Title: Charatheodory and Smirnov type theorem for harmonic mappings
Abstract: We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and Riesz--Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions of the boundary.


Title: Theoretical guarantees on the best-of-n alignment policy
Abstract: A simple and effective method for the alignment of generative models is the best-of-$n$ policy, where $n$ samples are drawn from a base policy, and ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-$n$ policy and the base policy is equal to $\log (n) - (n-1)/n.$ We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes. Finally, we propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.


Title: On instability of Type (II) Lawson-Osserman Cones
Abstract: We obtain the instability of Type (II) Lawson-Osserman cones in Euclidean spaces, and thus provide a family of (uncountably many) unstable solutions with singularity to the Dirichlet problem for minimal graphs of high codimension versus smooth unstable ones by Lawson-Osserman through a min-max technique. To our knowledge, these are the first examples of non-smooth unstable minimal graphs and unlikely detectible through the mean curvature flow or min-max theory.


Title: Synthetic Data in AI: Challenges, Applications, and Ethical Implications
Abstract: In the rapidly evolving field of artificial intelligence, the creation and utilization of synthetic datasets have become increasingly significant. This report delves into the multifaceted aspects of synthetic data, particularly emphasizing the challenges and potential biases these datasets may harbor. It explores the methodologies behind synthetic data generation, spanning traditional statistical models to advanced deep learning techniques, and examines their applications across diverse domains. The report also critically addresses the ethical considerations and legal implications associated with synthetic datasets, highlighting the urgent need for mechanisms to ensure fairness, mitigate biases, and uphold ethical standards in AI development.


Title: Evaluating Trustworthiness of Online News Publishers via Article Classification
Abstract: The proliferation of low-quality online information in today's era has underscored the need for robust and automatic mechanisms to evaluate the trustworthiness of online news publishers. In this paper, we analyse the trustworthiness of online news media outlets by leveraging a dataset of 4033 news stories from 40 different sources. We aim to infer the trustworthiness level of the source based on the classification of individual articles' content. The trust labels are obtained from NewsGuard, a journalistic organization that evaluates news sources using well-established editorial and publishing criteria. The results indicate that the classification model is highly effective in classifying the trustworthiness levels of the news articles. This research has practical applications in alerting readers to potentially untrustworthy news sources, assisting journalistic organizations in evaluating new or unfamiliar media outlets and supporting the selection of articles for their trustworthiness assessment.


Title: REDriver: Runtime Enforcement for Autonomous Vehicles
Abstract: Autonomous driving systems (ADSs) integrate sensing, perception, drive control, and several other critical tasks in autonomous vehicles, motivating research into techniques for assessing their safety. While there are several approaches for testing and analysing them in high-fidelity simulators, ADSs may still encounter additional critical scenarios beyond those covered once they are deployed on real roads. An additional level of confidence can be established by monitoring and enforcing critical properties when the ADS is running. Existing work, however, is only able to monitor simple safety properties (e.g., avoidance of collisions) and is limited to blunt enforcement mechanisms such as hitting the emergency brakes. In this work, we propose REDriver, a general and modular approach to runtime enforcement, in which users can specify a broad range of properties (e.g., national traffic laws) in a specification language based on signal temporal logic (STL). REDriver monitors the planned trajectory of the ADS based on a quantitative semantics of STL, and uses a gradient-driven algorithm to repair the trajectory when a violation of the specification is likely. We implemented REDriver for two versions of Apollo (i.e., a popular ADS), and subjected it to a benchmark of violations of Chinese traffic laws. The results show that REDriver significantly improves Apollo's conformance to the specification with minimal overhead.


Title: Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation
Abstract: We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the universal function approximation capability of ESN, it is shown that the reconstruction problem can be formulated as a fixed-point problem, in which the trajectory of the dynamical system is a fixed point of the ESN. An under-relaxed fixed-point iteration is proposed to reconstruct the nonlinear dynamics from a sparse observation. The proposed fixed-point ESN is tested against both univariate and multivariate chaotic dynamical systems by randomly removing up to 95% of the data. It is shown that the fixed-point ESN is able to reconstruct the complex dynamics from only 5 ~ 10% of the data. For a relatively simple non-chaotic dynamical system, the numerical experiments on a forced van der Pol oscillator show that it is possible to reconstruct the nonlinear dynamics from only 1~2% of the data.


Title: A Novel Dual-Stage Evolutionary Algorithm for Finding Robust Solutions
Abstract: In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient search process would benefit from increased opportunities to explore promising regions where global optima or good local optima are situated. In this paper, we introduce a novel robust evolutionary algorithm named the dual-stage robust evolutionary algorithm (DREA) aimed at discovering robust solutions. DREA operates in two stages: the peak-detection stage and the robust solution-searching stage. The primary objective of the peak-detection stage is to identify peaks in the fitness landscape of the original optimization problem. Conversely, the robust solution-searching stage focuses on swiftly identifying the robust optimal solution using information obtained from the peaks discovered in the initial stage. These two stages collectively enable the proposed DREA to efficiently obtain the robust optimal solution for the optimization problem. This approach achieves a balance between solution optimality and robustness by separating the search processes for optimal and robust optimal solutions. Experimental results demonstrate that DREA significantly outperforms five state-of-the-art algorithms across 18 test problems characterized by diverse complexities. Moreover, when evaluated on higher-dimensional robust optimization problems (100-$D$ and 200-$D$), DREA also demonstrates superior performance compared to all five counterpart algorithms.


Title: Faster optimal univariate microgaggregation
Abstract: Microaggregation is a method to coarsen a dataset, by optimally clustering data points in groups of at least $k$ points, thereby providing a $k$-anonymity type disclosure guarantee for each point in the dataset. Previous algorithms for univariate microaggregation had a $O(k n)$ time complexity. By rephrasing microaggregation as an instance of the concave least weight subsequence problem, in this work we provide improved algorithms that provide an optimal univariate microaggregation on sorted data in $O(n)$ time and space. We further show that our algorithms work not only for sum of squares cost functions, as typically considered, but seamlessly extend to many other cost functions used for univariate microaggregation tasks. In experiments we show that the presented algorithms lead to real world performance improvements.


Title: A Bayesian Model for Discovering Typological Implications
Abstract: A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such implications are typically discovered by painstaking hand analysis over a small sample of languages. We propose a computational model for assisting at this process. Our model is able to discover both well-known implications as well as some novel implications that deserve further study. Moreover, through a careful application of hierarchical analysis, we are able to cope with the well-known sampling problem: languages are not independent.


Title: Evaluating Fairness in Self-supervised and Supervised Models for Sequential Data
Abstract: Self-supervised learning (SSL) has become the de facto training paradigm of large models where pre-training is followed by supervised fine-tuning using domain-specific data and labels. Hypothesizing that SSL models would learn more generic, hence less biased, representations, this study explores the impact of pre-training and fine-tuning strategies on fairness (i.e., performing equally on different demographic breakdowns). Motivated by human-centric applications on real-world timeseries data, we interpret inductive biases on the model, layer, and metric levels by systematically comparing SSL models to their supervised counterparts. Our findings demonstrate that SSL has the capacity to achieve performance on par with supervised methods while significantly enhancing fairness--exhibiting up to a 27% increase in fairness with a mere 1% loss in performance through self-supervision. Ultimately, this work underscores SSL's potential in human-centric computing, particularly high-stakes, data-scarce application domains like healthcare.


Title: Weaving continuous generalized frames for operators
Abstract: Recently, Bemrose et al. \cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the known results in continuous $L$-frames, weaving continuous and weaving continuous $ g$-frames, also we study weaving continuous $ L$-$g$-frames in Hilbert spaces. Moreover, we study the behaviour continuous $ L$-$g$-frames under some perturbations, and we show that approximate $L$-duals are stable under small perturbation and that it is possible to remove some elements of a woven continuous $ L$-$g$-frame and still have a woven continuous $ L$-$g$-frame.


Title: Recursive sequences attached to modular representations of finite groups
Abstract: The core of a finite-dimensional modular representation $M$ of a finite group $G$ is its largest non-projective summand. We prove that the dimensions of the cores of $M^{\otimes n}$ have algebraic Hilbert series when $M$ is Omega-algebraic, in the sense that the non-projective summands of $M^{\otimes n}$ fall into finitely many orbits under the action of the syzygy operator $\Omega$. Similarly, we prove that these dimension sequences are eventually linearly recursive when $M$ is what we term $\Omega^{+}$-algebraic. This partially answers a conjecture by Benson and Symonds. Along the way, we also prove a number of auxiliary permanence results for linear recurrence under operations on multi-variable sequences.


Title: Learning Knowledge Representation with Meta Knowledge Distillation for Single Image Super-Resolution
Abstract: Knowledge distillation (KD), which can efficiently transfer knowledge from a cumbersome network (teacher) to a compact network (student), has demonstrated its advantages in some computer vision applications. The representation of knowledge is vital for knowledge transferring and student learning, which is generally defined in hand-crafted manners or uses the intermediate features directly. In this paper, we propose a model-agnostic meta knowledge distillation method under the teacher-student architecture for the single image super-resolution task. It provides a more flexible and accurate way to help the teachers transmit knowledge in accordance with the abilities of students via knowledge representation networks (KRNets) with learnable parameters. In order to improve the perception ability of knowledge representation to students' requirements, we propose to solve the transformation process from intermediate outputs to transferred knowledge by employing the student features and the correlation between teacher and student in the KRNets. Specifically, the texture-aware dynamic kernels are generated and then extract texture features to be improved and the corresponding teacher guidance so as to decompose the distillation problem into texture-wise supervision for further promoting the recovery quality of high-frequency details. In addition, the KRNets are optimized in a meta-learning manner to ensure the knowledge transferring and the student learning are beneficial to improving the reconstructed quality of the student. Experiments conducted on various single image super-resolution datasets demonstrate that our proposed method outperforms existing defined knowledge representation related distillation methods, and can help super-resolution algorithms achieve better reconstruction quality without introducing any inference complexity.


Title: A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball
Abstract: We show that the half-ball in $\mathbb{R}^4$ can be conformally changed so that the only contribution to the Gauss--Bonnet formula is a constant term at the corner. This may be seen as a fourth-order Cherrier--Escobar-type problem on the half-ball.


Title: Relative Fourier transforms and expectations on coideal subalgebras
Abstract: For an algebraic compact quantum group $H$ we establish a bijection between the set of right coideal $*$-subalgebras $A\to H$ and that of left module quotient $*$-coalgebras $H\to C$. It turns out that the inclusion $A\to H$ always splits as a map of right $A$-modules and right $H$-comodules, and the resulting expectation $E:H\to A$ is positive (and lifts to a positive map on the full $C^*$ completion on $H$) if and only if $A$ is invariant under the squared antipode of $H$. The proof proceeds by Tannaka-reconstructing the coalgebra $C$ corresponding to $A\to H$ by means of a fiber functor from $H$-equivariant $A$-modules to Hilbert spaces, while the characterization of those $A\to H$ which admit positive expectations makes use of a Fourier transform turning elements of $H$ into functions on $C$.


Title: Matching of Users and Creators in Two-Sided Markets with Departures
Abstract: Many online platforms of today, including social media sites, are two-sided markets bridging content creators and users. Most of the existing literature on platform recommendation algorithms largely focuses on user preferences and decisions, and does not simultaneously address creator incentives. We propose a model of content recommendation that explicitly focuses on the dynamics of user-content matching, with the novel property that both users and creators may leave the platform permanently if they do not experience sufficient engagement. In our model, each player decides to participate at each time step based on utilities derived from the current match: users based on alignment of the recommended content with their preferences, and creators based on their audience size. We show that a user-centric greedy algorithm that does not consider creator departures can result in arbitrarily poor total engagement, relative to an algorithm that maximizes total engagement while accounting for two-sided departures. Moreover, in stark contrast to the case where only users or only creators leave the platform, we prove that with two-sided departures, approximating maximum total engagement within any constant factor is NP-hard. We present two practical algorithms, one with performance guarantees under mild assumptions on user preferences, and another that tends to outperform algorithms that ignore two-sided departures in practice.


Title: Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower bounds
Abstract: The Polynomial-Time Hierarchy ($\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers. Quantumly, however, despite the fact that at least \emph{four} definitions of quantum $\mathsf{PH}$ exist, it has been challenging to prove analogues for these of even basic facts from $\mathsf{PH}$. This work studies three quantum-verifier based generalizations of $\mathsf{PH}$, two of which are from [Gharibian, Santha, Sikora, Sundaram, Yirka, 2022] and use classical strings ($\mathsf{QCPH}$) and quantum mixed states ($\mathsf{QPH}$) as proofs, and one of which is new to this work, utilizing quantum pure states ($\mathsf{pureQPH}$) as proofs. We first resolve several open problems from [GSSSY22], including a collapse theorem and a Karp-Lipton theorem for $\mathsf{QCPH}$. Then, for our new class $\mathsf{pureQPH}$, we show one-sided error reduction for $\mathsf{pureQPH}$, as well as the first bounds relating these quantum variants of $\mathsf{PH}$, namely $\mathsf{QCPH}\subseteq \mathsf{pureQPH} \subseteq \mathsf{EXP}^{\mathsf{PP}}$.


Title: Limit Theorems for the Fractional Non-homogeneous Poisson Process
Abstract: The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $\alpha$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional non-homogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.


Title: Universal Homotopy Theories and Associated Homological Algebras
Abstract: Let $\mathscr{C}$ be a small category. For every commutative ring $R$ with unity, we associate an $R\mathrm{-linear}$ abelian category with the universal homotopy category of $\mathscr{C}$, where we can do the corresponding homological algebra.


Title: Roth-type Theorem for high-power system in Piatetski-Shapiro primes (II)
Abstract: We consider the nonlinear system $c_1p_1^d +c_2p_2^d + \dots + c_s p_s^d = 0$ with $c_1, c_2,\dots, c_s\in\mathbb Z$ being nonzero and satisfying $c_1 +c_2 + \dots + c_s = 0$. We show that for $s\ge 2\lfloor \frac{d^2}2\rfloor+1$ and $c\in\left(1, 1+c(d,s)\right)$, if the system has only $K$-trivial solutions in subset $\mathcal{A}$ of Piatetski-Shapiro primes up to $x$ and corresponding to $c$, then $|\mathcal{A}| \ll \frac{x^{\frac1c}}{\log x} $$\left(\log \log \log \log x\right)^{\frac{2-s}{dc}+\varepsilon}$.


Title: Randomly coupled differential equations with elliptic correlations
Abstract: We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our previous work [14] that was restricted to the independent case. In particular, we analyze a recent model in the theory of neural networks [27] that specifically focused on the effect of the distributional asymmetry in the random connectivity matrix $X$. We rigorously prove and slightly correct the explicit formula from [28] on the time decay as a function of the asymmetry parameter. Our main tool is an asymptotically precise formula for the normalized trace of $f(X) g(X^*)$, in the large $N$ limit, where $f$ and $g$ are analytic functions.


Title: R(3,10) <= 41
Abstract: We improve the upper bound on the Ramsey number R(3,10) from 42 to 41. Hence R(3,10) is equal to 40 or 41.


Title: BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories
Abstract: We determine the structure of the BPS algebra of $2$-Calabi-Yau Abelian categories whose stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of the enveloping algebra of a generalised Kac-Moody Lie algebra generated by the intersection cohomology of certain connected components (corresponding to roots) of the good moduli space. Some major examples include the BPS algebras of (1) the category of semistable coherent sheaves of given slope on a K3 surface or, more generally, quasiprojective symplectic surface, (2) semistable Higgs bundles on smooth projective curves, (3) preprojective algebras of quivers, (4) multiplicative preprojective algebras and (5) fundamental groups of (quiver) Riemann surfaces. We define the BPS Lie algebras of $2$-Calabi-Yau categories and prove that they coincide with the ones obtained by dimensional reduction from the critical cohomological Hall algebra in the case in which the 2-Calabi-Yau category is the category of representations of a preprojective algebra. Consequences include (1) A proof in full generality of the Bozec-Schiffmann positivity conjecture for absolutely cuspidal polynomials, a strengthening of the Kac positivity conjecture (2) A proof of the cohomological integrality conjecture for the category of semistable coherent sheaves on local K3 surfaces (3) A description of the cohomology (in all degrees) of Nakajima quiver varieties as direct sums of irreducible lowest weight representations over the BPS Lie algebra.


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


Title: On a conjecture of George Beck
Abstract: In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.


Title: Generative Optimization Networks for Memory Efficient Data Generation
Abstract: In standard generative deep learning models, such as autoencoders or GANs, the size of the parameter set is proportional to the complexity of the generated data distribution. A significant challenge is to deploy resource-hungry deep learning models in devices with limited memory to prevent system upgrade costs. To combat this, we propose a novel framework called generative optimization networks (GON) that is similar to GANs, but does not use a generator, significantly reducing its memory footprint. GONs use a single discriminator network and run optimization in the input space to generate new data samples, achieving an effective compromise between training time and memory consumption. GONs are most suited for data generation problems in limited memory settings. Here we illustrate their use for the problem of anomaly detection in memory-constrained edge devices arising from attacks or intrusion events. Specifically, we use a GON to calculate a reconstruction-based anomaly score for input time-series windows. Experiments on a Raspberry-Pi testbed with two existing and a new suite of datasets show that our framework gives up to 32% higher detection F1 scores and 58% lower memory consumption, with only 5% higher training overheads compared to the state-of-the-art.


Title: On infinitesimal generators of sublinear Markov semigroups
Abstract: We establish a Dynkin formula and a Courr\`ege-von Waldenfels theorem for sublinear Markov semigroups. In particular, we show that any sublinear operator $A$ on $C_c^{\infty}(\mathbb{R}^d)$ satisfying the positive maximum principle can be represented as supremum of a family of pseudo-differential operators: $$Af(x) = \sup_{\alpha \in I} (-q_{\alpha}(x,D) f)(x).$$ As an immediate consequence, we obtain a representation formula for infinitesimal generators of sublinear Markov semigroups with a sufficiently rich domain. We give applications in the theory of non-linear Hamilton--Jacobi--Bellman equations and L\'evy processes for sublinear expectations.


Title: Morphisms of rational motivic homotopy types
Abstract: We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphisms of motivic dga's can reasonably be thought of as a nonabelian analog of motivic cohomology. Just as abelian motivic cohomology is a homotopy group of a spectrum coming from K-theory, the space of morphisms of motivic dga's is a certain limit of such spectra; we give an explicit formula for this limit --- a possible first step towards explicit computations or dimension bounds. We also consider commutative comonoids in Chow motives, which we call ``motivic Chow coalgebras''. We discuss the relationship between motivic Chow coalgebras and motivic dga's of smooth proper schemes. As a small first application of our results, we show that among schemes which are finite \'etale over a number field, morphisms of associated motivic dga's are no different than morphisms of schemes. This may be regarded as a small consequence of a plausible generalization of Kim's relative unipotent section conjecture, hence as an ounce of evidence for the latter.


Title: Principled network extraction from images
Abstract: Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal definition of a network in terms of sets of nodes and edges. Instead, this information should be suitably extracted from the raw image data. Motivated by this, we present a principled model to extract network topologies from images that is scalable and efficient. We map this goal into solving a routing optimization problem where the solution is a network that minimizes an energy function which can be interpreted in terms of an operational and infrastructural cost. Our method relies on recent results from optimal transport theory and is a principled alternative to standard image-processing techniques that are based on heuristics. We test our model on real images of the retinal vascular system, slime mold and river networks and compare with routines combining image-processing techniques. Results are tested in terms of a similarity measure related to the amount of information preserved in the extraction. We find that our model finds networks from retina vascular network images that are more similar to hand-labeled ones, while also giving high performance in extracting networks from images of rivers and slime mold for which there is no ground truth available. While there is no unique method that fits all the images the best, our approach performs consistently across datasets, its algorithmic implementation is efficient and can be fully automatized to be run on several datasets with little supervision.


Title: The Balkans Continued Fraction
Abstract: In a previous escapade we gave a collection of continued fractions involving Catalan's constant. This paper provides more general formulae governing those continued fractions. Having distinguished different cases associated to regions in the plan, we nickname those continued fractions \enquote{The Balkans} as they divide into areas which are related but still different in nature. Because we do not provide formal proofs of those machine-constructed formulae we do not claim them to be theorems. Still, each and every proposed formula was extensively tested numerically.


Title: Entropy-based Discovery of Summary Causal Graphs in Time Series
Abstract: This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this measure relates to an entropy reduction principle that can be seen as a special case of the probability raising principle. We finally combine these two ingredients in PC-like and FCI-like algorithms to construct the summary causal graph. There algorithm are evaluated on several datasets, which shows both their efficacy and efficiency.


Title: Non-Atomic Arbitrage in Decentralized Finance
Abstract: The prevalence of maximal extractable value (MEV) in the Ethereum ecosystem has led to a characterization of the latter as a dark forest. Studies of MEV have thus far largely been restricted to purely on-chain MEV, i.e., sandwich attacks, cyclic arbitrage, and liquidations. In this work, we shed light on the prevalence of non-atomic arbitrage on decentralized exchanges (DEXes) on the Ethereum blockchain. Importantly, non-atomic arbitrage exploits price differences between DEXes on the Ethereum blockchain as well as exchanges outside the Ethereum blockchain (i.e., centralized exchanges or DEXes on other blockchains). Thus, non-atomic arbitrage is a type of MEV that involves actions on and off the Ethereum blockchain. In our study of non-atomic arbitrage, we uncover that more than a fourth of the volume on Ethereum's biggest five DEXes from the merge until 31 October 2023 can likely be attributed to this type of MEV. We further highlight that only eleven searchers are responsible for more than 80% of the identified non-atomic arbitrage volume sitting at a staggering 137 billion US$ and draw a connection between the centralization of the block construction market and non-atomic arbitrage. Finally, we discuss the security implications of these high-value transactions that account for more than 10% of Ethereum's total block value and outline possible mitigations.


Title: Semi-supervised Contrastive Outlier removal for Pseudo Expectation Maximization (SCOPE)
Abstract: Semi-supervised learning is the problem of training an accurate predictive model by combining a small labeled dataset with a presumably much larger unlabeled dataset. Many methods for semi-supervised deep learning have been developed, including pseudolabeling, consistency regularization, and contrastive learning techniques. Pseudolabeling methods however are highly susceptible to confounding, in which erroneous pseudolabels are assumed to be true labels in early iterations, thereby causing the model to reinforce its prior biases and thereby fail to generalize to strong predictive performance. We present a new approach to suppress confounding errors through a method we describe as Semi-supervised Contrastive Outlier removal for Pseudo Expectation Maximization (SCOPE). Like basic pseudolabeling, SCOPE is related to Expectation Maximization (EM), a latent variable framework which can be extended toward understanding cluster-assumption deep semi-supervised algorithms. However, unlike basic pseudolabeling which fails to adequately take into account the probability of the unlabeled samples given the model, SCOPE introduces an outlier suppression term designed to improve the behavior of EM iteration given a discrimination DNN backbone in the presence of outliers. Our results show that SCOPE greatly improves semi-supervised classification accuracy over a baseline, and furthermore when combined with consistency regularization achieves the highest reported accuracy for the semi-supervised CIFAR-10 classification task using 250 and 4000 labeled samples. Moreover, we show that SCOPE reduces the prevalence of confounding errors during pseudolabeling iterations by pruning erroneous high-confidence pseudolabeled samples that would otherwise contaminate the labeled set in subsequent retraining iterations.


Title: Brain-Conditional Multimodal Synthesis: A Survey and Taxonomy
Abstract: In the era of Artificial Intelligence Generated Content (AIGC), conditional multimodal synthesis technologies (e.g., text-to-image, text-to-video, text-to-audio, etc) are gradually reshaping the natural content in the real world. The key to multimodal synthesis technology is to establish the mapping relationship between different modalities. Brain signals, serving as potential reflections of how the brain interprets external information, exhibit a distinctive One-to-Many correspondence with various external modalities. This correspondence makes brain signals emerge as a promising guiding condition for multimodal content synthesis. Brian-conditional multimodal synthesis refers to decoding brain signals back to perceptual experience, which is crucial for developing practical brain-computer interface systems and unraveling complex mechanisms underlying how the brain perceives and comprehends external stimuli. This survey comprehensively examines the emerging field of AIGC-based Brain-conditional Multimodal Synthesis, termed AIGC-Brain, to delineate the current landscape and future directions. To begin, related brain neuroimaging datasets, functional brain regions, and mainstream generative models are introduced as the foundation of AIGC-Brain decoding and analysis. Next, we provide a comprehensive taxonomy for AIGC-Brain decoding models and present task-specific representative work and detailed implementation strategies to facilitate comparison and in-depth analysis. Quality assessments are then introduced for both qualitative and quantitative evaluation. Finally, this survey explores insights gained, providing current challenges and outlining prospects of AIGC-Brain. Being the inaugural survey in this domain, this paper paves the way for the progress of AIGC-Brain research, offering a foundational overview to guide future work.


Title: 3D Open-Vocabulary Panoptic Segmentation with 2D-3D Vision-Language Distillation
Abstract: 3D panoptic segmentation is a challenging perception task, which aims to predict both semantic and instance annotations for 3D points in a scene. Although prior 3D panoptic segmentation approaches have achieved great performance on closed-set benchmarks, generalizing to novel categories remains an open problem. For unseen object categories, 2D open-vocabulary segmentation has achieved promising results that solely rely on frozen CLIP backbones and ensembling multiple classification outputs. However, we find that simply extending these 2D models to 3D does not achieve good performance due to poor per-mask classification quality on novel categories. In this paper, we propose the first method to tackle 3D open-vocabulary panoptic segmentation. Our model takes advantage of the fusion between learnable LiDAR features and dense frozen vision CLIP features, using a single classification head to make predictions for both base and novel classes. To further improve the classification performance on novel classes and leverage the CLIP model, we propose two novel loss functions: object-level distillation loss and voxel-level distillation loss. Our experiments on the nuScenes and SemanticKITTI datasets show that our method outperforms strong baselines by a large margin.


Title: Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem
Abstract: In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator.


Title: Effective descent morphisms of filtered preorders
Abstract: We characterize effective descent morphisms of what we call filtered preorders, and apply these results to slightly improve a known result, due to the first author and F. Lucatelli Nunes, on the effective descent morphisms in lax comma categories of preorders. A filtered preorder, over a fixed preorder $X$, is defined as a preorder $A$ equipped with a profunctor $X\to A$ and, equivalently, as a set $A$ equipped with a family $(A_x)_{x\in X}$ of upclosed subsets of $A$ with $x'\leqslant x\Rightarrow A_x\subseteq A_{x'}$.


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


Title: Watkins' conjecture for elliptic curves over function fields
Abstract: In 2002 Watkins conjectured that given an elliptic curve defined over $\mathbb{Q}$, its Mordell-Weil rank is at most the $2$-adic valuation of its modular degree. We consider the analogous problem over function fields of positive characteristic, and we prove it in several cases. More precisely, every modular semi-stable elliptic curve over $\mathbb{F}_q(T)$ after extending constant scalars, and every quadratic twist of a modular elliptic curve over $\mathbb{F}_q(T)$ by a polynomial with sufficiently many prime factors satisfy the analogue of Watkins' conjecture. Furthermore, for a well-known family of elliptic curves with unbounded rank due to Ulmer, we prove the analogue of Watkins' conjecture.


Title: Search Games with Predictions
Abstract: We study search games between a mobile Searcher and an immobile Hider in which the Searcher aims to minimize some payoff, which is either the time to find the Hider (the search time), or a normalized search time. We consider a new setting in which the Searcher has some potentially erroneous information, or prediction on the Hider's position. Specifically, we study tradeoffs between the consistency of a search strategy (i.e., its worst case expected payoff assuming the prediction is correct) and the robustness (i.e., the worst case expected payoff assuming that the prediction is adversarially generated). We show how to apply this framework in search games over both discrete and continuous, as well as bounded and unbounded spaces. Specifically, we prove optimal consistency/robustness tradeoffs for three fundamental search games, namely searching in a number of discrete locations, expanding search in a tree network, and searching in the infinite line. Our study is the first to address the full power of mixed (randomized) strategies; previous work focused only on deterministic strategies, or relied on stochastic assumptions that do not guarantee worst-case robustness in adversarial situations.


Title: A fractional conformal curvature flow on the unit sphere
Abstract: We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $\sigma \in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere.


Title: Positroids, knots, and $q,t$-Catalan numbers
Abstract: We relate the mixed Hodge structure on the cohomology of open positroid varieties (in particular, their Betti numbers over $\mathbb{C}$ and point counts over $\mathbb{F}_q$) to Khovanov--Rozansky homology of associated links. We deduce that the mixed Hodge polynomials of top-dimensional open positroid varieties are given by rational $q,t$-Catalan numbers. Via the curious Lefschetz property of cluster varieties, this implies the $q,t$-symmetry and unimodality properties of rational $q,t$-Catalan numbers. We show that the $q,t$-symmetry phenomenon is a manifestation of Koszul duality for category $\mathcal{O}$, and discuss relations with open Richardson varieties and extension groups of Verma modules.


Title: Periodic solutions of one-dimensional cellular automata with random rules
Abstract: We study cellular automata with randomly selected rules. Our setting are two-neighbor rules with a large number $n$ of states. The main quantity we analyze is the asymptotic probability, as $n \to \infty$, that the random rule has a periodic solution with given spatial and temporal periods. We prove that this limiting probability is non-trivial when the spatial and temporal periods are confined to a finite range. The main tool we use is the Chen-Stein method for Poisson approximation. The limiting probability distribution of the smallest temporal period for a given spatial period is deduced as a corollary and relevant empirical simulations are presented.


Title: Federated Class-Incremental Learning with Prototype Guided Transformer
Abstract: Existing federated learning methods have effectively addressed decentralized learning in scenarios involving data privacy and non-IID data. However, in real-world situations, each client dynamically learns new classes, requiring the global model to maintain discriminative capabilities for both new and old classes. To effectively mitigate the effects of catastrophic forgetting and data heterogeneity under low communication costs, we designed a simple and effective method named PLoRA. On the one hand, we adopt prototype learning to learn better feature representations and leverage the heuristic information between prototypes and class features to design a prototype re-weight module to solve the classifier bias caused by data heterogeneity without retraining the classification layer. On the other hand, our approach utilizes a pre-trained model as the backbone and utilizes LoRA to fine-tune with a tiny amount of parameters when learning new classes. Moreover, PLoRA does not rely on similarity-based module selection strategies, thereby further reducing communication overhead. Experimental results on standard datasets indicate that our method outperforms the state-of-the-art approaches significantly. More importantly, our method exhibits strong robustness and superiority in various scenarios and degrees of data heterogeneity. Our code will be publicly available.


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


Title: AERIAL-CORE: AI-Powered Aerial Robots for Inspection and Maintenance of Electrical Power Infrastructures
Abstract: Large-scale infrastructures are prone to deterioration due to age, environmental influences, and heavy usage. Ensuring their safety through regular inspections and maintenance is crucial to prevent incidents that can significantly affect public safety and the environment. This is especially pertinent in the context of electrical power networks, which, while essential for energy provision, can also be sources of forest fires. Intelligent drones have the potential to revolutionize inspection and maintenance, eliminating the risks for human operators, increasing productivity, reducing inspection time, and improving data collection quality. However, most of the current methods and technologies in aerial robotics have been trialed primarily in indoor testbeds or outdoor settings under strictly controlled conditions, always within the line of sight of human operators. Additionally, these methods and technologies have typically been evaluated in isolation, lacking comprehensive integration. This paper introduces the first autonomous system that combines various innovative aerial robots. This system is designed for extended-range inspections beyond the visual line of sight, features aerial manipulators for maintenance tasks, and includes support mechanisms for human operators working at elevated heights. The paper further discusses the successful validation of this system on numerous electrical power lines, with aerial robots executing flights over 10 kilometers away from their ground control stations.


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.


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


Title: Location Aware Modular Biencoder for Tourism Question Answering
Abstract: Answering real-world tourism questions that seek Point-of-Interest (POI) recommendations is challenging, as it requires both spatial and non-spatial reasoning, over a large candidate pool. The traditional method of encoding each pair of question and POI becomes inefficient when the number of candidates increases, making it infeasible for real-world applications. To overcome this, we propose treating the QA task as a dense vector retrieval problem, where we encode questions and POIs separately and retrieve the most relevant POIs for a question by utilizing embedding space similarity. We use pretrained language models (PLMs) to encode textual information, and train a location encoder to capture spatial information of POIs. Experiments on a real-world tourism QA dataset demonstrate that our approach is effective, efficient, and outperforms previous methods across all metrics. Enabled by the dense retrieval architecture, we further build a global evaluation baseline, expanding the search space by 20 times compared to previous work. We also explore several factors that impact on the model's performance through follow-up experiments. Our code and model are publicly available at https://github.com/haonan-li/LAMB.


Title: A network-level transport model of tau progression in the Alzheimer's brain
Abstract: One of the hallmarks of Alzheimer's disease (AD) is the accumulation and spread of toxic aggregates of tau protein. The progression of AD tau pathology is thought to be highly stereotyped, which is in part due to the fact that tau can spread between regions via the white matter tracts that connect them. Mathematically, this phenomenon has been described using models of "network diffusion", where the rate of spread of tau between brain regions is proportional to its concentration gradient and the amount of white matter between them. Although these models can robustly predict the progression of pathology in a wide variety of neurodegenerative diseases, including AD, an under explored aspect of tau spreading is that it is governed not simply by diffusion but also active transport along axonal microtubules. Spread can therefore take on a directional bias, resulting in distinct patterns of deposition, but current models struggle to capture this phenomenon. Recently, we have developed a mathematical model of the axonal transport of toxic tau proteins that takes into account the effects tau exerts on the molecular motors. Here we describe and implement a macroscopic version of this model, which we call the Network Transport Model (NTM). A key feature of this model is that, while it predicts tau dynamics at a regional level, it is parameterized in terms of only microscopic processes such as aggregation and transport rates; that is, differences in brain-wide tau progression can be explained by its microscopic properties. We provide numerical evidence that, as with the two-neuron model that the NTM extends, there are distinct and rich dynamics with respect to the overall rate of spread and the staging of pathology when we simulated the NTM on the hippocampal subnetwork. The theoretical insights provided by the NTM have broad implications for understanding AD pathophysiology more generally.


Title: Stochastic Broadcast Control of Multi-Agent Swarms
Abstract: We present a model for controlling swarms of mobile agents via broadcast control, assumed to be detected by a random set of agents in the swarm. The agents that detect the control signal become ad-hoc leaders of the swarm. The agents are assumed to be velocity controlled, identical, anonymous, memory-less units with limited capabilities of sensing their neighborhood. Each agent is programmed to behave according to a linear local gathering process, based on the relative position of all its neighbors. The detected exogenous control, which is a desired velocity vector, is added by the leaders to the local gathering control. The graph induced by the agents adjacency is referred to as the visibility graph. We show that for piece-wise constant system parameters and a connected visibility graph, the swarm asymptotically aligns in each time-interval on a line in the direction of the exogenous control signal, and all the agents move with identical speed. These results hold for two models of pairwise influence in the gathering process, uniform and scaled. The impact of the influence model is mostly evident when the visibility graph is incomplete. These results are conditioned by the preservation of the connectedness of the visibility graph. In the second part of the report we analyze sufficient conditions for preserving the connectedness of the visibility graph. We show that if the visibility graph is complete then certain bounds on the control signal suffice to preserve the completeness of the graph. However, when the graph is incomplete, general conditions, independent of the leaders topology, could not be found.


Title: Towards High Fidelity Face Relighting with Realistic Shadows
Abstract: Existing face relighting methods often struggle with two problems: maintaining the local facial details of the subject and accurately removing and synthesizing shadows in the relit image, especially hard shadows. We propose a novel deep face relighting method that addresses both problems. Our method learns to predict the ratio (quotient) image between a source image and the target image with the desired lighting, allowing us to relight the image while maintaining the local facial details. During training, our model also learns to accurately modify shadows by using estimated shadow masks to emphasize on the high-contrast shadow borders. Furthermore, we introduce a method to use the shadow mask to estimate the ambient light intensity in an image, and are thus able to leverage multiple datasets during training with different global lighting intensities. With quantitative and qualitative evaluations on the Multi-PIE and FFHQ datasets, we demonstrate that our proposed method faithfully maintains the local facial details of the subject and can accurately handle hard shadows while achieving state-of-the-art face relighting performance.


Title: Toward 6G: From New Hardware Design to Wireless Semantic and Goal-Oriented Communication Paradigms
Abstract: Several speculative visions are conjecturing on what 6G services will be able to offer at the horizon of 2030. Nevertheless, the 6G design process is at its preliminary stages. The reality today is that hardware, technologies and new materials required to effectively meet the unprecedented performance targets required for future 6G services and network operation, have not been designed, tested or even do not exist yet. Today, a solid vision on the cost-benefit trade-offs of machine learning and artificial intelligence support for 6G network and services operation optimization is missing. This includes the possible support from hardware efficiency, operation effectiveness and, the immeasurable cost due to data acquisition-transfer-processing. The contribution of this paper is three-fold. This is the first paper deriving crucial 6G key performance indicators on hardware and technology design. Second, we present a new hardware technologies design methodology conceived to enable the effective software-hardware components integration required to meet the challenging performance envisioned for future 6G networks. Third, we suggest a paradigm shift towards goal-oriented and semantic communications, in which a totally new opportunity of joint design of hardware, artificial intelligence and effective communication is offered. The proposed vision is consolidated by our recent results on hardware, technology and machine learning performance.


Title: Consistent estimation of non-bandlimited spectral density from uniformly spaced samples
Abstract: In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular (uniform) sampling. A major reason for this preference is the well-known problem of inconsistency of estimators based on regular sampling, when the underlying power spectral density is not bandlimited. It is argued in this paper that, in consideration of a large sample property like consistency, it is natural to allow the sampling rate to go to infinity as the sample size goes to infinity. Through appropriate asymptotic calculations under this scenario, it is shown that the smoothed periodogram based on regularly spaced data is a consistent estimator of the spectral density, even when the latter is not band-limited. It transpires that, under similar assumptions, the estimators based on uniformly sampled and Poisson-sampled data have about the same rate of convergence. Apart from providing this reassuring message, the paper also gives a guideline for practitioners regarding appropriate choice of the sampling rate. Theoretical calculations for large samples and Monte-Carlo simulations for small samples indicate that the smoothed periodogram based on uniformly sampled data have less variance and more bias than its counterpart based on Poisson sampled data.


Title: Complete Geodesic Metrics in Big Classes
Abstract: Let $(X,\omega)$ be a compact K\"ahler manifold and $\theta$ be a smooth closed real $(1,1)$-form that represents a big cohomology class. In this paper, we show that for $p\geq 1$, the high energy space $\mathcal{E}^{p}(X,\theta)$ can be endowed with a metric $d_{p}$ that makes $(\mathcal{E}^{p}(X,\theta),d_{p})$ a complete geodesic metric space. The weak geodesics in $\mathcal{E}^{p}(X,\theta)$ are the metric geodesic for $(\mathcal{E}^{p}(X,\theta), d_{p})$. Moreover, for $p > 1$, the geodesic metric space $(\mathcal{E}^{p}(X,\theta), d_{p})$ is uniformly convex.


Title: Algebraic trace functions over the primes
Abstract: We study sums over primes of trace functions of $\ell$-adic sheaves. Using an extension of our earlier results on algebraic twist of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of the Riemann Hypothesis over finite fields, we prove general estimates with power-saving for such sums. We then derive various concrete applications.


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


Title: Section Rings of $\mathbb{Q}$-Divisors on Genus-$1$ Curves
Abstract: We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique is a generalization of \cite{O'Dorney} and \cite{VZB} that accounts for the additional subtlety that genus one curves pose: their group structure. We give explicit minimal presentations for section rings of divisors supported at one point and for section rings of effective divisors supported at two points. Our results for one-point divisors are quite similar to the corresponding case in genus zero from \cite{O'Dorney}, and are a combination of the one-point cases in genera one and zero for two-point effective divisors.


Title: Using Schur Rings to Produce GRRs for Dihedral Groups
Abstract: In this paper we shall be looking at several results relating Schur rings to sufficient conditions for a graph to be a graphical regular representation (GRR) of a finite group, and then applying these specifically in the case of certain subfamilies of dihedral groups. Numerical methods are given for constructing trivalent GRRs for these dihedral groups very quickly.


Title: Fiber criteria for flatness and homomorphisms of flat affine group schemes
Abstract: A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finiteness'' assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.


Title: Periodicity of Adams operations on the Green ring of a finite group
Abstract: The Adams operations $\psi_\Lambda^n$ and $\psi_S^n$ on the Green ring of a group $G$ over a field $K$ provide a framework for the study of the exterior powers and symmetric powers of $KG$-modules. When $G$ is finite and $K$ has prime characteristic $p$ we show that $\psi_\Lambda^n$ and $\psi_S^n$ are periodic in $n$ if and only if the Sylow $p$-subgroups of $G$ are cyclic. In the case where $G$ is a cyclic $p$-group we find the minimum periods and use recent work of Symonds to express $\psi_S^n$ in terms of $\psi_\Lambda^n$.


Title: On the existence of analytic families of stable lattices in trianguline representations and their reductions
Abstract: In this article, we prove the existence of rigid analytic families of $G$-stable lattices with locally constant reductions inside families of representations of a topologically compact group $G$, extending a result of Hellman obtained in the semi-simple residual case. Implementing this generalization in the context of Galois representations, we prove a local constancy result for reductions modulo prime powers of trianguline representations of generic dimension $d$. Moreover, we present two explicit applications. First, in dimension two, we extend to a prime power setting and to the whole rigid projective line a recent result of Bergdall, Levin and Liu concerning reductions of semi-stable representations of $\text{Gal}(\overline{\mathbb{Q}}_p / \mathbb{Q}_p)$ with fixed Hodge-Tate weights and large $\mathcal{L}$-invariant. Second, in dimension $d$, let $V_n$ be a sequence of crystalline representations converging in a certain geometric sense to a crystalline representation $V$. We show that for any refined version $(V, \sigma)$ of $V$ (or equivalently for any chosen triangulation of its attached $(\varphi, \Gamma)$-module $D_{\text{rig}} (V)$ over the Robba ring), there exists a sequence of refinement $\sigma_n$ of each of the $V_n$ such that the limit as refined representations $(V_n , \sigma_n )$ converges to the $(V, \sigma)$. This result does not hold under the weaker assumption that $V_n$ converges only uniformly $p$-adically to $V$ (in the sense of Chenevier, Khare and Larsen).


Title: Persistent components in Canny's resultant
Abstract: When using resultants for elimination, one standard issue is that the resultant vanishes if the variety contains components of dimension larger than the expected dimension. J. Canny proposed an elegant construction, generalized characteristic polynomial, to address this issue by symbolically perturbing the system before the resultant computation. Such perturbed resultant would typically involve artefact components only loosely related to the geometry of the variety of interest. For removing these components, J.M. Rojas proposed to take the greatest common divisor of the results of two different perturbations. In this paper, we investigate this construction, and show that the extra components persistent under taking different perturbations must come either from singularities or from positive-dimensional fibers.


Title: Discriminants of stable rank two sheaves on some general type surfaces
Abstract: We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We then proceed to describe the surface itself as a moduli space of rank two vector bundles on it. Lastly, we give a proof of the Bogomolov inequality for semistable rank two sheaves on integral surfaces in three-dimensional projective space in all characteristics.


Title: Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought
Abstract: Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.


Title: Globalizing and stabilizing global $\infty$-categories
Abstract: We consider the question of cocompleting partially presentable parametrized $\infty$-categories in the sense of arXiv:2307.11001. As our main result we show that in certain cases one may compute such relative cocompletions via a very explicit formula given in terms of partially lax limits. We then apply this to equivariant homotopy theory, building on the work of op. cit. and arXiv:2301.08240, to conclude that the global $\infty$-category of globally equivariant spectra is the relative cocompletion of the global $\infty$-category of equivariant spectra. Evaluating at a group $G$ we obtain a description of the $\infty$-category of $G$-global spectra as a partially lax limit, extending the main result of arXiv:2206.01556 for finite groups to $G$-global homotopy theory. Finally we investigate the question of stabilizing global $\infty$-categories by inverting the action of representation spheres, and deduce a second universal property for the global $\infty$-category of globally equivariant spectra, similar to that of arXiv:2302.06207.


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


Title: On the number of hyperbolic Dehn fillings of a given volume
Abstract: Let M be a 1-cusped hyperbolic 3-manifold whose cusp shape is quadratic. We show that there exists c=c(M) such that the number of hyperbolic Dehn fillings of M with any given volume v is uniformly bounded by c.


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.


Title: Computing higher symplectic capacities I
Abstract: We present recursive formulas which compute the recently defined "higher symplectic capacities" for all convex toric domains. In the special case of four-dimensional ellipsoids, we apply homological perturbation theory to the associated filtered L-infinity algebras and prove that the resulting structure coefficients count punctured pseudoholomorphic curves in cobordisms between ellipsoids. As sample applications, we produce new previously inaccessible obstructions for stabilized embeddings of ellipsoids and polydisks, and we give new counts of curves with tangency constraints.


Title: On Augmenting Scenario-Based Modeling with Generative AI
Abstract: The manual modeling of complex systems is a daunting task; and although a plethora of methods exist that mitigate this issue, the problem remains very difficult. Recent advances in generative AI have allowed the creation of general-purpose chatbots, capable of assisting software engineers in various modeling tasks. However, these chatbots are often inaccurate, and an unstructured use thereof could result in erroneous system models. In this paper, we outline a method for the safer and more structured use of chatbots as part of the modeling process. To streamline this integration, we propose leveraging scenario-based modeling techniques, which are known to facilitate the automated analysis of models. We argue that through iterative invocations of the chatbot and the manual and automatic inspection of the resulting models, a more accurate system model can eventually be obtained. We describe favorable preliminary results, which highlight the potential of this approach.


Title: Toroidal orbifolds, destackification, and Kummer blowings up
Abstract: We show that any toroidal DM stack $X$ with finite diagonalizable inertia possesses a maximal toroidal coarsening $X_{tcs}$ such that the morphism $X\to X_{tcs}$ is logarithmically smooth. Further, we use torification results of [AT17] to construct a destackification functor, a variant of the main result of Bergh [Ber17], on the category of such toroidal stacks $X$. Namely, we associate to $X$ a sequence of blowings up of toroidal stacks $\widetilde{\mathcal{F}}_X\:Y\longrightarrow X$ such that $Y_{tc}$ coincides with the usual coarse moduli space $Y_{cs}$. In particular, this provides a toroidal resolution of the algebraic space $X_{cs}$. Both $X_{tcs}$ and $\widetilde{\mathcal{F}}_X$ are functorial with respect to strict inertia preserving morphisms $X'\to X$. Finally, we use coarsening morphisms to introduce a class of non-representable birational modifications of toroidal stacks called Kummer blowings up. These modifications, as well as our version of destackification, are used in our work on functorial toroidal resolution of singularities.


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.


Title: Adams spectral sequences and Franke's algebraicity conjecture
Abstract: To any well-behaved homology theory we associate a derived $\infty$-category which encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on algebraicity of certain homotopy categories and establish homotopy-coherent monoidality of the Adams filtration.


Title: On the center of near-group fusion category of type $\mathbb{Z}_3+6$
Abstract: Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence $\mathcal{Z}(\mathcal{A})\cong\mathcal{C}(\mathbb{Z}_3,\eta)\boxtimes\mathcal{C}(\mathfrak{sl}_3,9)_{\mathbb{Z}_3}^0$. Moreover, we construct two non-trivial faithful extensions of $\mathcal{A}$ explicitly, whose Drinfeld centers can also be obtained from representation categories quantum groups at root of unity.


Title: On the error term in a mixed moment of L-functions
Abstract: There has recently been some interest in optimizing the error term in the asymptotic for the fourth moment of Dirichlet L-functions and a closely related mixed moment of L-functions involving automorphic L-functions twisted by Dirichlet characters. We obtain an improvement for the error term of the latter.


Title: FairGridSearch: A Framework to Compare Fairness-Enhancing Models
Abstract: Machine learning models are increasingly used in critical decision-making applications. However, these models are susceptible to replicating or even amplifying bias present in real-world data. While there are various bias mitigation methods and base estimators in the literature, selecting the optimal model for a specific application remains challenging. This paper focuses on binary classification and proposes FairGridSearch, a novel framework for comparing fairness-enhancing models. FairGridSearch enables experimentation with different model parameter combinations and recommends the best one. The study applies FairGridSearch to three popular datasets (Adult, COMPAS, and German Credit) and analyzes the impacts of metric selection, base estimator choice, and classification threshold on model fairness. The results highlight the significance of selecting appropriate accuracy and fairness metrics for model evaluation. Additionally, different base estimators and classification threshold values affect the effectiveness of bias mitigation methods and fairness stability respectively, but the effects are not consistent across all datasets. Based on these findings, future research on fairness in machine learning should consider a broader range of factors when building fair models, going beyond bias mitigation methods alone.


Title: An algorithm for estimating the crossing number of dense graphs, and continuous analogs of the crossing and rectilinear crossing numbers
Abstract: We present a deterministic $n^{2+o(1)}$-time algorithm that approximates the crossing number of any graph $G$ of order $n$ up to an additive error of $o(n^4)$. We also provide a randomized polynomial-time algorithm that constructs a drawing of $G$ with $\text{cr}(G)+o(n^4)$ crossings. These results are made interesting by the well known fact that every dense $n$-vertex graph has crossing number $\Theta(n^4)$. Our work builds on a technique developed by Fox, Pach and S\'uk, who obtained very similar results for the rectilinear crossing number. The results by the aforementioned authors and in this paper imply that the (normalized) crossing and rectilinear crossing numbers are estimable parameters. Motivated by this, we introduce two graphon parameters, the \textit{crossing density} and the \textit{rectilinear crossing density}, and then we prove that, in a precise sense, these are the correct continuous analogs of the crossing and rectilinear crossing numbers of graphs.


Title: Core equality of real sequences
Abstract: Given an ideal $\mathcal{I}$ on $\omega$ and a bounded real sequence $\textbf{x}$, we denote by $\text{core}_{\textbf{x}}(\mathcal{I})$ the smallest interval $[a,b]$ such that $\{n \in \omega: x_n \notin [a-\varepsilon,b+\varepsilon]\} \in \mathcal{I}$ for all $\varepsilon>0$ (which corresponds to the interval $[\,\liminf \textbf{x}, \limsup \textbf{x}\,]$ if $\mathcal{I}$ is the ideal $\text{Fin}$ of finite subsets of $\omega$). First, we characterize all the infinite real matrices $A$ such that $$ \text{core}_{A\textbf{x}}(\mathcal{J})=\text{core}_{\textbf{x}}(\mathcal{I}) $$ for all bounded sequences $\textbf{x}$, provided that $\mathcal{J}$ is a countably generated ideal on $\omega$ and $A$ maps bounded sequences into bounded sequences. Such characterization fails if both $\mathcal{I}$ and $\mathcal{J}$ are the ideal of asymptotic density zero sets. Next, we show that such equality is possible for distinct ideals $\mathcal{I}, \mathcal{J}$, answering an open question in [J.~Math.~Anal.~Appl.~\textbf{321} (2006), 515--523]. Lastly, we prove that, if $\mathcal{J}=\text{Fin}$, the above equality holds for some matrix $A$ if and only if $\mathcal{I}=\text{Fin}$ or $\mathcal{I}=\text{Fin}\oplus \mathcal{P}(\omega)$.


Title: Post-Processed Posteriors for Banded Covariances
Abstract: We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior which does not satisfy any structural restrictions. In the second step, the posterior samples are transformed to satisfy the structural restriction through a post-processing function. The conceptually straightforward procedure of the post-processed posterior makes its computation efficient and can render interval estimators of functionals of covariance matrices. We show that it has nearly optimal minimax rates for banded covariances among all possible pairs of priors and post-processing functions. Furthermore, we prove that the expected coverage probability of the $(1-\alpha)100\%$ highest posterior density region of the post-processed posterior is asymptotically $1-\alpha$ with respect to a conventional posterior distribution. It implies that the highest posterior density region of the post-processed posterior is, on average, a credible set of a conventional posterior. The advantages of the post-processed posterior are demonstrated by a simulation study and a real data analysis.


Title: On the local density problem for graphs of given odd-girth
Abstract: Erd\H{o}s conjectured that every $n$-vertex triangle-free graph contains a subset of $\lfloor n/2\rfloor$ vertices that spans at most $n^2/50$ edges. Extending a recent result of Norin and Yepremyan, we confirm this conjecture for graphs homomorphic to so-called Andr\'asfai graphs. As a consequence, Erd\H{o}s' conjecture holds for every triangle-free graph $G$ with minimum degree $\delta (G)>10n/29$ and if $\chi (G)\leq 3$ the degree condition can be relaxed to $\delta (G)> n/3$. In fact, we obtain a more general result for graphs of higher odd-girth.


Title: Are LLMs Robust for Spoken Dialogues?
Abstract: Large Pre-Trained Language Models have demonstrated state-of-the-art performance in different downstream tasks, including dialogue state tracking and end-to-end response generation. Nevertheless, most of the publicly available datasets and benchmarks on task-oriented dialogues focus on written conversations. Consequently, the robustness of the developed models to spoken interactions is unknown. In this work, we have evaluated the performance of LLMs for spoken task-oriented dialogues on the DSTC11 test sets. Due to the lack of proper spoken dialogue datasets, we have automatically transcribed a development set of spoken dialogues with a state-of-the-art ASR engine. We have characterized the ASR-error types and their distributions and simulated these errors in a large dataset of dialogues. We report the intrinsic (perplexity) and extrinsic (human evaluation) performance of fine-tuned GPT-2 and T5 models in two subtasks of response generation and dialogue state tracking, respectively. The results show that LLMs are not robust to spoken noise by default, however, fine-tuning/training such models on a proper dataset of spoken TODs can result in a more robust performance.


Title: Evasive Hardware Trojan through Adversarial Power Trace
Abstract: The globalization of the Integrated Circuit (IC) supply chain, driven by time-to-market and cost considerations, has made ICs vulnerable to hardware Trojans (HTs). Against this threat, a promising approach is to use Machine Learning (ML)-based side-channel analysis, which has the advantage of being a non-intrusive method, along with efficiently detecting HTs under golden chip-free settings. In this paper, we question the trustworthiness of ML-based HT detection via side-channel analysis. We introduce a HT obfuscation (HTO) approach to allow HTs to bypass this detection method. Rather than theoretically misleading the model by simulated adversarial traces, a key aspect of our approach is the design and implementation of adversarial noise as part of the circuitry, alongside the HT. We detail HTO methodologies for ASICs and FPGAs, and evaluate our approach using TrustHub benchmark. Interestingly, we found that HTO can be implemented with only a single transistor for ASIC designs to generate adversarial power traces that can fool the defense with 100% efficiency. We also efficiently implemented our approach on a Spartan 6 Xilinx FPGA using 2 different variants: (i) DSP slices-based, and (ii) ring-oscillator-based design. Additionally, we assess the efficiency of countermeasures like spectral domain analysis, and we show that an adaptive attacker can still design evasive HTOs by constraining the design with a spectral noise budget. In addition, while adversarial training (AT) offers higher protection against evasive HTs, AT models suffer from a considerable utility loss, potentially rendering them unsuitable for such security application. We believe this research represents a significant step in understanding and exploiting ML vulnerabilities in a hardware security context, and we make all resources and designs openly available online: https://dev.d18uu4lqwhbmka.amplifyapp.com


Title: Stability and instability of Kelvin waves
Abstract: The $m$-waves of Kelvin are uniformly rotating patch solutions of the 2D Euler equations with $m$-fold rotational symmetry for $m\geq 2$. For Kelvin waves sufficiently close to the disc, we prove a nonlinear stability result up to an arbitrarily long time in the $L^1$ norm of the vorticity, for $m$-fold symmetric perturbations. To obtain this result, we first prove that the Kelvin wave is a strict local maximizer of the energy functional in some admissible class of patches, which had been claimed by Wan in 1986. This gives an orbital stability result with a support condition on the evolution of perturbations, but using a Lagrangian bootstrap argument which traces the particle trajectories of the perturbation, we are able to drop the condition on the evolution. Based on this unconditional stability result, we establish that long time filamentation, or formation of long arms, occurs near the Kelvin waves, which have been observed in various numerical simulations. Additionally, we discuss stability of annular patches in the same variational framework.


Title: Isometric Dilations for Representations of Product Systems
Abstract: We discuss representations of product systems (of $W^*$-correspondences) over the semigroup $\mathbb{Z}^n_+$ and show that, under certain pureness and Szego positivity conditions, a completely contractive representation can be dilated to an isometric representation. For $n=1,2$ this is known to hold in general (without assuming the conditions) but, for $n\geq 3$, it does not hold in general (as is known for the special case of isometric dilations of a tuple of commuting contractions). Restricting to the case of tuples of commuting contractions, our result reduces to a result of Barik, Das, Haria and Sarkar. Our dilation is explicitly constructed and we present some applications.


Title: Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks
Abstract: The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem supports using neural networks for various applications, including regression and classification tasks. Furthermore, it is valid for real-valued neural networks and some hypercomplex-valued neural networks such as complex-, quaternion-, tessarine-, and Clifford-valued neural networks. However, hypercomplex-valued neural networks are a type of vector-valued neural network defined on an algebra with additional algebraic or geometric properties. This paper extends the universal approximation theorem for a wide range of vector-valued neural networks, including hypercomplex-valued models as particular instances. Precisely, we introduce the concept of non-degenerate algebra and state the universal approximation theorem for neural networks defined on such algebras.


Title: Carleman estimates for third order operators of KdV and non KdV-type and applications
Abstract: In this paper we study a class of variable coefficient third order partial differential operators on $\mathbb{R}^{n+1}$, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of $\mathbb{R}^{n+1}$. A discussion of possible applications in the context of dispersive equations is provided.


Title: A convergence result for a local planning problem for mean field games and rigorous proof of a Freidlin-Ventchel-type Large Deviations Principle for the $1+1$ KPZ equation
Abstract: We prove the convergence of a viscous approximation to an one dimensional local mean field type planning problem with singular initial and terminal measures. Then we use this result to give a rigorous proof to a Freidlin-Ventchel-type Large Deviations Principle for the height of the $1+1$ KPZ equation.


Title: Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix
Abstract: We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc, Dembo and Jiang (2006). The main tool used in the proof is a spectral averaging technique from the theory of random Schr\"{o}dinger operators. The similar question for Hankel matrices remains open.


Title: Revisiting Norm Estimation in Data Streams
Abstract: The problem of estimating the pth moment F_p (p nonnegative and real) in data streams is as follows. There is a vector x which starts at 0, and many updates of the form x_i <-- x_i + v come sequentially in a stream. The algorithm also receives an error parameter 0 < eps < 1. The goal is then to output an approximation with relative error at most eps to F_p = ||x||_p^p. Previously, it was known that polylogarithmic space (in the vector length n) was achievable if and only if p <= 2. We make several new contributions in this regime, including: (*) An optimal space algorithm for 0 < p < 2, which, unlike previous algorithms which had optimal dependence on 1/eps but sub-optimal dependence on n, does not rely on a generic pseudorandom generator. (*) A near-optimal space algorithm for p = 0 with optimal update and query time. (*) A near-optimal space algorithm for the "distinct elements" problem (p = 0 and all updates have v = 1) with optimal update and query time. (*) Improved L_2 --> L_2 dimensionality reduction in a stream. (*) New 1-pass lower bounds to show optimality and near-optimality of our algorithms, as well as of some previous algorithms (the "AMS sketch" for p = 2, and the L_1-difference algorithm of Feigenbaum et al.). As corollaries of our work, we also obtain a few separations in the complexity of moment estimation problems: F_0 in 1 pass vs. 2 passes, p = 0 vs. p > 0, and F_0 with strictly positive updates vs. arbitrary updates.


Title: On the Hankel Transform of Bessel Functions on Complex Numbers and Explicit Spectral Formulae over the Gaussian Field
Abstract: In this paper, on the complex field $\mathbb{C}$, we prove two integral formulae for the Hankel-Mellin transform and the double Fourier-Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications, we use the former integral formula to make explicit the spectral formula of Bruggeman and Motohashi for the fourth moment of Dedekind zeta function over the Gaussian number field $\mathbb{Q}(i)$ and to establish a spectral formula for the Hecke-eigenvalue twisted second moment of central $L$-values for the Picard group $\mathrm{PGL}_2 (\mathbb{Z}[i])$. Moreover, we develop the theory of distributional Hankel transform on $\mathbb{C} \smallsetminus \{0\}$.


Title: Almost periodic invariant tori for the NLS on the circle
Abstract: In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain (2005) on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract "counter-term theorem" `a la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find "many more" almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.


Title: Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations
Abstract: We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in $L^\infty$, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space.


Title: A note on a Sung-Wang's paper
Abstract: The purpose of this note is to study the connectedness at infinity of manifold by using the theory of $p$-harmonic functions. We show that if the first eigenvalue $\lambda_{1,p}$ for the $p$-Laplacian achievies its maximal value on a K\"{a}hler manifold or a quaternionic K\"{a}hler manifold then such a manifold must be connected at infinity unless it is a topological cylinder with an explicit warped product metric.


Title: Sampling Acquisition Functions for Batch Bayesian Optimization
Abstract: We present Acquisition Thompson Sampling (ATS), a novel technique for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model hyper-parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function or to make existing parallel methods scale further. We present experiments on a variety of benchmark functions and on the hyper-parameter optimization of a popular gradient boosting tree algorithm. These demonstrate the advantages of ATS with respect to classical parallel Thompson Sampling for BO, its competitiveness with two state-of-the-art batch BO methods, and its effectiveness if applied to existing parallel BO algorithms.


Title: Higher Order Model Checking in Isabelle for Human Centric Infrastructure Security
Abstract: In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to considering security attacks, we achieve an efficient executable specification of a model checking algorithm for attack trees. We provide the existing background, the necessary theory and illustrate its application. Theory and application are fully formalized in Isabelle thus providing an executable model checking algorithm.


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


Title: Symmetry and asymmetry between positive and negative square energies of graphs
Abstract: The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. We answer some questions previously asked about $s^{+}$ and $s^{-}$ and suggest several further avenues of research.


Title: Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
Abstract: A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed subclass of quasi Doob transformations is presented. The theoretical results are applied to stochastic models relevant in the applications.


Title: Reciprocity formulas for certain generalized Hardy sums
Abstract: In this paper, we establish some reciprocity formulas for certain generalized Hardy sums by using the Fourier series technique and some properties of the periodic zeta function and Lerch zeta function. It turns out that one of Hardy's reciprocity theorems is deduced as a special case.