Title: Fano threefolds with noncyclic torsion in the divisor class group
Abstract: In this note we study Fano threefolds with noncyclic torsion in the divisor class group. Since they can all be obtained as quotients of Fano threefolds, we get also all examples that can be obtained as quotients of low codimension Fanos in the weighted projective space.


Title: An Adjusted Nearest Neighbor Algorithm Maximizing the F-Measure from Imbalanced Data
Abstract: In this paper, we address the challenging problem of learning from imbalanced data using a Nearest-Neighbor (NN) algorithm. In this setting, the minority examples typically belong to the class of interest requiring the optimization of specific criteria, like the F-Measure. Based on simple geometrical ideas, we introduce an algorithm that reweights the distance between a query sample and any positive training example. This leads to a modification of the Voronoi regions and thus of the decision boundaries of the NN algorithm. We provide a theoretical justification about the weighting scheme needed to reduce the False Negative rate while controlling the number of False Positives. We perform an extensive experimental study on many public imbalanced datasets, but also on large scale non public data from the French Ministry of Economy and Finance on a tax fraud detection task, showing that our method is very effective and, interestingly, yields the best performance when combined with state of the art sampling methods.


Title: Two dimensional gravity waves at low regularity II: Global solutions
Abstract: This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such solutions have been proved to exist earlier in [15, 7, 10, 12] in much higher regularity. Our goal in this paper is to improve these results and prove global well-posedness under minimal regularity and decay assumptions for the initial data. One key ingredient here is represented by the balanced cubic estimates in our first paper. Another is the nonlinear vector field Sobolev inequalities, an idea first introduced by the last two authors in the context of the Benjamin-Ono equations [14].


Title: Quantiles on global non-positive curvature spaces
Abstract: This paper develops a notion of geometric quantiles on Hadamard spaces, also known as global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary condition on the gradient of the quantile loss function at quantiles on Hadamard manifolds, we investigate asymptotic properties of sample quantiles on Hadamard manifolds, such as strong consistency and joint asymptotic normality. We provide a detailed description of how to compute quantiles using a gradient descent algorithm in hyperbolic space and, in particular, an explicit formula for the gradient of the quantile loss function, along with experiments using simulated and real single-cell RNA sequencing data.


Title: The uniform companion for fields with free operators in characteristic zero
Abstract: Generalising the uniform companion for large fields with a single derivation, we construct a theory $\text{UC}_{\mathcal{D}}$ of fields of characteristic $0$ with free operators -- operators determined by a homomorphism from the field to its tensor product with $\mathcal{D}$, a finite-dimensional $\mathbb{Q}$-algebra -- which is the model companion of any theory of a field with free operators whose associated difference field is difference large and model complete. Under the assumption that $\mathcal{D}$ is a local ring, we show that simplicity is transferred from the theory of the underlying field to the theory of the field with operators, and we use this to study the model theory of bounded, PAC fields with free operators.


Title: Advanced Determinant Calculus: A Complement
Abstract: This is a complement to my previous article "Advanced Determinant Calculus" (S\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441-456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.


Title: Full instability of boundary layers with the Navier boundary condition
Abstract: We consider the problem of the stability of the Navier-Stokes equations in $\mathbb{T}\times \mathbb{R}_+$ near shear flows which are linearly unstable for the Euler equation. In \cite{greniernguyen}, the authors prove an $L^{\infty}$ instability result for the no-slip boundary condition which also denies the validity of the Prandtl boundary layer expansion. In this paper, we generalise this result to a Navier slip boundary condition with viscosity dependent slip length: $\partial_y u =\nu^{-\gamma}u$ at $y=0$, where $\gamma >1/2$. This range includes the physical slip rate $\gamma=1$.


Title: Large Language Models Relearn Removed Concepts
Abstract: Advances in model editing through neuron pruning hold promise for removing undesirable concepts from large language models. However, it remains unclear whether models have the capacity to reacquire pruned concepts after editing. To investigate this, we evaluate concept relearning in models by tracking concept saliency and similarity in pruned neurons during retraining. Our findings reveal that models can quickly regain performance post-pruning by relocating advanced concepts to earlier layers and reallocating pruned concepts to primed neurons with similar semantics. This demonstrates that models exhibit polysemantic capacities and can blend old and new concepts in individual neurons. While neuron pruning provides interpretability into model concepts, our results highlight the challenges of permanent concept removal for improved model \textit{safety}. Monitoring concept reemergence and developing techniques to mitigate relearning of unsafe concepts will be important directions for more robust model editing. Overall, our work strongly demonstrates the resilience and fluidity of concept representations in LLMs post concept removal.


Title: Deep AUC Maximization for Medical Image Classification: Challenges and Opportunities
Abstract: In this extended abstract, we will present and discuss opportunities and challenges brought about by a new deep learning method by AUC maximization (aka \underline{\bf D}eep \underline{\bf A}UC \underline{\bf M}aximization or {\bf DAM}) for medical image classification. Since AUC (aka area under ROC curve) is a standard performance measure for medical image classification, hence directly optimizing AUC could achieve a better performance for learning a deep neural network than minimizing a traditional loss function (e.g., cross-entropy loss). Recently, there emerges a trend of using deep AUC maximization for large-scale medical image classification. In this paper, we will discuss these recent results by highlighting (i) the advancements brought by stochastic non-convex optimization algorithms for DAM; (ii) the promising results on various medical image classification problems. Then, we will discuss challenges and opportunities of DAM for medical image classification from three perspectives, feature learning, large-scale optimization, and learning trustworthy AI models.


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: Exploring Boundary of GPT-4V on Marine Analysis: A Preliminary Case Study
Abstract: Large language models (LLMs) have demonstrated a powerful ability to answer various queries as a general-purpose assistant. The continuous multi-modal large language models (MLLM) empower LLMs with the ability to perceive visual signals. The launch of GPT-4 (Generative Pre-trained Transformers) has generated significant interest in the research communities. GPT-4V(ison) has demonstrated significant power in both academia and industry fields, as a focal point in a new artificial intelligence generation. Though significant success was achieved by GPT-4V, exploring MLLMs in domain-specific analysis (e.g., marine analysis) that required domain-specific knowledge and expertise has gained less attention. In this study, we carry out the preliminary and comprehensive case study of utilizing GPT-4V for marine analysis. This report conducts a systematic evaluation of existing GPT-4V, assessing the performance of GPT-4V on marine research and also setting a new standard for future developments in MLLMs. The experimental results of GPT-4V show that the responses generated by GPT-4V are still far away from satisfying the domain-specific requirements of the marine professions. All images and prompts used in this study will be available at https://github.com/hkust-vgd/Marine_GPT-4V_Eval


Title: Index concepts for linear differential-algebraic equations in finite and infinite dimensions
Abstract: Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are equivalent. For infinite-dimensional systems, the situation is more complex. It is proven that although some indices imply others, in general they are not equivalent. The situation is illustrated with a number of examples.


Title: Ahlfors' contribution to the theory of meromorphic functions
Abstract: This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. It contains a survey of his work on meromorphic functions and related topics written in 1929-1941.


Title: Lower bounds for the eigenvalue estimates of the submanifold Dirac operator
Abstract: We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets several known results in this direction.


Title: On Higher-Order Extensions of the Weighted Projection Body Operator
Abstract: For a convex body $K$ in $\mathbb{R}^n$, the inequalities of Rogers-Shephard and Zhang, written succinctly, are $\text{vol}_n(DK)\leq \binom{2n}{n} \text{vol}_n(K) \leq \text{vol}_n(n\text{vol}_n(K)\Pi^\circ K).$ Here, $DK=\{x\in\mathbb{R}^n:K\cap(K+x)\neq \emptyset\}$ is the difference body of $K$, and $\Pi^\circ K$ is the polar projection body of $K$. There is equality in either if, and only if, $K$ is a $n$-dimensional simplex. In fact, there exists a collection of convex bodies, the so-called radial mean bodies $R_p K$ introduced by Gardner and Zhang, which continuously interpolates between $DK$ and $\Pi^\circ K$. Schneider defined the higher-order difference body as, for $m\in\mathbb{N}$, $$D^m(K)=\{(x_1,\dots,x_m)\in\mathbb{R}^{nm}:K\cap_{i=1}^m(K+x_i)\neq \emptyset\}\subset \mathbb{R}^{nm}$$ and proved a higher-order version of the Rogers-Shephard inequality. In a prequel to this work, the authors, working with Haddad, extended the higher-order concept to the radial mean bodies and the polar projection body, establishing the associated Zhang-type inequality. In this work, we introduce weighted versions of the above-mentioned operators by replacing the Lebesgue measure with measures that have density. The weighted version of these operators in the $m=1$ case was first done by Roysdon (difference body), Langharst-Roysdon-Zvavitch (polar projection body) and Langharst-Putterman (radial mean bodies). This work can be seen as a sequel to all those works, generalizing them to the higher-order setting. In the last section, we extend many of these ideas to the setting of generalized volume, first introduced by Gardner-Hug-Weil-Xing-Ye.


Title: Learning circuits with few negations
Abstract: Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions. We study this generalization of monotonicity from the vantage point of learning theory, giving near-matching upper and lower bounds on the uniform-distribution learnability of circuits in terms of the number of negations they contain. Our upper bounds are based on a new structural characterization of negation-limited circuits that extends a classical result of A. A. Markov. Our lower bounds, which employ Fourier-analytic tools from hardness amplification, give new results even for circuits with no negations (i.e. monotone functions).


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: Nilpotent polynomials over $\mathbb{Z}$
Abstract: For a polynomial $u(x)$ in $\mathbb{Z}[x]$ and $r\in\mathbb{Z}$, we consider the orbit of $u$ at $r$ denoted and defined by $\mathcal{O}_u(r):=\{u^{(n)}(r)~|~n\in\mathbb{N}\}$. Here we study polynomials for which $0$ is in the orbit for a given $r$. We provide a complete classification of these polynomials when $|r|\le 4$, with $|r|\le 1$ already done in \cite{SS23}. The central goal of this paper is to study the following questions: (i) relationship between the integers $r$ and $m$, for a polynomial $u$ in $N_{r,m}$; (ii) classification of the polynomials with nilpotency index $|r|$ for large enough $|r|$; and (iii) integer sequences with a generating polynomial.


Title: On Model Compression for Neural Networks: Framework, Algorithm, and Convergence Guarantee
Abstract: Model compression is a crucial part of deploying neural networks (NNs), especially when the memory and storage of computing devices are limited in many applications. This paper focuses on two model compression techniques: low-rank approximation and weight pruning in neural networks, which are very popular nowadays. However, training NN with low-rank approximation and weight pruning always suffers significant accuracy loss and convergence issues. In this paper, a holistic framework is proposed for model compression from a novel perspective of nonconvex optimization by designing an appropriate objective function. Then, we introduce NN-BCD, a block coordinate descent (BCD) algorithm to solve the nonconvex optimization. One advantage of our algorithm is that an efficient iteration scheme can be derived with closed-form, which is gradient-free. Therefore, our algorithm will not suffer from vanishing/exploding gradient problems. Furthermore, with the Kurdyka-{\L}ojasiewicz (K{\L}) property of our objective function, we show that our algorithm globally converges to a critical point at the rate of O(1/k), where k denotes the number of iterations. Lastly, extensive experiments with tensor train decomposition and weight pruning demonstrate the efficiency and superior performance of the proposed framework. Our code implementation is available at https://github.com/ChenyangLi-97/NN-BCD


Title: Graph Neural Network Based Access Point Selection for Cell-Free Massive MIMO Systems
Abstract: A graph neural network (GNN) based access point (AP) selection algorithm for cell-free massive multiple-input multiple-output (MIMO) systems is proposed. Two graphs, a homogeneous graph which includes only AP nodes representing the structure of the APs in the network, and a heterogeneous graph which includes both AP nodes and user equipment (UE) nodes are constructed to represent a cell-free massive MIMO network. A GNN based on the inductive graph learning framework GraphSAGE is used to obtain the embeddings which are then used to predict the links between the nodes. The numerical results show that compared to the proximity-based AP selection algorithms, the proposed GNN based algorithm predicts the potential APs with more accuracy. Compared to the large scale fading coefficient based AP selection algorithms, the proposed algorithm does not require measured and sorted signal strengths of all the neighbouring APs. Furthermore, the proposed algorithm is scalable in terms of the number of users in the cell-free system.


Title: Finite subgraphs of an extension graph
Abstract: Let $\Gamma$ be a finite graph and let $\Gamma^{\mathrm{e}}$ be its extension graph. We inductively define a sequence $\{\Gamma_i\}$ of finite induced subgraphs of $\Gamma^{\mathrm{e}}$ through successive applications of an operation called "doubling along a star". Then we show that every finite induced subgraph of $\Gamma^{\mathrm{e}}$ is isomorphic to an induced subgraph of some $\Gamma_i$.


Title: Joint Beamforming and Offloading Design for Integrated Sensing, Communication and Computation System
Abstract: Mobile edge computing (MEC) is powerful to alleviate the heavy computing tasks in integrated sensing and communication (ISAC) systems. In this paper, we investigate joint beamforming and offloading design in a three-tier integrated sensing, communication and computation (ISCC) framework comprising one cloud server, multiple mobile edge servers, and multiple terminals. While executing sensing tasks, the user terminals can optionally offload sensing data to either MEC server or cloud servers. To minimize the execution latency, we jointly optimize the transmit beamforming matrices and offloading decision variables under the constraint of sensing performance. An alternating optimization algorithm based on multidimensional fractional programming is proposed to tackle the non-convex problem. Simulation results demonstrates the superiority of the proposed mechanism in terms of convergence and task execution latency reduction, compared with the state-of-the-art two-tier ISCC framework.


Title: Bayesian Neural Network Versus Ex-Post Calibration For Prediction Uncertainty
Abstract: Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on non-probabilistic neural networks which by default do not capture this inherent uncertainty. This well-known problem has led to the development of post-hoc calibration procedures, such as Platt scaling (logistic), isotonic and beta calibration, which transforms the scores into well calibrated empirical probabilities. A plausible alternative to the calibration approach is to use Bayesian neural networks, which directly models a predictive distribution. Although they have been applied to images and text datasets, they have seen limited adoption in the tabular and small data regime. In this paper, we demonstrate that Bayesian neural networks yields competitive performance when compared to calibrated neural networks and conduct experiments across a wide array of datasets.


Title: A Preliminary Exploration of Floating Point Grammatical Evolution
Abstract: Current GP frameworks are highly effective on a range of real and simulated benchmarks. However, due to the high dimensionality of the genotypes for GP, the task of visualising the fitness landscape for GP search can be difficult. This paper describes a new framework: Floating Point Grammatical Evolution (FP-GE) which uses a single floating point genotype to encode an individual program. This encoding permits easier visualisation of the fitness landscape arbitrary problems by providing a way to map fitness against a single dimension. The new framework also makes it trivially easy to apply continuous search algorithms, such as Differential Evolution, to the search problem. In this work, the FP-GE framework is tested against several regression problems, visualising the search landscape for these and comparing different search meta-heuristics.


Title: A note on the equidistribution of $3$-colour partitions
Abstract: In this short note, we prove equidistribution results regarding three families of three-colour partitions recently introduced by Schlosser and Zhou. To do so, we prove an asymptotic formula for the infinite product $F_{a,c}(\zeta ; {\rm e}^{-z}) := \prod_{n \geq 0} \big(1- \zeta {\rm e}^{-(a+cn)z}\big)$ ($a,c \in \mathbb{N}$ with $0<a\leq c$ and $\zeta$ a root of unity) when $z$ lies in certain sectors in the right half-plane, which may be useful in studying similar problems. As a corollary, we obtain the asymptotic behaviour of the three-colour partition families at hand.


Title: On the maximal and minimal degree components of the cocenter of the cyclotomic KLR algebras
Abstract: Let $\mathscr{R}_\alpha^\Lambda$ be the cyclotomic KLR algebra associated to a symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$ and polynomials $\{Q_{ij}(u,v)\}_{i,j\in I}$. Shan, Varagnolo and Vasserot show that, when the ground field $K$ has characteristic $0$, the degree $d$ component of the cocenter $Tr(\mathscr{R}_\alpha^\Lambda)$ is nonzero only if $0\leq d\leq d_{\Lambda,\alpha}$. In this paper we show that this holds true for arbitrary ground field $K$, arbitrary $\mathfrak{g}$ and arbitrary polynomials $\{Q_{ij}(u,v)\}_{i,j\in I}$. We generalize our earlier results on the $K$-linear generators of $Tr(\mathscr{R}_\alpha^\Lambda), Tr(\mathscr{R}_\alpha^\Lambda)_0, Tr(\mathscr{R}_\alpha^\Lambda)_{d_{\Lambda,\alpha}}$ to arbitrary ground field $K$. Moreover, we show that the dimension of the degree $0$ component $Tr(\mathscr{R}_\alpha^\Lambda)_0$ is always equal to $\dim V(\Lambda)_{\Lambda-\alpha}$, where $V(\Lambda)$ is the integrable highest weight $U(\mathfrak{g})$-module with highest weight $\Lambda$, and we obtain a basis for $Tr(\mathscr{R}_\alpha^\Lambda)_0$.


Title: Geometric structures of late points of a two-dimensional simple random walk
Abstract: We consider the problem, as suggested by Dembo ($2003$, $2006$), of late points of a simple random walk in two dimensions. It has been shown that the exponents for the numbers of pairs of late points coincide with those of nearly favorite points and high points in the Gaussian free field, whose exact values are known. We estimate the exponents for the numbers of a multipoint set of late points in average. While there have been observed certain similarities between among three classes of points, our results exhibit a difference.


Title: Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator
Abstract: We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov{\'a}sz--Schrijver SDP operator $\LS_+$, with a particular focus on a search for relatively small graphs with high $\LS_+$-rank (the least number of iterations of the $\LS_+$ operator on the fractional stable set polytope to compute the stable set polytope). We provide families of graphs whose $\LS_+$-rank is asymptotically a linear function of its number of vertices, which is the best possible up to improvements in the constant factor (previous best result in this direction, from 1999, yielded graphs whose $\LS_+$-rank only grew with the square root of the number of vertices).


Title: Introducing an experimental distortion-tolerant speech encryption scheme for secure voice communication
Abstract: The current increasing need for privacy-preserving voice communications is leading to new ideas for securing voice transmission. This paper refers to a relatively new concept of sending encrypted speech as pseudo-speech in the audio domain over digital voice communication infrastructures, like 3G cellular network and VoIP. This work presents a novel distortion-tolerant speech encryption scheme for secure voice communications over voice channels that combines the robustness of analog speech scrambling and elevated security offered by digital ciphers like AES-CTR. The system scrambles vocal parameters of a speech signal (loudness, pitch, timbre) using distance-preserving pseudo-random translations and rotations on a hypersphere of parameters. Next, scrambled parameters are encoded to a pseudo-speech signal adapted to transmission over digital voice channels equipped with voice activity detection. Upon reception of this pseudo-speech signal, the legitimate receiver restores distorted copies of the initial vocal parameters. Despite some deciphering errors, an integrated neural-based vocoder based on the LPCNet architecture reconstructs an intelligible speech. The experimental implementation of this speech encryption scheme has been tested by simulations and sending an encrypted signal over FaceTime between two iPhones 6 connected to the same WiFi network. Moreover, speech excerpts restored from encrypted signals were evaluated by a speech quality assessment on a group of about 40 participants. The experiments demonstrated that the proposed scheme produces intelligible speech with a gracefully progressive quality degradation depending on the channel noise. Finally, the preliminary computational analysis suggested that the presented setting may operate on high-end portable devices in nearly real-time.


Title: Bayesian optimization for backpropagation in Monte-Carlo tree search
Abstract: In large domains, Monte-Carlo tree search (MCTS) is required to estimate the values of the states as efficiently and accurately as possible. However, the standard update rule in backpropagation assumes a stationary distribution for the returns, and particularly in min-max trees, convergence to the true value can be slow because of averaging. We present two methods, Softmax MCTS and Monotone MCTS, which generalize previous attempts to improve upon the backpropagation strategy. We demonstrate that both methods reduce to finding optimal monotone functions, which we do so by performing Bayesian optimization with a Gaussian process (GP) prior. We conduct experiments on computer Go, where the returns are given by a deep value neural network, and show that our proposed framework outperforms previous methods.


Title: An analysis of the logic of Riesz Spaces with strong unit
Abstract: We study \L ukasiewicz logic enriched with a scalar multiplication with scalars taken in $[0,1]$. Its algebraic models, called {\em Riesz MV-algebras}, are, up to isomorphism, unit intervals of Riesz spaces with a strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of {\em DMV-algebras} and a corresponding logical system. Our research follows two objectives. The first one is to deepen the connections between functional analysis and the logic of Riesz MV-algebras. The second one is to study the finitely presented MV-algebras, DMV-algebras and Riesz MV-algebras, connecting them from logical, algebraic and geometric perspective.


Title: A survey on set-theoretical solutions to the pentagon equation
Abstract: This survey aims to collect the main results of the theory of the set-theoretical solutions to the pentagon equation obtained up to now in the literature. In particular, we present some classes of these solutions and raise some questions.


Title: Chordal graphs, even-hole-free graphs and sparse obstructions to bounded treewidth
Abstract: We present and study the following conjecture: for an integer $t\geq 4$ and a graph $H$, every even-hole-free graph of large enough treewidth has an induced subgraph isomorphic to either $K_t$ or $H$, if (and only if) $H$ is a $K_4$-free chordal graph. The ``only if'' part follows from the properties of the so-called layered wheels due to Sintiari and Trotignon. Alecu, Chudnovsky, Spirkl and the author recently proved the conjecture in two special cases: (a) when $t=4$; and (b) when $H=cone (F)$ for some forest $F$; that is, $H$ is obtained from $F$ by adding a universal vertex. Our first result is a common strengthening: for an integer $t\geq 4$ and graphs $F$ and $H$, (even-hole, $cone(cone (F))$, $H$, $K_t$)-free graphs have bounded treewidth if and only if $F$ is a forest and $H$ is a $K_4$-free chordal graph. For general $t\geq 4$, we push the current state of the art further than (b) by settling the conjecture for the smallest choices of $H$ that are not coned forests. This follows from our second result: we prove the conjecture when $H$ is a crystal; that is, a graph obtained from several coned double stars by gluing them together along the middle edges of the double stars. We also propose another conjecture motivated by the following observation: except for complete graphs and complete bipartite graphs, all the constructions of graphs with unbounded treewidth which have been discovered so far are $2$-degenerate. Specifically, we conjecture that for every $t\geq 1$, every graph of sufficiently large treewidth has an induced subgraph of treewidth $t$ which is either complete, complete bipartite, or $2$-degenerate. This conjecture is the first to predict a grid-type theorem for induced subgraphs, and what makes it even more relevant is somewhat serendipitous: if true, it would imply our former conjecture by reducing it to (a).


Title: Rethinking Response Evaluation from Interlocutor's Eye for Open-Domain Dialogue Systems
Abstract: Open-domain dialogue systems have started to engage in continuous conversations with humans. Those dialogue systems are required to be adjusted to the human interlocutor and evaluated in terms of their perspective. However, it is questionable whether the current automatic evaluation methods can approximate the interlocutor's judgments. In this study, we analyzed and examined what features are needed in an automatic response evaluator from the interlocutor's perspective. The first experiment on the Hazumi dataset revealed that interlocutor awareness plays a critical role in making automatic response evaluation correlate with the interlocutor's judgments. The second experiment using massive conversations on X (formerly Twitter) confirmed that dialogue continuity prediction can train an interlocutor-aware response evaluator without human feedback while revealing the difficulty in evaluating generated responses compared to human responses.


Title: An Inversion Formula for the Gaussian Radon Transform for Banach Spaces
Abstract: We provide a disintegration theorem for the Gaussian Radon transform Gf on Banach spaces and use the Segal-Bargmann transform on abstract Wiener spaces to find a procedure to obtain f from its Gaussian Radon transform Gf.


Title: Permawound Unipotent Groups
Abstract: We introduce the class of permawound unipotent groups, and show that they simultaneously satisfy certain "ubiquity" and "rigidity" properties that in combination render them very useful in the study of general wound unipotent groups. As an illustration of their utility, we present two applications: We prove that nonsplit smooth unipotent groups over (infinite) finitely-generated fields have infinite first cohomology; and we show that every commutative p-torsion wound unipotent group over a field of degree of imperfection 1 is the maximal unipotent quotient of a commutative pseudo-reductive group, thus partially answering a question of Totaro.


Title: The ZFC analogue of the Halpern-Levy theorem
Abstract: Here we present ZFC theorems yielding the Halpern-L\a"uchli theorem and avoiding metamathematical notions in their formulations.


Title: Word-Representability of Graphs with respect to Split Recomposition
Abstract: In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the class of parity graphs is word-representable. Further, we obtain a characteristic property by which the recomposition of comparability graphs is a comparability graph. Consequently, we also establish the permutation-representation number (prn) of the resulting comparability graph. We also introduce a subclass of comparability graphs, called prn-irreducible graphs. We provide a criterion such that the split recomposition of two prn-irreducible graphs is a comparability graph and determine the prn of the resultant graph.


Title: Void Shape Identification in a 2D Point Distribution
Abstract: We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm. Our methodology initiates with the computational determination of the Convex Hull vertices within the point cloud, followed by a systematic selection of optimal line segments, strategically chosen for their likelihood of intersecting internal void regions. We then utilize Delaunay triangulation in conjunction with Voronoi diagrams to ascertain the initial points for the construction of the maximal internal curve envelope by adopting a pseudo-recursive approach for higher-order void identification. In each iteration, the existing collection of maximal internal curve envelope points serves as a basis for identifying additional candidate points. This iterative process is inherently self-converging, ensuring progressive refinement of the void's shape with each successive computation cycle. The mathematical robustness of this method allows for an efficient convergence to a stable solution, reflecting both the geometric intricacies and the topological characteristics of the voids within the point cloud. Our findings introduce a method that aims to balance geometric accuracy with computational practicality. The approach is designed to improve the understanding of void shapes within point clouds and suggests a potential framework for exploring more complex, multi-dimensional data analysis.


Title: On PFH and HF spectral invariants
Abstract: In this note, we define the link spectral invariants by using the cylindrical formulation of the quantitative Heegaard Floer homology. We call them HF spectral invariants. We deduce a relation between the HF spectral invariants and the PFH spectral invariants by using closed-open morphisms and open-closed morphisms. For the sphere, we prove that the homogenized HF spectral invariants at the unit are equal to the homogenized PFH spectral invariants. Moreover, we show that the homogenized PFH spectral invariants are quasimorphisms.


Title: Precise Regret Bounds for Log-loss via a Truncated Bayesian Algorithm
Abstract: We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper bounds for the sequential minimax regret that are defined as the excess loss it incurs over a class of experts. After proving a general upper bound, we consider some specific classes of experts from Lipschitz class to bounded Hessian class and derive matching lower and upper bounds with provably optimal constants. Our bounds work for a wide range of values of the data dimension and the number of rounds. To derive lower bounds, we use tools from information theory (e.g., Shtarkov sum) and for upper bounds, we resort to new "smooth truncated covering" of the class of experts. This allows us to find constructive proofs by applying a simple and novel truncated Bayesian algorithm. Our proofs are substantially simpler than the existing ones and yet provide tighter (and often optimal) bounds.


Title: Fluctuation of the Largest Eigenvalue of a Kernel Matrix with application in Graphon-based Random Graphs
Abstract: In this article, we explore the spectral properties of general random kernel matrices $[K(U_i,U_j)]_{1\leq i\neq j\leq n}$ from a Lipschitz kernel $K$ with $n$ independent random variables $U_1,U_2,\ldots, U_n$ distributed uniformly over $[0,1]$. In particular we identify a dichotomy in the extreme eigenvalue of the kernel matrix, where, if the kernel $K$ is degenerate, the largest eigenvalue of the kernel matrix (after proper normalization) converges weakly to a weighted sum of independent chi-squared random variables. In contrast, for non-degenerate kernels, it converges to a normal distribution extending and reinforcing earlier results from Koltchinskii and Gin\'e (2000). Further, we apply this result to show a dichotomy in the asymptotic behavior of extreme eigenvalues of $W$-random graphs, which are pivotal in modeling complex networks and analyzing large-scale graph behavior. These graphs are generated using a kernel $W$, termed as graphon, by connecting vertices $i$ and $j$ with probability $W(U_i, U_j)$. Our results show that for a Lipschitz graphon $W$, if the degree function is constant, the fluctuation of the largest eigenvalue (after proper normalization) converges to the weighted sum of independent chi-squared random variables and an independent normal distribution. Otherwise, it converges to a normal distribution.


Title: Bernstein components via Bernstein center
Abstract: Let G be a reductive p-adic group. Let $\Phi$ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that $\Phi$ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr(G); in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modiification of the arguments of J.F.Dat who proved our result in one direction.


Title: Two kinds of partial Motzkin paths with air pockets
Abstract: Motzkin paths with air pockets (MAP) are defined as a generalization of Dyck paths with air pockets by adding some horizontal steps with certain conditions. In this paper, we introduce two generalizations. The first one consists of lattice paths in $\Bbb{N}^2$ starting at the origin made of steps $U=(1,1)$, $D_k=(1,-k)$, $k\geq 1$ and $H=(1,0)$, where two down steps cannot be consecutive, while the second one are lattice paths in $\Bbb{N}^2$ starting at the origin, made of steps $U$, $D_k$ and $H$, where each step $D_k$ and $H$ is necessarily followed by an up step, except for the last step of the path. We provide enumerative results for these paths according to the length, the type of the last step, and the height of its end-point. A similar study is made for these paths read from right to left. As a byproduct, we obtain new classes of paths counted by the Motzkin numbers. Finally, we express our results using Riordan arrays.


Title: The Influence of Biomedical Research on Future Business Funding: Analyzing Scientific Impact and Content in Industrial Investments
Abstract: This paper investigates the relationship between scientific innovation in biomedical sciences and its impact on industrial activities, focusing on how the historical impact and content of scientific papers influenced future funding and innovation grant application content for small businesses. The research incorporates bibliometric analyses along with SBIR (Small Business Innovation Research) data to yield a holistic view of the science-industry interface. By evaluating the influence of scientific innovation on industry across 10,873 biomedical topics and taking into account their taxonomic relationships, we present an in-depth exploration of science-industry interactions where we quantify the temporal effects and impact latency of scientific advancements on industrial activities, spanning from 2010 to 2021. Our findings indicate that scientific progress substantially influenced industrial innovation funding and the direction of industrial innovation activities. Approximately 76% and 73% of topics showed a correlation and Granger-causality between scientific interest in papers and future funding allocations to relevant small businesses. Moreover, around 74% of topics demonstrated an association between the semantic content of scientific abstracts and future grant applications. Overall, the work contributes to a more nuanced and comprehensive understanding of the science-industry interface, opening avenues for more strategic resource allocation and policy developments aimed at fostering innovation.


Title: Von Neumann entropy of the angle operator between a pair of intermediate subalgebras
Abstract: Given a pair of intermediate $C^*$-subalgebras of a unital inclusion of simple $C^*$-algebras with a conditional expectation of finite Watatani index, we discuss the corresponding angle operator and its Fourier transform. We provide a calculable formula for the von Neumann entropy of the (Fourier) dual angle operator for a large class of quadruple of simple $C^*$-algebras.


Title: Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies
Abstract: In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.


Title: Parsing using a grammar of word association vectors
Abstract: This paper was was first drafted in 2001 as a formalization of the system described in U.S. patent U.S. 7,392,174. It describes a system for implementing a parser based on a kind of cross-product over vectors of contextually similar words. It is being published now in response to nascent interest in vector combination models of syntax and semantics. The method used aggressive substitution of contextually similar words and word groups to enable product vectors to stay in the same space as their operands and make entire sentences comparable syntactically, and potentially semantically. The vectors generated had sufficient representational strength to generate parse trees at least comparable with contemporary symbolic parsers.


Title: Marked random graphs with given degree sequence: large deviations on the local topology
Abstract: We investigate the behavior of the empirical neighbourhood distribution of marked graphs in the framework of local weak convergence. We establish a large deviation principle for such families of empirical measures. The proof builds on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's 2019 introduction of BC entropy, relying on combinatorial lemmas that allow one to construct suitable approximations of measures supported on marked trees.


Title: Diabetic Retinopathy Using Gaussian Filter
Abstract: The retina is an essential component of the visual system, and maintaining eyesight depends on the timely and correct detection of disorders. This research specifically addresses the early-stage detection and severity classification of diabetic retinopathy (DR), a serious public health hazard. We compare the results of different deep learning models such as InceptionV3, DenseNet121 and other CNN based models by using different image filters, such as Gaussian, grayscale and Gabor. These models could detect subtle pathological alterations and use that information to estimate the risk of retinal illnesses. The objective is to improve the diagnostic processes for diabetic retinopathy, the primary cause of diabetes-related blindness, by utilizing deep learning models. A comparative analysis between Greyscale, Gaussian and Gabor filters has been provided after applying these filters on the retinal images. The Gaussian filter resulted to be the most promising filter giving the best accuracies for all the models. The best performing model was InceptionV3 which gave an accuracy of 96% on Gaussian images, therefore Gaussian filter emerged as our most promising filter.


Title: Group actions on stacks and applications to equivariant string topology for stacks
Abstract: This paper is a continuations of the project initiated in the book string topology for stacks. We construct string operations on the SO(2)-equivariant homology of the (free) loop space $L(X)$ of an oriented differentiable stack $X$ and show that $H^{SO(2)}_{*+dim(X) -2}(L(X))$ is a graded Lie algebra. In the particular case where $X$ is a 2-dimensional orbifold we give a Goldman-type description for the string bracket. To prove these results, we develop a machinery of (weak) group actions on topological stacks which should be of independent interest. We explicitly construct the quotient stack of a group acting on a stack and show that it is a topological stack. Then use its homotopy type to define equivariant (co)homology for stacks, transfer maps, and so on.


Title: On Brown-York mass and compactly conformal deformations of scalar curvature
Abstract: In this article, we found a connection between Brown-York mass and the first Dirichlet Eigenvalue of a Schr\"odingier type operator. In particular, we proved a local positive mass type theorem for metrics conformal to the background one with suitable presumptions. As applications, we investigated compactly conformal deformations which either increase or decrease scalar curvature. We found local conformal rigidity phenomena occur in both cases for small domains and as for manifolds with nonpositive scalar curvature it is even more rigid in particular. On the other hand, such deformations exist for closed manifolds with positive scalar curvature. We also constructed such kind of deformations on a type of product manifolds that either increase or decrease their scalar curvature compactly and conformally. These results together answered a natural question arises in \cite{Corvino, Lohkamp}.


Title: Symmetry Breaking in Symmetric Tensor Decomposition
Abstract: In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by standard gradient based methods are \emph{symmetry breaking} with respect to the target tensor. The phenomena, seen for different choices of target tensors and norms, make possible the use of recently developed analytic and algebraic tools for studying nonconvex optimization landscapes exhibiting symmetry breaking phenomena of similar nature.


Title: A sample iterated small cancellation theory for groups of Burnside type
Abstract: We develop yet another technique to present the free Burnside group $B(m,n)$ of odd exponent $n$ with $m\ge2$ generators as a group satisfying a certain iterated small cancellation condition. Using the approach, we provide a reasonably accessible proof that $B(m,n)$ is infinite with a moderate bound $n > 2000$ on the odd exponent $n$.


Title: A Geometry-Sensitive Approach for Photographic Style Classification
Abstract: Photographs are characterized by different compositional attributes like the Rule of Thirds, depth of field, vanishing-lines etc. The presence or absence of one or more of these attributes contributes to the overall artistic value of an image. In this work, we analyze the ability of deep learning based methods to learn such photographic style attributes. We observe that although a standard CNN learns the texture and appearance based features reasonably well, its understanding of global and geometric features is limited by two factors. First, the data-augmentation strategies (cropping, warping, etc.) distort the composition of a photograph and affect the performance. Secondly, the CNN features, in principle, are translation-invariant and appearance-dependent. But some geometric properties important for aesthetics, e.g. the Rule of Thirds (RoT), are position-dependent and appearance-invariant. Therefore, we propose a novel input representation which is geometry-sensitive, position-cognizant and appearance-invariant. We further introduce a two-column CNN architecture that performs better than the state-of-the-art (SoA) in photographic style classification. From our results, we observe that the proposed network learns both the geometric and appearance-based attributes better than the SoA.


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: Mobile ALOHA: Learning Bimanual Mobile Manipulation with Low-Cost Whole-Body Teleoperation
Abstract: Imitation learning from human demonstrations has shown impressive performance in robotics. However, most results focus on table-top manipulation, lacking the mobility and dexterity necessary for generally useful tasks. In this work, we develop a system for imitating mobile manipulation tasks that are bimanual and require whole-body control. We first present Mobile ALOHA, a low-cost and whole-body teleoperation system for data collection. It augments the ALOHA system with a mobile base, and a whole-body teleoperation interface. Using data collected with Mobile ALOHA, we then perform supervised behavior cloning and find that co-training with existing static ALOHA datasets boosts performance on mobile manipulation tasks. With 50 demonstrations for each task, co-training can increase success rates by up to 90%, allowing Mobile ALOHA to autonomously complete complex mobile manipulation tasks such as sauteing and serving a piece of shrimp, opening a two-door wall cabinet to store heavy cooking pots, calling and entering an elevator, and lightly rinsing a used pan using a kitchen faucet. Project website: https://mobile-aloha.github.io


Title: Propagation Path Loss Models for 5G Urban Micro- and Macro-Cellular Scenarios
Abstract: This paper presents and compares two candidate large-scale propagation path loss models, the alpha-beta-gamma (ABG) model and the close-in (CI) free space reference distance model, for the design of fifth generation (5G) wireless communication systems in urban micro- and macro-cellular scenarios. Comparisons are made using the data obtained from 20 propagation measurement campaigns or ray-tracing studies from 2 GHz to 73.5 GHz over distances ranging from 5 m to 1429 m. The results show that the one-parameter CI model has a very similar goodness of fit (i.e., the shadow fading standard deviation) in both line-of-sight and non-line-of-sight environments, while offering substantial simplicity and more stable behavior across frequencies and distances, as compared to the three-parameter ABG model. Additionally, the CI model needs only one very subtle and simple modification to the existing 3GPP floating-intercept path loss model (replacing a constant with a close-in free space reference value) in order to provide greater simulation accuracy, more simplicity, better repeatability across experiments, and higher stability across a vast range of frequencies.


Title: On the connected (sub)partition polytope
Abstract: Let $k$ be a positive integer and let $G$ be a graph with $n$ vertices. A connected $k$-subpartition of $G$ is a collection of $k$ pairwise disjoint sets (a.k.a. classes) of vertices in $G$ such that each set induces a connected subgraph. The connected $k$-partition polytope of $G$, denoted by $P(G,k)$, is defined as the convex hull of the incidence vectors of all connected $k$-subpartitions of $G$. Many applications arising in off-shore oil-drilling, forest planning, image processing, cluster analysis, political districting, police patrolling, and biology are modeled in terms of finding connected (sub)partitions of a graph. This study focus on the facial structure of $P(G,k)$ and the computational complexity of the corresponding separation problems. We first propose a set of valid inequalities having non-null coefficients associated with a single class that extends and generalizes the ones in the literature of related problems, show sufficient conditions for these inequalities to be facet-defining, and design a polynomial-time separation algorithm for them. We also devise two sets of inequalities that consider multiple classes, prove when they define facets, and study the computational complexity of associated separation problems.


Title: Ramsey numbers for bipartite graphs with small bandwidth
Abstract: We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. In particular we determine asymptotically the two and three color Ramsey numbers for grid graphs. More generally, we determine asymptotically the two color Ramsey number for bipartite graphs with small bandwidth and bounded maximum degree and the three color Ramsey number for such graphs with the additional assumption that the bipartite graph is balanced.


Title: Kempe equivalence and quadratic toric rings
Abstract: Perfectly contractile graphs form a typical class of perfect graphs. In particular, all $k$-colorings of a perfectly contractile graph are Kempe equivalent. Everett and Reed conjectured that a graph is perfectly contractile if and only if it contains no odd holes, no antiholes and no odd prisms. On the other hand the authors and Shibata conjectured that a perfect graph is perfectly contractile if and only if its toric ring, which is called the stable set ring, is quadratic. In the present paper, we characterize when the stable set ring of a (not necessarily perfect) graph is quadratic by using Kempe equivalence. As applications of this characterization, we can claim that if Everett and Reed conjecture is true, then the conjecture of the authors and Shibata is also true. Moreover, we can show that for several important classes of perfectly contractile graphs, the stable set rings are quadratic.


Title: A collection of integrals, products and series
Abstract: This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental constants.


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: Path-based Explanation for Knowledge Graph Completion
Abstract: Graph Neural Networks (GNNs) have achieved great success in Knowledge Graph Completion (KGC) by modelling how entities and relations interact in recent years. However, the explanation of the predicted facts has not caught the necessary attention. Proper explanations for the results of GNN-based KGC models increase model transparency and help researchers develop more reliable models. Existing practices for explaining KGC tasks rely on instance/subgraph-based approaches, while in some scenarios, paths can provide more user-friendly and interpretable explanations. Nonetheless, the methods for generating path-based explanations for KGs have not been well-explored. To address this gap, we propose Power-Link, the first path-based KGC explainer that explores GNN-based models. We design a novel simplified graph-powering technique, which enables the generation of path-based explanations with a fully parallelisable and memory-efficient training scheme. We further introduce three new metrics for quantitative evaluation of the explanations, together with a qualitative human evaluation. Extensive experiments demonstrate that Power-Link outperforms the SOTA baselines in interpretability, efficiency, and scalability.


Title: A new approach to convergence analysis of iterative models with optimal error bounds
Abstract: In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called \emph{optimal error bounds}, which established some necessary and sufficient conditions for convergence and derived both the error estimates and bounds on the convergence rates for iterative schemes. Although a special interest here is devoted to the Ishikawa and modified Ishikawa iterative sequences, the theory of \emph{optimal error bounds} proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of non-expansive mappings.


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: Density bounds for unit ball packings relative to their outer parallel domains
Abstract: We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This generalizes some earlier (classical) results. Sharp upper bounds are proved for the analogue problem on congruent circular disks in the spherical (resp., hyperbolic) plane and on congruent balls in Euclidean $3$-space.


Title: Moduli spaces of orthogonal bundles over an algebraic curve
Abstract: We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the invariants on the representation space of a quiver under the action of a product of classical groups.


Title: Distillation-based fabric anomaly detection
Abstract: Unsupervised texture anomaly detection has been a concerning topic in a vast amount of industrial processes. Patterned textures inspection, particularly in the context of fabric defect detection, is indeed a widely encountered use case. This task involves handling a diverse spectrum of colors and textile types, encompassing a wide range of fabrics. Given the extensive variability in colors, textures, and defect types, fabric defect detection poses a complex and challenging problem in the field of patterned textures inspection. In this article, we propose a knowledge distillation-based approach tailored specifically for addressing the challenge of unsupervised anomaly detection in textures resembling fabrics. Our method aims to redefine the recently introduced reverse distillation approach, which advocates for an encoder-decoder design to mitigate classifier bias and to prevent the student from reconstructing anomalies. In this study, we present a new reverse distillation technique for the specific task of fabric defect detection. Our approach involves a meticulous design selection that strategically highlights high-level features. To demonstrate the capabilities of our approach both in terms of performance and inference speed, we conducted a series of experiments on multiple texture datasets, including MVTEC AD, AITEX, and TILDA, alongside conducting experiments on a dataset acquired from a textile manufacturing facility. The main contributions of this paper are the following: a robust texture anomaly detector utilizing a reverse knowledge-distillation technique suitable for both anomaly detection and domain generalization and a novel dataset encompassing a diverse range of fabrics and defects.


Title: Behavior of Totally Positive Differential Systems Near a Periodic Solution
Abstract: A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field of a TPDS is T-periodic then every bounded trajectory converges to a T-periodic solution. In particular, when the vector field is time-invariant every bounded trajectory of a TPDS converges to an equlbrium. Here, we use the spectral theory of oscillatory matrices to analyze the behavior near a periodic solution of a TPDS. This yields information on the perturbation directions that lead to the fastest and slowest convergence to or divergence from the periodic solution. We demonstrate the theoretical results using a model from systems biology called the ribosome flow model.


Title: Mining Temporal Attack Patterns from Cyberthreat Intelligence Reports
Abstract: Defending from cyberattacks requires practitioners to operate on high-level adversary behavior. Cyberthreat intelligence (CTI) reports on past cyberattack incidents describe the chain of malicious actions with respect to time. To avoid repeating cyberattack incidents, practitioners must proactively identify and defend against recurring chain of actions - which we refer to as temporal attack patterns. Automatically mining the patterns among actions provides structured and actionable information on the adversary behavior of past cyberattacks. The goal of this paper is to aid security practitioners in prioritizing and proactive defense against cyberattacks by mining temporal attack patterns from cyberthreat intelligence reports. To this end, we propose ChronoCTI, an automated pipeline for mining temporal attack patterns from cyberthreat intelligence (CTI) reports of past cyberattacks. To construct ChronoCTI, we build the ground truth dataset of temporal attack patterns and apply state-of-the-art large language models, natural language processing, and machine learning techniques. We apply ChronoCTI on a set of 713 CTI reports, where we identify 124 temporal attack patterns - which we categorize into nine pattern categories. We identify that the most prevalent pattern category is to trick victim users into executing malicious code to initiate the attack, followed by bypassing the anti-malware system in the victim network. Based on the observed patterns, we advocate organizations to train users about cybersecurity best practices, introduce immutable operating systems with limited functionalities, and enforce multi-user authentications. Moreover, we advocate practitioners to leverage the automated mining capability of ChronoCTI and design countermeasures against the recurring attack patterns.


Title: Existence of solutions to the nonlinear equations characterizing the precise error of M-estimators
Abstract: Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional asymptotic regime where the sample size $n$ and the number of features $p$ are increasing simultaneously such that $n/p\to \delta \in(0,\infty)$, using powerful tools such as Approximate Message Passing or the Convex Gaussian Min-Max Theorem (CGMT). The asymptotic error and behavior of the regularized M-estimator is then typically described by a system of nonlinear equations with a few scalar unknowns, and the solution to this system precisely characterize the asymptotic error. Application of the CGMT and related machinery requires the existence of a solution to this low-dimensional system of equations. This paper resolves the question of existence of solution to this low-dimensional system for the case of linear models with independent additive noise, when both the data-fitting loss function and regularization penalty are separable and convex. Such existence result for solution to the nonlinear system were previously known under strong convexity for specific estimators such as the Lasso. The main idea behind this existence result is inspired by an argument developed \cite{montanari2019generalization,celentano2020lasso} in different contexts: By constructing an ad-hoc convex minimization problem in an infinite dimensional Hilbert space, the existence of the Lagrange multiplier for this optimization problem makes it possible to construct explicitly solutions to the low-dimensional system of interest. The conditions under which we derive this existence result exactly correspond to the side of the phase transition where perfect recovery $\hat x= x_0$ fails, so that these conditions are optimal.


Title: Optimal Placement of Dynamic Var Sources by Using Empirical Controllability Covariance
Abstract: In this paper, the empirical controllability covariance (ECC), which is calculated around the considered operating condition of a power system, is applied to quantify the degree of controllability of system voltages under specific dynamic var source locations. An optimal dynamic var source placement method addressing fault-induced delayed voltage recovery (FIDVR) issues is further formulated as an optimization problem that maximizes the determinant of ECC. The optimization problem is effectively solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search algorithm. The proposed method is tested on an NPCC 140-bus system and the results show that the proposed method with fault specified ECC can solve the FIDVR issue caused by the most severe contingency with fewer dynamic var sources than the Voltage Sensitivity Index (VSI) based method. The proposed method with fault unspecified ECC does not depend on the settings of the contingency and can address more FIDVR issues than VSI method when placing the same number of SVCs under different fault durations. It is also shown that the proposed method can help mitigate voltage collapse.


Title: Better and Simpler Lower Bounds for Differentially Private Statistical Estimation
Abstract: We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\alpha \le O\left(\frac{1}{\sqrt{d}}\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\tilde{\Omega}\left(\frac{d}{\alpha^{k/(k-1)} \varepsilon} + \frac{d}{\alpha^2}\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.


Title: The Cayley Plane and the Witten Genus
Abstract: This paper defines a new genus, the Cayley plane genus. By definition it is the universal multiplicative genus for oriented Cayley plane bundles. The main result (Theorem 2) is that it factors (tensor Q) through the product of the Ochanine elliptic genus and the Witten genus---revealing a synergy between these two genera---and that its image is the homogeneous coordinate ring Q[Kum,HP^2,HP^3,CaP^2]/(CaP^3).(HP^3,CaP^2-(HP^2)^2) of the union of the curve of Ochanine elliptic genera and the surface of Witten genera meeting with multiplicity 2 at the point CaP^2=HP^3=HP^2=0 corresponding to the \^A-genus. This all remains true if the word "oriented" is replaced with the word "spin" (Theorem 3). This paper also characterizes the Witten genus (tensor Q) as the universal genus vanishing on total spaces of Cayley plane bundles (Theorem 1, a result proved independently by Dessai in [Des09].)


Title: Existence and uniqueness of solutions to rate independent systems with history variable of integral type
Abstract: This paper investigates rate independent systems (RIS), where the dissipation functional depends not only on the rate but also on the history of the state. The latter is expressed in terms of a Volterra integral operator. We establish an existence result for the original problem and for the control thereof, without resorting to smallness assumptions. Under a smoothness condition, we prove the uniqueness of solutions to a certain class of history dependent RIS with unbounded dissipation potentials. In this context, we derive an essential estimate that opens the door to future research on the topic of optimization.


Title: Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems
Abstract: We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for small problems with very few hyperparameters but are not computationally feasible for problems with a very large number of unknown parameters. In this work, we describe an empirical Bayesian (EB) method to estimate hyperparameters that maximize the marginal posterior, i.e., the probability density of the hyperparameters conditioned on the data, and then we use the estimated values to compute the posterior of the inverse parameters. For problems where the computation of the square root and inverse of prior covariance matrices are not feasible, we describe an approach based on the generalized Golub-Kahan bidiagonalization to approximate the marginal posterior and seek hyperparameters that minimize the approximate marginal posterior. Numerical results from seismic and atmospheric tomography demonstrate the accuracy, robustness, and potential benefits of the proposed approach.


Title: Planar Para Algebras, Reflection Positivity
Abstract: We define a planar para algebra, which arises naturally from combining planar algebras with the idea of $\mathbb{Z}_{N}$ para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects, that are invariant under para isotopy. For each $\mathbb{Z}_{N}$, we construct a family of subfactor planar para algebras which play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), that we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity, by relating the two reflections through the string Fourier transform.


Title: Cambrian triangulations and their tropical realizations
Abstract: This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on $\nu$-Tamari lattices and their tropical realizations. For any signature $\varepsilon \in \{\pm\}^n$, we consider a family of $\varepsilon$-trees in bijection with the triangulations of the $\varepsilon$-polygon. These $\varepsilon$-trees define a flag regular triangulation $\mathcal{T}^\varepsilon$ of the subpolytope $\operatorname{conv} \{(\mathbf{e}_{i_\bullet}, \mathbf{e}_{j_\circ}) \, | \, 0 \le i_\bullet < j_\circ \le n+1 \}$ of the product of simplices $\triangle_{\{0_\bullet, \dots, n_\bullet\}} \times \triangle_{\{1_\circ, \dots, (n+1)_\circ\}}$. The oriented dual graph of the triangulation $\mathcal{T}^\varepsilon$ is the Hasse diagram of the (type $A$) $\varepsilon$-Cambrian lattice of N. Reading. For any $I_\bullet \subseteq \{0_\bullet, \dots, n_\bullet\}$ and $J_\circ \subseteq \{1_\circ, \dots, (n+1)_\circ\}$, we consider the restriction $\mathcal{T}^\varepsilon_{I_\bullet, J_\circ}$ of the triangulation $\mathcal{T}^\varepsilon$ to the face $\triangle_{I_\bullet} \times \triangle_{J_\circ}$. Its dual graph is naturally interpreted as the increasing flip graph on certain $(\varepsilon, I_\bullet, J_\circ)$-trees, which is shown to be a lattice generalizing in particular the $\nu$-Tamari lattices in the Cambrian setting. Finally, we present an alternative geometric realization of $\mathcal{T}^\varepsilon_{I_\bullet, J_\circ}$ as a polyhedral complex induced by a tropical hyperplane arrangement.


Title: Convex Clustering via Optimal Mass Transport
Abstract: We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations of a cardinality function which penalizes the size of the support set. We establish that a certain relaxation provides the tightest convex lower approximation to the cardinality penalty. We compare the performance of alternative relaxations on a numerical study on clustering.


Title: A stochastic representation theorem for sublinear semigroups with non-local generators
Abstract: In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-Bellman operators. Our main result provides a stochastic representation in terms of a family of sublinear (conditional) expectations that can be understood as a nonlinear Markov family with uncertain local characteristics. The proofs are based on viscosity methods.


Title: Complementing Model Learning with Mutation-Based Fuzzing
Abstract: An ongoing challenge for learning algorithms formulated in the Minimally Adequate Teacher framework is to efficiently obtain counterexamples. In this paper we compare and combine conformance testing and mutation-based fuzzing methods for obtaining counterexamples when learning finite state machine models for the reactive software systems of the Rigorous Exampination of Reactive Systems (RERS) challenge. We have found that for the LTL problems of the challenge the fuzzer provided an independent confirmation that the learning process had been successful, since no additional counterexamples were found. For the reachability problems of the challenge, however, the fuzzer discovered more reachable error states than the learner and tester, albeit in some cases the learner and tester found some that were not discovered by the fuzzer. This leads us to believe that these orthogonal approaches are complementary in the context of model learning.


Title: Periodic Strategies II: Generalizations and Extensions
Abstract: At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.


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: Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines
Abstract: We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to $L_p$-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the $L_2$-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images.


Title: Gesture-to-Gesture Translation in the Wild via Category-Independent Conditional Maps
Abstract: Recent works have shown Generative Adversarial Networks (GANs) to be particularly effective in image-to-image translations. However, in tasks such as body pose and hand gesture translation, existing methods usually require precise annotations, e.g. key-points or skeletons, which are time-consuming to draw. In this work, we propose a novel GAN architecture that decouples the required annotations into a category label - that specifies the gesture type - and a simple-to-draw category-independent conditional map - that expresses the location, rotation and size of the hand gesture. Our architecture synthesizes the target gesture while preserving the background context, thus effectively dealing with gesture translation in the wild. To this aim, we use an attention module and a rolling guidance approach, which loops the generated images back into the network and produces higher quality images compared to competing works. Thus, our GAN learns to generate new images from simple annotations without requiring key-points or skeleton labels. Results on two public datasets show that our method outperforms state of the art approaches both quantitatively and qualitatively. To the best of our knowledge, no work so far has addressed the gesture-to-gesture translation in the wild by requiring user-friendly annotations.


Title: Hierarchical Aligned Multimodal Learning for NER on Tweet Posts
Abstract: Mining structured knowledge from tweets using named entity recognition (NER) can be beneficial for many down stream applications such as recommendation and intention understanding. With tweet posts tending to be multimodal, multimodal named entity recognition (MNER) has attracted more attention. In this paper, we propose a novel approach, which can dynamically align the image and text sequence and achieve the multi-level cross-modal learning to augment textual word representation for MNER improvement. To be specific, our framework can be split into three main stages: the first stage focuses on intra-modality representation learning to derive the implicit global and local knowledge of each modality, the second evaluates the relevance between the text and its accompanying image and integrates different grained visual information based on the relevance, the third enforces semantic refinement via iterative cross-modal interactions and co-attention. We conduct experiments on two open datasets, and the results and detailed analysis demonstrate the advantage of our model.


Title: Force-Based Atomistic/Continuum Blending for Multilattices
Abstract: We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone--Wales defect in graphene.


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: Simplified Information Geometry Approach for Massive MIMO-OFDM Channel Estimation -- Part I: Algorithm and Fixed Point Analysis
Abstract: In this two-part paper, we investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. In Part I, we revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude property of the entries of the measurement matrix in the massive MIMO-OFDM channel estimation and the asymptotic analysis, we find that the second-order natural parameters of the distributions on all the auxiliary manifolds are equivalent to each other at each iteration of IGA, and the first-order natural parameters of the distributions on all the auxiliary manifolds are asymptotically equivalent to each other at the fixed point of IGA. Motivated by these results, we simplify the iterative process of IGA and propose a simplified IGA for massive MIMO-OFDM channel estimation. It is proved that at the fixed point, the a posteriori mean obtained by the simplified IGA is asymptotically optimal. The simplified IGA allows efficient implementation with fast Fourier transformation (FFT). Simulations confirm that the simplified IGA can achieve near the optimal performance with low complexity in a limited number of iterations.


Title: Significance of Anatomical Constraints in Virtual Try-On
Abstract: The system of Virtual Try-ON (VTON) allows a user to try a product virtually. In general, a VTON system takes a clothing source and a person's image to predict the try-on output of the person in the given clothing. Although existing methods perform well for simple poses, in case of bent or crossed arms posture or when there is a significant difference between the alignment of the source clothing and the pose of the target person, these methods fail by generating inaccurate clothing deformations. In the VTON methods that employ Thin Plate Spline (TPS) based clothing transformations, this mainly occurs for two reasons - (1)~the second-order smoothness constraint of TPS that restricts the bending of the object plane. (2)~Overlaps among different clothing parts (e.g., sleeves and torso) can not be modeled by a single TPS transformation, as it assumes the clothing as a single planar object; therefore, disregards the independence of movement of different clothing parts. To this end, we make two major contributions. Concerning the bending limitations of TPS, we propose a human AnaTomy-Aware Geometric (ATAG) transformation. Regarding the overlap issue, we propose a part-based warping approach that divides the clothing into independently warpable parts to warp them separately and later combine them. Extensive analysis shows the efficacy of this approach.


Title: The relationship between the negative inertia index of graph $G$ and its girth $g$ and diameter $d$
Abstract: Let $G$ be a simple connected graph. We use $n(G)$, $p(G)$, and $\eta(G)$ to denote the number of negative eigenvalues, positive eigenvalues, and zero eigenvalues of the adjacency matrix $A(G)$ of $G$, respectively. In this paper, we prove that $2n(G)\geq d(G) + 1$ when $d(G)$ is odd, and $n(G) \geq \lceil \frac{g}{2}\rceil - 1$ for a graph containing cycles, where $d(G)$ and $g$ are the diameter and girth of the graph $G$, respectively. Furthermore, we characterize the extremal graphs for the cases of $2n(G) = d(G) + 1$, $n(G) = \lceil \frac{g}{2}\rceil$, and $n(G) = \lceil \frac{g}{2}\rceil - 1$.


Title: Fading memory as inductive bias in residual recurrent networks
Abstract: Residual connections have been proposed as an architecture-based inductive bias to mitigate the problem of exploding and vanishing gradients and increased task performance in both feed-forward and recurrent networks (RNNs) when trained with the backpropagation algorithm. Yet, little is known about how residual connections in RNNs influence their dynamics and fading memory properties. Here, we introduce weakly coupled residual recurrent networks (WCRNNs) in which residual connections result in well-defined Lyapunov exponents and allow for studying properties of fading memory. We investigate how the residual connections of WCRNNs influence their performance, network dynamics, and memory properties on a set of benchmark tasks. We show that several distinct forms of residual connections yield effective inductive biases that result in increased network expressivity. In particular, those are residual connections that (i) result in network dynamics at the proximity of the edge of chaos, (ii) allow networks to capitalize on characteristic spectral properties of the data, and (iii) result in heterogeneous memory properties. In addition, we demonstrate how our results can be extended to non-linear residuals and introduce a weakly coupled residual initialization scheme that can be used for Elman RNNs.


Title: $F$-finiteness of homomorphisms and its descent
Abstract: Let $p$ be a prime number. We define the notion of $F$-finiteness of homomorphisms of $\mathbb F_p$-algebras, and discuss some basic properties. In particular, we prove a sort of descent theorem on $F$-finiteness of homomorphisms of $\mathbb F_p$-algebras. As a corollary, we prove the following. Let $g:B\to C$ be a homomorphism of Noetherian $\mathbb F_p$-algebras. If $g$ is faithfully flat reduced, and $C$ is $F$-finite, then $B$ is $F$-finite. This is a generalization of Seydi's result on excellent local rings of characteristic $p$.


Title: Error Forward-Propagation: Reusing Feedforward Connections to Propagate Errors in Deep Learning
Abstract: We introduce Error Forward-Propagation, a biologically plausible mechanism to propagate error feedback forward through the network. Architectural constraints on connectivity are virtually eliminated for error feedback in the brain; systematic backward connectivity is not used or needed to deliver error feedback. Feedback as a means of assigning credit to neurons earlier in the forward pathway for their contribution to the final output is thought to be used in learning in the brain. How the brain solves the credit assignment problem is unclear. In machine learning, error backpropagation is a highly successful mechanism for credit assignment in deep multilayered networks. Backpropagation requires symmetric reciprocal connectivity for every neuron. From a biological perspective, there is no evidence of such an architectural constraint, which makes backpropagation implausible for learning in the brain. This architectural constraint is reduced with the use of random feedback weights. Models using random feedback weights require backward connectivity patterns for every neuron, but avoid symmetric weights and reciprocal connections. In this paper, we practically remove this architectural constraint, requiring only a backward loop connection for effective error feedback. We propose reusing the forward connections to deliver the error feedback by feeding the outputs into the input receiving layer. This mechanism, Error Forward-Propagation, is a plausible basis for how error feedback occurs deep in the brain independent of and yet in support of the functionality underlying intricate network architectures. We show experimentally that recurrent neural networks with two and three hidden layers can be trained using Error Forward-Propagation on the MNIST and Fashion MNIST datasets, achieving $1.90\%$ and $11\%$ generalization errors respectively.


Title: Arithmetic progression in a finite field with prescribed norms
Abstract: Given a prime power $q$ and a positive integer $n$, let $\mathbb{F}_{q^{n}}$ represents a finite extension of degree $n$ of the finite field ${\mathbb{F}_{q}}$. In this article, we investigate the existence of $m$ elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for $n\geq6,q=3^k,m=2$ we establish that there are only $10$ possible exceptions.


Title: Reciprocity between partitions and compositions
Abstract: In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by them satisfy certain reciprocal relations.


Title: Linked partition ideals, directed graphs and $q$-multi-summations
Abstract: Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs with an ``empty'' vertex, we then turn our attention to a $q$-difference system. This $q$-difference system eventually yields a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Finally, using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews--Gordon type generating function identities. These proofs also have an interesting connection with binary trees.


Title: Miscellaneous problems about packing and covering
Abstract: In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest path problems and questions about stability of packings.


Title: A parametricity-based formalization of semi-simplicial and semi-cubical sets
Abstract: Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of n-simplices or n-cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call indexed. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively in its unary and binary variants. We exploit this correspondence to develop an original uniform indexed definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.


Title: On perturbations of singular complex analytic curves
Abstract: Suppose $V$ is a singular complex analytic curve inside $\mathbb{C}^{2}$. We investigate when a singular or non-singular complex analytic curve $W$ inside $\mathbb{C}^{2}$ with sufficiently small Hausdorff distance $d_{H}(V, W)$ from $V$ must intersect $V$. We obtain a sufficient condition on $W$ which when satisfied gives an affirmative answer to our question. More precisely, we show the intersection is non-empty for any such $W$ that admits at most one non-normal crossing type discriminant point associated with some proper projection. As an application, we prove a special case of the higher-dimensional analog, and also a holomorphic multifunction analog of a result by Lyubich-Peters.


Title: Properly Outer and Strictly Outer Actions of Finite Groups on Prime C*-algebras
Abstract: An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper I define the notion of strictly outer action (similar to the definition for von Neumann factors in [11]) and prove that for finite groups it is equivalent with proper outerness of the action. For finite abelian groups this is equivalent with other relevant properities of the action.