Title: Energy based diffusion generator for efficient sampling of Boltzmann distributions
Abstract: We introduce a novel sampler called the energy based diffusion generator for generating samples from arbitrary target distributions. The sampling model employs a structure similar to a variational autoencoder, utilizing a decoder to transform latent variables from a simple distribution into random variables approximating the target distribution, and we design an encoder based on the diffusion model. Leveraging the powerful modeling capacity of the diffusion model for complex distributions, we can obtain an accurate variational estimate of the Kullback-Leibler divergence between the distributions of the generated samples and the target. Moreover, we propose a decoder based on generalized Hamiltonian dynamics to further enhance sampling performance. Through empirical evaluation, we demonstrate the effectiveness of our method across various complex distribution functions, showcasing its superiority compared to existing methods.


Title: Nonexistence of Exceptional 5-class Association Schemes with Two $Q$-polynomial Structures
Abstract: In [H. Suzuki, Association schemes with multiple $Q$-polynomial structures, J. Algebraic Combin. 7 (1998) 181-196], Suzuki gave a classification of association schemes with multiple $Q$-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzuki's theorem mirrors exactly the well-known counterpart for association schemes with multiple $P$-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980.


Title: Discrete Uniqueness Sets for Functions with Spectral Gaps
Abstract: It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces have this property whenever $S$ is a set of infinite measure having "periodic gaps". The periodicity condition is crucial. For sets $S$ with randomly distributed gaps, we show that the uniformly discrete sets $\Lambda$ satisfy a strong non-uniqueness property: Every discrete function $c(\lambda)\in l^2(\Lambda)$ can be interpolated by an analytic $L^2$-function with spectrum in $S$.


Title: Big pictures of motivic and classical homotopy theories
Abstract: Motivic homotopy theory is meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. As proved by Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to Voevodsky's triangulated category of motives. A connection that is the motivic analogue of the connection between algebraic topology and homological algebra. In this paper, we try to understand the big picture of motivic homotopy theory and its connection to Voevodsky's motives by comparison to the classical counterpart.


Title: Mutual-visibility problems on graphs of diameter two
Abstract: The mutual-visibility problem in a graph $G$ asks for the cardinality of a largest set of vertices $S\subseteq V(G)$ so that for any two vertices $x,y\in S$ there is a shortest $x,y$-path $P$ so that all internal vertices of $P$ are not in $S$. This is also said as $x,y$ are visible with respect to $S$, or $S$-visible for short. Variations of this problem are known, based on the extension of the visibility property of vertices that are in and/or outside $S$. Such variations are called total, outer and dual mutual-visibility problems. This work is focused on studying the corresponding four visibility parameters in graphs of diameter two, throughout showing bounds and/or closed formulae for these parameters. The mutual-visibility problem in the Cartesian product of two complete graphs is equivalent to (an instance of) the celebrated Zarankievicz's problem. Here we study the dual and outer mutual-visibility problem for the Cartesian product of two complete graphs and all the mutual-visibility problems for the direct product of such graphs as well. We also study all the mutual-visibility problems for the line graphs of complete and complete bipartite graphs. As a consequence of this study, we present several relationships between the mentioned problems and some instances of the classical Tur\'an problem. Moreover, we study the visibility problems for cographs and several non-trivial diameter-two graphs of minimum size.


Title: Centers of categorified endomorphism rings
Abstract: We prove that for a large class of well-behaved cocomplete categories $\mathcal C$ the weak and strong Drinfeld centers of the monoidal category $\mathcal{E}$ of cocontinuous endofunctors of $\mathcal{C}$ coincide. This generalizes similar results in the literature, where $\mathcal{C}$ is the category of modules over a ring $A$ and hence $\mathcal{E}$ is the category of $A$-bimodules.


Title: Large volume limit fibrations over fanifolds
Abstract: We lift the stratified torus fibration over a fanifold constructed by Gammage--Shende to the associated Weinstein manifold-with-boundary, which is homotopic to a filtered stratified integrable system with noncompact fibers. When the fanifold admits a dual stratified space in a suitable sense, we give a stratified fibration over it completing SYZ picture. For the fanifold associated with a very affine hypersurface, we realize the latter fibration as a restriction of SYZ fibrations over the tropical hypersurface proposed by Abouzaid--Auroux--Katzarkov.


Title: Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thiémard to compute bounds for the star discrepancy
Abstract: We improve the best known upper bound for the bracketing number of $d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, of lower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$). More precisely, we provide a better upper bound for the cardinality of an algorithmic bracketing cover construction due to Eric Thi\'emard, which forms the core of his algorithm to approximate the star discrepancy of arbitrary point sets from [E. Thi\'emard, An algorithm to compute bounds for the star discrepancy, J.~Complexity 17 (2001), 850 -- 880]. Moreover, the new upper bound for the bracketing number of anchored axis-parallel boxes yields an improved upper bound for the bracketing number of arbitrary axis-parallel boxes in $[0,1]^d$. In our upper bounds all constants are fully explicit.


Title: InternVid: A Large-scale Video-Text Dataset for Multimodal Understanding and Generation
Abstract: This paper introduces InternVid, a large-scale video-centric multimodal dataset that enables learning powerful and transferable video-text representations for multimodal understanding and generation. The InternVid dataset contains over 7 million videos lasting nearly 760K hours, yielding 234M video clips accompanied by detailed descriptions of total 4.1B words. Our core contribution is to develop a scalable approach to autonomously build a high-quality video-text dataset with large language models (LLM), thereby showcasing its efficacy in learning video-language representation at scale. Specifically, we utilize a multi-scale approach to generate video-related descriptions. Furthermore, we introduce ViCLIP, a video-text representation learning model based on ViT-L. Learned on InternVid via contrastive learning, this model demonstrates leading zero-shot action recognition and competitive video retrieval performance. Beyond basic video understanding tasks like recognition and retrieval, our dataset and model have broad applications. They are particularly beneficial for generating interleaved video-text data for learning a video-centric dialogue system, advancing video-to-text and text-to-video generation research. These proposed resources provide a tool for researchers and practitioners interested in multimodal video understanding and generation.


Title: Disentangle Estimation of Causal Effects from Cross-Silo Data
Abstract: Estimating causal effects among different events is of great importance to critical fields such as drug development. Nevertheless, the data features associated with events may be distributed across various silos and remain private within respective parties, impeding direct information exchange between them. This, in turn, can result in biased estimations of local causal effects, which rely on the characteristics of only a subset of the covariates. To tackle this challenge, we introduce an innovative disentangle architecture designed to facilitate the seamless cross-silo transmission of model parameters, enriched with causal mechanisms, through a combination of shared and private branches. Besides, we introduce global constraints into the equation to effectively mitigate bias within the various missing domains, thereby elevating the accuracy of our causal effect estimation. Extensive experiments conducted on new semi-synthetic datasets show that our method outperforms state-of-the-art baselines.


Title: Riemann surface of the Riemann zeta function
Abstract: In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex $\adyn$-dimensional, customly denoted as $s$, another two are complex infinite dimensional, we denote it as $\b = \{b_n\}_{n=1}^{\infty}$ and $\z =\{z_n\}_{n=1}^{\infty}$. When $\b = \{1\}_{n=1}^{\infty}$ and $\z = \{\frac{1}{n}\}_{n=1}^{\infty}$ one gets the usual Riemann zeta function. Our goal in this paper is to study the meromorphic continuation of $\zeta (\b , \z ,s)$ as a function of the triple $(\a , \z , s)$. Minor corrections, to appear in the Journal of Mathematical Analysis and Applications.


Title: Characters of Representations of Quantum Groups of Type $A_n$
Abstract: We introduce the notion of characters of comodules over coribbon Hopf algebras. The case of quantum groups of type $A_n$ is studied. We establish a characteristic equation for the quantum matrix and a q-analogue of Harish-Chandra- Itzykson-Zuber integral


Title: Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints
Abstract: We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity of fair allocations. We study the problem of finding an allocation that is Pareto-optimal. While it is easy to find an efficient allocation when the underlying graph is a path or a star, the problem is NP-hard for many other graph topologies, even for trees of bounded pathwidth or of maximum degree 3. We show that on a path, there are instances where no Pareto-optimal allocation satisfies envy-freeness up to one good, and that it is NP-hard to decide whether such an allocation exists, even for binary valuations. We also show that, for a path, it is NP-hard to find a Pareto-optimal allocation that satisfies maximin share, but show that a moving-knife algorithm can find such an allocation when agents have binary valuations that have a non-nested interval structure.


Title: Random walk on the high-dimensional IIC
Abstract: We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.


Title: Bounded diameter tree-decompositions
Abstract: When does a graph admit a tree-decomposition in which every bag has small diameter? For finite graphs, this is a property of interest in algorithmic graph theory, where it is called having bounded ``tree-length''. We will show that this is equivalent to being ``boundedly quasi-isometric to a tree'', which for infinite graphs is a much-studied property from metric geometry. One object of this paper is to tie these two areas together. We will prove that there is a tree-decomposition in which each bag has small diameter, if and only if there is a map $\phi$ from $V(G)$ into the vertex set of a tree $T$, such that for all $u,v\in V(G)$, the distances $d_G(u,v), d_T(\phi(u),\phi(v))$ differ by at most a constant. A ``geodesic loaded cycle'' in $G$ is a pair $(C,F)$, where $C$ is a cycle of $G$ and $F\subseteq E(C)$, such that for every pair $u,v$ of vertices of $C$, one of the paths of $C$ between $u,v$ contains at most $d_G(u,v)$ $F$-edges, where $d_G(u,v)$ is the distance between $u,v$ in $G$. We will show that a graph $G$ admits a tree-decomposition in which every bag has small diameter, if and only if $|F|$ is small for every geodesic loaded cycle $(C,F)$. Our proof is an extension of an algorithm to approximate tree-length in finite graphs by Dourisboure and Gavoille. In metric geometry, there is a similar theorem that characterizes when a graph is quasi-isometric to a tree, ``Manning's bottleneck criterion''. The goal of this paper is to tie all these concepts together, and add a few more related ideas. For instance, we prove a conjecture of Rose McCarty, that $G$ admits a tree-decomposition in which every bag has small diameter, if and only if for all vertices $u,v,w$ of $G$, some ball of small radius meets every path joining two of $u,v,w$.


Title: Sharp weighted inequalities for iterated commutators of a class of multilinear operators
Abstract: In this paper, the sharp quantitative weighted bounds for the iterated commutators of a class of multilinear operators were systematically studied. This class of operators contains multilinear Calder\'{o}n-Zygmund operators, multilinear Fourier integral operators, and multilinear Littlewood-Paley square operators as its typical examples. These were done only under two pretty much general assumptions of pointwise sparse domination estimates. We first established local decay estimates and quantitative weak $A_\infty$ decay estimates for iterated commutators of this class of operators. Then, we considered the corresponding Coifman-Fefferman inequalities and the mixed weak type estimates associated with Sawyer's conjecture. Beyond that, the Fefferman-Stein inequalities with respect to arbitrary weights and weighted modular inequalities were also given. As applications, it was shown that all the conclusions aforementioned can be applied to multilinear $\omega$-Calder\'{o}n-Zygmund operators, multilinear maximal singular integral operators, multilinear pseudo-differential operators, Stein's square functions, and higher order Calder\'{o}n commutators.


Title: A note on Jones polynomial and cosmetic surgery
Abstract: We show that two Dehn surgeries on a knot $K$ never yield manifolds that are homeomorphic as oriented manifolds if $V_K''(1)\neq 0$ or $V_K'''(1)\neq 0$. As an application, we verify the cosmetic surgery conjecture for all knots with no more than $11$ crossings except for three $10$-crossing knots and five $11$-crossing knots. We also compute the finite type invariant of order $3$ for two-bridge knots and Whitehead doubles, from which we prove several nonexistence results of purely cosmetic surgery.


Title: Real-Time 2D Temperature Field Prediction in Metal Additive Manufacturing Using Physics-Informed Neural Networks
Abstract: Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical to preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions and online control in iterative design scenarios. Conversely, machine learning models rely heavily on high-quality datasets, which can be costly and challenging to obtain within the metal AM domain. Our work addresses this by introducing a physics-informed neural network framework specifically designed for temperature field prediction in metal AM. This framework incorporates a physics-informed input, physics-informed loss function, and a Convolutional Long Short-Term Memory (ConvLSTM) architecture. Utilizing real-time temperature data from the process, our model predicts 2D temperature fields for future timestamps across diverse geometries, deposition patterns, and process parameters. We validate the proposed framework in two scenarios: full-field temperature prediction for a thin wall and 2D temperature field prediction for cylinder and cubic parts, demonstrating errors below 3% and 1%, respectively. Our proposed framework exhibits the flexibility to be applied across diverse scenarios with varying process parameters, geometries, and deposition patterns.


Title: Taming the Beast: Fully Automated Unit Testing with Coyote C++
Abstract: In this paper, we present Coyote C++, a fully automated white-box unit testing tool for C and C++. Whereas existing tools have struggled to realize unit test generation for C++, Coyote C++ is able to produce high coverage results from unit test generation at a testing speed of over 10,000 statements per hour. This impressive feat is made possible by the combination of a powerful concolic execution engine with sophisticated automated test harness generation. Additionally, the GUI of Coyote C++ displays detailed code coverage visualizations and provides various configuration features for users seeking to manually optimize their coverage results. Combining potent one-click automated testing with rich support for manual tweaking, Coyote C++ is the first automated testing tool that is practical enough to make automated testing of C++ code truly viable in industrial applications.


Title: Asynchronous Downlink Massive MIMO Networks: A Stochastic Geometry Approach
Abstract: Massive multiple-input multiple-output (MIMO) is recognized as a promising technology for the next generation of wireless networks because of its potential to increase the spectral efficiency. In initial studies of massive MIMO, the system has been considered to be perfectly synchronized throughout the entire cells. However, perfect synchronization may be hard to attain in practice. Therefore, we study a massive MIMO system whose cells are not synchronous to each other, while transmissions in a cell are still synchronous. We analyze an asynchronous downlink massive MIMO system in terms of the coverage probability and the ergodic rate by means of the stochastic geometry tool. For comparison, we also obtain the results for the synchronous systems. In addition, we investigate the effect of the uplink power control and the number of pilot symbols on the downlink ergodic rate, and we observe that there is an optimal value for the number of pilot symbols maximizing the downlink ergodic rate of a cell. Our results also indicate that, compared to the cases with synchronous transmission, the downlink ergodic rate is more sensitive to the uplink power control in the asynchronous mode.


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


Title: Limit theorems for a supercritical remaining-lifetime age-structured branching process
Abstract: In a previous paper [9] we studied an age-structured branching model without immigration. Here we consider a special case of the model, where the system is founded by a single particle with a random lifetime and the reproduction regime is supercritical. We show that there is a necessary and sufficient condition for the convergence of the Malthus normalized random measures $e^{-\tilde{\alpha}t} X_t$, where $\tilde{\alpha}$ is a strictly positive Malthusian parameter. The convergence of $e^{-\tilde{\alpha}t} \langle X_t,f\rangle$ can be strengthened to hold with probability one under conditions weaker than those given in Jagers [24]. A central limit theorem of $\langle X_t,f\rangle$ is further proved.


Title: DHOT-GM: Robust Graph Matching Using A Differentiable Hierarchical Optimal Transport Framework
Abstract: Graph matching is one of the most significant graph analytic tasks in practice, which aims to find the node correspondence across different graphs. Most existing approaches rely on adjacency matrices or node embeddings when matching graphs, whose performances are often sub-optimal because of not fully leveraging the multi-modal information hidden in graphs, such as node attributes, subgraph structures, etc. In this study, we propose a novel and effective graph matching method based on a differentiable hierarchical optimal transport (HOT) framework, called DHOT-GM. Essentially, our method represents each graph as a set of relational matrices corresponding to the information of different modalities. Given two graphs, we enumerate all relational matrix pairs and obtain their matching results, and accordingly, infer the node correspondence by the weighted averaging of the matching results. This method can be implemented as computing the HOT distance between the two graphs -- each matching result is an optimal transport plan associated with the Gromov-Wasserstein (GW) distance between two relational matrices, and the weights of all matching results are the elements of an upper-level optimal transport plan defined on the matrix sets. We propose a bi-level optimization algorithm to compute the HOT distance in a differentiable way, making the significance of the relational matrices adjustable. Experiments on various graph matching tasks demonstrate the superiority and robustness of our method compared to state-of-the-art approaches.


Title: New Perspective on Progressive GANs Distillation for One-class Novelty Detection
Abstract: One-class novelty detection is conducted to identify anomalous instances, with different distributions from the expected normal instances. In this paper, the Generative Adversarial Network based on the Encoder-Decoder-Encoder scheme (EDE-GAN) achieves state-of-the-art performance. The two factors bellow serve the above purpose: 1) The EDE-GAN calculates the distance between two latent vectors as the anomaly score, which is unlike the previous methods by utilizing the reconstruction error between images. 2) The model obtains best results when the batch size is set to 1. To illustrate their superiority, we design a new GAN architecture, and compare performances according to different batch sizes. Moreover, with experimentation leads to discovery, our result implies there is also evidence of just how beneficial constraint on the latent space are when engaging in model training. In an attempt to learn compact and fast models, we present a new technology, Progressive Knowledge Distillation with GANs (P-KDGAN), which connects two standard GANs through the designed distillation loss. Two-step progressive learning continuously augments the performance of student GANs with improved results over single-step approach. Our experimental results on CIFAR-10, MNIST, and FMNIST datasets illustrate that P-KDGAN improves the performance of the student GAN by 2.44%, 1.77%, and 1.73% when compressing the computationat ratios of 24.45:1, 311.11:1, and 700:1, respectively.


Title: On upper bounds on expectations of gOSs based on DFR and DFRA distributions
Abstract: We focus on the problem of establishing the optimal upper bounds on generalized order statistics which are based on the underlying cdf belonging to the family of distributions with decreasing failure rate and decreasing failure rate on the average. This issue has been previously considered by Bieniek [Projection bounds on expectations of generalized order statistics from DFR and DFRA families, Statistics, 2006; 40: 339--351], who established upper nonnegative mean-variance bounds with use of the projections of the compositions of density functions of the uniform generalized order statistic and the exponential distribution function onto the properly chosen convex cones. In this paper we obtain possibly negative upper bounds, by improving the zero bounds obtained by Bieniek for some particular cases of gOSs. We express the bounds in the scale units generated by the central absolute moments of arbitrary orders. We also describe the attainability conditions.


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


Title: Filtered fiber functors over a general base
Abstract: We prove that every filtered fiber functor on the category of dualizable representations of a smooth affine group scheme with enough dualizable representations comes from a graded fiber functor.


Title: An insertion algorithm for catabolizability
Abstract: Motivated by our recent work relating canonical bases to combinatorics of Garsia-Procesi modules \cite{B}, we give an insertion algorithm that computes the catabolizability of the insertion tableau of a standard word. This allows us to characterize catabolizability as the statistic on words invariant under Knuth transformations, certain (co)rotations, and a new operation called a catabolism transformation. We also prove a Greene's Theorem-like characterization of catabolizability, and a result about how cocyclage changes catabolizability, strengthening a similar result in \cite{SW}.


Title: Optimal jump set in hyperbolic conservation laws
Abstract: This paper deals with some qualitative properties of entropy solutions to hyperbolic conservation laws. In [11] the jump set of entropy solution to conservation laws has been introduced. We find an entropy solution to scalar conservation laws for which the jump set is not closed, in particular, it is dense in a space-time domain. In the later part of this article, we obtain a similar result for the hyperbolic system. We give two different approaches for scalar conservation laws and hyperbolic system to obtain the results. For the scalar case, obtained solutions are more explicitly calculated.


Title: On semigroups of orientation-preserving partial permutations with restricted range
Abstract: Let $\Omega_n$ be a finite chain with $n$ elements $(n\in\mathbb{N})$, and let $\mathcal{POPI}_{n}$ be the semigroup of all injective orientation-preserving partial transformations of $\Omega_n$. In this paper, for any nonempty subset $Y$ of $\Omega_n$, we consider the subsemigroup $\mathcal{POPI}_{n}(Y)$ of $\mathcal{POPI}_{n}$ of all transformations with range contained in $Y$. We describe the Green's relations and study the regularity of $\mathcal{POPI}_{n}(Y)$. Moreover, we calculate the rank of $\mathcal{POPI}_{n}(Y)$ and determine when two semigroups of this type are isomorphic.


Title: Reconstruction from Substrings with Partial Overlap
Abstract: This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous works considered two extreme cases in which \emph{all} substrings of some fixed length are read or substrings are read with no overlap, this work considers the setup in which consecutive substrings are read with some given minimum overlap. First, upper bounds are provided on the attainable rates of codes that guarantee unique reconstruction. Then, we present efficient constructions of asymptotically optimal codes that meet the upper bound.


Title: Log-concave Density Estimation with Independent Components
Abstract: We propose a method for estimating a log-concave density on $\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave density estimation is hard both computationally and statistically, the independent components assumption alleviates both issues, while still maintaining a large non-parametric class. We prove that under mild conditions, at most $\tilde{\mathcal{O}}(\epsilon^{-4})$ samples (suppressing constants and log factors) suffice for our proposed estimator to be within $\epsilon$ of the original density in squared Hellinger distance. On the computational front, while the usual log-concave maximum likelihood estimate can be obtained via a finite-dimensional convex program, it is slow to compute -- especially in higher dimensions. We demonstrate through numerical experiments that our estimator can be computed efficiently, making it more practical to use.


Title: Hadwiger's conjecture and topological bounds
Abstract: The Odd Hadwiger's conjecture, formulated by Gerards and Seymour in 1995, is a substantial strengthening of Hadwiger's famous coloring conjecture from 1943. We investigate whether the hierarchy of topological lower bounds on the chromatic number, introduced by Matou\v{s}ek and Ziegler (2003) and refined recently by Daneshpajouh and Meunier (2023), forms a potential avenue to a disproof of Hadwiger's conjecture or its odd-minor variant. In this direction, we prove that, in a very general sense, every graph $G$ that admits a topological lower bound of $t$ on its chromatic number, contains $K_{\lfloor t/2\rfloor +1}$ as an odd-minor. This solves a problem posed by Simonyi and Zsb\'{a}n [European Journal of Combinatorics, 31(8), 2110--2119 (2010)]. We also prove that if for a graph $G$ the Dol'nikov-K\v{r}\'{i}\v{z} lower bound on the chromatic number (one of the lower bounds in the aforementioned hierarchy) attains a value of at least $t$, then $G$ contains $K_t$ as a minor. Finally, extending results by Simonyi and Zsb\'{a}n, we show that the Odd Hadwiger's conjecture holds for Schrijver and Kneser graphs for any choice of the parameters. The latter are canonical examples of graphs for which topological lower bounds on the chromatic number are tight.


Title: Absence of Lavrentiev's gap for anisotropic functionals
Abstract: We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect to the last variable. This fact results from new results on good approximation properties of the natural underlying unconventional function space. Scalar and vector-valued problems are studied.


Title: On the embedding complexity of Liouville manifolds
Abstract: We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and its L-infinity structure. As our primary application, we investigate embeddings between normal crossing divisor complements in complex projective space, giving a complete characterization in many cases. Our main embedding results are deduced explicitly from pseudoholomorphic curves, without appealing to Hamiltonian or virtual perturbations.


Title: Minimum Weight Pairwise Distance Preservers
Abstract: In this paper, we study the Minimum Weight Pairwise Distance Preservers (MWPDP) problem. Consider a positively weighted undirected/directed connected graph $G = (V, E, c)$ and a subset $P$ of pairs of vertices, also called demand pairs. A subgraph $G'$ is a distance preserver with respect to $P$ if and only if every pair $(u, w) \in P$ satisfies $dist_{G'} (u, w) = dist_{G}(u, w)$. In MWPDP problem, we aim to find the minimum-weight subgraph $G^*$ that is a distance preserver with respect to $P$. Taking a shortest path between each pair in $P$ gives us a trivial solution with the weight of at most $U=\sum_{(u,v) \in P} dist_{G} (u, w)$. Subsequently, we ask how much improvement we can make upon $U$. In other words, we opt to find a distance preserver $G^*$ that maximizes $U-c(G^*)$. Denote this problem as Cost Sharing Pairwise Distance Preservers (CSPDP), which has several applications in the planning and operations of transportation systems. The only known work that can provide a nontrivial solution for CSPDP is that of Chlamt\'a\v{c} et al. (SODA, 2017). This algorithm works for unweighted graphs and guarantees a non-zero objective only if the optimal solution is extremely sparse with respect to the trivial solution. We address this issue by proposing an $O(|E|^{1/2+\epsilon})$-approximation algorithm for CSPDP in weighted graphs that runs in $O((|P||E|)^{2.38} (1/\epsilon))$ time. Moreover, we prove CSPDP is at least as hard as $\text{LABEL-COVER}_{\max}$. This implies that CSPDP cannot be approximated within $O(|E|^{1/6-\epsilon})$ factor in polynomial time, unless there is an improvement in the notoriously difficult $\text{LABEL-COVER}_{\max}$.


Title: Quadratic relations of the deformed $W$-algebra
Abstract: The deformed $W$-algebra is a quantum deformation of the $W$-algebra ${\cal W}_\beta(\mathfrak{g})$ in conformal field theory. Using the free field construction, we obtain a closed set of quadratic relations of the $W$-currents of the deformed $W$-algebra. This allows us to define the deformed $W$-algebra by generators and relations. In this review, we study two types of deformed $W$-algebra. One is the deformed $W$-algebra ${\cal W}_{x,r}\big(A_{2N}^{(2)}\big)$, and the other is the $q$-deformed corner vertex algebra $q$-$Y_{L_1, L_2, L_3}$ that is a generalization of the deformed $W$-algebra ${\cal W}_{x,r}\big(A(M,N)^{(1)}\big)$ via the quantum toroidal algebra.


Title: Joint symbolic aggregate approximation of time series
Abstract: The increasing availability of temporal data poses a challenge to time-series and signal-processing domains due to its high numerosity and complexity. Symbolic representation outperforms raw data in a variety of engineering applications due to its storage efficiency, reduced numerosity, and noise reduction. The most recent symbolic aggregate approximation technique called ABBA demonstrates outstanding performance in preserving essential shape information of time series and enhancing the downstream applications. However, ABBA cannot handle multiple time series with consistent symbols, i.e., the same symbols from distinct time series are not identical. Also, working with appropriate ABBA digitization involves the tedious task of tuning the hyperparameters, such as the number of symbols or tolerance. Therefore, we present a joint symbolic aggregate approximation that has symbolic consistency, and show how the hyperparameter of digitization can itself be optimized alongside the compression tolerance ahead of time. Besides, we propose a novel computing paradigm that enables parallel computing of symbolic approximation. The extensive experiments demonstrate its superb performance and outstanding speed regarding symbolic approximation and reconstruction.


Title: UstanceBR: a multimodal language resource for stance prediction
Abstract: This work introduces UstanceBR, a multimodal corpus in the Brazilian Portuguese Twitter domain for target-based stance prediction. The corpus comprises 86.8 k labelled stances towards selected target topics, and extensive network information about the users who published these stances on social media. In this article we describe the corpus multimodal data, and a number of usage examples in both in-domain and zero-shot stance prediction based on text- and network-related information, which are intended to provide initial baseline results for future studies in the field.


Title: Approximate innerness and central triviality of endomorphisms
Abstract: We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by Kawahigashi-Sutherland-Takesaki in automorphism case.


Title: On Codes for the Noisy Substring Channel
Abstract: We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems, interest in this channel has renewed in recent years. In contrast to existing literature, we consider a noisy channel model where information is subject to noise before its substrings are sampled, motivated by in-vivo storage. We study two separate noise models, substitutions or deletions. In both cases, we examine families of codes which may be utilized for error-correction and present combinatorial bounds on their sizes. Through a generalization of the concept of repeat-free strings, we show that the added required redundancy due to this imperfect observation assumption is sublinear, either when the fraction of errors in the observed substring length is sufficiently small, or when that length is sufficiently long. This suggests that no asymptotic cost in rate is incurred by this channel model in these cases. Moreover, we develop an efficient encoder for such constrained strings in some cases. Finally, we show how a similar encoder can be used to avoid formation of secondary-structures in coded DNA strands, even when accounting for imperfect structures.


Title: On the complexity of the generalized Q2R automaton
Abstract: We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a block sequential update scheme. Furthermore, we show that the decision problem consisting in determine if a given node in the network changes its state is \textbf{P}-Hard.


Title: Depth-Regularized Optimization for 3D Gaussian Splatting in Few-Shot Images
Abstract: In this paper, we present a method to optimize Gaussian splatting with a limited number of images while avoiding overfitting. Representing a 3D scene by combining numerous Gaussian splats has yielded outstanding visual quality. However, it tends to overfit the training views when only a small number of images are available. To address this issue, we introduce a dense depth map as a geometry guide to mitigate overfitting. We obtained the depth map using a pre-trained monocular depth estimation model and aligning the scale and offset using sparse COLMAP feature points. The adjusted depth aids in the color-based optimization of 3D Gaussian splatting, mitigating floating artifacts, and ensuring adherence to geometric constraints. We verify the proposed method on the NeRF-LLFF dataset with varying numbers of few images. Our approach demonstrates robust geometry compared to the original method that relies solely on images. Project page: robot0321.github.io/DepthRegGS


Title: A quick probability-oriented introduction to operator splitting methods
Abstract: This paper is an extended and reworked version of a short course given by the author at ''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was prepared for a special issue of ''Theory of stochastic processes'', devoted to publishing lecture notes from the aforementioned workshop. The survey is devoted to operator splitting methods in the abstract formulation and their applications in probability. While the survey is focused on multiplicative methods, the BCH formula is used to discuss exponential splitting methods and a short informal introduction to additive splitting is presented. We introduce frameworks and available deterministic and probabilistic results and concentrate on constructing a wide picture of the field of operator splitting methods, providing a rigorous description in the setting of abstract Cauchy problems and an informal discussion for further and parallel advances. Some limitations and common difficulties are listed, as well as examples of works that provide solutions or hints. No new results are given. The bibliography contains illustrative deterministic examples and a selection of probability-related works.


Title: A Note on the Two Approaches to Stringy Functors for Orbifolds
Abstract: In this note, we reconcile two approaches that have been used to construct stringy multiplications. The pushing forward after pulling back that has been used to give a global stringy extension of the functors K_0,K^{top},A^*,H^* [CR, FG, AGV, JKK2], and the pulling back after having pushed forward, which we have previously used in our (re)-construction program for G-Frobenius algebras, notably in considerations of singularities with symmetries and for symmetric products. A similar approach was also used by [CH] in their considerations of the Chen-Ruan product in a deRham setting for Abelian orbifolds. We show that the pull-push formalism has a solution by the push-pull equations in two situations. The first is a deRham formalism with Thom push-forward maps and the second is the setting of cyclic twisted sectors, which was at the heart of the (re)-construction program. We go on to do formal calculations using fractional Euler classes which allows us to formally treat all the stringy multiplications mentioned above in the general setting. The upshot is the formal trivialization of the co-cycles of the reconstruction program using the presentation of the obstruction bundle of [JKK2].


Title: Short Squeeze in DeFi Lending Market: Decentralization in Jeopardy?
Abstract: Anxiety levels in the Aave community spiked in November 2022 as Avi Eisenberg performed an attack on Aave. Eisenberg attempted to short the CRV token by using funds borrowed on the protocol to artificially deflate the value of CRV. While the attack was ultimately unsuccessful, it left the Aave community scared and even raised question marks regarding the feasibility of large lending platforms under decentralized governance. In this work, we analyze Avi Eisenberg's actions and show how he was able to artificially lower the price of CRV by selling large quantities of borrowed CRV for stablecoins on both decentralized and centralized exchanges. Despite the failure of his attack, it still led to irretrievable debt worth more than 1.5 Mio USD at the time and, thereby, quadrupled the protocol's irretrievable debt. Furthermore, we highlight that his attack was enabled by the vast proportion of CRV available to borrow as well as Aave's lending protocol design hindering rapid intervention. We stress Eisenberg's attack exposes a predicament of large DeFi lending protocols: limit the scope or compromise on 'decentralization'.


Title: The Case for Bayesian Deep Learning
Abstract: The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian marginalization. (3) The structure of neural networks gives rise to a structured prior in function space, which reflects the inductive biases of neural networks that help them generalize. (4) The observed correlation between parameters in flat regions of the loss and a diversity of solutions that provide good generalization is further conducive to Bayesian marginalization, as flat regions occupy a large volume in a high dimensional space, and each different solution will make a good contribution to a Bayesian model average. (5) Recent practical advances for Bayesian deep learning provide improvements in accuracy and calibration compared to standard training, while retaining scalability.


Title: Wide Neural Networks Forget Less Catastrophically
Abstract: A primary focus area in continual learning research is alleviating the "catastrophic forgetting" problem in neural networks by designing new algorithms that are more robust to the distribution shifts. While the recent progress in continual learning literature is encouraging, our understanding of what properties of neural networks contribute to catastrophic forgetting is still limited. To address this, instead of focusing on continual learning algorithms, in this work, we focus on the model itself and study the impact of "width" of the neural network architecture on catastrophic forgetting, and show that width has a surprisingly significant effect on forgetting. To explain this effect, we study the learning dynamics of the network from various perspectives such as gradient orthogonality, sparsity, and lazy training regime. We provide potential explanations that are consistent with the empirical results across different architectures and continual learning benchmarks.


Title: On Memorization and Privacy Risks of Sharpness Aware Minimization
Abstract: In many recent works, there is an increased focus on designing algorithms that seek flatter optima for neural network loss optimization as there is empirical evidence that it leads to better generalization performance in many datasets. In this work, we dissect these performance gains through the lens of data memorization in overparameterized models. We define a new metric that helps us identify which data points specifically do algorithms seeking flatter optima do better when compared to vanilla SGD. We find that the generalization gains achieved by Sharpness Aware Minimization (SAM) are particularly pronounced for atypical data points, which necessitate memorization. This insight helps us unearth higher privacy risks associated with SAM, which we verify through exhaustive empirical evaluations. Finally, we propose mitigation strategies to achieve a more desirable accuracy vs privacy tradeoff.


Title: Cartan calculus for $C^\infty$-ringed spaces
Abstract: In an earlier paper (arXiv:2212.11163) I constructed a complex of differential forms on a local $C^\infty$-ringed space. In this paper I define a sheaf of vector fields (``the tangent sheaf'') on a local $C^\infty$-ringed space, define contractions of vector fields and forms, Lie derivatives of forms with respect to vector fields, and show that the standard equations of Cartan calculus hold for vector fields and differential forms on local $C^\infty$-ringed spaces.


Title: Large and moderate deviations for Gaussian neural networks
Abstract: We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e., when the model has more than one hidden layer) and hold for bounded and continuous pre-activation functions. However, for deep neural networks fed by a single input, we have results even if the pre-activation is ReLU. When the network is shallow (i.e., there is exactly one hidden layer) the large and moderate principles hold for quite general pre-activations and in an infinite-dimensional setting.


Title: Higher dimensional Calabi-Yau manifolds of Kummer type
Abstract: Based on Cynk-Hulek method we construct complex Calabi-Yau varieties of arbitrary dimensions using elliptic curves with automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize result of Katsura and Sch\"utt to obtain arbitrarily dimensional Calabi-Yau manifolds which are Zariski in any characteristic $p\not\equiv 1\pmod{12}.$


Title: Application of the Cartier Operator in Coding Theory
Abstract: The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. We use the Cartier operator on $H^0(\mathcal{A}_2,\Omega^1)$ to find a closed formula for the $a$-number of the form $\mathcal{A}_2 = v(Y^{\sqrt{q}}+Y-x^{\frac{\sqrt{q}+1}{2}})$ where $q=p^s$ over the finite field $\mathbb{F}_{q^2}$. The application of the computed $a$-number in coding theory is illustrated by the relationship between the algebraic properties of the curve and the parameters of codes that are supported by it.


Title: Cohomology of fixed point sets of anti-symplectic involutions in the Hilbert scheme of points on a surface
Abstract: Let $S$ be a smooth, quasi-projective complex surface with complex symplectic form $\omega \in H^0(S, K_S)$. This determines a symplectic form $\omega_n$ on the Hilbert scheme of points $S^{[n]}$ for $n \geq 1$. Let $\tau$ be an anti-symplectic involution of $(S,\omega)$: an order two automorphism of $S$ such that $ \tau^*\omega=-\omega$. Then $\tau$ induces an anti-symplectic involution on $(S^{[n]},\omega_n)$ and the fixed point set $(S^{[n]})^\tau$ is a smooth Lagrangian subvariety of $S^{[n]}$. In this paper, we calculate the mixed Hodge structure of $H^*( (S^{[n]})^\tau; \mathbb{Q})$ in terms of the mixed Hodge structures of $H^*( S^\tau;\mathbb{Q})$ and of $H^*( S / \tau; \mathbb{Q})$. We also classify the connected components of $(S^{[n]})^\tau$ and determine their mixed Hodge structures. Our results apply more generally whenever $S$ is a smooth quasi-projective surface, and $\tau$ is an involution of $S$ for which $S^\tau$ is a curve.


Title: Beyond Information Exchange: An Approach to Deploy Network Properties for Information Diffusion
Abstract: Information diffusion in Online Social Networks is a new and crucial problem in social network analysis field and requires significant research attention. Efficient diffusion of information are of critical importance in diverse situations such as; pandemic prevention, advertising, marketing etc. Although several mathematical models have been developed till date, but previous works lacked systematic analysis and exploration of the influence of neighborhood for information diffusion. In this paper, we have proposed Common Neighborhood Strategy (CNS) algorithm for information diffusion that demonstrates the role of common neighborhood in information propagation throughout the network. The performance of CNS algorithm is evaluated on several real-world datasets in terms of diffusion speed and diffusion outspread and compared with several widely used information diffusion models. Empirical results show CNS algorithm enables better information diffusion both in terms of diffusion speed and diffusion outspread.


Title: The Constrained Round Robin Algorithm for Fair and Efficient Allocation
Abstract: We consider a multi-agent resource allocation setting that models the assignment of papers to reviewers. A recurring issue in allocation problems is the compatibility of welfare/efficiency and fairness. Given an oracle to find a welfare-achieving allocation, we embed such an oracle into a flexible algorithm called the Constrained Round Robin (CRR) algorithm, that achieves the required welfare level. Our algorithm also allows the system designer to lower the welfare requirements in order to achieve a higher degree of fairness. If the welfare requirement is lowered enough, a strengthening of envy-freeness up to one item is guaranteed. Hence, our algorithm can be viewed as a computationally efficient way to interpolate between welfare and approximate envy-freeness in allocation problems.


Title: Disjointness for measurably distal group actions and applications
Abstract: We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving system. As a corollary we obtain easy to check necessary and sufficient conditions for two systems to be disjoint, provided one of them is measurably distal. We also obtain a Wiener--Wintner type theorem for countable amenable groups with distal weights and applications to weighted multiple ergodic averages and multiple recurrence.


Title: STAS: Spatial-Temporal Return Decomposition for Multi-agent Reinforcement Learning
Abstract: Centralized Training with Decentralized Execution (CTDE) has been proven to be an effective paradigm in cooperative multi-agent reinforcement learning (MARL). One of the major challenges is credit assignment, which aims to credit agents by their contributions. While prior studies have shown great success, their methods typically fail to work in episodic reinforcement learning scenarios where global rewards are revealed only at the end of the episode. They lack the functionality to model complicated relations of the delayed global reward in the temporal dimension and suffer from inefficiencies. To tackle this, we introduce Spatial-Temporal Attention with Shapley (STAS), a novel method that learns credit assignment in both temporal and spatial dimensions. It first decomposes the global return back to each time step, then utilizes the Shapley Value to redistribute the individual payoff from the decomposed global reward. To mitigate the computational complexity of the Shapley Value, we introduce an approximation of marginal contribution and utilize Monte Carlo sampling to estimate it. We evaluate our method on an Alice & Bob example and MPE environments across different scenarios. Our results demonstrate that our method effectively assigns spatial-temporal credit, outperforming all state-of-the-art baselines.


Title: Optimal Synthesis of Finite State Machines with Universal Gates using Evolutionary Algorithm
Abstract: This work presents an optimization method for the synthesis of finite state machines. The focus is on the reduction in the on-chip area and the cost of the circuit. A list of finite state machines from MCNC91 benchmark circuits have been evolved using Cartesian Genetic Programming. On the average, almost 30% of reduction in the total number of gates has been achieved. The effects of some parameters on the evolutionary process have also been discussed in the paper.


Title: The "exponential" torsion of superelliptic Jacobians
Abstract: Let $J$ be the Jacobian of a superelliptic curve defined by the equation $y^{\ell} = f(x)$, where $f$ is a separable polynomial of degree non-divisible by $\ell$. In this article we study the "exponential" (i.e. $\ell$-power) torsion of $J$. In particular, under some mild conditions on the polynomial $f$, we determine the image of the associated $\ell$-adic representation up to the determinant. We show also that the image of the determinant is contained in an explicit $\mathbb Z_{\ell}$-lattice with a finite index. As an application, we prove the Mumford-Tate conjecture for a generic superelliptic Jacobian of the above type.


Title: Dynamics of point-vortex systems near thermal equilibrium: relaxation or not?
Abstract: This article is devoted to the long-time dynamics of point-vortex systems near thermal equilibrium and to the possible emergence of collisional relaxation. More precisely, we consider a tagged particle coupled to a large number of background particles that are initially at equilibrium, and we analyze its resulting slow dynamics. On the one hand, in the spirit of the Lenard-Balescu relaxation for plasmas, we establish in a generic setting the outset of the slow thermalization of the tagged particle. On the other hand, we show that a completely different phenomenology is also possible in some degenerate regime: the slow dynamics of the tagged particle then remains conservative and the thermalization no longer holds in a strict sense. We provide the first detailed description of this degenerate regime and of its mixing properties. Note that it is particularly delicate to handle due to statistical closure problems, which manifest themselves as a lack of self-adjointness of the effective Hamiltonian.


Title: Positive Semidefinite Metric Learning with Boosting
Abstract: The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. \BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.


Title: A rewriting-logic-with-SMT-based formal analysis and parameter synthesis framework for parametric time Petri nets
Abstract: This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.


Title: Error Approximation and Bias Correction in Dynamic Problems using a Recurrent Neural Network/Finite Element Hybrid Model
Abstract: This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to perform bias correction of the low-fidelity models. The hybrid model uses FE basis functions as a spatial basis and RNNs for the approximation of the time dependencies of the FE basis' degrees of freedom. The training data sets consist of sparse, non-uniformly sampled snapshots of the discrepancy function, pre-computed from trajectory data of low- and high-fidelity dynamic FE models. To account for data sparsity and prevent overfitting, data upsampling and local weighting factors are employed, to instigate a trade-off between physically conforming model behavior and neural network regression. The proposed hybrid modeling methodology is showcased in three highly non-trivial engineering test-cases, all featuring transient FE models, namely, heat diffusion out of a heat sink, eddy-currents in a quadrupole magnet, and sound wave propagation in a cavity. The results show that the proposed hybrid model is capable of approximating model discrepancies to a high degree of accuracy and accordingly correct low-fidelity models.


Title: Deep Learning based Multi-Label Image Classification of Protest Activities
Abstract: With the rise of internet technology amidst increasing rates of urbanization, sharing information has never been easier thanks to globally-adopted platforms for digital communication. The resulting output of massive amounts of user-generated data can be used to enhance our understanding of significant societal issues particularly for urbanizing areas. In order to better analyze protest behavior, we enhanced the GSR dataset and manually labeled all the images. We used deep learning techniques to analyze social media data to detect social unrest through image classification, which performed good in predict multi-attributes, then also used map visualization to display protest behaviors across the country.


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


Title: Collective Choice Theory in Collaborative Computing
Abstract: This paper presents some fundamental collective choice theory for information system designers, particularly those working in the field of computer-supported cooperative work. This paper is focused on a presentation of Arrow's Possibility and Impossibility theorems which form the fundamental boundary on the efficacy of collective choice: voting and selection procedures. It restates the conditions that Arrow placed on collective choice functions in more rigorous second-order logic, which could be used as a set of test conditions for implementations, and a useful probabilistic result for analyzing votes on issue pairs. It also describes some simple collective choice functions. There is also some discussion of how enterprises should approach putting their resources under collective control: giving an outline of a superstructure of performative agents to carry out this function and what distributing processing technology would be needed.


Title: Galois subspaces for smooth projective curves
Abstract: Given an embedding of a smooth projective curve $X$ of genus $g\geq1$ into $\mathbb{P}^N$, we study the locus of linear subspaces of $\mathbb{P}^N$ of codimension 2 such that projection from said subspace, composed with the embedding, gives a Galois morphism $X\to\mathbb{P}^1$. For genus $g\geq2$ we prove that this locus is a smooth projective variety with components isomorphic to projective spaces. If $g=1$ and the embedding is given by a complete linear system, we prove that this locus is also a smooth projective variety whose positive-dimensional components are isomorphic to projective bundles over \'etale quotients of the elliptic curve, and we describe these components explicitly.


Title: Primitive elements in infinitesimal bialgebras
Abstract: For any set S, the free magmatic algebra spanned by card(S) binary products is the vector space spanned by the set of all planar rooted binary trees with the internal nodes colored by the elements of S, graded by the number of leaves of a tree. We show that it has a unique structure of coassociative coalgebra such that the coproduct satisfies the unital infinitesimal condition with each magmatic product, and prove an analog of Aguiar-Sottile formula in this context, describing the coproduct in terms of the Moebius basis for the Tamari order. The last result allows us to compute the subspace of primitive elements of any unital infinitesimal S-magmatic bialgebra. As an example, we construct a set of generators of the dual of Pilaud and Pons bialgebra of integer relations and compute an explicit basis of its subspace of primitive elements.


Title: Towards understanding the Pierce-Birkhoff conjecture via MV-algebras
Abstract: Our main issue was to understand the connection between \L ukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we define the class of \textit{f}MV-algebras, which are MV-algebras endowed with both an internal binary product and a scalar product with scalars from $[0,1]$. The proper quasi-variety generated by $[0,1]$, with both products interpreted as the real product, provides the desired framework: the normal form theorem of its corresponding logical system can be seen as a local version of the Pierce-Birkhoff conjecture.


Title: A noncommutative Davis' decomposition for martingales
Abstract: We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \h_1. We further extend this latter result to the case 1<p<2.


Title: Global well-posedness for the Euler alignment system with mildly singular interactions
Abstract: We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutions was proved in\cite{do2018global,shvydkoy2017eulerian1,shvydkoy2017eulerian2,shvydkoy2017eulerian3}. Here, we consider a class of less singular interaction kernels and establish the global regularity of solutions as long as the interaction kernels are not integrable. The proof relies on modulus of continuity estimates for a class of parabolic integro-differential equations with a drift and mildly singular kernels.


Title: On the relations between Auerbach or almost Auberbach Markushevich systems and Schauder bases
Abstract: We establish that the summability of the series $\sum\varepsilon_n$ is the necessary and sufficient criterion ensuring that every $(1+\varepsilon_n)$ Markushevich basis in a separable Hilbert space is a Riesz basis. Further we show that if $n\varepsilon_n\to \infty$, then in $\ell_2$ there exists a $(1+\varepsilon_n)$ Markushevich basis that under any permutation is non-equivalent to a Schauder basis. We extend this result to any separable Banach space. Finally we provide examples of Auerbach bases in 1-symmetric separable Banach spaces whose no permutations are equivalent to any Schauder basis or (depending on the space) any unconditional Schauder basis.


Title: A Decentralized Multiagent-Based Task Scheduling Framework for Handling Uncertain Events in Fog Computing
Abstract: Fog computing has become an attractive research topic in recent years. As an extension of the cloud, fog computing provides computing resources for Internet of Things (IoT) applications through communicative fog nodes located at the network edge. Fog nodes assist cloud services in handling real-time and mobile applications by bringing the processing capability to where the data is generated. However, the introduction of fog nodes can increase scheduling openness and uncertainty. The scheduling issues in fog computing need to consider the geography, load balancing, and network latency between IoT devices, fog nodes, as well as the parent cloud. Besides, the scheduling methods also need to deal with the occurrence of uncertain events in real-time so as to ensure service reliability. This paper proposes an agent-based framework with a decentralized structure to construct the architecture of fog computing, while three agent-based algorithms are proposed to implement the scheduling, load balance, and rescheduling processes. The proposed framework is implemented by JADE and evaluated on the iFogSim toolkit. Experimental results show that the proposed scheduling framework can adaptively schedule tasks and resources for different service requests in fog computing and can also improve the task success rate when uncertain events occur.


Title: Stochastic Analysis of an Adaptive Cubic Regularisation Method under Inexact Gradient Evaluations and Dynamic Hessian Accuracy
Abstract: We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still considered, this novel variant inherits the innovative use of adaptive accuracy requirements for Hessian approximations introduced in [3] and additionally employs inexact computations of the gradient. Without restrictions on the variance of the errors, we assume that these approximations are available within a sufficiently large, but fixed, probability and we extend, in the spirit of [18], the deterministic analysis of the framework to its stochastic counterpart, showing that the expected number of iterations to reach a first-order stationary point matches the well known worst-case optimal complexity. This is, in fact, still given by O(epsilon^(-3/2)), with respect to the first-order epsilon tolerance. Finally, numerical tests on nonconvex finite-sum minimisation confirm that using inexact first and second-order derivatives can be beneficial in terms of the computational savings.


Title: Propagation of Chaos for Mean Field Interacting Particle System with Multiplicative Noise
Abstract: In this paper, the quantitative propagation of chaos for mean field interacting particle system with multiplicative noise in $L^2$-Wasserstein distance is derived. When the diffusion is distribution free, the quantitative propagation of chaos in relative entropy as well as total variation distance is also obtained, where the initial distribution of mean field interacting particles is allowed to be singular with that of the limit equation. Furthermore, a general result on the long time quantitative propagation of chaos in relative entropy as well as in $L^2$-Wasserstein distance is provided and is applied in (path dependent) mean field interacting particle system as well as stochastic Hamiltonian system under dissipative condition.


Title: Balancing Adaptability and Non-exploitability in Repeated Games
Abstract: We study the problem of guaranteeing low regret in repeated games against an opponent with unknown membership in one of several classes. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to use an algorithm against which we cannot achieve rewards exceeding some "fair" value. Our solution is an expert algorithm (LAFF) that searches within a set of sub-algorithms that are optimal for each opponent class and uses a punishment policy upon detecting evidence of exploitation by the opponent. With benchmarks that depend on the opponent class, we show that LAFF has sublinear regret uniformly over the possible opponents, except exploitative ones, for which we guarantee that the opponent has linear regret. To our knowledge, this work is the first to provide guarantees for both regret and non-exploitability in multi-agent learning.


Title: On a new method for the stochastic perturbation of the disease transmission coefficient in SIS Models
Abstract: In this study we investigate a novel approach to stochastically perturb the disease transmission coefficient, which is a key parameter in susceptible-infected-susceptible (SIS) models. Motivated by the papers [2] and [5], we perturb the disease transmission coefficient with a Gaussian white noise, formally modelled as the time derivative of a mean reverting Ornstein-Uhlenbeck process. We remark that, thanks to a suitable representation of the solution to the deterministic SIS model, this perturbation is rigorous and supported by a Wong-Zakai approximation argument that consists in smoothing the singular Gaussian white noise and then taking limit of the solution from the approximated model. We prove that the stochastic version of the classic SIS model obtained this way preserves a crucial feature of the deterministic equation: the reproduction number dictating the two possible asymptotic regimes for the infection, i.e. extinction and persistence, remains unchanged. We then identify the class of perturbing noises for which this property holds and propose simple sufficient conditions for that. All the theoretical discoveries are illustrated and discussed with the help of several numerical simulations.


Title: Theta divisors whose Gauss map has a fiber of positive dimension
Abstract: We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor is only generically finite and not finite. That is, the Gauss map in these cases has at least one positive-dimensional fiber. We also obtain lower-bounds on the dimension of Andreotti-Mayer loci.


Title: Quantum rigidity of negatively curved manifolds
Abstract: We show that an isometric action of a compact quantum group on the underlying geodesic metric space of a compact connected Riemannian manifold $(M,g)$ with strictly negative curvature is automatically classical, in the sense that it factors through the action of the isometry group of $(M,g)$. This partially answers a question by D. Goswami.


Title: Weyl modules for the hyperspecial current algebra
Abstract: We develop the theory of global and local Weyl modules for the hyperspecial maximal parabolic subalgebra of type $A_{2n}^{(2)}$. We prove that the dimension of a local Weyl module depends only on its highest weight, thus establishing a freeness result for global Weyl modules. Furthermore, we show that the graded local Weyl modules are level one Demazure modules for the corresponding affine Lie algebra. In the last section we derive the same results for the special maximal parabolic subalgebras of the twisted affine Lie algebras not of type $A_{2n}^{(2)}$.


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


Title: A note on odd partition numbers
Abstract: Ramanujan's celebrated partition congruences modulo $\ell\in \{5, 7, 11\}$ assert that $$ p(\ell n+\delta_{\ell})\equiv 0\pmod{\ell}, $$ where $0<\delta_{\ell}<\ell$ satisfies $24\delta_{\ell}\equiv 1\pmod{\ell}.$ By proving Subbarao's Conjecture, Radu showed that there are no such congruences when it comes to parity. There are infinitely many odd (resp. even) partition numbers in every arithmetic progression. For primes $\ell \geq 5,$ we give a new proof of the conclusion that there are infinitely many $m$ for which $p(\ell m+\delta_{\ell})$ is odd. This proof uses a generalization, due to the second author and Ramsey, of a result of Mazur in his classic paper on the Eisenstein ideal. We also refine a classical criterion of Sturm for modular form congruences, which allows us to show that the smallest such $m$ satisfies $m<(\ell^2-1)/24,$ representing a significant improvement to the previous bound.


Title: Radio Map-Based Spectrum Sharing for Joint Communication and Sensing
Abstract: The sixth-generation (6G) network is expected to provide both communication and sensing (C&S) services. However, spectrum scarcity poses a major challenge to the harmonious coexistence of C&S systems. Without effective cooperation, the interference resulting from spectrum sharing impairs the performance of both systems. This paper addresses C&S interference within a distributed network. Different from traditional schemes that require pilot-based high-frequency interactions between C&S systems, we introduce a third party named the radio map to provide the large-scale channel state information (CSI). With large-scale CSI, we optimize the transmit power of C&S systems to maximize the signal-to-interference-plus-noise ratio (SINR) for the radar detection, while meeting the ergodic rate requirement of the interfered user. Given the non-convexity of both the objective and constraint, we employ the techniques of auxiliary-function-based scaling and fraction programming for simplification. Subsequently, we propose an iterative algorithm to solve this problem. Simulation results collaborate our idea that the extrinsic information, i.e., positions and surroundings, is effective to decouple C&S interference.


Title: Agile Behaviour Design: A Design Approach for Structuring Game Characters and Interactions
Abstract: In this paper, a novel design methodology-Agile Behaviour Design-is presented that accommodates the requirements for developing complex game agents suitable for industrial environments. An essential part of the design approach is to support independent work of both designers and programmers by reducing bottleneck situations. The approach fosters the creation of more loose and fluid interactions between design and implementation, leaving more freedom for creative expression.


Title: Online codes for analog signals
Abstract: This paper revisits a classical scenario in communication theory: a waveform sampled at regular intervals is to be encoded so as to minimize distortion in its reconstruction, despite noise. This transformation must be online (causal), to enable real-time signaling; and should use no more power than the original signal. The noise model we consider is an "atomic norm" convex relaxation of the standard (discrete alphabet) Hamming-weight-bounded model: namely, adversarial $\ell_1$-bounded. In the "block coding" (noncausal) setting, such encoding is possible due to the existence of large almost-Euclidean sections in $\ell_1$ spaces, a notion first studied in the work of Dvoretzky in 1961. Our main result is that an analogous result is achievable even causally. Equivalently, our work may be seen as a "lower triangular" version of $\ell_1$ Dvoretzky theorems. In terms of communication, the guarantees are expressed in terms of certain time-weighted norms: the time-weighted $\ell_2$ norm imposed on the decoder forces increasingly accurate reconstruction of the distant past signal, while the time-weighted $\ell_1$ norm on the noise ensures vanishing interference from distant past noise. Encoding is linear (hence easy to implement in analog hardware). Decoding is performed by an LP analogous to those used in compressed sensing.


Title: From Function to Distribution Modeling: A PAC-Generative Approach to Offline Optimization
Abstract: This paper considers the problem of offline optimization, where the objective function is unknown except for a collection of ``offline" data examples. While recent years have seen a flurry of work on applying various machine learning techniques to the offline optimization problem, the majority of these work focused on learning a surrogate of the unknown objective function and then applying existing optimization algorithms. While the idea of modeling the unknown objective function is intuitive and appealing, from the learning point of view it also makes it very difficult to tune the objective of the learner according to the objective of optimization. Instead of learning and then optimizing the unknown objective function, in this paper we take on a less intuitive but more direct view that optimization can be thought of as a process of sampling from a generative model. To learn an effective generative model from the offline data examples, we consider the standard technique of ``re-weighting", and our main technical contribution is a probably approximately correct (PAC) lower bound on the natural optimization objective, which allows us to jointly learn a weight function and a score-based generative model. The robustly competitive performance of the proposed approach is demonstrated via empirical studies using the standard offline optimization benchmarks.


Title: An optimization-based reformulation of the classical displacement approach for state update of non-linear material models
Abstract: In this paper, we build on recent work using a mathematical programming approach for incremental state update in analysis of non-linear mechanics models. In particular, we consider quasi-static analysis of continuum problems in the linearized kinematics regime, with non-linear material models described using convex energy functions. We find in this case that the classical displacement-based nested approach for incremental state update can be reformulated as solving a reduced dual optimization problem. This reformulation provides insights into the working of the algorithm, and eliminates the need for some heuristics. An important purpose of this paper is to further illustrate the unifying nature of the mathematical programming approach. We therefore present relationships with several of these types of algorithms recently presented in the literature for incremental state update.


Title: Concentration of maximum degree in random planar graphs
Abstract: Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $[n]:=\left\{1, \ldots, n\right\}$ with $m=m(n)$ edges. We show that in the sparse regime, when $m/n\leq 1$, with high probability the maximum degree of $P(n,m)$ takes at most two different values. In contrast, this is not true anymore in the dense regime, when $m/n>1$, where the maximum degree of $P(n,m)$ is not concentrated on any subset of $[n]$ with bounded size.


Title: Craig's Interpolation Theorem formalised and mechanised in Isabelle/HOL
Abstract: We formalise and mechanise a construtive, proof theoretic proof of Craig's Interpolation Theorem in Isabelle/HOL. We give all the definitions and lemma statements both formally and informally. We also transcribe informally the formal proofs. We detail the main features of our mechanisation, such as the formalisation of binding for first order formulae. We also give some applications of Craig's Interpolation Theorem.


Title: Non-commutative ambits and equivariant compactifications
Abstract: We prove that an action $\rho:A\to M(C_0(\mathbb{G})\otimes A)$ of a locally compact quantum group on a $C^*$-algebra has a universal equivariant compactification, and prove a number of other category-theoretic results on $\mathbb{G}$-equivariant compactifications: that the categories compactifications of $\rho$ and $A$ respectively are locally presentable (hence complete and cocomplete), that the forgetful functor between them is a colimit-creating left adjoint, and that epimorphisms therein are surjective and injections are regular monomorphisms. When $\mathbb{G}$ is regular coamenable we also show that the forgetful functor from unital $\mathbb{G}$-$C^*$-algebras to unital $C^*$-algebras creates finite limits and is comonadic, and that the monomorphisms in the former category are injective.


Title: Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables
Abstract: The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi{\'c} et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90\% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package \url{https://github.com/jakobrunge/tigramite}.


Title: Sorting by Reversals and the Theory of 4-Regular Graphs
Abstract: We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we expose strong connections between the two theories that have not been fully appreciated before. We also discuss a generalization of sorting by reversals involving the double-cut-and-join (DCJ) operation. Finally, we also show that the theory of sorting by reversals is closely related to that of gene assembly in ciliates.


Title: Perfect matchings and Hamilton cycles in uniform attachment graphs
Abstract: We study Hamilton cycles and perfect matchings in a uniform attachment graph. In this random graph, vertices are added sequentially, and when a vertex $t$ is created, it makes $k$ independent and uniform choices from $\{1,\dots,t-1\}$ and attaches itself to these vertices. Improving the results of Frieze, P\'erez-Gim\'enez, Pra\l{}at and Reiniger (2019), we show that, with probability approaching 1 as $n$ tends to infinity, a uniform attachment graph on $n$ vertices has a perfect matching for $k \ge 5$ and a Hamilton cycle for $k\ge 13$. One of the ingredients in our proofs is the identification of a subset of vertices that is least likely to expand, which provides us with better expansion rates than the existing ones.


Title: A Moebius inversion formula to discard tangled hyperbolic surfaces
Abstract: Recent literature on Weil-Petersson random hyperbolic surfaces has met a consistent obstacle: the necessity to condition the model, prohibiting certain rare geometric patterns (which we call tangles), such as short closed geodesics or embedded surfaces of short boundary length. The main result of this article is a Moebius inversion formula, allowing to integrate the indicator function of the set of tangle-free surfaces in a systematic, tractable way. It is inspired by a key step of Friedman's celebrated proof of Alon's conjecture. We further prove that our tangle-free hypothesis significantly reduces the number of local topological types of short geodesics, replacing the exponential proliferation observed on tangled surfaces by a polynomial growth.


Title: Box complexes: at the crossroad of graph theory and topology
Abstract: Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their topological properties. They provide thus a fascinating topic mixing topology and discrete mathematics. This paper is intended to provide an up-do-date survey on box complexes. It is based on classical results and recent findings from the literature, but also establishes new results improving our current understanding of the topic, and identifies several challenging open questions.


Title: Markov modulated fluid network process: Tail asymptotics of the stationary distribution
Abstract: We consider a Markov modulated fluid network with a finite number of stations. We are interested in the tail asymptotics behavior of the stationary distribution of its buffer content process. Using two different approaches, we derive upper and lower bounds for the stationary tail decay rate in various directions. Both approaches are based on a well-known time-evolution formula of a Markov process, so-called Dynkin's formula, where a key ingredient is a suitable choice of test functions. Those results show how multidimensional tail asymptotics can be studied for the more than two-dimensional case, which is known as a hard problem.


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


Title: A load balanced chemistry model with analytical Jacobian for faster reactive simulations in OpenFOAM
Abstract: In this study, we introduce a novel open-source chemistry model for OpenFOAM to speed-up the reactive computational fluid dynamics (CFD) simulations using finite-rate chemistry. First, a dynamic load balancing model called DLBFoam is introduced to balance the chemistry load during runtime in parallel simulations. In addition, the solution of the cell-based chemistry problem is improved by utilizing an analytical Jacobian using an open-source library called pyJac and an efficient linear algebra library LAPACK. Combination of the aforementioned efforts yields a speed-up factor 200 for a high-fidelity large-eddy simulation spray combustion case compared to the standard OpenFOAM implementation. It is worth noting that the present implementation does not compromise the solution accuracy.


Title: Debiased Cross-modal Matching for Content-based Micro-video Background Music Recommendation
Abstract: Micro-video background music recommendation is a complicated task where the matching degree between videos and uploader-selected background music is a major issue. However, the selection of the user-generated content (UGC) is biased caused by knowledge limitations and historical preferences among music of each uploader. In this paper, we propose a Debiased Cross-Modal (DebCM) matching model to alleviate the influence of such selection bias. Specifically, we design a teacher-student network to utilize the matching of segments of music videos, which is professional-generated content (PGC) with specialized music-matching techniques, to better alleviate the bias caused by insufficient knowledge of users. The PGC data is captured by a teacher network to guide the matching of uploader-selected UGC data of the student network by KL-based knowledge transfer. In addition, uploaders' personal preferences of music genres are identified as confounders that spuriously correlate music embeddings and background music selections, resulting in the learned recommender system to over-recommend music from the majority groups. To resolve such confounders in the UGC data of the student network, backdoor adjustment is utilized to deconfound the spurious correlation between music embeddings and prediction scores. We further utilize Monte Carlo (MC) estimator with batch-level average as the approximations to avoid integrating the entire confounder space calculated by the adjustment. Extensive experiments on the TT-150k-genre dataset demonstrate the effectiveness of the proposed method towards the selection bias. The code is publicly available on: \url{https://github.com/jing-1/DebCM}.


Title: Task and Explanation Network
Abstract: Explainability in deep networks has gained increased importance in recent years. We argue herein that an AI must be tasked not just with a task but also with an explanation of why said task was accomplished as such. We present a basic framework -- Task and Explanation Network (TENet) -- which fully integrates task completion and its explanation. We believe that the field of AI as a whole should insist -- quite emphatically -- on explainability.


Title: Packing graphs of bounded codegree
Abstract: Two graphs $G_1$ and $G_2$ on $n$ vertices are said to pack if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\'as and Eldridge and, independently, Catlin, asserts that, if $(\Delta_1(G)+1) (\Delta_2(G)+1) \le n+1$, then $G_1$ and $G_2$ pack. We consider the validity of this assertion under the additional assumption that $G_1$ or $G_2$ has bounded codegree. In particular, we prove for all $t \ge 2$ that, if $G_1$ contains no copy of the complete bipartite graph $K_{2,t}$ and $\Delta_1 > 17 t \cdot \Delta_2$, then $(\Delta_1(G)+1) (\Delta_2(G)+1) \le n+1$ implies that $G_1$ and $G_2$ pack. We also provide a mild improvement if moreover $G_2$ contains no copy of the complete tripartite graph $K_{1,1,s}$, $s\ge 1$.


Title: Explore Human Parsing Modality for Action Recognition
Abstract: Multimodal-based action recognition methods have achieved high success using pose and RGB modality. However, skeletons sequences lack appearance depiction and RGB images suffer irrelevant noise due to modality limitations. To address this, we introduce human parsing feature map as a novel modality, since it can selectively retain effective semantic features of the body parts, while filtering out most irrelevant noise. We propose a new dual-branch framework called Ensemble Human Parsing and Pose Network (EPP-Net), which is the first to leverage both skeletons and human parsing modalities for action recognition. The first human pose branch feeds robust skeletons in graph convolutional network to model pose features, while the second human parsing branch also leverages depictive parsing feature maps to model parsing festures via convolutional backbones. The two high-level features will be effectively combined through a late fusion strategy for better action recognition. Extensive experiments on NTU RGB+D and NTU RGB+D 120 benchmarks consistently verify the effectiveness of our proposed EPP-Net, which outperforms the existing action recognition methods. Our code is available at: https://github.com/liujf69/EPP-Net-Action.


Title: Which Quantum Circuit Mutants Shall Be Used? An Empirical Evaluation of Quantum Circuit Mutations
Abstract: As a new research area, quantum software testing lacks systematic testing benchmarks to assess testing techniques' effectiveness. Recently, some open-source benchmarks and mutation analysis tools have emerged. However, there is insufficient evidence on how various quantum circuit characteristics (e.g., circuit depth, number of quantum gates), algorithms (e.g., Quantum Approximate Optimization Algorithm), and mutation characteristics (e.g., mutation operators) affect the most mutant detection in quantum circuits. Studying such relations is important to systematically design faulty benchmarks with varied attributes (e.g., the difficulty in detecting a seeded fault) to facilitate assessing the cost-effectiveness of quantum software testing techniques efficiently. To this end, we present a large-scale empirical evaluation with more than 700K faulty benchmarks (quantum circuits) generated by mutating 382 real-world quantum circuits. Based on the results, we provide valuable insights for researchers to define systematic quantum mutation analysis techniques. We also provide a tool to recommend mutants to users based on chosen characteristics (e.g., a quantum algorithm type) and the required difficulty of killing mutants. Finally, we also provide faulty benchmarks that can already be used to assess the cost-effectiveness of quantum software testing techniques.


Title: A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three
Abstract: We use local limits of Galton-Watson trees to establish local limit theorems for permutations conditioned to avoid a pattern of length three. In the case of 321-avoiding permutations our results resolve an open problem of Pinsky. In the other cases our results give new descriptions of the limiting objects in terms of size-biased Galton-Watson trees.