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Title: Convergence of the discrete Redner-Ben-Avraham-Kahng coagulation equation Abstract: This article looks at the relationship between the discrete and the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation models. On the basis of a priori estimation, a weak stability principle and the weak compactness in $L_1$ for the continuous RBK model is shown. By employing a sequence of discrete models to approximate the continuous one, we show that how discrete model eventually converges to the the modified continuous one using the stability principle.

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Title: Beyond Regrets: Geometric Metrics for Bayesian Optimization Abstract: Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the performance of Bayesian optimization is assessed by regret-based metrics such as instantaneous, simple, and cumulative regrets. These metrics only rely on function evaluations, so that they do not consider geometric relationships between query points and global solutions, or query points themselves. Notably, they cannot discriminate if multiple global solutions are successfully found. Moreover, they do not evaluate Bayesian optimization's abilities to exploit and explore a search space given. To tackle these issues, we propose four new geometric metrics, i.e., precision, recall, average degree, and average distance. These metrics allow us to compare Bayesian optimization algorithms considering the geometry of both query points and global optima, or query points. However, they are accompanied by an extra parameter, which needs to be carefully determined. We therefore devise the parameter-free forms of the respective metrics by integrating out the additional parameter. Finally, we empirically validate that our proposed metrics can provide more convincing interpretation and understanding of Bayesian optimization algorithms from distinct perspectives, compared to the conventional metrics.

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Title: Hereditary completeness of Exponential systems $\{e^{λ_n t}\}_{n=1}^{\infty}$ in their closed span in $L^2 (a, b)$ and Spectral Synthesis Abstract: Suppose that $\{\lambda_n\}_{n=1}^{\infty}$ is a sequence of distinct positive real numbers satisfying the conditions inf$\{\lambda_{n+1}-\lambda_n \}>0,$ and $\sum_{n=1}^{\infty}\lambda_n^{-1}<\infty.$ We prove that the exponential system $\{e^{\lambda_n t}\}_{n=1}^{\infty}$ is hereditarily complete in the closure of the subspace spanned by $\{e^{\lambda_n t}\}_{n=1}^{\infty}$ in the space $L^2 (a,b)$. We also give an example of a class of compact non-normal operators defined on this closure which admit spectral synthesis.

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Title: NODEC: Neural ODE For Optimal Control of Unknown Dynamical Systems Abstract: Controlling complex dynamical systems is generally associated with minimizing certain control objectives with known dynamics under the variational calculus framework. For systems with unknown dynamics, an additional step of dynamics modeling is required. However, any inaccuracy in dynamics modeling will lead to sub-optimality in the resulting control function. Another set of approaches for controlling unknown dynamical systems - reinforcement learning, folds the dynamics modeling into controller training via value function approximation or policy gradient through extensively interacting with the environment, but it suffers from low data efficiency. To address these, we introduce NODEC, a novel framework for controlling unknown dynamical systems, which combines dynamics modelling and controller training using a coupled neural ODE model. Through an intriguing interplay between the two coupled neural networks, NODEC learns system dynamics as well as optimal controls that guides the unknown dynamical system towards target states. Our experiments demonstrate the effectiveness and data efficiency of NODEC for learning optimal control of unknown dynamical systems.

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Title: Feature Selection for Discovering Distributional Treatment Effect Modifiers Abstract: Finding the features relevant to the difference in treatment effects is essential to unveil the underlying causal mechanisms. Existing methods seek such features by measuring how greatly the feature attributes affect the degree of the {\it conditional average treatment effect} (CATE). However, these methods may overlook important features because CATE, a measure of the average treatment effect, cannot detect differences in distribution parameters other than the mean (e.g., variance). To resolve this weakness of existing methods, we propose a feature selection framework for discovering {\it distributional treatment effect modifiers}. We first formulate a feature importance measure that quantifies how strongly the feature attributes influence the discrepancy between potential outcome distributions. Then we derive its computationally efficient estimator and develop a feature selection algorithm that can control the type I error rate to the desired level. Experimental results show that our framework successfully discovers important features and outperforms the existing mean-based method.

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Title: Uncertainty in GNN Learning Evaluations: A Comparison Between Measures for Quantifying Randomness in GNN Community Detection Abstract: (1) The enhanced capability of Graph Neural Networks (GNNs) in unsupervised community detection of clustered nodes is attributed to their capacity to encode both the connectivity and feature information spaces of graphs. The identification of latent communities holds practical significance in various domains, from social networks to genomics. Current real-world performance benchmarks are perplexing due to the multitude of decisions influencing GNN evaluations for this task. (2) Three metrics are compared to assess the consistency of algorithm rankings in the presence of randomness. The consistency and quality of performance between the results under a hyperparameter optimisation with the default hyperparameters is evaluated. (3) The results compare hyperparameter optimisation with default hyperparameters, revealing a significant performance loss when neglecting hyperparameter investigation. A comparison of metrics indicates that ties in ranks can substantially alter the quantification of randomness. (4) Ensuring adherence to the same evaluation criteria may result in notable differences in the reported performance of methods for this task. The $W$ Randomness coefficient, based on the Wasserstein distance, is identified as providing the most robust assessment of randomness.

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Title: Characterizing Fake News Targeting Corporations Abstract: Misinformation proliferates in the online sphere, with evident impacts on the political and social realms, influencing democratic discourse and posing risks to public health and safety. The corporate world is also a prime target for fake news dissemination. While recent studies have attempted to characterize corporate misinformation and its effects on companies, their findings often suffer from limitations due to qualitative or narrative approaches and a narrow focus on specific industries. To address this gap, we conducted an analysis utilizing social media quantitative methods and crowd-sourcing studies to investigate corporate misinformation across a diverse array of industries within the S\&P 500 companies. Our study reveals that corporate misinformation encompasses topics such as products, politics, and societal issues. We discovered companies affected by fake news also get reputable news coverage but less social media attention, leading to heightened negativity in social media comments, diminished stock growth, and increased stress mentions among employee reviews. Additionally, we observe that a company is not targeted by fake news all the time, but there are particular times when a critical mass of fake news emerges. These findings hold significant implications for regulators, business leaders, and investors, emphasizing the necessity to vigilantly monitor the escalating phenomenon of corporate misinformation.

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Title: SPHARMA approximations for stationary functional time series on the sphere Abstract: In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in [8, 7]; more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.

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Title: On a variety of right-symmetric algebras Abstract: We construct a finite-dimensional metabelian right-symmetric algebra over an arbitrary field that does not have a finite basis of identities.

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Title: Limit pretrees for free group automorphisms: existence Abstract: To any free group automorphism, we associate a real pretree with several nice properties. First, it has a rigid/non-nesting action of the free group with trivial arc stabilizers. Secondly, there is an expanding pretree-automorphism of the real pretree that represents the free group automorphism. Finally and crucially, the loxodromic elements are exactly those whose (conjugacy class) length grows exponentially under iteration of the automorphism; thus, the action on the real pretree is able to detect the growth type of an element. This construction extends the theory of metric trees that has been used to study free group automorphisms. The new idea is that one can equivariantly blow up an isometric action on a real tree with respect to other real trees and get a rigid action on a treelike structure known as a real pretree. Topology plays no role in this construction as all the work is done in the language of pretrees.

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Title: Attacks in Adversarial Machine Learning: A Systematic Survey from the Life-cycle Perspective Abstract: Adversarial machine learning (AML) studies the adversarial phenomenon of machine learning, which may make inconsistent or unexpected predictions with humans. Some paradigms have been recently developed to explore this adversarial phenomenon occurring at different stages of a machine learning system, such as backdoor attack occurring at the pre-training, in-training and inference stage; weight attack occurring at the post-training, deployment and inference stage; adversarial attack occurring at the inference stage. However, although these adversarial paradigms share a common goal, their developments are almost independent, and there is still no big picture of AML. In this work, we aim to provide a unified perspective to the AML community to systematically review the overall progress of this field. We firstly provide a general definition about AML, and then propose a unified mathematical framework to covering existing attack paradigms. According to the proposed unified framework, we build a full taxonomy to systematically categorize and review existing representative methods for each paradigm. Besides, using this unified framework, it is easy to figure out the connections and differences among different attack paradigms, which may inspire future researchers to develop more advanced attack paradigms. Finally, to facilitate the viewing of the built taxonomy and the related literature in adversarial machine learning, we further provide a website, \ie, \url{http://adversarial-ml.com}, where the taxonomies and literature will be continuously updated.

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

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

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Title: A stratification of moduli of arbitrarily singular curves Abstract: We introduce a new moduli stack $\mathscr{E}_{g,n}$ of ``equinormalized curves" which is a minor modification of the moduli space of all reduced, connected curves. We construct a stratification $\bigsqcup_\Gamma \mathscr{E}_\Gamma$ of $\mathscr{E}_{g,n}$ indexed by generalized dual graphs and prove that each stratum $\mathscr{E}_{\Gamma}$ is a fiber bundle over a finite quotient of a product of $\mathcal{M}_{g,n}$'s. The fibers are moduli schemes parametrizing subalgebras of a fixed algebra, and are in principle explicitly computable as locally closed subschemes of products of Grassmannians. We thus obtain a remarkably explicit geometric description of moduli of reduced curves with arbitrary singularities.

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Title: On the construction of Cohn's universal localization Abstract: For an associative ring we investigate a construction of Cohn's universal ring of fractions defined relative to a multiplicative set of matrices. The construction avoids the Ore condition, which is necessary to construct a ring of fractions relative to a multiplicative set of elements. But a similar condition, which we call the ``pseudo-Ore'' condition, plays an important role in the construction of Cohn's localization. We show that this condition in fact determines the equivalence relation used in the construction.

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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 $\text{LABEL-COVER}_{\max}$.

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Title: On the delooping of (framed) embedding spaces Abstract: It is known that the bimodule derived mapping spaces between two operads have a delooping in terms of the operadic mapping space. We show a relative version of that statement. The result has applications to the spaces of disc embeddings fixed near the boundary and framed disc embeddings.

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Title: Prompt Decoupling for Text-to-Image Person Re-identification Abstract: Text-to-image person re-identification (TIReID) aims to retrieve the target person from an image gallery via a textual description query. Recently, pre-trained vision-language models like CLIP have attracted significant attention and have been widely utilized for this task due to their robust capacity for semantic concept learning and rich multi-modal knowledge. However, recent CLIP-based TIReID methods commonly rely on direct fine-tuning of the entire network to adapt the CLIP model for the TIReID task. Although these methods show competitive performance on this topic, they are suboptimal as they necessitate simultaneous domain adaptation and task adaptation. To address this issue, we attempt to decouple these two processes during the training stage. Specifically, we introduce the prompt tuning strategy to enable domain adaptation and propose a two-stage training approach to disentangle domain adaptation from task adaptation. In the first stage, we freeze the two encoders from CLIP and solely focus on optimizing the prompts to alleviate domain gap between the original training data of CLIP and downstream tasks. In the second stage, we maintain the fixed prompts and fine-tune the CLIP model to prioritize capturing fine-grained information, which is more suitable for TIReID task. Finally, we evaluate the effectiveness of our method on three widely used datasets. Compared to the directly fine-tuned approach, our method achieves significant improvements.

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Title: Locally differentially private estimation of nonlinear functionals of discrete distributions Abstract: We study the problem of estimating non-linear functionals of discrete distributions in the context of local differential privacy. The initial data $x_1,\ldots,x_n \in [K]$ are supposed i.i.d. and distributed according to an unknown discrete distribution $p = (p_1,\ldots,p_K)$. Only $\alpha$-locally differentially private (LDP) samples $z_1,...,z_n$ are publicly available, where the term 'local' means that each $z_i$ is produced using one individual attribute $x_i$. We exhibit privacy mechanisms (PM) that are interactive (i.e. they are allowed to use already published confidential data) or non-interactive. We describe the behavior of the quadratic risk for estimating the power sum functional $F_{\gamma} = \sum_{k=1}^K p_k^{\gamma}$, $\gamma >0$ as a function of $K, \, n$ and $\alpha$. In the non-interactive case, we study two plug-in type estimators of $F_{\gamma}$, for all $\gamma >0$, that are similar to the MLE analyzed by Jiao et al. (2017) in the multinomial model. However, due to the privacy constraint the rates we attain are slower and similar to those obtained in the Gaussian model by Collier et al. (2020). In the interactive case, we introduce for all $\gamma >1$ a two-step procedure which attains the faster parametric rate $(n \alpha^2)^{-1/2}$ when $\gamma \geq 2$. We give lower bounds results over all $\alpha$-LDP mechanisms and all estimators using the private samples.

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Title: Kronecker coefficients and noncommutative super Schur functions Abstract: The theory of noncommutative Schur functions can be used to obtain positive combinatorial formulae for the Schur expansion of various classes of symmetric functions, as shown by Fomin and Greene. We develop a theory of noncommutative super Schur functions and use it to prove a positive combinatorial rule for the Kronecker coefficients where one of the partitions is a hook, recovering previous results of the two authors. This method also gives a precise connection between this rule and a heuristic for Kronecker coefficients first investigated by Lascoux.

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Title: Cross-linguistically Consistent Semantic and Syntactic Annotation of Child-directed Speech Abstract: While corpora of child speech and child-directed speech (CDS) have enabled major contributions to the study of child language acquisition, semantic annotation for such corpora is still scarce and lacks a uniform standard. We compile two CDS corpora with sentential logical forms, one in English and the other in Hebrew. In compiling the corpora we employ a methodology that enforces a cross-linguistically consistent representation, building on recent advances in dependency representation and semantic parsing. The corpora are based on a sizable portion of Brown's Adam corpus from CHILDES (about 80% of its child-directed utterances), and to all child-directed utterances from Berman's Hebrew CHILDES corpus Hagar. We begin by annotating the corpora with the Universal Dependencies (UD) scheme for syntactic annotation, motivated by its applicability to a wide variety of domains and languages. We then proceed by applying an automatic method for transducing sentential logical forms (LFs) from UD structures. The two representations have complementary strengths: UD structures are language-neutral and support direct annotation, whereas LFs are neutral as to the interface between syntax and semantics, and transparently encode semantic distinctions. We verify the quality of the annotated UD annotation using an inter-annotator agreement study. We then demonstrate the utility of the compiled corpora through a longitudinal corpus study of the prevalence of different syntactic and semantic phenomena.

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Title: Borel structurability on the 2-shift of a countable group Abstract: We show that for any infinite countable group $G$ and for any free Borel action $G \curvearrowright X$ there exists an equivariant class-bijective Borel map from $X$ to the free part $\mathrm{Free}(2^G)$ of the $2$-shift $G \curvearrowright 2^G$. This implies that any Borel structurability which holds for the equivalence relation generated by $G \curvearrowright \mathrm{Free}(2^G)$ must hold a fortiori for all equivalence relations coming from free Borel actions of $G$. A related consequence is that the Borel chromatic number of $\mathrm{Free}(2^G)$ is the maximum among Borel chromatic numbers of free actions of $G$. This answers a question of Marks. Our construction is flexible and, using an appropriate notion of genericity, we are able to show that in fact the generic $G$-equivariant map to $2^G$ lands in the free part. As a corollary we obtain that for every $\epsilon > 0$, every free pmp action of $G$ has a free factor which admits a $2$-piece generating partition with Shannon entropy less than $\epsilon$. This generalizes a result of Danilenko and Park.

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Title: On metric dimension of cube of trees Abstract: Let $G=(V,E)$ be a connected graph and $d_{G}(u,v)$ be the shortest distance between the vertices $u$ and $v$ in $G$. A set $S=\{s_{1},s_{2},\cdots,s_{n}\}\subset V(G)$ is said to be a {\em resolving set} if for all distinct vertices $u,v$ of $G$, there exist an element $s\in S$ such that $d(s,u)\neq d(s,v)$. The minimum cardinality of a resolving set for a graph $G$ is called the {\em metric dimension} of $G$ and it is denoted by $\beta{(G)}$. A resolving set having $\beta{(G)}$ number of vertices is named as {\em metric basis} of $G$. The metric dimension problem is to find a metric basis in a graph $G$, and it has several real-life applications in network theory, telecommunication, image processing, pattern recognition, and many other fields. In this article, we consider {\em cube of trees} $T^{3}=(V, E)$, where any two vertices $u,v$ are adjacent if and only if the distance between them is less than equal to three in $T$. We establish the necessary and sufficient conditions of a vertex subset of $V$ to become a resolving set for $T^{3}$. This helps determine the tight bounds (upper and lower) for the metric dimension of $T^{3}$. Then, for certain well-known cubes of trees, such as caterpillars, lobsters, spiders, and $d$-regular trees, we establish the boundaries of the metric dimension. Further, we characterize some restricted families of cube of trees satisfying $\beta{(T^{3})}=\beta{(T)}$. We provide a construction showing the existence of a cube of tree attaining every positive integer value as their metric dimension.

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Title: On the computation of coarse cohomology Abstract: The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the boundedly supported cohomology. Boundedly supported cohomology coincides with compactly supported Alexander--Spanier cohomology if the space is proper and contractible. Our work generalizes an earlier result of Roe which says that the coarse cohomology is isomorphic to the compactly supported Alexander-Spanier cohomology if the space is uniformly contractible. As an application of our main theorem, we obtain that coarse cohomology of the complement can be computed in terms of Alexander-Spanier cohomology for many spaces.

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Title: Performance Analysis of Clustered LoRa Networks Abstract: In this paper, we investigate the uplink transmission performance of low-power wide-area (LPWA) networks with regards to coexisting radio modules. We adopt long range (LoRa) radio technique as an example of the network of focus even though our analysis can be easily extended to other situations. We exploit a new topology to model the network, where the node locations of LoRa follow a Poisson cluster process (PCP) while other coexisting radio modules follow a Poisson point process (PPP). Unlike most of the performance analysis based on stochastic geometry, we take noise into consideration. More specifically, two models, with a fixed and a random number of active LoRa nodes in each cluster, respectively, are considered. To obtain insights, both the exact and simple approximated expressions for coverage probability are derived. Based on them, area spectral efficiency and energy efficiency are obtained. From our analysis, we show how the performance of LPWA networks can be enhanced through adjusting the density of LoRa nodes around each LoRa receiver. Moreover, the simulation results unveil that the optimal number of active LoRa nodes in each cluster exists to maximize the area spectral efficiency.

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Title: Noncompact $n$-dimensional Einstein spaces as attractors for the Einstein flow Abstract: We prove that along with the Einstein flow, any small perturbations of an $n(n \geq 4)$-dimensional, non-compact negative Einstein space with some "non-positive Weyl tensor" lead to a unique and global solution, and the solution will be attracted to a noncompact Einstein space that is close to the background one. The $n=3$ case has been addressed in [30], while in dimension $n \geq 4$, as we know, negative Einstein metrics in general have non-trivial moduli spaces. This fact is reflected on the structure of Einstein equations, which further indicates no decay for the spatial Weyl tensor. Furthermore, it is suggested in the proof that the mechanic preventing the metric from flowing back to the original Einstein metric lies in the non-decaying character of spatial Weyl tensor. In contrary to the compact case considered in Andersson-Moncrief [4], our proof is independent of the theory of infinitesimal Einstein deformations. Instead, we take advantage of the inherent geometric structures of Einstein equations and develop an approach of energy estimates for a hyperbolic system of Maxwell type.

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Title: Wasserstein Nonnegative Tensor Factorization with Manifold Regularization Abstract: Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.

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Title: Beyond Self-Promotion: How Software Engineering Research Is Discussed on LinkedIn Abstract: LinkedIn is the largest professional network in the world. As such, it can serve to build bridges between practitioners, whose daily work is software engineering (SE), and researchers, who work to advance the field of software engineering. We know that such a metaphorical bridge exists: SE research findings are sometimes shared on LinkedIn and commented on by software practitioners. Yet, we do not know what state the bridge is in. Therefore, we quantitatively and qualitatively investigate how SE practitioners and researchers approach each other via public LinkedIn discussions and what both sides can contribute to effective science communication. We found that a considerable proportion of LinkedIn posts on SE research are written by people who are not the paper authors (39%). Further, 71% of all comments in our dataset are from people in the industry, but only every second post receives at least one comment at all. Based on our findings, we formulate concrete advice for researchers and practitioners to make sharing new research findings on LinkedIn more fruitful.

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Title: Formal manifolds: foundations, function spaces, and Poincaré's lemma Abstract: This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the notion of formal manifolds in the context of differential geometry, inspired by the notion of formal schemes in algebraic geometry. We develop the basic theory for formal manifolds, including a generalization of the theory of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. Additionally, we establish Poincar\'e's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions.

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Title: Mechanism Design for Time Critical and Cost Critical Task Execution via Crowdsourcing Abstract: An exciting application of crowdsourcing is to use social networks in complex task execution. In this paper, we address the problem of a planner who needs to incentivize agents within a network in order to seek their help in executing an {\em atomic task} as well as in recruiting other agents to execute the task. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We identify a set of desirable properties that should ideally be satisfied by a crowdsourcing mechanism. In particular, {\em sybil-proofness} and {\em collapse-proofness} are two complementary properties in our desiderata. We prove that no mechanism can satisfy all the desirable properties simultaneously. This leads us naturally to explore approximate versions of the critical properties. We focus our attention on approximate sybil-proofness and our exploration leads to a parametrized family of payment mechanisms which satisfy collapse-proofness. We characterize the approximate versions of the desirable properties in cost critical and time critical domain.

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Title: Reference-less Measure of Faithfulness for Grammatical Error Correction Abstract: We propose USim, a semantic measure for Grammatical Error Correction (GEC) that measures the semantic faithfulness of the output to the source, thereby complementing existing reference-less measures (RLMs) for measuring the output's grammaticality. USim operates by comparing the semantic symbolic structure of the source and the correction, without relying on manually-curated references. Our experiments establish the validity of USim, by showing that (1) semantic annotation can be consistently applied to ungrammatical text; (2) valid corrections obtain a high USim similarity score to the source; and (3) invalid corrections obtain a lower score.

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Title: A Note on Minimax Robustness of Designs Against Correlated or Heteroscedastic Responses Abstract: We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.

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

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Title: Universality in block dependent linear models with applications to nonparametric regression Abstract: Over the past decade, characterizing the exact asymptotic risk of regularized estimators in high-dimensional regression has emerged as a popular line of work. This literature considers the proportional asymptotics framework, where the number of features and samples both diverge, at a rate proportional to each other. Substantial work in this area relies on Gaussianity assumptions on the observed covariates. Further, these studies often assume the design entries to be independent and identically distributed. Parallel research investigates the universality of these findings, revealing that results based on the i.i.d.~Gaussian assumption extend to a broad class of designs, such as i.i.d.~sub-Gaussians. However, universality results examining dependent covariates so far focused on correlation-based dependence or a highly structured form of dependence, as permitted by right rotationally invariant designs. In this paper, we break this barrier and study a dependence structure that in general falls outside the purview of these established classes. We seek to pin down the extent to which results based on i.i.d.~Gaussian assumptions persist. We identify a class of designs characterized by a block dependence structure that ensures the universality of i.i.d.~Gaussian-based results. We establish that the optimal values of the regularized empirical risk and the risk associated with convex regularized estimators, such as the Lasso and ridge, converge to the same limit under block dependent designs as they do for i.i.d.~Gaussian entry designs. Our dependence structure differs significantly from correlation-based dependence, and enables, for the first time, asymptotically exact risk characterization in prevalent nonparametric regression problems in high dimensions. Finally, we illustrate through experiments that this universality becomes evident quite early, even for relatively moderate sample sizes.

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Title: Stable sets of primes in number fields Abstract: We define a new class of sets -- stable sets -- of primes in number fields. For example, Chebotarev sets $P_{M/K}(\sigma)$, with $M/K$ Galois and $\sigma \in \Gal(M/K)$, are very often stable. These sets have positive (but arbitrary small) Dirichlet density and generalize sets with density 1 in the sense that arithmetic theorems like certain Hasse principles, the Grunwald-Wang theorem, the Riemann's existence theorem, etc. hold for them. Geometrically this allows to give examples of infinite sets $S$ with arbitrary small positive density such that $\Spec \mathcal{O}_{K,S}$ is algebraic $K(\pi,1)$ (for all $p$ simultaneous).

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Title: Counting Finite Topologies Abstract: In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

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Title: Eigenvalues Distributions and Control Theory Abstract: This work deals with the isogeometric Galerkin discretization of the eigenvalue problem related to the Laplace operator subject to homogeneous Dirichlet boundary conditions on bounded intervals. This paper uses GLT theory to study the behavior of the gap of discrete spectra toward the uniform gap condition needed for the uniform boundary observability/controllability problems. The analysis refers to a regular $B$-spline basis and concave or convex reparametrizations. Under suitable assumptions on the reparametrization transformation, we prove that structure emerges within the distribution of the eigenvalues once we reframe the problem into GLT-symbol analysis. We also demonstrate numerically, that the necessary average gap condition proposed in \cite{bianchi2018spectral} is not equivalent to the uniform gap condition. However, by improving the result in \cite{bianchi2021analysis} we construct sufficient criteria that guarantee the uniform gap property.

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Title: Generalizations of quasielliptic curves Abstract: We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all characteristics and having higher genera. This relies on the study of certain infinitesimal group schemes acting on the affine line and certain compactifications. The group schemes are defined in terms of invertible additive polynomials over rings with nilpotent elements, and the compactification is constructed with the theory of numerical semigroups. The existence of regular twisted forms relies on Brion's recent theory of equivariant normalization. Furthermore, extending results of Serre from the realm of group cohomology, we describe non-abelian cohomology for semidirect products, to compute in special cases the collection of all twisted forms.

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Title: Tuple-Independent Representations of Infinite Probabilistic Databases Abstract: Probabilistic databases (PDBs) are probability spaces over database instances. They provide a framework for handling uncertainty in databases, as occurs due to data integration, noisy data, data from unreliable sources or randomized processes. Most of the existing theory literature investigated finite, tuple-independent PDBs (TI-PDBs) where the occurrences of tuples are independent events. Only recently, Grohe and Lindner (PODS '19) introduced independence assumptions for PDBs beyond the finite domain assumption. In the finite, a major argument for discussing the theoretical properties of TI-PDBs is that they can be used to represent any finite PDB via views. This is no longer the case once the number of tuples is countably infinite. In this paper, we systematically study the representability of infinite PDBs in terms of TI-PDBs and the related block-independent disjoint PDBs. The central question is which infinite PDBs are representable as first-order views over tuple-independent PDBs. We give a necessary condition for the representability of PDBs and provide a sufficient criterion for representability in terms of the probability distribution of a PDB. With various examples, we explore the limits of our criteria. We show that conditioning on first order properties yields no additional power in terms of expressivity. Finally, we discuss the relation between purely logical and arithmetic reasons for (non-)representability.

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Title: The multicolour size-Ramsey number of powers of paths Abstract: Given a positive integer $s$, a graph $G$ is $s$-Ramsey for a graph $H$, denoted $G\rightarrow (H)_s$, if every $s$-colouring of the edges of $G$ contains a monochromatic copy of $H$. The $s$-colour size-Ramsey number ${\hat{r}}_s(H)$ of a graph $H$ is defined to be ${\hat{r}}_s(H)=\min\{|E(G)|\colon G\rightarrow (H)_s\}$. We prove that, for all positive integers $k$ and $s$, we have ${\hat{r}}_s(P_n^k)=O(n)$, where $P_n^k$ is the $k$th power of the $n$-vertex path $P_n$.

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Title: Improved Training of Sparse Coding Variational Autoencoder via Weight Normalization Abstract: Learning a generative model of visual information with sparse and compositional features has been a challenge for both theoretical neuroscience and machine learning communities. Sparse coding models have achieved great success in explaining the receptive fields of mammalian primary visual cortex with sparsely activated latent representation. In this paper, we focus on a recently proposed model, sparse coding variational autoencoder (SVAE) (Barello et al., 2018), and show that the end-to-end training scheme of SVAE leads to a large group of decoding filters not fully optimized with noise-like receptive fields. We propose a few heuristics to improve the training of SVAE and show that a unit $L_2$ norm constraint on the decoder is critical to produce sparse coding filters. Such normalization can be considered as local lateral inhibition in the cortex. We verify this claim empirically on both natural image patches and MNIST dataset and show that projection of the filters onto unit norm drastically increases the number of active filters. Our results highlight the importance of weight normalization for learning sparse representation from data and suggest a new way of reducing the number of inactive latent components in VAE learning.

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Title: Use of Jordan forms for convection-pressure split Euler solvers Abstract: In this study, we analyze convection-pressure split Euler flux functions which contain genuine weakly hyperbolic convection subsystems. A system is said to be a genuine weakly hyperbolic if all eigenvalues are real with no complete set of linearly independent (LI) eigenvectors. To construct an upwind solver based on flux difference splitting (FDS) framework, we require to generate complete set of LI eigenvectors. This can be done through addition of generalized eigenvectors which can be computed from theory of Jordan canonical forms. Once we have complete set of LI generalized eigenvectors, we construct upwind solvers in convection-pressure splitting framework. Since generalized eigenvectors are not unique, we take extra care to ensure no direct contribution of generalized eigenvectors in the final formulation of both the newly developed numerical schemes. First scheme is based on Zha and Bilgen type splitting approach, while second is based on Toro and V\'azquez splitting. Both the schemes are tested on several bench-mark test problems on 1-D and one of them is tested on some typical 2-D test problems which involve shock instabilities. The concept of generalized eigenvector based on Jordan forms is found to be useful in dealing with the genuine weakly hyperbolic parts of the considered Euler systems.

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

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Title: An invariant for homogeneous spaces of compact quantum groups Abstract: The central notion in Connes' formulation of non commutative geometry is that of a spectral triple. Given a homogeneous space of a compact quantum group, restricting our attention to all spectral triples that are `well behaved' with respect to the group action, we construct a certain dimensional invariant. In particular, taking the (quantum) group itself as the homogeneous space, this gives an invariant for a compact quantum group. Computations of this invariant in several cases, including all type A quantum groups, are given.

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Title: Somos-4 and a quartic Surface in $\mathbb{RP}^{3}$ Abstract: The Somos-4 equation defines the sequences with this name. Looking at these sequences with an additional property we get a quartic polynomial in 4 variables. This polynomial defines a rational, projective surface in $\mathbb{RP}^{3}$. Here some generators of the subgroup of $Cr_3 (\mathbb{R})$ are determined, whose birational maps are automorphisms of the quartic surface.

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Title: Synchronized CTL over One-Counter Automata Abstract: We consider the model-checking problem of Synchronized Computation-Tree Logic (CTL+Sync) over One-Counter Automata (OCAs). CTL+Sync augments CTL with temporal operators that require several paths to satisfy properties in a synchronous manner, e.g., the property "all paths should eventually see $p$ at the same time". The model-checking problem for CTL+Sync over finite-state Kripke structures was shown to be in $\mathsf{P}^{\mathsf{NP}^{\mathsf{NP}}}$. OCAs are labelled transition systems equipped with a non-negative counter that can be zero-tested. Thus, they induce infinite-state systems whose computation trees are not regular. The model-checking problem for CTL over OCAs was shown to be $\mathsf{PSPACE}$-complete. We show that the model-checking problem for CTL+Sync over OCAs is decidable. However, the upper bound we give is non-elementary. We therefore proceed to study the problem for a central fragment of CTL+Sync, extending CTL with operators that require all paths to satisfy properties in a synchronous manner, and show that it is in $\mathsf{EXP}^\mathsf{NEXP}$ (and in particular in $\mathsf{EXPSPACE}$), by exhibiting a certain "segmented periodicity" in the computation trees of OCAs.

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Title: Taking Complete Finite Prefixes To High Level, Symbolically Abstract: Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net's unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.

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Title: Monotonicity Formulas for Bakry-Emery Ricci Curvature Abstract: Motivated and inspired by the recent work of Colding [5] and Colding-Minicozzi [6] we derive several families of monotonicity formulas for manifolds with nonnegative Bakry-Emery Ricci curvature, extending the formulas in [5, 6].

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Title: Subtraction games in more than one dimension Abstract: This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966), with finite subtraction sets. In case of two move rulesets we find a complete solution, via a certain \P-to-\P\ principle (where \P \ means that the previous player wins). Namely $x \in \P$ if and only if $x +a +b \in \P$, where $a$ and $b$ are the two move options. Flammenkamp 1997 observed that, already in one dimension, rulesets with three moves can be hard to analyze, and still today his related conjecture remains open. Here, we solve instances of rulesets with three moves in two dimensions, and conjecture that they all have regular outcomes. Through several computer visualizations of outcomes of multi-move two-dimensional rulesets, we observe that they tend to partition the game board into periodic mosaics on very few regions/segments, which can depend on the number of moves in a ruleset. For example, we have found a five-move ruleset with an outcome segmentation into six semi-infinite slices. In this spirit, we develop a coloring automaton that generalizes the \P-to-\P\ principle. Given an initial set of colored positions, it quickly paints the \P-positions in segments of the game board. Moreover, we prove that two-dimensional rulesets have row/column eventually periodic outcomes. We pose open problems on the generic hardness of two-dimensional rulesets; several regularity conjectures are provided, but we also conjecture that not all rulesets have regular outcomes.

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Title: Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey Abstract: This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors of neural networks and their datasets. We discuss different strategies to obtain topological information from data and neural networks by means of TDA. Additionally, we review how topological information can be leveraged to analyze properties of neural networks, such as their generalization capacity or expressivity. We explore practical implications of deep learning, specifically focusing on areas like adversarial detection and model selection. Our survey organizes the examined works into four broad domains: 1. Characterization of neural network architectures; 2. Analysis of decision regions and boundaries; 3. Study of internal representations, activations, and parameters; 4. Exploration of training dynamics and loss functions. Within each category, we discuss several articles, offering background information to aid in understanding the various methodologies. We conclude with a synthesis of key insights gained from our study, accompanied by a discussion of challenges and potential advancements in the field.

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Title: Modeling and analysis of pooled stepped chutes Abstract: We consider an application of pooled stepped chutes where the transport in each pooled step is described by the shallow--water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze the mathematical conditions coupling the flows between different chutes taken from the engineering literature. We present the solution to a Riemann problem in the large and also a well--posedness result for the coupled problem. We finally report on some numerical experiments.

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Title: On the intermittency front of stochastic heat equation driven by colored noises Abstract: We study the propagation of high peaks (intermittency front) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in $\mathbb{R}^d$. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, based on a moment formula of the solution. When the space covariance is given by a Riesz kernel, we give more precise bounds for the propagation speed.

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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.

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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.

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Title: Neural Network Complexity of Chaos and Turbulence Abstract: Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations, and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.

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Title: To Save Mobile Crowdsourcing from Cheap-talk: A Game Theoretic Learning Approach Abstract: Today mobile crowdsourcing platforms invite users to provide anonymous reviews about service experiences, yet many reviews are found biased to be extremely positive or negative. The existing methods find it difficult to learn from biased reviews to infer the actual service state, as the state can also be extreme and the platform cannot verify the truthfulness of reviews immediately. Further, reviewers can hide their (positive or negative) bias types and proactively adjust their anonymous reviews against the platform's inference. To our best knowledge, we are the first to study how to save mobile crowdsourcing from cheap-talk and strategically learn from biased users' reviews. We formulate the problem as a dynamic Bayesian game, including users' service-type messaging and the platform's follow-up rating/inference. Our closed-form PBE shows that an extremely-biased user may still honestly message to convince the platform of listening to his review. Such Bayesian game-theoretic learning obviously outperforms the latest common schemes especially when there are multiple diversely-biased users to compete. For the challenging single-user case, we further propose a time-evolving mechanism with the platform's commitment inferences to ensure the biased user's truthful messaging all the time, whose performance improves with more time periods to learn from more historical data.

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Title: Support theorem for the transverse ray transform of tensor fields of rank 2 Abstract: Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given a symmetric tensor field f of rank 2, we show that if the transverse ray transform of f vanishes over an appropriate open set of maximal geodesics of M , then the support of f vanishes on the points of M that lie on the union of the aforementioned open set of geodesics.

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Title: From transient elastic linkages to friction: a complete study of a penalized fourth order equation with delay Abstract: In this paper we consider a fourth order nonlinear parabolic delayed problem modelling a quasi-instantaneous turn-over of linkages in the context of cell-motility. The model depends on a small parameter $\epsilon$ which represents a typical time scale of the memory effect. We first prove global existence and uniqueness of solutions for $\epsilon$ fixed. This is achieved by combining suitable fixed-point and energy arguments and by uncovering a nonlocal in time, integral conserved quantity. After giving a complete classification of steady states in terms of elliptic functions, we next show that every solution converges to a steady state as $t \to \infty$. When $\epsilon \to 0$, we then establish convergence results on finite time intervals, showing that the solution tends in a suitable sense towards the solution of a parabolic problem without delay. Moreover, we establish the convergence of energies as $\epsilon \to 0$, which enables us to show that, for $\epsilon$ small enough, the $\epsilon$-dependent problem inherits part of the large time asymptotics of the limiting parabolic problem.

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Title: Temporal Matrix Factorization for Tracking Concept Drift in Individual User Preferences Abstract: The matrix factorization (MF) technique has been widely adopted for solving the rating prediction problem in recommender systems. The MF technique utilizes the latent factor model to obtain static user preferences (user latent vectors) and item characteristics (item latent vectors) based on historical rating data. However, in the real world user preferences are not static but full of dynamics. Though there are several previous works that addressed this time varying issue of user preferences, it seems (to the best of our knowledge) that none of them is specifically designed for tracking concept drift in individual user preferences. Motivated by this, we develop a Temporal Matrix Factorization approach (TMF) for tracking concept drift in each individual user latent vector. There are two key innovative steps in our approach: (i) we develop a modified stochastic gradient descent method to learn an individual user latent vector at each time step, and (ii) by the Lasso regression we learn a linear model for the transition of the individual user latent vectors. We test our method on a synthetic dataset and several real datasets. In comparison with the original MF, our experimental results show that our temporal method is able to achieve lower root mean square errors (RMSE) for both the synthetic and real datasets. One interesting finding is that the performance gain in RMSE is mostly from those users who indeed have concept drift in their user latent vectors at the time of prediction. In particular, for the synthetic dataset and the Ciao dataset, there are quite a few users with that property and the performance gains for these two datasets are roughly 20% and 5%, respectively.

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Title: Predators and altruists arriving on jammed Riviera Abstract: The Riviera model is a combinatorial model for a settlement along a coastline, introduced recently by the authors. Of most interest are the so-called jammed states, where no more houses can be built without violating the condition that every house needs to have free space to at least one of its sides. In this paper, we introduce new agents (predators and altruists) that want to build houses once the settlement is already in the jammed state. Their behavior is governed by a different set of rules, and this allows them to build new houses even though the settlement is jammed. Our main focus is to detect jammed configurations that are resistant to predators, to altruists, and to both predators and altruists. We provide bivariate generating functions, and complexity functions (configurational entropies) for such jammed configurations. We also discuss this problem in the two-dimensional setting of a combinatorial settlement planning model that was also recently introduced by the authors, and of which the Riviera model is just a special case.

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Title: The Local Queue Number of Graphs with Bounded Treewidth Abstract: A queue layout of a graph $G$ consists of a vertex ordering of $G$ and a partition of the edges into so-called queues such that no two edges in the same queue nest, i.e., have their endpoints ordered in an ABBA-pattern. Continuing the research on local ordered covering numbers, we introduce the local queue number of a graph $G$ as the minimum $\ell$ such that $G$ admits a queue layout with each vertex having incident edges in no more than $\ell$ queues. Similarly to the local page number [Merker, Ueckerdt, GD'19], the local queue number is closely related to the graph's density and can be arbitrarily far from the classical queue number. We present tools to bound the local queue number of graphs from above and below, focusing on graphs of treewidth $k$. Using these, we show that every graph of treewidth $k$ has local queue number at most $k+1$ and that this bound is tight for $k=2$, while a general lower bound is $\lceil k/2\rceil+1$. Our results imply, inter alia, that the maximum local queue number among planar graphs is either 3 or 4.

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Title: Balancing Continual Learning and Fine-tuning for Human Activity Recognition Abstract: Wearable-based Human Activity Recognition (HAR) is a key task in human-centric machine learning due to its fundamental understanding of human behaviours. Due to the dynamic nature of human behaviours, continual learning promises HAR systems that are tailored to users' needs. However, because of the difficulty in collecting labelled data with wearable sensors, existing approaches that focus on supervised continual learning have limited applicability, while unsupervised continual learning methods only handle representation learning while delaying classifier training to a later stage. This work explores the adoption and adaptation of CaSSLe, a continual self-supervised learning model, and Kaizen, a semi-supervised continual learning model that balances representation learning and down-stream classification, for the task of wearable-based HAR. These schemes re-purpose contrastive learning for knowledge retention and, Kaizen combines that with self-training in a unified scheme that can leverage unlabelled and labelled data for continual learning. In addition to comparing state-of-the-art self-supervised continual learning schemes, we further investigated the importance of different loss terms and explored the trade-off between knowledge retention and learning from new tasks. In particular, our extensive evaluation demonstrated that the use of a weighting factor that reflects the ratio between learned and new classes achieves the best overall trade-off in continual learning.

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Title: On Completely Edge-Independent Spanning Trees in Locally Twisted Cubes Abstract: A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if any two of them are pairwisely edge-disjoint, they are called completely edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many network functionalities, and constructing CEISTs as maximally allowed as possible in a given network is a worthy undertaking. In this paper, we establish the maximal number of CEISTs in the locally twisted cube network, and propose an algorithm to construct $\lfloor \frac{n}{2} \rfloor$ CEISTs in $LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has been actually implemented, and we present the outputs. Network broadcasting in the $LTQ_n$ was simulated using $\lfloor\frac{n}{2}\rfloor$ CEISTs, and the performance compared with broadcasting using a single tree.

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Title: Membrane-Dependent Neuromorphic Learning Rule for Unsupervised Spike Pattern Detection Abstract: Several learning rules for synaptic plasticity, that depend on either spike timing or internal state variables, have been proposed in the past imparting varying computational capabilities to Spiking Neural Networks. Due to design complications these learning rules are typically not implemented on neuromorphic devices leaving the devices to be only capable of inference. In this work we propose a unidirectional post-synaptic potential dependent learning rule that is only triggered by pre-synaptic spikes, and easy to implement on hardware. We demonstrate that such a learning rule is functionally capable of replicating computational capabilities of pairwise STDP. Further more, we demonstrate that this learning rule can be used to learn and classify spatio-temporal spike patterns in an unsupervised manner using individual neurons. We argue that this learning rule is computationally powerful and also ideal for hardware implementations due to its unidirectional memory access.

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Title: Specific Emitter Identification Based on Joint Variational Mode Decomposition Abstract: Specific emitter identification (SEI) technology is significant in device administration scenarios, such as self-organized networking and spectrum management, owing to its high security. For nonlinear and non-stationary electromagnetic signals, SEI often employs variational modal decomposition (VMD) to decompose the signal in order to effectively characterize the distinct device fingerprint. However, the trade-off of VMD between the robustness to noise and the ability to preserve signal information has not been investigated in the current literature. Moreover, the existing VMD algorithm does not utilize the stability of the intrinsic distortion of emitters within a certain temporal span, consequently constraining its practical applicability in SEI. In this paper, we propose a joint variational modal decomposition (JVMD) algorithm, which is an improved version of VMD by simultaneously implementing modal decomposition on multi-frame signals. The consistency of multi-frame signals in terms of the central frequencies and the inherent modal functions (IMFs) is exploited, which effectively highlights the distinctive characteristics among emitters and reduces noise. Additionally, the complexity of JVMD is analyzed, which is proven to be more computational-friendly than VMD. Simulations of both modal decomposition and SEI that involve real-world datasets are presented to illustrate that when compared with VMD, the JVMD algorithm improves the accuracy of device classification and the robustness towards noise.

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Title: Imperfect Delayed CSIT can be as Useful as Perfect Delayed CSIT: DoF Analysis and Constructions for the BC Abstract: In the setting of the two-user broadcast channel, where a two-antenna transmitter communicates information to two single-antenna receivers, recent work by Maddah-Ali and Tse has shown that perfect knowledge of delayed channel state information at the transmitter (perfect delayed CSIT) can be useful, even in the absence of any knowledge of current CSIT. Similar benefits of perfect delayed CSIT were revealed in recent work by Kobayashi et al., Yang et al., and Gou and Jafar, which extended the above to the case of perfect delayed CSIT and imperfect current CSIT. The work here considers the general problem of communicating, over the aforementioned broadcast channel, with imperfect delayed and imperfect current CSIT, and reveals that even substantially degraded and imperfect delayed-CSIT is in fact sufficient to achieve the aforementioned gains previously associated to perfect delayed CSIT. The work proposes novel multi-phase broadcasting schemes that properly utilize knowledge of imperfect delayed and imperfect current CSIT, to match in many cases the optimal degrees-of-freedom (DoF) region achieved with perfect delayed CSIT. In addition to the theoretical limits and explicitly constructed precoders, the work applies towards gaining practical insight as to when it is worth improving CSIT quality.

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Title: A Hybrid Neural Network Model For Predicting The Nitrate Concentration In The Recirculating Aquaculture System Abstract: This study was groundbreaking in its application of neural network models for nitrate management in the Recirculating Aquaculture System (RAS). A hybrid neural network model was proposed, which accurately predicted daily nitrate concentration and its trends using six water quality parameters. We conducted a 105-day aquaculture experiment, during which we collected 450 samples from five sets of RAS to train our model (C-L-A model) which incorporates Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and self-Attention. Furthermore, we obtained 90 samples from a standalone RAS as the testing data to evaluate the performance of the model in practical applications. The experimental results proved that the C-L-A model accurately predicted nitrate concentration in RAS and maintained good performance even with a reduced proportion of training data. We recommend using water quality parameters from the past 7 days to forecast future nitrate concentration, as this timeframe allows the model to achieve maximum generalization capability. Additionally, we compared the performance of the C-L-A model with three basic neural network models (CNN, LSTM, self-Attention) as well as three hybrid neural network models (CNN-LSTM, CNN-Attention, LSTM-Attention). The results demonstrated that the C-L-A model (R2=0.956) significantly outperformed the other neural network models (R2=0.901-0.927). Our study suggests that the utilization of neural network models, specifically the C-L-A model, could potentially assist the RAS industry in conserving resources for daily nitrate monitoring.

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Title: Efficient Continuous Relaxations for Dense CRF Abstract: Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range interactions, dense CRFs provide a more detailed labelling compared to their sparse counterparts. Variational inference in these dense models is performed using a filtering-based mean-field algorithm in order to obtain a fully-factorized distribution minimising the Kullback-Leibler divergence to the true distribution. In contrast to the continuous relaxation-based energy minimisation algorithms used for sparse CRFs, the mean-field algorithm fails to provide strong theoretical guarantees on the quality of its solutions. To address this deficiency, we show that it is possible to use the same filtering approach to speed-up the optimisation of several continuous relaxations. Specifically, we solve a convex quadratic programming (QP) relaxation using the efficient Frank-Wolfe algorithm. This also allows us to solve difference-of-convex relaxations via the iterative concave-convex procedure where each iteration requires solving a convex QP. Finally, we develop a novel divide-and-conquer method to compute the subgradients of a linear programming relaxation that provides the best theoretical bounds for energy minimisation. We demonstrate the advantage of continuous relaxations over the widely used mean-field algorithm on publicly available datasets.

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Title: The configuration category of a covering space Abstract: We investigate the relationship between the configuration category of a manifold and the configuration category of a covering space of that manifold.

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Title: Characterizing Boundedness in Chase Variants Abstract: Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions. This paper is under consideration for publication in Theory and Practice of Logic Programming.

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Title: Signal reconstruction from the magnitude of subspace components Abstract: We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature conditions, that require at least a quadratic number of subspaces. Moreover, we address reconstruction under the erasure of a subset of the norms; using the concepts of $p$-fusion frames and list decoding, we propose an algorithm that outputs a finite list of candidate signals, one of which is the correct one. In the random setting, we show that a set of subspaces chosen at random and of cardinality scaling linearly in the ambient dimension allows for exact reconstruction with high probability by solving the feasibility problem of a semidefinite program.

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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.

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Title: Continuous Credit Networks and Layer 2 Blockchains: Monotonicity and Sampling Abstract: To improve transaction rates, many cryptocurrencies have implemented so-called ''Layer-2'' transaction protocols, where payments are routed across networks of private payment channels. However, for a given transaction, not every network state provides a feasible route to perform the payment; in this case, the transaction must be put on the public ledger. The payment channel network thus multiplies the transaction rate of the overall system; the less frequently it fails, the higher the multiplier. We build on earlier work on credit networks and show that this network liquidity problem is connected to the combinatorics of graphical matroids. Earlier work could only analyze the (unnatural) scenario where transactions had discrete sizes. Superficially, it might seem like the continuous case would be harder to examine. However, removing this assumption lets us make progress in two important directions. First, we give a partial answer to the ``monotonicity conjecture'' that previous work left open. This conjecture asks that the network's performance not degrade as capacity on any edge increases. And second, we construct here a network state sampling procedure with much faster asymptotic performance than off-the-shelf Markov chains ($O(\vert E\vert \beta(\vert E\vert))$, where $\beta(x)$ is the complexity of solving a linear program on $x$ constraints.) We obtain our results by mapping the underlying graphs to convex bodies and then showing that the liquidity and sampling problems reduce to bounding and computing the volumes of these bodies. The transformation relies crucially on the combinatorial properties of the underlying graphic matroid, as do the proofs of monotonicity and fast sampling.

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Title: The relationship between Biological and Artificial Intelligence Abstract: Intelligence can be defined as a predominantly human ability to accomplish tasks that are generally hard for computers and animals. Artificial Intelligence [AI] is a field attempting to accomplish such tasks with computers. AI is becoming increasingly widespread, as are claims of its relationship with Biological Intelligence. Often these claims are made to imply higher chances of a given technology succeeding, working on the assumption that AI systems which mimic the mechanisms of Biological Intelligence should be more successful. In this article I will discuss the similarities and differences between AI and the extent of our knowledge about the mechanisms of intelligence in biology, especially within humans. I will also explore the validity of the assumption that biomimicry in AI systems aids their advancement, and I will argue that existing similarity to biological systems in the way Artificial Neural Networks [ANNs] tackle tasks is due to design decisions, rather than inherent similarity of underlying mechanisms. This article is aimed at people who understand the basics of AI (especially ANNs), and would like to be better able to evaluate the often wild claims about the value of biomimicry in AI.

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Title: Jumping numbers of a unibranch curve on a smooth surface Abstract: A formula for the jumping numbers of a curve unibranch at a singular point is established. The jumping numbers are expressed in terms of the Enriques diagram of the log resolution of the singularity, or equivalently in terms of the canonical set of generators of the semigroup of the curve at the singular point.

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Title: Harvesting of interacting stochastic populations Abstract: We analyze the optimal harvesting problem for an ecosystem of species that experience environmental stochasticity. Our work generalizes the current literature significantly by taking into account non-linear interactions between species, state-dependent prices, and species injections. The key generalization is making it possible to not only harvest, but also `seed' individuals into the ecosystem. This is motivated by how fisheries and certain endangered species are controlled. The harvesting problem becomes finding the optimal harvesting-seeding strategy that maximizes the expected total income from the harvest minus the lost income from the species injections. Our analysis shows that new phenomena emerge due to the possibility of species injections. It is well-known that multidimensional harvesting problems are very hard to tackle. We are able to make progress, by characterizing the value function as a viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equations. Moreover, we provide a verification theorem, which tells us that if a function has certain properties, then it will be the value function. This allows us to show heuristically, as was shown in Lungu and $\O$ksendal (Bernoulli '01), that it is almost surely never optimal to harvest or seed from more than one population at a time. We approximate the continuous-time systems by Markov chains and show that the optimal harvesting-seeding strategies of the Markov chain approximations converge to the correct optimal harvesting strategy. This is used to provide numerical approximations to the optimal harvesting-seeding strategies and is a first step towards a full understanding of the intricacies of how one should harvest and seed interacting species. In particular, we look at three examples: one species modeled by a Verhulst-Pearl diffusion, two competing species and a two-species predator-prey system.

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Title: A 3-skeleton for a classifying space for the symmetric group Abstract: We construct a 3-dimensional cell complex that is the 3-skeleton for an Eilenberg--MacLane classifying space for the symmetric group $\mathfrak{S}_n$. Our complex starts with the presentation for $\mathfrak{S}_n$ with $n-1$ adjacent transpositions with squaring, commuting, and braid relations, and adds seven classes of 3-cells that fill in certain 2-spheres bounded by these relations. We use a rewriting system and a combinatorial method of K. Brown to prove the correctness of our construction. Our main application is a computation of the second cohomology of $\mathfrak{S}_n$ in certain twisted coefficient modules; we use this computation in a companion paper to study splitting of extensions related to braid groups. As another application, we give a concrete description of the third homology of $\mathfrak{S}_n$ with untwisted coefficients in $\mathbb{Z}$.

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Title: Improving Deep Pancreas Segmentation in CT and MRI Images via Recurrent Neural Contextual Learning and Direct Loss Function Abstract: Deep neural networks have demonstrated very promising performance on accurate segmentation of challenging organs (e.g., pancreas) in abdominal CT and MRI scans. The current deep learning approaches conduct pancreas segmentation by processing sequences of 2D image slices independently through deep, dense per-pixel masking for each image, without explicitly enforcing spatial consistency constraint on segmentation of successive slices. We propose a new convolutional/recurrent neural network architecture to address the contextual learning and segmentation consistency problem. A deep convolutional sub-network is first designed and pre-trained from scratch. The output layer of this network module is then connected to recurrent layers and can be fine-tuned for contextual learning, in an end-to-end manner. Our recurrent sub-network is a type of Long short-term memory (LSTM) network that performs segmentation on an image by integrating its neighboring slice segmentation predictions, in the form of a dependent sequence processing. Additionally, a novel segmentation-direct loss function (named Jaccard Loss) is proposed and deep networks are trained to optimize Jaccard Index (JI) directly. Extensive experiments are conducted to validate our proposed deep models, on quantitative pancreas segmentation using both CT and MRI scans. Our method outperforms the state-of-the-art work on CT [11] and MRI pancreas segmentation [1], respectively.

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Title: Cross-Layer Modeling of Randomly Spread CDMA Using Stochastic Network Calculus Abstract: Code-division multiple-access (CDMA) has the potential to support traffic sources with a wide range of quality of service (QoS) requirements. The traffic carrying capacity of CDMA channels under QoS constraints (such as delay guarantee) is, however, less well-understood. In this work, we propose a method based on stochastic network calculus and large system analysis to quantify the maximum traffic that can be carried by a multiuser CDMA network under the QoS constraints. At the physical layer, we have linear minimum-mean square error receivers and adaptive modulation and coding, while the channel service process is modeled by using a finite-state Markov chain. We study the impact of delay requirements, violation probability and the user load on the traffic carrying capacity under different signal strengths. A key insight provided by the numerical results is as to how much one has to back-off from capacity under the different delay requirements.

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Title: Neural Ensemble Search via Bayesian Sampling Abstract: Recently, neural architecture search (NAS) has been applied to automate the design of neural networks in real-world applications. A large number of algorithms have been developed to improve the search cost or the performance of the final selected architectures in NAS. Unfortunately, these NAS algorithms aim to select only one single well-performing architecture from their search spaces and thus have overlooked the capability of neural network ensemble (i.e., an ensemble of neural networks with diverse architectures) in achieving improved performance over a single final selected architecture. To this end, we introduce a novel neural ensemble search algorithm, called neural ensemble search via Bayesian sampling (NESBS), to effectively and efficiently select well-performing neural network ensembles from a NAS search space. In our extensive experiments, NESBS algorithm is shown to be able to achieve improved performance over state-of-the-art NAS algorithms while incurring a comparable search cost, thus indicating the superior performance of our NESBS algorithm over these NAS algorithms in practice.

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Title: Polynomial Bound and Nonlinear Smoothing for the Benjamin-Ono Equation on the Circle Abstract: For initial data in Sobolev spaces $H^s(\mathbb T)$, $\frac 12 < s \leqslant 1$, the solution to the Cauchy problem for the Benjamin-Ono equation on the circle is shown to grow at most polynomially in time at a rate $(1+t)^{3(s-\frac 12) + \epsilon}$, $0<\epsilon \ll 1$. Key to establishing this result is the discovery of a nonlinear smoothing effect for the Benjamin-Ono equation, according to which the solution to the equation satisfied by a certain gauge transform, which is widely used in the well-posedness theory of the Cauchy problem, becomes smoother once its free solution is removed.

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Title: How to Apply Markov Chains for Modeling Sequential Edit Patterns in Collaborative Ontology-Engineering Projects Abstract: With the growing popularity of large-scale collaborative ontology-engineering projects, such as the creation of the 11th revision of the International Classification of Diseases, we need new methods and insights to help project- and community-managers to cope with the constantly growing complexity of such projects. In this paper, we present a novel application of Markov chains to model sequential usage patterns that can be found in the change-logs of collaborative ontology-engineering projects. We provide a detailed presentation of the analysis process, describing all the required steps that are necessary to apply and determine the best fitting Markov chain model. Amongst others, the model and results allow us to identify structural properties and regularities as well as predict future actions based on usage sequences. We are specifically interested in determining the appropriate Markov chain orders which postulate on how many previous actions future ones depend on. To demonstrate the practical usefulness of the extracted Markov chains we conduct sequential pattern analyses on a large-scale collaborative ontology-engineering dataset, the International Classification of Diseases in its 11th revision. To further expand on the usefulness of the presented analysis, we show that the collected sequential patterns provide potentially actionable information for user-interface designers, ontology-engineering tool developers and project-managers to monitor, coordinate and dynamically adapt to the natural development processes that occur when collaboratively engineering an ontology. We hope that presented work will spur a new line of ontology-development tools, evaluation-techniques and new insights, further taking the interactive nature of the collaborative ontology-engineering process into consideration.

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Title: Wittgenstein, Peirce, and paradoxes of mathematical proof Abstract: Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following skepticism. We argue that his intuitions rather reflect resistance to treating meaning as fixed content, and are better understood in the light of C.S. Peirce's distinction between corollarial and theorematic proofs. We show how Peirce's insight that "all necessary reasoning is diagrammatic", vindicated in modern epistemic logic and semantic information theory, helps explain the paradoxical ability of deduction to generate new knowledge and meaning.

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Title: U-Mixer: An Unet-Mixer Architecture with Stationarity Correction for Time Series Forecasting Abstract: Time series forecasting is a crucial task in various domains. Caused by factors such as trends, seasonality, or irregular fluctuations, time series often exhibits non-stationary. It obstructs stable feature propagation through deep layers, disrupts feature distributions, and complicates learning data distribution changes. As a result, many existing models struggle to capture the underlying patterns, leading to degraded forecasting performance. In this study, we tackle the challenge of non-stationarity in time series forecasting with our proposed framework called U-Mixer. By combining Unet and Mixer, U-Mixer effectively captures local temporal dependencies between different patches and channels separately to avoid the influence of distribution variations among channels, and merge low- and high-levels features to obtain comprehensive data representations. The key contribution is a novel stationarity correction method, explicitly restoring data distribution by constraining the difference in stationarity between the data before and after model processing to restore the non-stationarity information, while ensuring the temporal dependencies are preserved. Through extensive experiments on various real-world time series datasets, U-Mixer demonstrates its effectiveness and robustness, and achieves 14.5\% and 7.7\% improvements over state-of-the-art (SOTA) methods.

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Title: Hot Streaks on Social Media Abstract: Measuring the impact and success of human performance is common in various disciplines, including art, science, and sports. Quantifying impact also plays a key role on social media, where impact is usually defined as the reach of a user's content as captured by metrics such as the number of views, likes, retweets, or shares. In this paper, we study entire careers of Twitter users to understand properties of impact. We show that user impact tends to have certain characteristics: First, impact is clustered in time, such that the most impactful tweets of a user appear close to each other. Second, users commonly have 'hot streaks' of impact, i.e., extended periods of high-impact tweets. Third, impact tends to gradually build up before, and fall off after, a user's most impactful tweet. We attempt to explain these characteristics using various properties measured on social media, including the user's network, content, activity, and experience, and find that changes in impact are associated with significant changes in these properties. Our findings open interesting avenues for future research on virality and influence on social media.

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Title: Density estimation using the perceptron Abstract: We propose a new density estimation algorithm. Given $n$ i.i.d. samples from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose ''perceptron discrepancy'' with the empirical distribution is at most $O(\sqrt{d/n})$. The perceptron discrepancy between two distributions is defined as the largest difference in mass that they place on any halfspace of $\mathbb{R}^d$. It is shown that this estimator achieves expected total variation distance to the truth that is almost minimax optimal over the class of densities with bounded Sobolev norm and Gaussian mixtures. This suggests that regularity of the prior distribution could be an explanation for the efficiency of the ubiquitous step in machine learning that replaces optimization over large function spaces with simpler parametric classes (e.g. in the discriminators of GANs). We generalize the above to show that replacing the ''perceptron discrepancy'' with the generalized energy distance of Sz\'ekeley-Rizzo further improves total variation loss. The generalized energy distance between empirical distributions is easily computable and differentiable, thus making it especially useful for fitting generative models. To the best of our knowledge, it is the first example of a distance with such properties for which there are minimax statistical guarantees.

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Title: The Impact of Distance on Performance and Scalability of Distributed Database Systems in Hybrid Clouds Abstract: The increasing need for managing big data has led the emergence of advanced database management systems. There has been increased efforts aimed at evaluating the performance and scalability of NoSQL and Relational databases hosted by either private or public cloud datacenters. However, there has been little work on evaluating the performance and scalability of these databases in hybrid clouds, where the distance between private and public cloud datacenters can be one of the key factors that can affect their performance. Hence, in this paper, we present a detailed evaluation of throughput, scalability, and VMs size vs. VMs number for six modern databases in a hybrid cloud, consisting of a private cloud in Adelaide and Azure based datacenter in Sydney, Mumbai, and Virginia regions. Based on results, as the distance between private and public clouds increases, the throughput performance of most databases reduces. Second, MongoDB obtains the best throughput performance, followed by MySQL C luster, whilst Cassandra exposes the most fluctuation in through performance. Third, vertical scalability improves the throughput of databases more than the horizontal scalability. Forth, exploiting bigger VMs rather than more VMs with less cores can increase throughput performance for Cassandra, Riak, and Redis.

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

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Title: A note on $t$-designs in isodual codes Abstract: In the present paper, we construct 3-designs using extended binary quadratic residue codes and their dual codes.

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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.

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Title: Inference with System W Satisfies Syntax Splitting Abstract: In this paper, we investigate inductive inference with system W from conditional belief bases with respect to syntax splitting. The concept of syntax splitting for inductive inference states that inferences about independent parts of the signature should not affect each other. This was captured in work by Kern-Isberner, Beierle, and Brewka in the form of postulates for inductive inference operators expressing syntax splitting as a combination of relevance and independence; it was also shown that c-inference fulfils syntax splitting, while system P inference and system Z both fail to satisfy it. System W is a recently introduced inference system for nonmonotonic reasoning that captures and properly extends system Z as well as c-inference. We show that system W fulfils the syntax splitting postulates for inductive inference operators by showing that it satisfies the required properties of relevance and independence. This makes system W another inference operator besides c-inference that fully complies with syntax splitting, while in contrast to c-inference, also extending rational closure.

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Title: On the use of the M-quantiles for outlier detection in multivariate data Abstract: Defining a successful notion of a multivariate quantile has been an open problem for more than half a century, motivating a plethora of possible solutions. Of these, the approach of [8] and [25] leading to M-quantiles, is very appealing for its mathematical elegance combining elements of convex analysis and probability theory. The key idea is the description of a convex function (the K-function) whose gradient (the K-transform) is in one-to-one correspondence between all of R^d and the unit ball in R^d. By analogy with the d=1 case where the K-transform is a cumulative distribution function-like object (an M-distribution), the fact that its inverse is guaranteed to exist lends itself naturally to providing the basis for the definition of a quantile function for all d>=1. Over the past twenty years the resulting M-quantiles have seen applications in a variety of fields, primarily for the purpose of detecting outliers in multidimensional spaces. In this article we prove that for odd d>=3, it is not the gradient but a poly-Laplacian of the K-function that is (almost everywhere) proportional to the density function. For d even one cannot establish a differential equation connecting the K-function with the density. These results show that usage of the K-transform for outlier detection in higher odd-dimensions is in principle flawed, as the K-transform does not originate from inversion of a true M-distribution. We demonstrate these conclusions in two dimensions through examples from non-standard asymmetric distributions. Our examples illustrate a feature of the K-transform whereby regions in the domain with higher density map to larger volumes in the co-domain, thereby producing a magnification effect that moves inliers closer to the boundary of the co-domain than outliers. This feature obviously disrupts any outlier detection mechanism that relies on the inverse K-transform.

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Title: Properties of Mean Value Sets: Angle Conditions, Blowup Solutions, and Nonconvexity Abstract: We study the mean values sets of the second order divergence form elliptic operator with principal coefficients defined as $$a^{ij}_k(x):= \begin{cases} \alpha_k \delta^{ij}(x) &x_n>0 \beta_k \delta^{ij}(x) &x_n<0. \end{cases}$$ In particular, we will show that the mean value sets associated to such an operator need not be convex as $\alpha_k$ and $\beta_k$ converge to 1. This example then leads to an example of nonconvex mean value sets for smooth $a^{ij}(x)$.

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Title: Moduli of non-commutative polarized schemes Abstract: We construct, using geometric invariant theory, a quasi-projective Deligne-Mumford stack of stable graded algebras. We also construct a derived enhancement, which classifies twisted bundles of stable graded A-infinity-algebras. The tangent complex of the derived scheme is given by graded Hochschild cohomology, which we relate to ordinary Hochschild cohomology. We obtain a version of Hilbert stability for non-commutative projective schemes.

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Title: Approximating Numerical Flux by Fourier Neural Operators for the Hyperbolic Conservation Laws Abstract: Classical numerical schemes exist for solving PDEs numerically, and recently, neural network-based methods have been developed. However, methodologies using neural networks, such as PINN and neural operators, lack robustness and generalization power. To compensate for such drawbacks, there are many types of research combining classical numerical schemes and machine learning methods by replacing a small portion of the numerical schemes with neural networks. In this work, we focus on hyperbolic conservation laws and replace numerical fluxes in the numerical schemes by neural operator. For this, we construct losses that are motivated by numerical schemes for conservation laws and approximate numerical flux by FNO. Through experiments, we show that our methodology has advantages of both numerical schemes and FNO by comparing with original methods. For instance, we demonstrate our method gains robustness, resolution invariance property, and feasibility of a data-driven method. Our method especially has the ability to predict continuously in time and generalization power on the out-of-distribution samples, which are challenges to be tackled for existing neural operator methods.

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

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Title: Reproducing formulas for generalized translation invariant systems on locally compact abelian groups Abstract: In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\Gamma_j$, $j \in J$, be a countable family of closed, co-compact subgroups of a second countable locally compact abelian group $G$ and study systems of the form $\cup_{j \in J}\{g_{j,p}(\cdot - \gamma)\}_{\gamma \in \Gamma_j, p \in P_j}$ with generators $g_{j,p}$ in $L^2(G)$ and with each $P_j$ being a countable or an uncountable index set. We refer to systems of this form as generalized translation invariant (GTI) systems. Many of the familiar transforms, e.g., the wavelet, shearlet and Gabor transform, both their discrete and continuous variants, are GTI systems. Under a technical $\alpha$ local integrability condition ($\alpha$-LIC) we characterize when GTI systems constitute tight and dual frames that yield reproducing formulas for $L^2(G)$. This generalizes results on generalized shift invariant systems, where each $P_j$ is assumed to be countable and each $\Gamma_j$ is a uniform lattice in $G$, to the case of uncountably many generators and (not necessarily discrete) closed, co-compact subgroups. Furthermore, even in the case of uniform lattices $\Gamma_j$, our characterizations improve known results since the class of GTI systems satisfying the $\alpha$-LIC is strictly larger than the class of GTI systems satisfying the previously used local integrability condition. As an application of our characterization results, we obtain new characterizations of translation invariant continuous frames and Gabor frames for $L^2(G)$. In addition, we will see that the admissibility conditions for the continuous and discrete wavelet and Gabor transform in $L^2(\mathbb{R}^n)$ are special cases of the same general characterizing equations.

math

Title: Center of Mass Technique and Affine Geometry Abstract: The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be defined for sets whose total mass equals zero. In the paper we improve this disadvantage and assign to an n-dimensional affine space L over any field k the (n+1)-dimensional vector space over the field k of weighty points and mass dipoles in L. In this space, the sum of weighted points with nonzero total mass is equal to the center of mass of these points equipped with their total mass. We present several interpretations of the space of weighty points and mass dipoles in L, and a couple of its applications to geometry. The paper is self-contained and is accessible for undergraduate students.

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Title: Profinite equivariant spectra and their tensor-triangular geometry Abstract: We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all other models in the literature. We describe the Balmer spectrum of finite $G$-spectra up to the ambiguity that is present in the finite group case; in particular, we obtain a thick subcategory theorem when $G$ is abelian. By verifying the bijectivity hypothesis for $\mathsf{Sp}_G$, we prove a nilpotence theorem for all profinite groups. Our study then moves to the realm of rational $G$-equivariant spectra. By exploiting the continuity of our model, we construct an equivalence between the category of rational $G$-spectra and the algebraic model of the second author and Sugrue, which improves their result to the symmetric monoidal and $\infty$-categorical level. Furthermore, we prove that the telescope conjecture holds in this category. Finally, we characterize when the category of rational $G$-spectra is stratified, resulting in a classification of the localizing ideals in terms of conjugacy classes of subgroups. To facilitate these results, we develop some foundational aspects of pro-tt-geometry. For instance, we establish and use the continuity of the homological spectrum and introduce a notion of von Neumann regular tt-categories, of which rational $G$-spectra is an example.

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Title: Theory of sexes by Geodakian as it is advanced by Iskrin Abstract: In 1960s V.Geodakian proposed a theory that explains sexes as a mechanism for evolutionary adaptation of the species to changing environmental conditions. In 2001 V.Iskrin refined and augmented the concepts of Geodakian and gave a new and interesting explanation to several phenomena which involve sex, and sex ratio, including the war-years phenomena. He also introduced a new concept of the "catastrophic sex ratio." This note is an attempt to digest technical aspects of the new ideas by Iskrin.

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