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We study the non-equilibrium dynamics of the superconducting order parameter in the Hatsugai-Kohmoto (HK) model. In the absence of superconductivity, its ground state is a non-Fermi liquid, whose properties are controlled by the HK interaction. Our protocol involves quantum quenching the HK interaction but leaving the interaction responsible for superconductivity unchanged. We map out the non-equilibrium dynamical phase diagram of the interacting model which contains three phases where, at long times, the order parameter amplitude vanishes, approaches a constant value or persistently oscillates. We also investigate the Loschmidt echo in searching for dynamical quantum phase transition, and find no significant correlation between the three phases and the non-analytic temporal behaviour of the Loschmidt echo. The momentum space entanglement entropy between positive and negative momentum modes, relevant for Coopair pairing, is calculated. Counterintuitively, this momentum space entanglement does not change significantly during the quench dynamics and its value remains reasonably large even for vanishing superconducting order parameter. Nevertheless, its derivative with respect to the HK interaction signals the dynamical phase transition associated to the late time vanishing of superconductivity., Comment: 10 pages, 8 figures

Regulatory frameworks for the use of AI are emerging. However, they trail behind the fast-evolving malicious AI technologies that can quickly cause lasting societal damage. In response, we introduce a pioneering Assistive AI framework designed to enhance human decision-making capabilities. This framework aims to establish a trust network across various fields, especially within legal contexts, serving as a proactive complement to ongoing regulatory efforts. Central to our framework are the principles of privacy, accountability, and credibility. In our methodology, the foundation of reliability of information and information sources is built upon the ability to uphold accountability, enhance security, and protect privacy. This approach supports, filters, and potentially guides communication, thereby empowering individuals and communities to make well-informed decisions based on cutting-edge advancements in AI. Our framework uses the concept of Boards as proxies to collectively ensure that AI-assisted decisions are reliable, accountable, and in alignment with societal values and legal standards. Through a detailed exploration of our framework, including its main components, operations, and sample use cases, the paper shows how AI can assist in the complex process of decision-making while maintaining human oversight. The proposed framework not only extends regulatory landscapes but also highlights the synergy between AI technology and human judgement, underscoring the potential of AI to serve as a vital instrument in discerning reality from fiction and thus enhancing the decision-making process. Furthermore, we provide domain-specific use cases to highlight the applicability of our framework., Comment: 37 pages, 6 figures

The emerging zero-shot capabilities of Large Language Models (LLMs) have led to their applications in areas extending well beyond natural language processing tasks. In reinforcement learning, while LLMs have been extensively used in text-based environments, their integration with continuous state spaces remains understudied. In this paper, we investigate how pre-trained LLMs can be leveraged to predict in context the dynamics of continuous Markov decision processes. We identify handling multivariate data and incorporating the control signal as key challenges that limit the potential of LLMs' deployment in this setup and propose Disentangled In-Context Learning (DICL) to address them. We present proof-of-concept applications in two reinforcement learning settings: model-based policy evaluation and data-augmented off-policy reinforcement learning, supported by theoretical analysis of the proposed methods. Our experiments further demonstrate that our approach produces well-calibrated uncertainty estimates. We release the code at https://github.com/abenechehab/dicl.

Calibrating verbalized probabilities presents a novel approach for reliably assessing and leveraging outputs from black-box Large Language Models (LLMs). Recent methods have demonstrated improved calibration by applying techniques like Platt scaling or temperature scaling to the confidence scores generated by LLMs. In this paper, we explore the calibration of verbalized probability distributions for discriminative tasks. First, we investigate the capability of LLMs to generate probability distributions over categorical labels. We theoretically and empirically identify the issue of re-softmax arising from the scaling of verbalized probabilities, and propose using the invert softmax trick to approximate the "logit" by inverting verbalized probabilities. Through extensive evaluation on three public datasets, we demonstrate: (1) the robust capability of LLMs in generating class distributions, and (2) the effectiveness of the invert softmax trick in estimating logits, which, in turn, facilitates post-calibration adjustments., Comment: 21 pages

Federated learning is increasingly popular as it enables multiple parties with limited datasets and resources to train a high-performing machine learning model collaboratively. However, similarly to other collaborative systems, federated learning is vulnerable to free-riders -- participants who do not contribute to the training but still benefit from the shared model. Free-riders not only compromise the integrity of the learning process but also slow down the convergence of the global model, resulting in increased costs for the honest participants. To address this challenge, we propose FRIDA: free-rider detection using privacy attacks, a framework that leverages inference attacks to detect free-riders. Unlike traditional methods that only capture the implicit effects of free-riding, FRIDA directly infers details of the underlying training datasets, revealing characteristics that indicate free-rider behaviour. Through extensive experiments, we demonstrate that membership and property inference attacks are effective for this purpose. Our evaluation shows that FRIDA outperforms state-of-the-art methods, especially in non-IID settings.

Ensemble data assimilation techniques form an indispensable part of numerical weather prediction. As the ensemble size grows and model resolution increases, the amount of required storage becomes a major issue. Data compression schemes may come to the rescue not only for operational weather prediction, but also for weather history archives. In this paper, we present the design and implementation of an easy-to-use framework for evaluating the impact of lossy data compression in large scale ensemble data assimilation. The framework leverages robust statistical qualifiers to determine which compression parameters can be safely applied to the climate variables. Furthermore, our proposal can be used to apply the best parameters during operation, while monitoring data integrity. We perform an exemplary study on the Lorenz96 model to identify viable compression parameters and achieve a 1/3 saving in storage space and an effective speedup of 6% per assimilation cycle, while monitoring the state integrity., Comment: 12 pages, 6 figures

Studying structural brain networks has witnessed significant advancement in recent decades. Findings have revealed a geometric principle, the exponential distance rule (EDR) showing that the number of neurons decreases exponentially with the length of their axons. An EDR based network model explained various characteristics of inter-areal cortical networks in macaques, mice, and rats. The complete connectome of the Drosophila fruit fly has recently been mapped at the neuronal level. Our study demonstrates that the EDR holds true in Drosophila, and the EDR model effectively accounts for numerous binary and weighted properties of neuropil networks, also called projectome. Our study illustrates that the EDR model is a suitable null model for analyzing networks of brain regions, as it captures geometric and physical constraints in very different species. The importance of the null model lies in its ability to facilitate the identification of functionally significant features that are not caused by inevitable geometric constraints, as we illustrate with the pronounced asymmetry of connection weights important for functional hierarchy., Comment: 40 pages in total (34 main article + 4 pages the SI); 8 figures in the main text and 7 figures in the supplementary information

Maintaining numerical stability in machine learning models is crucial for their reliability and performance. One approach to maintain stability of a network layer is to integrate the condition number of the weight matrix as a regularizing term into the optimization algorithm. However, due to its discontinuous nature and lack of differentiability the condition number is not suitable for a gradient descent approach. This paper introduces a novel regularizer that is provably differentiable almost everywhere and promotes matrices with low condition numbers. In particular, we derive a formula for the gradient of this regularizer which can be easily implemented and integrated into existing optimization algorithms. We show the advantages of this approach for noisy classification and denoising of MNIST images., Comment: Accepted at ICML24 Workshop: Differentiable Almost Everything: Differentiable Relaxations, Algorithms, Operators, and Simulators

For several decades now, Bayesian inference techniques have been applied to theories of particle physics, cosmology and astrophysics to obtain the probability density functions of their free parameters. In this study, we review and compare a wide range of Markov Chain Monte Carlo (MCMC) and nested sampling techniques to determine their relative efficacy on functions that resemble those encountered most frequently in the particle astrophysics literature. Our first series of tests explores a series of high-dimensional analytic test functions that exemplify particular challenges, for example highly multimodal posteriors or posteriors with curving degeneracies. We then investigate two real physics examples, the first being a global fit of the $\Lambda$CDM model using cosmic microwave background data from the Planck experiment, and the second being a global fit of the Minimal Supersymmetric Standard Model using a wide variety of collider and astrophysics data. We show that several examples widely thought to be most easily solved using nested sampling approaches can in fact be more efficiently solved using modern MCMC algorithms, but the details of the implementation matter. Furthermore, we also provide a series of useful insights for practitioners of particle astrophysics and cosmology., Comment: 45 pages, 8 figures, 20 tables

We calculate the gravitational wave spectrum generated by sound waves during a cosmological phase transition, incorporating several advancements beyond the current state-of-the-art. Rather than relying on the bag model or similar approximations, we derive the equation of state directly from the effective potential. This approach enables us to accurately determine the hydrodynamic quantities, which serve as initial conditions in a generalised hybrid simulation. This simulation tracks the fluid evolution after bubble collisions, leading to the generation of gravitational waves. Our work is the first self-consistent numerical calculation of gravitational waves for the real singlet extension of the standard model. Our computational method is adaptable to any particle physics model, offering a fast and reliable way to calculate gravitational waves generated by sound waves. With fewer approximations, our approach provides a robust foundation for precise gravitational wave calculations and allows for the exploration of model-independent features of gravitational waves from phase transitions., Comment: 31 pages, 8 figures, 1 table

In this paper we show that the random degree constrained process (a time-evolving random graph model with degree constraints) has a local weak limit, provided that the underlying host graphs are high degree almost regular. We, moreover, identify the limit object as a multi-type branching process, by combining coupling arguments with the analysis of a certain recursive tree process. Using a spectral characterization, we also give an asymptotic expansion of the critical time when the giant component emerges in the so-called random $d$-process, resolving a problem of Warnke and Wormald for large $d$., Comment: 53 pages, 3 figures

We trained denoiser autoencoding neural networks on medium resolution simulated optical spectra of late-type stars to demonstrate that the reconstruction of the original flux is possible at a typical relative error of a fraction of a percent down to a typical signal-to-noise ratio of 10 per pixel. We show that relatively simple networks are capable of learning the characteristics of stellar spectra while still flexible enough to adapt to different values of extinction and fluxing imperfections that modifies the overall shape of the continuum, as well as to different values of Doppler shift. Denoised spectra can be used to find initial values for traditional stellar template fitting algorithms and - since evaluation of pre-trained neural networks is significantly faster than traditional template fitting - denoiser networks can be useful when a fast analysis of the noisy spectrum is necessary, for example during observations, between individual exposures.

We study some representations of symmetric groups arising from a certain ideal in the coordinate ring of affine n-space. Our results give graded and representation-theoretic enhancements of sequence 337 of the Online Encyclopaedia of Integer Sequences, involving a symmetric version of the Bernoulli triangle., Comment: 8 pages. Main article by Nsibiet E. Udo, Praise Adeyemo and Balazs Szendroi; Appendix by Stavros Argyrios Papadakis

The least squares (LS) estimate is the archetypical solution of linear regression problems. The asymptotic Gaussianity of the scaled LS error is often used to construct approximate confidence ellipsoids around the LS estimate, however, for finite samples these ellipsoids do not come with strict guarantees, unless some strong assumptions are made on the noise distributions. The paper studies the distribution-free Sign-Perturbed Sums (SPS) ellipsoidal outer approximation (EOA) algorithm which can construct non-asymptotically guaranteed confidence ellipsoids under mild assumptions, such as independent and symmetric noise terms. These ellipsoids have the same center and orientation as the classical asymptotic ellipsoids, only their radii are different, which radii can be computed by convex optimization. Here, we establish high probability non-asymptotic upper bounds for the sizes of SPS outer ellipsoids for linear regression problems and show that the volumes of these ellipsoids decrease at the optimal rate. Finally, the difference between our theoretical bounds and the empirical sizes of the regions are investigated experimentally.

A classical result of Kleitman determines the maximum number $f(n,s)$ of subsets in a family $\mathcal{F}\subseteq 2^{[n]}$ of sets that do not contain distinct sets $F_1,F_2,\dots,F_s$ that are pairwise disjoint in the case $n\equiv 0,-1$ (mod $s$). Katona and Nagy determined the maximum size of a family of subsets of an $n$-element set that does not contain $A_1,A_2,\dots,A_t,B_1,B_2,\dots,B_t$ with $\bigcup_{i=1}^t A_i$ and $\bigcup_{i=1}^t B_i$ being disjoint. In this paper, we consider the problem of finding the maximum number $vex(n,K_{s\times t})$ in a family $\mathcal{F}\subseteq 2^{[n]}$ without sets $F^1_1,\dots,F^1_t,\dots,F^s_1,\dots,F^s_t$ such that $G_j=\bigcup_{i=1}^tF^j_i$ $j=1,2,\dots,s$ are pairwise disjoint. We determine the asymptotics of $2^n-vex(n,K_{s\times t})$ if $n\equiv -1$ (mod $s$) for all $t$, and if $n\equiv 0$ (mod $s$), $t\ge 3$ and show that in this latter case the asymptotics of the $t=2$ subcase is different from both the $t=1$ and $t\ge 3$ subcases.

Gravitational waves from cosmological phase transitions are novel probes of fundamental physics, making their precise calculation essential for revealing various mysteries of the early Universe. In this work we propose a framework that enables the consistent calculation of such gravitational waves sourced by sound waves. Starting from the Lagrangian, this framework integrates the calculation of the dynamics of first-order phase transitions in a self-consistent manner, eliminating various approximations typically introduced by conventional methods. At the heart of our approach is the congruous evaluation of the phase transition hydrodynamics that, at every step, is consistently informed by the Lagrangian. We demonstrate the application of our framework using the SM+$|H|^6$ model, deriving the corresponding gravitational wave spectrum. Our framework establishes a robust foundation for the precise prediction of gravitational waves from phase transitions., Comment: 8 pages, 4 figures, 1 table

The increasing accuracy reports of metric monocular depth estimation models lead to a growing interest from the automotive domain. Current model evaluations do not provide deeper insights into the models' performance, also in relation to safety-critical or unseen classes. Within this paper, we present a novel approach for the evaluation of depth estimation models. Our proposed metric leverages three components, a class-wise component, an edge and corner image feature component, and a global consistency retaining component. Classes are further weighted on their distance in the scene and on criticality for automotive applications. In the evaluation, we present the benefits of our metric through comparison to classical metrics, class-wise analytics, and the retrieval of critical situations. The results show that our metric provides deeper insights into model results while fulfilling safety-critical requirements. We release the code and weights on the following repository: https://github.com/leisemann/ca_mmde, Comment: Accepted at the European Conference on Computer Vision (ECCV) 2024 Workshop on Out Of Distribution Generalization in Computer Vision

The study of geometric hypergraphs gave rise to the notion of $ABAB$-free hypergraphs. A hypergraph $\mathcal{H}$ is called $ABAB$-free if there is an ordering of its vertices such that there are no hyperedges $A,B$ and vertices $v_1,v_2,v_3,v_4$ in this order satisfying $v_1,v_3\in A\setminus B$ and $v_2,v_4\in B\setminus A$. In this paper, we prove that it is NP-complete to decide if a hypergraph is $ABAB$-free. We show a number of analogous results for hypergraphs with similar forbidden patterns, such as $ABABA$-free hypergraphs. As an application, we show that deciding whether a hypergraph is realizable as the incidence hypergraph of points and pseudodisks is also NP-complete., Comment: 10 pages

We study stationary epidemic processes in scale-free networks with local awareness behavior adopted by only susceptible, only infected, or all nodes. We find that while the epidemic size in the susceptible-aware and the all-aware scenarios scales linearly with the network size, the scaling becomes sublinear in the infected-aware scenario, suggesting that fewer aware nodes may reduce the epidemic size more effectively. We explain this paradox via numerical and theoretical analysis, and highlight the role of influential nodes and their disassortativity to raise awareness in epidemic scenarios.

We study the sample complexity of the Sign-Perturbed Sums (SPS) method, which constructs exact, non-asymptotic confidence regions for the true system parameters under mild statistical assumptions, such as independent and symmetric noise terms. The standard version of SPS deals with linear regression problems, however, it can be generalized to stochastic linear (dynamical) systems, even with closed-loop setups, and to nonlinear and nonparametric problems, as well. Although the strong consistency of the method was rigorously proven, the sample complexity of the algorithm was only analyzed so far for scalar linear regression problems. In this paper we study the sample complexity of SPS for general linear regression problems. We establish high probability upper bounds for the diameters of SPS confidence regions for finite sample sizes and show that the SPS regions shrink at the same, optimal rate as the classical asymptotic confidence ellipsoids. Finally, the difference between the theoretical bounds and the empirical sizes of SPS confidence regions is investigated experimentally.

We calculate the phase diagram of the Aubry-Andr\'{e} model as a function of filling and potential strength ($W$). We apply periodic boundary conditions and calculate the geometric Binder cumulant to determine the transition between the extended and localized phases. For rational fillings the phase transition occurs at $W=2t$ ($t$ denotes the hopping parameter), but spikes occur in the phase diagram at fillings which correspond to ratios of Fibonacci numbers. In the thermodynamic limit these ratios tend to specific irrational numbers, and $W \rightarrow 0$ at these fillings. We also calculate the phase diagram of an extended Aubry-Andr\'{e} model with second nearest neighbor hoppings. In addition to spikes, this phase diagram also exhibits discontinuities (jumps) at some of the irrational fillings at which the spikes occur.

Convolutional layers with 1-D filters are often used as frontend to encode audio signals. Unlike fixed time-frequency representations, they can adapt to the local characteristics of input data. However, 1-D filters on raw audio are hard to train and often suffer from instabilities. In this paper, we address these problems with hybrid solutions, i.e., combining theory-driven and data-driven approaches. First, we preprocess the audio signals via a auditory filterbank, guaranteeing good frequency localization for the learned encoder. Second, we use results from frame theory to define an unsupervised learning objective that encourages energy conservation and perfect reconstruction. Third, we adapt mixed compressed spectral norms as learning objectives to the encoder coefficients. Using these solutions in a low-complexity encoder-mask-decoder model significantly improves the perceptual evaluation of speech quality (PESQ) in speech enhancement., Comment: Accepted at INTERSPEECH 2024

This paper argues that military buildups lead to a significant rise in greenhouse gas emissions and can disrupt the green transition. Identifying military spending shocks, I use local projections to show that a percentage point rise in the military spending share leads to a 0.9-2% rise in total emissions, as well as a 1% rise in emission intensity, depending on the economy's overall emission intensity. Using a dynamic production network model calibrated for the US, I find that a permanent shock of the same size would increase total emissions by between 0.36% and 1.81%, and emission intensity by between 0.22% and 1.5%. The empirical analysis indicates that green patenting is reduced by 10-25% following such a shock, and the model suggests that investment in renewables could be crowded out by defence spending, hindering the energy transition. These effects can significantly raise climate damages, temperatures, and can lead to a quicker exhaustion of the carbon budget.

We study Markov processes on weighted directed hypergraphs where the state of at most one vertex can change at a time. Our setting is general enough to include simplicial epidemic processes, processes on multilayered networks or even the dynamics of the edges of a graph. Our results are twofold. Firstly, we prove concentration bounds for the number of vertices in a certain state under mild assumptions. Our results imply that even the empirical averages of subpopulations of diverging but possibly sublinear size are well concentrated around their mean. In the case of undirected weighted graphs, we completely characterize when said averages concentrate around their expected value. Secondly, we prove (under assumptions which are tight in some significant cases) upper bounds for the error of the N-Intertwined Mean Field Approximation (NIMFA). In particular, for symmetric unweighted graphs, the error has the same order of magnitude as the reciprocal of the average degree, improving the previously known state of the art bound of the inverse square root of the average degree.

We study the finite size scaling of the bulk polarization in a quasiperiodic (Aubry-Andr\'{e}) model using the geometric analog of the Binder cumulant. As a proof of concept we show that the geometric Binder cumulant method described here can reproduce the known literature values for the flat and raised cosine distributions, which are the two distributions that occur in the delocalized phase. For the Aubry-Andr\'{e} model at half-filling the phase transition point is accurately reproduced. Not only is the correct size scaling exponent of the variance obtained in the extended and the localized phases, but the geometric Binder cumulant undergoes a sign change at the phase transition. We also calculate the state resolved Binder cumulant as a function of disorder strength to gain insight into the mechanism of the localization transition.

In the last years, many neural network-based approaches have been proposed to tackle combinatorial optimization problems such as routing problems. Many of these approaches are based on graph neural networks (GNNs) or related transformers, operating on the Euclidean coordinates representing the routing problems. However, GNNs are inherently not well suited to operate on dense graphs, such as in routing problems. Furthermore, models operating on Euclidean coordinates cannot be applied to non-Euclidean versions of routing problems that are often found in real-world settings. To overcome these limitations, we propose a novel GNN-related edge-based neural model called Graph Edge Attention Network (GREAT). We evaluate the performance of GREAT in the edge-classification task to predict optimal edges in the Traveling Salesman Problem (TSP). We can use such a trained GREAT model to produce sparse TSP graph instances, keeping only the edges GREAT finds promising. Compared to other, non-learning-based methods to sparsify TSP graphs, GREAT can produce very sparse graphs while keeping most of the optimal edges. Furthermore, we build a reinforcement learning-based GREAT framework which we apply to Euclidean and non-Euclidean asymmetric TSP. This framework achieves state-of-the-art results., Comment: 15 pages, 7 figures

We consider spin chain models with exotic symmetries that change the length of the spin chain. It is known that the XXZ Heisenberg spin chain at the supersymmetric point $\Delta=-1/2$ possesses such a symmetry: it is given by the supersymmetry generators, which change the length of the chain by one unit. We show that volume changing symmetries exist also in other spin chain models, and that they can be constructed using a special tensor network, which is a simple generalization of a Matrix Product Operator. As examples we consider the folded XXZ model and its perturbations, and also a new hopping model that is defined on constrained Hilbert spaces. We show that the volume changing symmetries are not related to integrability: the symmetries can survive even non-integrable perturbations. We also show that the known supersymmetry generator of the XXZ chain with $\Delta=-1/2$ can also be expressed as a generalized Matrix Product Operator., Comment: 17 pages, 7 figures

Anonymous messaging and payments have gained momentum recently due to their impact on individuals, society, and the digital landscape. Fuzzy Message Detection (FMD) is a privacy-preserving protocol where an untrusted server performs message anonymously filtering for its clients. To prevent the server from linking the sender and the receiver, the latter can set how much cover traffic they should download along with genuine messages. This could cause unwanted messages to appear on the user's end, thereby creating a need to balance one's bandwidth cost with the desired level of unlinkability. Previous work showed that FMD is not viable with selfish users. In this paper, we model and analyze FMD using the tools of empirical game theory and show that the system needs at least a few altruistic users to operate properly. Utilizing real-world communication datasets, we characterize the emerging equilibria, quantify the impact of different types and levels of altruism, and assess the efficiency of potential outcomes versus socially optimal allocations. Moreover, taking a mechanism design approach, we show how the betweenness centrality (BC) measure can be utilized to achieve the social optimum., Comment: Accepted at GameSec24

In this paper, we prove that spatially semi-discrete evolving finite element method for parabolic equations on a given evolving hypersurface of arbitrary dimensions preserves the maximal $L^p$-regularity at the discrete level. We first establish the results on a stationary surface and then extend them, via a perturbation argument, to the case where the underlying surface is evolving under a prescribed velocity field. The proof combines techniques in evolving finite element method, properties of Green's functions on (discretised) closed surfaces, and local energy estimates for finite element methods

Coupling latent diffusion based image generation with contextual bandits enables the creation of eye-catching personalized product images at scale that was previously either impossible or too expensive. In this paper we showcase how we utilized these technologies to increase user engagement with recommendations in online retargeting campaigns for e-commerce., Comment: Appearing in the Proceedings of the 18th ACM Conference on Recommender Systems (RecSys'24) as an Industry Track paper

We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two $XY$ spin chains that are coupled through Ising $ZZ$ interaction. The spin ladder model is then examined within the semiclassical limit using a spin-coherent state basis, where the dynamics is governed by a set of coupled Landau-Lifshitz-Gilbert equations. The non-Hermitian interactions in this model generate a spin-transfer torque term. We analyze the system's evolution toward several potential steady states, including a state of decoupled chains that is accessible when each chain has uniform initial conditions. Other possible steady states involve dimerized configurations with decoupled rungs, where the rung spins are either ferromagnetically or antiferromagnetically coupled, depending on the sign of the imaginary interactions. The spin dynamics is then studied in the infinite-temperature limit, which favors dimerized steady states. Despite the decoupled rungs, we observe the formation of ferromagnetic domains along each chain in the steady state. Additionally, we investigate the spin correlation functions and identify signatures of anomalous spin dynamics., Comment: 12 pages, 9 figures

We give a quadratic-time algorithm to compute the stretch factor and the invariant measured foliations for a pseudo-Anosov element of the mapping class group. As input, the algorithm accepts a word (in any given finite generating set for the mapping class group) representing a pseudo-Anosov mapping class, and the length of the word is our measure of complexity for the input. The output is a train track and an integer matrix where the stretch factor is the largest real eigenvalue and the unstable foliation is given by the corresponding eigenvector. This is the first algorithm to compute stretch factors and measured foliations that is known to terminate in sub-exponential time., Comment: 47 pages, 6 figures

We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the density imbalance are analyzed using bosonization and exact diagonalization. The energy becomes complex valued, despite the instantaneous Hamiltonian having the same real spectrum throughout. The adiabatic limit is approached very slowly through damped oscillations. The decay scales with $\tau^{-1}$ with $\tau$ the ramp duration, while the oscillation period is $2L/v$ with $v$ the Fermi velocity and $L$ the system length. Yet, without the need for auxiliary controls, a shortcut to adiabaticity is found for ramp times commensurate with the period. Our work highlights the intricate interplay of adiabaticity and non-Hermitian many-body physics., Comment: 11 pages, 4 figures

Maps are essential for diverse applications, such as vehicle navigation and autonomous robotics. Both require spatial models for effective route planning and localization. This paper addresses the challenge of road graph construction for autonomous vehicles. Despite recent advances, creating a road graph remains labor-intensive and has yet to achieve full automation. The goal of this paper is to generate such graphs automatically and accurately. Modern cars are equipped with onboard sensors used for today's advanced driver assistance systems like lane keeping. We propose using global navigation satellite system (GNSS) traces and basic image data acquired from these standard sensors in consumer vehicles to estimate road-level maps with minimal effort. We exploit the spatial information in the data by framing the problem as a road centerline semantic segmentation task using a convolutional neural network. We also utilize the data's time series nature to refine the neural network's output by using map matching. We implemented and evaluated our method using a fleet of real consumer vehicles, only using the deployed onboard sensors. Our evaluation demonstrates that our approach not only matches existing methods on simpler road configurations but also significantly outperforms them on more complex road geometries and topologies. This work received the 2023 Woven by Toyota Invention Award., Comment: This work will be presented at IROS 2024. Supplementary website: https://bazs.github.io/probe2road/

For an edge-ordered graph $G$, we say that an $n$-vertex edge-ordered graph $H$ is $G$-saturated if it is $G$-free and adding any new edge with any new label to $H$ introduces a copy of $G$. The saturation function describes the minimum number of edges of a $G$-saturated graph. In particular, we study the order of magnitude of these functions. For (unordered) graphs, $0$-$1$ matrices, and vertex-ordered graphs it was possible to show that the saturation functions are either $O(1)$ or $\Theta(n)$. We show that the saturation functions of edge-ordered graphs are also either $O(1)$ or $\Omega(n)$. However, by finding edge-ordered graphs whose saturation functions are superlinear, we show that such a dichotomy result does not hold in general. Additionally, we consider the semisaturation problem of edge-ordered graphs, a variant of the saturation problem where we do not require that $H$ is $G$-free. We show a general upper bound $O(n \log n)$ and characterize edge-ordered graphs with bounded semisaturation function. We also present various classes of graphs with bounded, linear and superlinear (semi)saturation functions. Along the way, we define a natural variant of the above problem, where the new edge must get the smallest label. The behaviour of the two variants shows many similarities, which motivated us to investigate the second variant extensively as well.

Advances in machine learning have led to the development of foundation models for atomistic materials chemistry, enabling quantum-accurate descriptions of interatomic forces across diverse compounds at reduced computational cost. Hitherto, these models have been benchmarked relying on descriptors based on atoms' interaction energies or harmonic vibrations; their accuracy and efficiency in predicting observable and technologically relevant heat-conduction properties remains unknown. Here, we introduce a framework that leverages foundation models and the Wigner formulation of heat transport to overcome the major bottlenecks of current methods for designing heat-management materials: high cost, limited transferability, or lack of physics awareness. We present the standards needed to achieve first-principles accuracy in conductivity predictions through model's fine-tuning, discussing benchmark metrics and precision/cost trade-offs. We apply our framework to a database of solids with diverse compositions and structures, demonstrating its potential to discover materials for next-gen technologies ranging from thermal insulation to neuromorphic computing., Comment: 15 pages, 10 figures

Recently, there has been increasing activity in using deep learning for software engineering, including tasks like code generation and summarization. In particular, the most recent coding Large Language Models seem to perform well on these problems. In this technical report, we aim to review how these models perform in code explanation/summarization, while also investigating their code generation capabilities (based on natural language descriptions)., Comment: technical report with 11 pages, 1 figure, 10 tables

A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order 1 to 5 in time. Optimal-order error estimates are proven. The error estimates are based on a consistency and stability analysis in an abstract framework, based on energy estimates exploiting the anti-symmetric structure of the second-order system.

In this article we introduce several new examples of Wiener pairs $\mathcal{A} \subseteq \mathcal{B}$, where $\mathcal{B} = \mathcal{B}(\ell^2(X;\mathcal{H}))$ is the Banach algebra of bounded operators acting on the Hilbert space-valued Bochner sequence space $\ell^2(X;\mathcal{H})$ and $\mathcal{A} = \mathcal{A}(X)$ is a Banach algebra consisting of operator-valued matrices indexed by some relatively separated set $X \subset \mathbb{R}^d$. In particular, we introduce $\mathcal{B}(\mathcal{H})$-valued versions of the Jaffard algebra, of certain weighted Schur-type algebras, of Banach algebras which are defined by more general off-diagonal decay conditions than polynomial decay, of weighted versions of the Baskakov-Gohberg-Sj\"ostrand algebra, and of anisotropic variations of all of these matrix algebras, and show that they are inverse-closed in $\mathcal{B}(\ell^2(X;\mathcal{H}))$. In addition, we obtain that each of these Banach algebras is symmetric.

In this paper, we address the challenge of fine-grained video event understanding in traffic scenarios, vital for autonomous driving and safety. Traditional datasets focus on driver or vehicle behavior, often neglecting pedestrian perspectives. To fill this gap, we introduce the WTS dataset, highlighting detailed behaviors of both vehicles and pedestrians across over 1.2k video events in hundreds of traffic scenarios. WTS integrates diverse perspectives from vehicle ego and fixed overhead cameras in a vehicle-infrastructure cooperative environment, enriched with comprehensive textual descriptions and unique 3D Gaze data for a synchronized 2D/3D view, focusing on pedestrian analysis. We also pro-vide annotations for 5k publicly sourced pedestrian-related traffic videos. Additionally, we introduce LLMScorer, an LLM-based evaluation metric to align inference captions with ground truth. Using WTS, we establish a benchmark for dense video-to-text tasks, exploring state-of-the-art Vision-Language Models with an instance-aware VideoLLM method as a baseline. WTS aims to advance fine-grained video event understanding, enhancing traffic safety and autonomous driving development., Comment: ECCV24. Website: https://woven-visionai.github.io/wts-dataset-homepage/

Monitoring the carrier-envelope phase (CEP) is of paramount importance for experiments involving few cycle intense laser fields. Common measurement techniques include f-2f interferometry or stereo-ATI setups. These approaches are adequate, but are challenging to implement on demand, at different locations as additional metrology tools, in intense few cycle laser-matter interaction experiments, such as those prevalent in sophisticated user beamlines. In addition there are inherent difficulties for CEP measured at non-conventional laser wavelengths (like e.g. mid infrared) and measurements above 10 kHz laser repetition rates, on single shot basis. Here we demonstrate both by simulations and by experiments a machine learning (ML) driven method for CEP estimation in the mid infrared, which is readily generalizable for any laser wavelength and possibly up to MHz repetition rates. The concept relies on the observation of the spectrum of high harmonic generation (HHG) in bulk material and the use of ML techniques to estimate the CEP of the laser. Once the ML model is trained, the method provides a way for cheap and compact real-time CEP tagging. This technique can complement the otherwise sophisticated monitoring of CEP, and is able to capture the complex correlation between the CEP and the observable HHG spectra.

GRBAlpha is a 1U CubeSat launched in March 2021 to a sun-synchronous LEO at an altitude of 550 km to perform an in-orbit demonstration of a novel gamma-ray burst detector developed for CubeSats. VZLUSAT-2 followed ten months later in a similar orbit carrying as a secondary payload a pair of identical detectors as used on the first mission. These instruments detecting gamma-rays in the range of 30-900 keV consist of a 56 cm2 5 mm thin CsI(Tl) scintillator read-out by a row of multi-pixel photon counters (MPPC or SiPM). The scientific motivation is to detect gamma-ray bursts and other HE transient events and serve as a pathfinder for a larger constellation of nanosatellites that could localize these events via triangulation. At the beginning of July 2024, GRBAlpha detected 140 such transients, while VZLUSAT-2 had 83 positive detections, confirmed by larger GRB missions. Almost a hundred of them are identified as gamma-ray bursts, including extremely bright GRB 221009A and GRB 230307A, detected by both satellites. We were able to characterize the degradation of SiPMs in polar orbit and optimize the duty cycle of the detector system also by using SatNOGS radio network for downlink., Comment: Presented at SPIE.Astronomical Telescopes and Instrumentations,2024

The goal of this paper is to show that fundamental concepts in higher-order Fourier analysis can be nauturally extended to the non-commutative setting. We generalize Gowers norms to arbitrary compact non-commutative groups. On the structural side, we show that nilspace theory (the algebraic part of higher-order Fourier analysis) can be naturally extended to include all non-commutative groups. To this end, we introduce generalized nilspaces called "groupspaces" and demonstrate that they possess properties very similar to nilspaces. We study $k$-th order generalizations of groups that are special groupspaces called {\it k-step} groupspaces. One step groupspaces are groups. We show that $k$-step groupspaces admit the structure of an iterated principal bundle with structure groups $G_1,G_2,\dots,G_k$. A similar, but somewhat more technical statement holds for general groupspaces, with possibly infinitely many structure groups. Structure groups of groupspaces are in some sense analogous to higher homotopy groups. In particular we use a version of the Eckmann-Hilton argument from homotopy theory to show that $G_i$ is abelian for $i\geq 2$. Groupspaces also show some similarities with $n$-groups from higher category theory (also used in physics) but the exact relationship between these concepts is a subject of future research.

We present a Spiking Neural Network (SNN) model that incorporates learnable synaptic delays using Dilated Convolution with Learnable Spacings (DCLS). We train this model on the Raw Heidelberg Digits keyword spotting benchmark using Backpropagation Through Time with surrogate gradients. Analysing the spatio-temporal structure of synaptic interactions in the network we observe that after training excitation and inhibition are grouped together both in space and time. To further enhance the efficiency and biological realism of our model, we implemented a dynamic pruning strategy that combines DEEP R for connection removal and RigL for connection reintroduction, ensuring that the network maintains optimal connectivity throughout training. Additionally, we incorporated Dale's Principle, enforcing each neuron to be exclusively excitatory or inhibitory -- aligning our model closer to biological neural networks. We observed that, after training, the spatio-temporal patterns of excitation and inhibition appeared in the more biologically plausible model as well. Our research demonstrates the potential of integrating learnable delays, dynamic pruning, and biological constraints to develop efficient SNN models for temporal data processing. Furthermore, our results enhance the understanding of spatio-temporal dynamics in SNNs -- suggesting that the spatio-temporal features which emerge from training are robust to both pruning and rewiring processes -- providing a solid foundation for future work in neuromorphic computing applications., Comment: 10 pages, 4 figures, submitted to Frontiers in Computational Neuroscience

This paper develops and discusses a residual-based a posteriori error estimate and a space--time adaptive algorithm for solving parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and the backward Euler method in time. The proposed error indicator bounds the error quantities globally in space from above and below, and globally in time from above and locally from below. A space--time adaptive algorithm is proposed using the derived error indicator. Numerical experiments illustrate and complement the theory., Comment: 18 pages, 4 figures

Injectivity is the defining property of a mapping that ensures no information is lost and any input can be perfectly reconstructed from its output. By performing hard thresholding, the ReLU function naturally interferes with this property, making the injectivity analysis of ReLU-layers in neural networks a challenging yet intriguing task that has not yet been fully solved. This article establishes a frame theoretic perspective to approach this problem. The main objective is to develop the most general characterization of the injectivity behavior of ReLU-layers in terms of all three involved ingredients: (i) the weights, (ii) the bias, and (iii) the domain where the data is drawn from. Maintaining a focus on practical applications, we limit our attention to bounded domains and present two methods for numerically approximating a maximal bias for given weights and data domains. These methods provide sufficient conditions for the injectivity of a ReLU-layer on those domains and yield a novel practical methodology for studying the information loss in ReLU layers. Finally, we derive explicit reconstruction formulas based on the duality concept from frame theory.

In this paper we study bifurcations in mass-action networks with two chemical species and reactant complexes of molecularity no more than two. We refer to these as planar, quadratic networks as they give rise to (at most) quadratic differential equations on the nonnegative quadrant of the plane. Our aim is to study bifurcations in networks in this class with the fewest possible reactions, and the lowest possible product molecularity. We fully characterise generic bifurcations of positive equilibria in such networks with up to four reactions, and product molecularity no higher than three. In these networks we find fold, Andronov--Hopf, Bogdanov--Takens and Bautin bifurcations, and prove the non-occurrence of any other generic bifurcations of positive equilibria. In addition, we present a number of results which go beyond planar, quadratic networks. For example, we show that mass-action networks without conservation laws admit no bifurcations of codimension greater than $m-2$, where $m$ is the number of reactions; we fully characterise quadratic, rank-one mass-action networks admitting fold bifurcations; and we write down some necessary conditions for Andronov--Hopf and cusp bifurcations in mass-action networks. Finally, we draw connections with a number of previous results in the literature on nontrivial dynamics, bifurcations, and inheritance in mass-action networks.

Geometric motivations warranted the study of hypergraphs on ordered vertices that have no pair of hyperedges that induce an alternation of some given length. Such hypergraphs are called ABA-free, ABAB-free and so on. Since then various coloring and other combinatorial results were proved about these families of hypergraphs. We prove a characterization in terms of their incidence matrices which avoids using the ordering of the vertices. Using this characterization, we prove new results about the dual hypergraphs of ABAB-free hypergraphs. In particular, we show that dual-ABAB-free hypergraphs are not always proper $2$-colorable even if we restrict ourselves to hyperedges that are larger than some parameter $m$.

In a quantum communication network, links represent entanglement between qubits located at different nodes. Even if two nodes are not directly linked by shared entanglement, communication channels can be established between them via quantum routing protocols. However, in contrast to classical communication networks, each communication event removes all participating links along the communication path, disrupting the quantum network. Here, we propose a simple model, where randomly selected pairs of nodes communicate through shortest paths. Each time such a path is used, all participating links are eliminated, leading to a correlated percolation process that we call ``path percolation.'' We study path percolation both numerically and analytically and present the phase diagram of the steady states as a function of the rate at which new links are being added to the quantum communication network. As a key result, the steady state is found to be independent from the initial network topology when new link are added randomly between disconnected components. We close by discussing extensions of path percolation and their potential applications., Comment: 10 pages, 5 figures

Considering the possibility of complex organic molecules and microbial life appearing under the ice shell of those satellites in the Solar system, this study investigates the possible analog sources (targeting the potential ice satellite hosting, Jupiter and Saturn-like planets in exoplanet databases) and the transport of such bioaerosols in an attempt to support or contradict Panspermia, a fringe theory about the fertilization of Earth. Along many general parameters of the candidate planets, the host star, and the star system, additional factors thought to be related to Panspermia were also considered (e.g., the evolution of icy satellites, the frequency of impact related ejection, the traveling time from a source, and so on), revealing the following results. Eleven exosystems, with candidate gas giants hosting icy satellites, were found in a database listing more than 5000 exoplanets. The exomoons of the oldest systems (c.a. > 8 Ga; HD 191939, HD 4203, and HD 34445) could have developed rapidly considering the short formation time (~100 Myrs), which may result in the overlap of the putative early biological evolution and asteroid bombardment phase, providing a higher chance to bioaerosol ejection to space due to frequent collisions. However, the direct transfer might have occurred too early, even before our Solar system was formed, which prevented the fertilization of the latter. A longer formation of the exomoons (~3 Gyrs) significantly reduces the chance of ejection into space by asteroid impacts, which become less frequent over time, but increased the chance of arrival in time to the Solar system. Younger systems, such as HD 217107, HD 219828, HD 140901, and HD 156279 (c.a. 4 to 6 Ga), are better candidates of putative microbe source if the short icy satellite formation, along the higher impact and ejection frequency are expected considering direct transport from those systems.