventional schemes.


Title: Transformers in Action Recognition: A Review on Temporal Modeling
Abstract: In vision-based action recognition, spatio-temporal features from different modalities are used for recognizing activities. Temporal modeling is a long challenge of action recognition. However, there are limited methods such as pre-computed motion features, three-dimensional (3D) filters, and recurrent neural networks (RNN) for modeling motion information in deep-based approaches. Recently, transformers success in modeling long-range dependencies in natural language processing (NLP) tasks has gotten great attention from other domains; including speech, image, and video, to rely entirely on self-attention without using sequence-aligned RNNs or convolutions. Although the application of transformers to action recognition is relatively new, the amount of research proposed on this topic within the last few years is astounding. This paper especially reviews recent progress in deep learning methods for modeling temporal variations. It focuses on action recognition methods that use transformers for temporal modeling, discussing their main features, used modalities, and identifying opportunities and challenges for future research.


Title: Fundamental groups, coregularity, and low dimensional klt Calabi-Yau pairs
Abstract: In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we conjecture that for a projective klt log pair $(X,D)$ of absolute coregularity $c$ (and arbitrary dimension) the fundamental group $\pi_1^{\rm reg}(X,D)$ admits a normal abelian subgroup of finite index and rank at most $2c$. We prove this conjecture in the cases $c\in \{0,1,2\}$, building on the almost abelianity of the fundamental groups of klt Calabi-Yau pairs of dimension $\leq 2$. In the cases $c \in \{0,1,2\}$ and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. In dimension three, we are able to prove almost abelianity for projective varieties with klt singularities and $\mathbb{Q}$-trivial canonical divisor.


Title: Accelerating Text-to-Image Editing via Cache-Enabled Sparse Diffusion Inference
Abstract: Due to the recent success of diffusion models, text-to-image generation is becoming increasingly popular and achieves a wide range of applications. Among them, text-to-image editing, or continuous text-to-image generation, attracts lots of attention and can potentially improve the quality of generated images. It's common to see that users may want to slightly edit the generated image by making minor modifications to their input textual descriptions for several rounds of diffusion inference. However, such an image editing process suffers from the low inference efficiency of many existing diffusion models even using GPU accelerators. To solve this problem, we introduce Fast Image Semantically Edit (FISEdit), a cached-enabled sparse diffusion model inference engine for efficient text-to-image editing. The key intuition behind our approach is to utilize the semantic mapping between the minor modifications on the input text and the affected regions on the output image. For each text editing step, FISEdit can automatically identify the affected image regions and utilize the cached unchanged regions' feature map to accelerate the inference process. Extensive empirical results show that FISEdit can be $3.4\times$ and $4.4\times$ faster than existing methods on NVIDIA TITAN RTX and A100 GPUs respectively, and even generates more satisfactory images.


Title: Approximation to multifractional Riemann-Liouville Brownian sheet
Abstract: In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence of I.I.D random variables.


Title: In Quest of Significance: Identifying Types of Twitter Sentiment Events that Predict Spikes in Sales
Abstract: We study the power of Twitter events to predict consumer sales events by analysing sales for 75 companies from the retail sector and over 150 million tweets mentioning those companies along with their sentiment. We suggest an approach for events identification on Twitter extending existing methodologies of event study. We also propose a robust method for clustering Twitter events into different types based on their shape, which captures the varying dynamics of information propagation through the social network. We provide empirical evidence that through events differentiation based on their shape we can clearly identify types of Twitter events that have a more significant power to predict spikes in sales than the aggregated Twitter signal.


Title: Context-Free TextSpotter for Real-Time and Mobile End-to-End Text Detection and Recognition
Abstract: In the deployment of scene-text spotting systems on mobile platforms, lightweight models with low computation are preferable. In concept, end-to-end (E2E) text spotting is suitable for such purposes because it performs text detection and recognition in a single model. However, current state-of-the-art E2E methods rely on heavy feature extractors, recurrent sequence modellings, and complex shape aligners to pursue accuracy, which means their computations are still heavy. We explore the opposite direction: How far can we go without bells and whistles in E2E text spotting? To this end, we propose a text-spotting method that consists of simple convolutions and a few post-processes, named Context-Free TextSpotter. Experiments using standard benchmarks show that Context-Free TextSpotter achieves real-time text spotting on a GPU with only three million parameters, which is the smallest and fastest among existing deep text spotters, with an acceptable transcription quality degradation compared to heavier ones. Further, we demonstrate that our text spotter can run on a smartphone with affordable latency, which is valuable for building stand-alone OCR applications.


Title: On the $δ$-chromatic numbers of the Cartesian products of graphs
Abstract: In this work, we study the $\delta$-chromatic number of a graph which is the chromatic number of the $\delta$-complement of a graph. We give a structure of the $\delta$-complements and sharp bounds on the $\delta$-chromatic numbers of the Cartesian products of graphs. Furthermore, we compute the $\delta$-chromatic numbers of various classes of Cartesian product graphs, including the Cartesian products between cycles, paths, and stars.


Title: Divides with cusps and symmetric links
Abstract: A Divide with cusps is the image of a proper generic immersion from finite intervals and circles into a $2$-disk which allows to have cusps. A divide with cusps is the generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in $S^3$. In this paper, we give the characterization of the link in $S^3$ which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and $2$-periodic link can be described as the link of a divide with cusps.


Title: Non-smoothable $\mathbb{Z}/p$-actions on nuclei
Abstract: In this article we construct examples of non-smoothable $\mathbb{Z}/p$-actions on indefinite spin 4-manifolds with boundary for all primes $p\geq 5$. For example, we show that for each prime $p\geq 5$ and each $n\geq 1$ there exists a locally linear $\mathbb{Z}/p$-action on the Gompf nucleus $N(2pn)$ which is not smoothable with respect to any smooth structure on $N(2pn)$. Furthermore we investigate the behavior of these actions under two different types of equivariant stabilizations with $S^{2}\times S^{2}$, namely \emph{free} and \emph{homologically trivial} stabilizations -- in particular we show that our non-smoothable $\mathbb{Z}/p$-action on $N(2pn)$ remains non-smoothable after $2n-2$ free stabilizations, and after arbitrarily many homologically trivial stabilizations. We also show that free stabilizations satisfy a Wall stabilization principle in the sense that any non-smoothable $\mathbb{Z}/p$-action becomes smoothable after some finite number free stabilizations (under certain assumptions), whereas our aforementioned result implies that homologically trivial stabilizations do not satisfy this property. The proofs of these results use equivariant $\kappa$-invariants defined by the author in \cite{Mon22}, calculations of equivariant $\eta$-invariants for the odd signature and Dirac operators on Seifert-fibered spaces, as well as an analysis of the geometric $S^{1}$-action on the Seiberg-Witten moduli spaces of Seifert-fibered spaces induced by rotation in the fibers, which may be of independent interest.


Title: Associators in mould theory
Abstract: By developing various techniques of mould theory, we introduce $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$, a mould theoretic formulation of Drinfeld's associator set. We give a mould-theoretical generalization of the result that associator relations imply double shuffle relations, namely, we explain that $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$ is embedded to Ecalle's set $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}\ast\mathsf{is}}$ which is a mould theoretic version of Racinet's double shuffle set.


Title: A Tiny CNN Architecture for Medical Face Mask Detection for Resource-Constrained Endpoints
Abstract: The world is going through one of the most dangerous pandemics of all time with the rapid spread of the novel coronavirus (COVID-19). According to the World Health Organisation, the most effective way to thwart the transmission of coronavirus is to wear medical face masks. Monitoring the use of face masks in public places has been a challenge because manual monitoring could be unsafe. This paper proposes an architecture for detecting medical face masks for deployment on resource-constrained endpoints having extremely low memory footprints. A small development board with an ARM Cortex-M7 microcontroller clocked at 480 Mhz and having just 496 KB of framebuffer RAM, has been used for the deployment of the model. Using the TensorFlow Lite framework, the model is quantized to further reduce its size. The proposed model is 138 KB post quantization and runs at the inference speed of 30 FPS.


Title: $q$-de Rham complexes of higher level
Abstract: In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on higher-level $q$-crystalline site, which was introduced in the previous article of the author. One complex is the $q$-analog of the higher de Rham complex constructed by Miyatani, and another complex is the $q$-analog of the jet complex constructed by Le Stum-Quir\'os. The complexes we constructed can also be regarded as the higher-level analogs of the $q$-de Rham complex.


Title: Unsupervised Program Synthesis for Images By Sampling Without Replacement
Abstract: Program synthesis has emerged as a successful approach to the image parsing task. Most prior works rely on a two-step scheme involving supervised pretraining of a Seq2Seq model with synthetic programs followed by reinforcement learning (RL) for fine-tuning with real reference images. Fully unsupervised approaches promise to train the model directly on the target images without requiring curated pretraining datasets. However, they struggle with the inherent sparsity of meaningful programs in the search space. In this paper, we present the first unsupervised algorithm capable of parsing constructive solid geometry (CSG) images into context-free grammar (CFG) without pretraining via non-differentiable renderer. To tackle the \emph{non-Markovian} sparse reward problem, we combine three key ingredients -- (i) a grammar-encoded tree LSTM ensuring program validity (ii) entropy regularization and (iii) sampling without replacement from the CFG syntax tree. Empirically, our algorithm recovers meaningful programs in large search spaces (up to $3.8 \times 10^{28}$). Further, even though our approach is fully unsupervised, it generalizes better than supervised methods on the synthetic 2D CSG dataset. On the 2D computer aided design (CAD) dataset, our approach significantly outperforms the supervised pretrained model and is competitive to the refined model.


Title: On embeddings of certain spherical homogeneous spaces in prime characteristic
Abstract: Let $\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\mc G$-spaces that are induced from the $G\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of $\mc G$. We show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen-Macaulay. Examples are the $G\times G$-orbits in normal reductive monoids with unit group $G$. Our class of homogeneous spaces also includes the open orbits of the well-known determinantal varieties and the varieties of (circular) complexes. We also show that all $G$-orbit closures in a spherical variety which is canonically Frobenius split are normal. Finally we study the Gorenstein property for the varieties of circular complexes and for a related reductive monoid.


Title: Integrability of moduli and regularity of Denjoy counterexamples
Abstract: We study the regularity of exceptional actions of groups by $C^{1,\alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of continuity $\alpha$. Let $G$ be a finitely generated group admitting a $C^{1,\alpha}$ action $\rho$ with a free orbit on the circle, and such that the logarithms of derivatives of group elements are uniformly bounded at some point of the circle. We prove that if $G$ has spherical growth bounded by $c n^{d-1}$ and if the function $1/\alpha^d$ is integrable near zero, then under some mild technical assumptions on $\alpha$, there is a sequence of exceptional $C^{1,\alpha}$ actions of $G$ which converge to $\rho$ in the $C^1$ topology. As a consequence for a single diffeomorphism, we obtain that if the function $1/\alpha$ is integrable near zero, then there exists a $C^{1,\alpha}$ exceptional diffeomorphism of the circle. This corollary accounts for all previously known moduli of continuity for derivatives of exceptional diffeomorphisms. We also obtain a partial converse to our main result. For finitely generated free abelian groups, the existence of an exceptional action, together with some natural hypotheses on the derivatives of group elements, puts integrability restrictions on the modulus $\alpha$. These results are related to a long-standing question of D. McDuff concerning the length spectrum of exceptional $C^1$ diffeomorphisms of the circle.


Title: Representative Families: A Unified Tradeoff-Based Approach
Abstract: Let $M=(E,{\cal I})$ be a matroid, and let $\cal S$ be a family of subsets of size $p$ of $E$. A subfamily $\widehat{\cal S}\subseteq{\cal S}$ represents ${\cal S}$ if for every pair of sets $X\in{\cal S}$ and $Y\subseteq E\setminus X$ such that $X\cup Y\in{\cal I}$, there is a set $\widehat{X}\in\widehat{\cal S}$ disjoint from $Y$ such that $\widehat{X}\cup Y\in{\cal I}$. Fomin et al. (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2014) introduced a powerful technique for fast computation of representative families for uniform matroids. In this paper, we show that this technique leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes, among others, $k$-Partial Cover, $k$-Internal Out-Branching, and Long Directed Cycle. Our approach exploits an interesting tradeoff between running time and the size of the representative families.


Title: An algebra structure for reproducing kernel Hilbert spaces
Abstract: Reproducing kernel Hilbert spaces (RKHSs) are Hilbert spaces of functions where pointwise evaluation is continuous. There are known examples of RKHSs that are Banach algebras under pointwise multiplication. These examples are built from weights on the dual of a locally compact abelian group. In this paper we define an algebra structure on an RKHS that is equivalent to subconvolutivity of the weight for known examples (referred to as reproducing kernel Hilbert algebras, or RKHAs). We show that the class of RKHAs is closed under the Hilbert space tensor product and the pullback construction on the category of RKHSs. The subcategory of RKHAs becomes a monoidal category with the spectrum as a monoidal functor to the category of topological spaces. The image of this functor is shown to contain all compact subspaces of $\mathbb R^n$ for $n>0$.


Title: Liouville formulas for quantum affine algebras and eigenvalues of quantum Gelfand invariants
Abstract: We construct new central elements in the quantum affine algebras of type $A$ and prove Liouville-type formulas relating them to the quantum determinants. We apply these formulas to calculate the eigenvalues of the quantum Gelfand invariants as introduced by Reshetikhin, Takhtadzhyan and Faddeev (1989) acting in irreducible highest weight representations of the quantized enveloping algebra for ${\mathfrak {gl}}_n$.


Title: Tarski's Least Fixed Point Theorem: A Type Theoretic Formulation
Abstract: We translate Giovanni Curi's predicative least fixed point theorem into type theory. There are multiple benefits of having a type theoretic formulation apart from the potential for routine formalization. By taking advantage of (higher) inductive types, we have skirted the painstaking set theoretic constructions and as a result believe our presentation is conceptually clearer. Additionally, due the predicative admissibility of (higher) inductive types we take a step towards the \say{system independent} derivation that Curi calls for in his conclusion. We also explore restrictions on monotone maps that guarantee they are \say{generated} in a sense we make precise. This allows for an alternative statement of the least fixed point theorem which goes beyond the version found in Curi's work.


Title: The effect of approximate coarsest-level solves on the convergence of multigrid V-cycle methods
Abstract: The multigrid V-cycle method is a popular method for solving systems of linear equations. It computes an approximate solution by using smoothing on fine levels and solving a system of linear equations on the coarsest level. Solving on the coarsest level depends on the size and difficulty of the problem. If the size permits, it is typical to use a direct method based on LU or Cholesky decomposition. In settings with large coarsest-level problems, approximate solvers such as iterative Krylov subspace methods, or direct methods based on low-rank approximation, are often used. The accuracy of the coarsest-level solver is typically determined based on the experience of the users with the concrete problems and methods. In this paper we present an approach to analyzing the effects of approximate coarsest-level solves on the convergence of the V-cycle method for symmetric positive definite problems. Using these results, we derive coarsest-level stopping criterion through which we may control the difference between the approximation computed by a V-cycle method with approximate coarsest-level solver and the approximation which would be computed if the coarsest-level problems were solved exactly. The coarsest-level stopping criterion may thus be set up such that the V-cycle method converges to a chosen finest-level accuracy in (nearly) the same number of V-cycle iterations as the V-cycle method with exact coarsest-level solver. We also utilize the theoretical results to discuss how the convergence of the V-cycle method may be affected by the choice of a tolerance in a coarsest-level stopping criterion based on the relative residual norm.


Title: On almost sure convergence of random variables with finite chaos decomposition
Abstract: Under mild conditions on a family of independent random variables $(X_n)$ we prove that almost sure convergence of a sequence of tetrahedral polynomial chaoses of uniformly bounded degrees in the variables $(X_n)$ implies the almost sure convergence of their homogeneous parts. This generalizes a recent result due to Poly and Zheng obtained under stronger integrability conditions. In particular for i.i.d. sequences we provide a simple necessary and sufficient condition for this property to hold. We also discuss similar phenomena for sums of multiple stochastic integrals with respect to Poisson processes, answering a question by Poly and Zheng.


Title: Bagchi's Theorem for families of automorphic forms
Abstract: We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem for family of primitive cusp forms of weight $2$ and prime level, and discuss under which conditions the argument will apply to general reasonable family of automorphic $L$-functions.


Title: Connections between K-stability and Vojta's conjecture
Abstract: In this note, we use recent advances concerning the K-stability of $\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.


Title: Quasi-invariant theorem on the Gaussian path space
Abstract: In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the case of the fractional Brownian motion. As applications, we will establish the integration by parts formula and Bismut-Elworthy-Li formula on the Gaussian path space, and by which some logarithmic Sobolev inequalities will be presented. Moreover, we will also provides some applications in the field of financial mathematics.


Title: Data Assimilation in Chaotic Systems Using Deep Reinforcement Learning
Abstract: Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF), which relies on linear updates to minimize variance among the ensemble of forecast states. Recent advancements have seen the emergence of deep learning approaches in this domain, primarily within a supervised learning framework. However, the adaptability of such models to untrained scenarios remains a challenge. In this study, we introduce a novel DA strategy that utilizes reinforcement learning (RL) to apply state corrections using full or partial observations of the state variables. Our investigation focuses on demonstrating this approach to the chaotic Lorenz '63 system, where the agent's objective is to minimize the root-mean-squared error between the observations and corresponding forecast states. Consequently, the agent develops a correction strategy, enhancing model forecasts based on available system state observations. Our strategy employs a stochastic action policy, enabling a Monte Carlo-based DA framework that relies on randomly sampling the policy to generate an ensemble of assimilated realizations. Results demonstrate that the developed RL algorithm performs favorably when compared to the EnKF. Additionally, we illustrate the agent's capability to assimilate non-Gaussian data, addressing a significant limitation of the EnKF.


Title: The primitive curve complex for a handlebody
Abstract: A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve transversely in a single point. The primitive curve complex is then defined to be the full subcomplex of the curve complex for the boundary surface, spanned by the vertices of primitive curves. Given any two primitive curves, we construct a sequence of primitive curves from one to the other one satisfying a certain property. As a consequence, we prove that the primitive curve complex for the handlebody is connected.


Title: A minimal Gröbner basis for simple $\mathfrak{sl}_n$- or $\mathfrak{sp}_n$-modules
Abstract: We explicitly provide minimal Gr\"obner bases for simple, finite-dimensional modules of complex Lie algebras of types A and C, using a weighted ordering that is compatible with the PBW filtration on the universal enveloping algebras.


Title: The Cytnx Library for Tensor Networks
Abstract: We introduce a tensor network library designed for classical and quantum physics simulations called Cytnx (pronounced as sci-tens). This library provides almost an identical interface and syntax for both C++ and Python, allowing users to effortlessly switch between two languages. Aiming at a quick learning process for new users of tensor network algorithms, the interfaces resemble the popular Python scientific libraries like NumPy, Scipy, and PyTorch. Not only multiple global Abelian symmetries can be easily defined and implemented, Cytnx also provides a new tool called Network that allows users to store large tensor networks and perform tensor network contractions in an optimal order automatically. With the integration of cuQuantum, tensor calculations can also be executed efficiently on GPUs. We present benchmark results for tensor operations on both devices, CPU and GPU. We also discuss features and higher-level interfaces to be added in the future.


Title: A direct approach for function approximation on data defined manifolds
Abstract: In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the approximation theory results are observed to be too conservative. In manifold learning, one assumes instead that the data is sampled from an unknown manifold; i.e., the manifold is defined by the data itself. Function approximation on this unknown manifold is then a two stage procedure: first, one approximates the Laplace-Beltrami operator (and its eigen-decomposition) on this manifold using a graph Laplacian, and next, approximates the target function using the eigen-functions. Alternatively, one estimates first some atlas on the manifold and then uses local approximation techniques based on the local coordinate charts. In this paper, we propose a more direct approach to function approximation on \emph{unknown}, data defined manifolds without computing the eigen-decomposition of some operator or an atlas for the manifold, and without any kind of training in the classical sense. Our constructions are universal; i.e., do not require the knowledge of any prior on the target function other than continuity on the manifold. We estimate the degree of approximation. For smooth functions, the estimates do not suffer from the so-called saturation phenomenon. We demonstrate via a property called good propagation of errors how the results can be lifted for function approximation using deep networks where each channel evaluates a Gaussian network on a possibly unknown manifold.


Title: The Security and Privacy of Mobile Edge Computing: An Artificial Intelligence Perspective
Abstract: Mobile Edge Computing (MEC) is a new computing paradigm that enables cloud computing and information technology (IT) services to be delivered at the network's edge. By shifting the load of cloud computing to individual local servers, MEC helps meet the requirements of ultralow latency, localized data processing, and extends the potential of Internet of Things (IoT) for end-users. However, the crosscutting nature of MEC and the multidisciplinary components necessary for its deployment have presented additional security and privacy concerns. Fortunately, Artificial Intelligence (AI) algorithms can cope with excessively unpredictable and complex data, which offers a distinct advantage in dealing with sophisticated and developing adversaries in the security industry. Hence, in this paper we comprehensively provide a survey of security and privacy in MEC from the perspective of AI. On the one hand, we use European Telecommunications Standards Institute (ETSI) MEC reference architecture as our based framework while merging the Software Defined Network (SDN) and Network Function Virtualization (NFV) to better illustrate a serviceable platform of MEC. On the other hand, we focus on new security and privacy issues, as well as potential solutions from the viewpoints of AI. Finally, we comprehensively discuss the opportunities and challenges associated with applying AI to MEC security and privacy as possible future research directions.


Title: The covariant functoriality of graph algebras
Abstract: In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories enjoying covariant functors to categories of algebras given by constructions of path algebras, Cohn path algebras, and Leavitt path algebras, respectively. Thus we obtain new tools to unravel homomorphisms between Leavitt path algebras and graph C*-algebras. In particular, a graph-algebraic presentation of the inclusion of the C*-algebra of a quantum real projective plane into the Toeplitz algebra allows us to determine a quantum CW-complex structure of the former. It comes as a mixed-pullback theorem where two $*$-homomorphisms are covariantly induced from path homomorphisms of graphs and the remaining two are contravariantly induced by admissible inclusions of graphs. As a main result and an application of new covariant-induction tools, we prove such a mixed-pullback theorem for arbitrary graphs whose all vertex-simple loops have exits, which substantially enlarges the scope of examples coming from noncommutative topology.


Title: ODIN: A Single Model for 2D and 3D Perception
Abstract: State-of-the-art models on contemporary 3D perception benchmarks like ScanNet consume and label dataset-provided 3D point clouds, obtained through post processing of sensed multiview RGB-D images. They are typically trained in-domain, forego large-scale 2D pre-training and outperform alternatives that featurize the posed RGB-D multiview images instead. The gap in performance between methods that consume posed images versus post-processed 3D point clouds has fueled the belief that 2D and 3D perception require distinct model architectures. In this paper, we challenge this view and propose ODIN (Omni-Dimensional INstance segmentation), a model that can segment and label both 2D RGB images and 3D point clouds, using a transformer architecture that alternates between 2D within-view and 3D cross-view information fusion. Our model differentiates 2D and 3D feature operations through the positional encodings of the tokens involved, which capture pixel coordinates for 2D patch tokens and 3D coordinates for 3D feature tokens. ODIN achieves state-of-the-art performance on ScanNet200, Matterport3D and AI2THOR 3D instance segmentation benchmarks, and competitive performance on ScanNet, S3DIS and COCO. It outperforms all previous works by a wide margin when the sensed 3D point cloud is used in place of the point cloud sampled from 3D mesh. When used as the 3D perception engine in an instructable embodied agent architecture, it sets a new state-of-the-art on the TEACh action-from-dialogue benchmark. Our code and checkpoints can be found at the project website: https://odin-seg.github.io.


Title: Characterization and Prediction of Deep Learning Workloads in Large-Scale GPU Datacenters
Abstract: Modern GPU datacenters are critical for delivering Deep Learning (DL) models and services in both the research community and industry. When operating a datacenter, optimization of resource scheduling and management can bring significant financial benefits. Achieving this goal requires a deep understanding of the job features and user behaviors. We present a comprehensive study about the characteristics of DL jobs and resource management. First, we perform a large-scale analysis of real-world job traces from SenseTime. We uncover some interesting conclusions from the perspectives of clusters, jobs and users, which can facilitate the cluster system designs. Second, we introduce a general-purpose framework, which manages resources based on historical data. As case studies, we design: a Quasi-Shortest-Service-First scheduling service, which can minimize the cluster-wide average job completion time by up to 6.5x; and a Cluster Energy Saving service, which improves overall cluster utilization by up to 13%.


Title: Autonomous Driving Implementation in an Experimental Environment
Abstract: Autonomous systems require identifying the environment and it has a long way to go before putting it safely into practice. In autonomous driving systems, the detection of obstacles and traffic lights are of importance as well as lane tracking. In this study, an autonomous driving system is developed and tested in the experimental environment designed for this purpose. In this system, a model vehicle having a camera is used to trace the lanes and avoid obstacles to experimentally study autonomous driving behavior. Convolutional Neural Network models were trained for Lane tracking. For the vehicle to avoid obstacles, corner detection, optical flow, focus of expansion, time to collision, balance calculation, and decision mechanism were created, respectively.


Title: Canonical and $n$-canonical modules on a Noetherian algebra
Abstract: We define canonical and $n$-canonical modules on a module-finite algebra over a Noether commutative ring and study their basic properties. Using $n$-canonical modules, we generalize a theorem on $(n,C)$-syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a non-commutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism. We also prove the codimension two-argument for modules over a coherent sheaf of algebras with a $2$-canonical module, generalizing a result of the author.


Title: EcoFed: Efficient Communication for DNN Partitioning-based Federated Learning
Abstract: Efficiently running federated learning (FL) on resource-constrained devices is challenging since they are required to train computationally intensive deep neural networks (DNN) independently. DNN partitioning-based FL (DPFL) has been proposed as one mechanism to accelerate training where the layers of a DNN (or computation) are offloaded from the device to the server. However, this creates significant communication overheads since the intermediate activation and gradient need to be transferred between the device and the server during training. While current research reduces the communication introduced by DNN partitioning using local loss-based methods, we demonstrate that these methods are ineffective in improving the overall efficiency (communication overhead and training speed) of a DPFL system. This is because they suffer from accuracy degradation and ignore the communication costs incurred when transferring the activation from the device to the server. This article proposes EcoFed - a communication efficient framework for DPFL systems. EcoFed eliminates the transmission of the gradient by developing pre-trained initialization of the DNN model on the device for the first time. This reduces the accuracy degradation seen in local loss-based methods. In addition, EcoFed proposes a novel replay buffer mechanism and implements a quantization-based compression technique to reduce the transmission of the activation. It is experimentally demonstrated that EcoFed can reduce the communication cost by up to 133x and accelerate training by up to 21x when compared to classic FL. Compared to vanilla DPFL, EcoFed achieves a 16x communication reduction and 2.86x training time speed-up. EcoFed is available from https://github.com/blessonvar/EcoFed.


Title: Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field
Abstract: We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite field, going beyond the Riemann hypothesis over finite fields. As the main tool to prove our bound on traces of Hecke operators, we develop a Petersson formula for newforms for general nebentype characters.


Title: Towards dense object tracking in a 2D honeybee hive
Abstract: From human crowds to cells in tissue, the detection and efficient tracking of multiple objects in dense configurations is an important and unsolved problem. In the past, limitations of image analysis have restricted studies of dense groups to tracking a single or subset of marked individuals, or to coarse-grained group-level dynamics, all of which yield incomplete information. Here, we combine convolutional neural networks (CNNs) with the model environment of a honeybee hive to automatically recognize all individuals in a dense group from raw image data. We create new, adapted individual labeling and use the segmentation architecture U-Net with a loss function dependent on both object identity and orientation. We additionally exploit temporal regularities of the video recording in a recurrent manner and achieve near human-level performance while reducing the network size by 94% compared to the original U-Net architecture. Given our novel application of CNNs, we generate extensive problem-specific image data in which labeled examples are produced through a custom interface with Amazon Mechanical Turk. This dataset contains over 375,000 labeled bee instances across 720 video frames at 2 FPS, representing an extensive resource for the development and testing of tracking methods. We correctly detect 96% of individuals with a location error of ~7% of a typical body dimension, and orientation error of 12 degrees, approximating the variability of human raters. Our results provide an important step towards efficient image-based dense object tracking by allowing for the accurate determination of object location and orientation across time-series image data efficiently within one network architecture.


Title: A Concrete View of Rule 110 Computation
Abstract: Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to the left and right are both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in (Cook, 2004) we showed that it is capable of emulating the activity of a Turing machine by encoding the Turing machine and its tape into a repeating left pattern, a central pattern, and a repeating right pattern, which Rule 110 then acts on. In this paper we provide an explicit compiler for converting a Turing machine into a Rule 110 initial state, and we present a general approach for proving that such constructions will work as intended. The simulation was originally assumed to require exponential time, but surprising results of Neary and Woods (2006) have shown that in fact, only polynomial time is required. We use the methods of Neary and Woods to exhibit a direct simulation of a Turing machine by a tag system in polynomial time.


Title: Near-Field Velocity Sensing and Predictive Beamforming
Abstract: The novel concept of near-field velocity sensing is proposed. In contrast to far-field velocity sensing, near-field velocity sensing enables the simultaneous estimation of both radial and transverse velocities of a moving target. A maximum-likelihood-based method is proposed for jointly estimating the radial and transverse velocities from the echo signals. Assisted by near-field velocity sensing, a predictive beamforming framework is proposed for a moving communication user, which requires no channel estimation but achieves seamless data transmission. Finally, numerical examples validate the proposed approaches.


Title: Towards a quality metric for dense light fields
Abstract: Light fields become a popular representation of three dimensional scenes, and there is interest in their processing, resampling, and compression. As those operations often result in loss of quality, there is a need to quantify it. In this work, we collect a new dataset of dense reference and distorted light fields as well as the corresponding quality scores which are scaled in perceptual units. The scores were acquired in a subjective experiment using an interactive light-field viewing setup. The dataset contains typical artifacts that occur in light-field processing chain due to light-field reconstruction, multi-view compression, and limitations of automultiscopic displays. We test a number of existing objective quality metrics to determine how well they can predict the quality of light fields. We find that the existing image quality metrics provide good measures of light-field quality, but require dense reference light- fields for optimal performance. For more complex tasks of comparing two distorted light fields, their performance drops significantly, which reveals the need for new, light-field-specific metrics.


Title: Tensorial structure of the lifting doctrine in constructive domain theory
Abstract: We present a survey of the two-dimensional and tensorial structure of the lifting doctrine in constructive domain theory. We establish the universal property of lifting of directed-complete partial orders (dcpos) as the Sierpi\'nski cone, from which we deduce (1) that lifting forms a Kock-Z\"oberlein doctrine, (2) that lifting algebras, pointed dcpos, and inductive partial orders form canonically equivalent locally posetal 2-categories, and (3) that the category of lifting algebras is cocomplete, with connected colimits created by the forgetful functor to dcpos. Finally we deduce the symmetric monoidal closure of the Eilenberg-Moore resolution of the lifting 2-monad by means of smash products; these are shown to classify both bilinear maps and strict maps, which we prove to coincide in the constructive setting. We provide several concrete computations of the smash product as dcpo coequalisers and lifting algebra coequalisers, and compare these with the more abstract results of Seal. Although all these results are well-known classically, the existing proofs do not apply in a constructive setting; indeed, the classical analysis of the Eilenberg-Moore category of the lifting monad relies on the fact that all lifting algebras are free, a condition that is not known to hold constructively.


Title: BA-SAM: Scalable Bias-Mode Attention Mask for Segment Anything Model
Abstract: In this paper, we address the challenge of image resolution variation for the Segment Anything Model (SAM). SAM, known for its zero-shot generalizability, exhibits a performance degradation when faced with datasets with varying image sizes. Previous approaches tend to resize the image to a fixed size or adopt structure modifications, hindering the preservation of SAM's rich prior knowledge. Besides, such task-specific tuning necessitates a complete retraining of the model, which is cost-expensive and unacceptable for deployment in the downstream tasks. In this paper, we reformulate this issue as a length extrapolation problem, where token sequence length varies while maintaining a consistent patch size for images of different sizes. To this end, we propose Scalable Bias-Mode Attention Mask (BA-SAM) to enhance SAM's adaptability to varying image resolutions while eliminating the need for structure modifications. Firstly, we introduce a new scaling factor to ensure consistent magnitude in the attention layer's dot product values when the token sequence length changes. Secondly, we present a bias-mode attention mask that allows each token to prioritize neighboring information, mitigating the impact of untrained distant information. Our BA-SAM demonstrates efficacy in two scenarios: zero-shot and fine-tuning. Extensive evaluation on diverse datasets, including DIS5K, DUTS, ISIC, COD10K, and COCO, reveals its ability to significantly mitigate performance degradation in the zero-shot setting and achieve state-of-the-art performance with minimal fine-tuning. Furthermore, we propose a generalized model and benchmark, showcasing BA-SAM's generalizability across all four datasets simultaneously.


Title: Infinite Eulerian trails are computable on graphs with vertices of infinite degree
Abstract: The Erd\H{o}s, Gr\"unwald and Weiszfeld theorem provides a characterization of infinite graphs which are Eulerian. That is, infinite graphs which admit infinite Eulerian trails. In this article we complement this theorem with a characterization of those finite trails that can be extended to infinite Eulerian trails. This allows us to prove an effective version of the Erd\H{o}s, Gr\"unwald and Weiszfeld theorem for a class of graphs that includes non locally finite ones, generalizing a theorem of D.Bean.


Title: Evolution of Retweet Rates in Twitter User Careers: Analysis and Model
Abstract: We study the evolution of the number of retweets received by Twitter users over the course of their "careers" on the platform. We find that on average the number of retweets received by users tends to increase over time. This is partly expected because users tend to gradually accumulate followers. Normalizing by the number of followers, however, reveals that the relative, per-follower retweet rate tends to be non-monotonic, maximized at a "peak age" after which it does not increase, or even decreases. We develop a simple mathematical model of the process behind this phenomenon, which assumes a constantly growing number of followers, each of whom loses interest over time. We show that this model is sufficient to explain the non-monotonic nature of per-follower retweet rates, without any assumptions about the quality of content posted at different times.


Title: TSGAN: An Optical-to-SAR Dual Conditional GAN for Optical based SAR Temporal Shifting
Abstract: In contrast to the well-investigated field of SAR-to-Optical translation, this study explores the lesser-investigated domain of Optical-to-SAR translation, a challenging field due to the ill-posed nature of this translation. The complexity arises as a single optical data can have multiple SAR representations based on the SAR viewing geometry. We propose a novel approach, termed SAR Temporal Shifting, which inputs an optical data from the desired timestamp along with a SAR data from a different temporal point but with a consistent viewing geometry as the expected SAR data, both complemented with a change map of optical data during the intervening period. This model modifies the SAR data based on the changes observed in optical data to generate the SAR data for the desired timestamp. Our model, a dual conditional Generative Adversarial Network (GAN), named Temporal Shifting GAN (TSGAN), incorporates a siamese encoder in both the Generator and the Discriminator. To prevent the model from overfitting on the input SAR data, we employed a change weighted loss function. Our approach surpasses traditional translation methods by eliminating the GAN's fiction phenomenon, particularly in unchanged regions, resulting in higher SSIM and PSNR in these areas. Additionally, modifications to the Pix2Pix architecture and the inclusion of attention mechanisms have enhanced the model's performance on all regions of the data. This research paves the way for leveraging legacy optical datasets, the most abundant and longstanding source of Earth imagery data, extending their use to SAR domains and temporal analyses. To foster further research, we provide the code, datasets used in our study, and a framework for generating paired SAR-Optical datasets for new regions of interest. These resources are available on github.com/moienr/TemporalGAN


Title: Limits of subcritical random graphs and random graphs with excluded minors
Abstract: We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a compactification of the space of countable (connected) rooted graphs, and use it to generalise the notion of Benjamini-Schramm convergence in order to allow for vertices of infinite degree in the limit object.


Title: One Shot Learning as Instruction Data Prospector for Large Language Models
Abstract: Aligning large language models(LLMs) with human is a critical step in effectively utilizing their pre-trained capabilities across a wide array of language tasks. Current instruction tuning practices often rely on expanding dataset size without a clear strategy for ensuring data quality, which can inadvertently introduce noise and degrade model performance. To address this challenge, we introduce Nuggets, a novel and efficient methodology that employs one shot learning to select high-quality instruction data from expansive datasets. Nuggets assesses the potential of individual instruction examples to act as effective one shot examples, thereby identifying those that can significantly enhance diverse task performance. Nuggets utilizes a scoring system based on the impact of candidate examples on the perplexity of a diverse anchor set, facilitating the selection of the most beneficial data for instruction tuning. Through rigorous testing on two benchmarks, including MT-Bench and Alpaca-Eval, we demonstrate that instruction tuning with the top 1% of Nuggets-curated examples substantially outperforms conventional methods that use the full dataset. These findings advocate for a data selection paradigm that prioritizes quality, offering a more efficient pathway to align LLMs with humans.


Title: A Note on Matching Variables to Equations
Abstract: We showed with J. P. Gollin that if a (possibly infinite) homogeneous linear equation system has only the trivial solution, then there exists an injective function from the variables to the equations such that each variable has non-zero coefficient in its image. Shortly after a more elementary proof was found by Aharoni and Guo. In this note we present a very short matroid-theoretic proof which we believe is the simplest possible proof of this theorem.


Title: A Dataset for Statutory Reasoning in Tax Law Entailment and Question Answering
Abstract: Legislation can be viewed as a body of prescriptive rules expressed in natural language. The application of legislation to facts of a case we refer to as statutory reasoning, where those facts are also expressed in natural language. Computational statutory reasoning is distinct from most existing work in machine reading, in that much of the information needed for deciding a case is declared exactly once (a law), while the information needed in much of machine reading tends to be learned through distributional language statistics. To investigate the performance of natural language understanding approaches on statutory reasoning, we introduce a dataset, together with a legal-domain text corpus. Straightforward application of machine reading models exhibits low out-of-the-box performance on our questions, whether or not they have been fine-tuned to the legal domain. We contrast this with a hand-constructed Prolog-based system, designed to fully solve the task. These experiments support a discussion of the challenges facing statutory reasoning moving forward, which we argue is an interesting real-world task that can motivate the development of models able to utilize prescriptive rules specified in natural language.


Title: Full quantum crossed products, invariant measures, and type-I lifting
Abstract: We show that for a closed embedding $\mathbb{H}\le \mathbb{G}$ of locally compact quantum groups (LCQGs) with $\mathbb{G}/\mathbb{H}$ admitting an invariant probability measure, a unitary $\mathbb{G}$-representation is type-I if its restriction to $\mathbb{H}$ is. On a related note, we also prove that if an action $\mathbb{G}\circlearrowright A$ of an LCQG on a unital $C^*$-algebra admits an invariant state then the full group algebra of $\mathbb{G}$ embeds into the resulting full crossed product (and into the multiplier algebra of that crossed product if the original algebra is not unital). We also prove a few other results on crossed products of LCQG actions, some of which seem to be folklore; among them are (a) the fact that two mutually dual quantum-group morphisms produce isomorphic full crossed products, and (b) the fact that full and reduced crossed products by dual-coamenable LCQGs are isomorphic.


Title: Deep Demosaicing for Edge Implementation
Abstract: Most digital cameras use sensors coated with a Color Filter Array (CFA) to capture channel components at every pixel location, resulting in a mosaic image that does not contain pixel values in all channels. Current research on reconstructing these missing channels, also known as demosaicing, introduces many artifacts, such as zipper effect and false color. Many deep learning demosaicing techniques outperform other classical techniques in reducing the impact of artifacts. However, most of these models tend to be over-parametrized. Consequently, edge implementation of the state-of-the-art deep learning-based demosaicing algorithms on low-end edge devices is a major challenge. We provide an exhaustive search of deep neural network architectures and obtain a pareto front of Color Peak Signal to Noise Ratio (CPSNR) as the performance criterion versus the number of parameters as the model complexity that beats the state-of-the-art. Architectures on the pareto front can then be used to choose the best architecture for a variety of resource constraints. Simple architecture search methods such as exhaustive search and grid search require some conditions of the loss function to converge to the optimum. We clarify these conditions in a brief theoretical study.


Title: Accurate Leukocyte Detection Based on Deformable-DETR and Multi-Level Feature Fusion for Aiding Diagnosis of Blood Diseases
Abstract: In standard hospital blood tests, the traditional process requires doctors to manually isolate leukocytes from microscopic images of patients' blood using microscopes. These isolated leukocytes are then categorized via automatic leukocyte classifiers to determine the proportion and volume of different types of leukocytes present in the blood samples, aiding disease diagnosis. This methodology is not only time-consuming and labor-intensive, but it also has a high propensity for errors due to factors such as image quality and environmental conditions, which could potentially lead to incorrect subsequent classifications and misdiagnosis. To address these issues, this paper proposes an innovative method of leukocyte detection: the Multi-level Feature Fusion and Deformable Self-attention DETR (MFDS-DETR). To tackle the issue of leukocyte scale disparity, we designed the High-level Screening-feature Fusion Pyramid (HS-FPN), enabling multi-level fusion. This model uses high-level features as weights to filter low-level feature information via a channel attention module and then merges the screened information with the high-level features, thus enhancing the model's feature expression capability. Further, we address the issue of leukocyte feature scarcity by incorporating a multi-scale deformable self-attention module in the encoder and using the self-attention and cross-deformable attention mechanisms in the decoder, which aids in the extraction of the global features of the leukocyte feature maps. The effectiveness, superiority, and generalizability of the proposed MFDS-DETR method are confirmed through comparisons with other cutting-edge leukocyte detection models using the private WBCDD, public LISC and BCCD datasets. Our source code and private WBCCD dataset are available at https://github.com/JustlfC03/MFDS-DETR.


Title: Multifunctions determined by integrable functions
Abstract: Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.


Title: Weighted extremal metrics on blowups
Abstract: We show that if a compact K\"ahler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo--Pacard--Singer and Sz\'ekelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of K\"ahler--Ricci solitons and $\mu$-cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds.


Title: Cross-modal Prototype Driven Network for Radiology Report Generation
Abstract: Radiology report generation (RRG) aims to describe automatically a radiology image with human-like language and could potentially support the work of radiologists, reducing the burden of manual reporting. Previous approaches often adopt an encoder-decoder architecture and focus on single-modal feature learning, while few studies explore cross-modal feature interaction. Here we propose a Cross-modal PROtotype driven NETwork (XPRONET) to promote cross-modal pattern learning and exploit it to improve the task of radiology report generation. This is achieved by three well-designed, fully differentiable and complementary modules: a shared cross-modal prototype matrix to record the cross-modal prototypes; a cross-modal prototype network to learn the cross-modal prototypes and embed the cross-modal information into the visual and textual features; and an improved multi-label contrastive loss to enable and enhance multi-label prototype learning. XPRONET obtains substantial improvements on the IU-Xray and MIMIC-CXR benchmarks, where its performance exceeds recent state-of-the-art approaches by a large margin on IU-Xray and comparable performance on MIMIC-CXR.


Title: Tensor Ranks and the Fine-Grained Complexity of Dynamic Programming
Abstract: Generalizing work of K\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a tensor of transition costs between nodes in the grid. This captures many classical problems which are solved using DP such as the knapsack problem, the airplane refueling problem, and the minimal-weight polygon triangulation problem. We observe that for many of these problems, the tensor naturally has low tensor rank or low slice rank. We then give new algorithms and a web of fine-grained reductions to tightly determine the complexity of these problems. For instance, we show that a polynomial speedup over the DP algorithm is possible when the tensor rank is a constant or the slice rank is 1, but that such a speedup is impossible if the tensor rank is slightly super-constant (assuming SETH) or the slice rank is at least 3 (assuming the APSP conjecture). We find that this characterizes the known complexities for many of these problems, and in some cases leads to new faster algorithms.


Title: On the joint distributions of succession and Eulerian statistics
Abstract: The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102--124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum. We discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and several Eulerian-type statistics.


Title: Adaptive Signal Variances: CNN Initialization Through Modern Architectures
Abstract: Deep convolutional neural networks (CNN) have achieved the unwavering confidence in its performance on image processing tasks. The CNN architecture constitutes a variety of different types of layers including the convolution layer and the max-pooling layer. CNN practitioners widely understand the fact that the stability of learning depends on how to initialize the model parameters in each layer. Nowadays, no one doubts that the de facto standard scheme for initialization is the so-called Kaiming initialization that has been developed by He et al. The Kaiming scheme was derived from a much simpler model than the currently used CNN structure having evolved since the emergence of the Kaiming scheme. The Kaiming model consists only of the convolution and fully connected layers, ignoring the max-pooling layer and the global average pooling layer. In this study, we derived the initialization scheme again not from the simplified Kaiming model, but precisely from the modern CNN architectures, and empirically investigated how the new initialization method performs compared to the de facto standard ones that are widely used today.


Title: Configuration space, moduli space and 3-fold covering space
Abstract: A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\phi: B_k \rightarrow \Gamma_{g,b}$ is induced by 3-fold branched covering over a disk with some branch points. In this thesis we give a concrete description of this map and show that it is injective by Birman-Hilden theory. This gives us a new interesting non-geometric embedding of braid group into mapping class group. On the other hand, we show that the map on the level of classifying spaces of groups is compatible with the action of little 2-cube operad so that it induces a trivial homomorphim between stable homology group of braid groups and that of mapping class groups(Harer conjecture). We also show how the lift $\tilde{\beta_i}$ acts on the fundamental group of the surface and through this we prove that $\tilde{\beta_i}$ equals the product of two inverse Dehn twists.