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In this chapter, we investigate the energy spectra as well as the bulk and surface states in a two-dimensional system composed of a coupled stack of one-dimensional dimerized chains in the presence of an external magnetic field. Specifically, we analyze the Hofstadter butterfly patterns that emerge in a 2D stack of coupled 1D Su-Schrieffer-Heeger (SSH) chains subject to an external transverse magnetic field. Depending on the parameter regime, we find that the energy spectra of this hybrid topological system can exhibit topologically non-trivial bulk bands separated by energy gaps. Upon introducing boundaries into the system, we observe topologically protected in-gap surface states, which are protected either by a non-trivial Chern number or by inversion symmetry. We examine the resilience of these surface states against perturbations, confirming their expected stability against local symmetry-preserving perturbations., Comment: Book chapter. 16 pages, 13 figures

We measure the performance of in-context learning as a function of task novelty and difficulty for open and closed questions. For that purpose, we created a novel benchmark consisting of hard scientific questions, each paired with a context of various relevancy. We show that counter-intuitively, a context that is more aligned with the topic does not always help more than a less relevant context. This effect is especially visible for open questions and questions of high difficulty or novelty. This result reveals a fundamental difference between the treatment of close-form and open-form questions by large-language models and shows a need for a more robust evaluation of in-context learning on the variety of different types of questions. It also poses a new question of how to optimally select a context for large language models, especially in the context of Retrieval Augmented Generation (RAG) systems. Our results suggest that the answer to this question can be highly application-dependent and might be contingent on factors including the format of the question, the perceived difficulty level of the questions, and the novelty or popularity of the information we seek., Comment: 8 pages plus references, 4 main figures, 6 pages of supplementary material

In this paper we describe the quotients of several plactic-like monoids by the least congruences containing the relations $a^{\sigma(a)} = a$ with $\sigma(a)\ge 2$ for every generator $a$. The starting point for this description is the recent paper of Abram and Reutenauer about the so-called stylic monoid which happens to be the quotient of the plactic monoid by the relations $a^2 = a$ for every letter $a$. The plactic-like monoids considered are the plactic monoid itself, the Chinese monoid, and the sylvester monoid. In each case we describe: a set of normal forms, and the idempotents; and obtain formulae for their size., Comment: In Proceedings GASCom 2024, arXiv:2406.14588

The sparse dictionary coding framework represents signals as a linear combination of a few predefined dictionary atoms. It has been employed for images, time series, graph signals and recently for 2-way (or 2D) spatio-temporal data employing jointly temporal and spatial dictionaries. Large and over-complete dictionaries enable high-quality models, but also pose scalability challenges which are exacerbated in multi-dictionary settings. Hence, an important problem that we address in this paper is: How to scale multi-dictionary coding for large dictionaries and datasets? We propose a multi-dictionary atom selection technique for low-rank sparse coding named LRMDS. To enable scalability to large dictionaries and datasets, it progressively selects groups of row-column atom pairs based on their alignment with the data and performs convex relaxation coding via the corresponding sub-dictionaries. We demonstrate both theoretically and experimentally that when the data has a low-rank encoding with a sparse subset of the atoms, LRMDS is able to select them with strong guarantees under mild assumptions. Furthermore, we demonstrate the scalability and quality of LRMDS in both synthetic and real-world datasets and for a range of coding dictionaries. It achieves 3X to 10X speed-up compared to baselines, while obtaining up to two orders of magnitude improvement in representation quality on some of the real world datasets given a fixed target number of atoms., Comment: Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, August 25--29, 2024, Barcelona, Spain

Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline a framework for discovering continuous symmetry in data beyond the affine transformation group. We also provide a similar framework for discovering discrete symmetry. We experimentally compare our method to an existing method known as LieGAN and show that our method is competitive at detecting affine symmetries for large sample sizes and superior than LieGAN for small sample sizes. We also show our method is able to detect continuous symmetries beyond the affine group and is generally more computationally efficient than LieGAN.

We use numerical simulations to demonstrate a local rheology for sheared, vibrated granular flows. We consider a granular assembly that is subjected to simple shear and harmonic vibration at the boundary. This configuration allows us to isolate the effects of vibration, as parameterized by granular temperature. We find that friction is reduced due to local velocity fluctuations of grains. All data obey a local rheology that relates the material friction coefficient, the granular temperature, and the dimensionless shear rate. We also observe that reduction in material friction due to granular temperature is associated with reduction in fabric anisotropy. We demonstrate that the temperature can be modeled by a heat equation with dissipation with appropriate boundary conditions, which provides complete closure of the system and allows a fully local continuum description of sheared, vibrated granular flows. This success suggests local rheology based on temperature, as suggested previously, combined with the new, empirical heat diffusion equation may provide a general strategy for dense granular flows.

Here we theoretically and computationally study the frequency dependence of phase speed and attenuation for marine sediments from the perspective of granular mechanics. We leverage recent theoretical insights from the granular physics community as well as discrete-element method simulations, where the granular material is treated as a packing of discrete objects that interact via pairwise forces. These pairwise forces include both repulsive contact forces as well as dissipative terms which may include losses from the fluid as well as losses from inelasticity at grain-grain contacts. We show that the structure of disordered granular packings leads to anomalous scaling laws for frequency-dependent phase speed and attenuation that do not follow from a continuum treatment. Our results demonstrate that granular packing structure, which is not explicitly considered in existing models, may play a crucial role in a complete theory of sediment acoustics. While this simple approach does not explicitly treat sound propagation or inertial effects in the interstitial fluid, it provides a starting point for future models that include these and other more complex features., Comment: Accepted for publication in the Journal of the Acoustical Society of America

This research paper explores ways to apply Federated Learning (FL) and Differential Privacy (DP) techniques to population-scale Electrocardiogram (ECG) data. The study learns a multi-label ECG classification model using FL and DP based on 1,565,849 ECG tracings from 7 hospitals in Alberta, Canada. The FL approach allowed collaborative model training without sharing raw data between hospitals while building robust ECG classification models for diagnosing various cardiac conditions. These accurate ECG classification models can facilitate the diagnoses while preserving patient confidentiality using FL and DP techniques. Our results show that the performance achieved using our implementation of the FL approach is comparable to that of the pooled approach, where the model is trained over the aggregating data from all hospitals. Furthermore, our findings suggest that hospitals with limited ECGs for training can benefit from adopting the FL model compared to single-site training. In addition, this study showcases the trade-off between model performance and data privacy by employing DP during model training. Our code is available at https://github.com/vikhyatt/Hospital-FL-DP., Comment: Accepted for ICMHI 2024

Machine learning has the potential to revolutionize passive acoustic monitoring (PAM) for ecological assessments. However, high annotation and compute costs limit the field's efficacy. Generalizable pretrained networks can overcome these costs, but high-quality pretraining requires vast annotated libraries, limiting its current applicability primarily to bird taxa. Here, we identify the optimum pretraining strategy for a data-deficient domain using coral reef bioacoustics. We assemble ReefSet, a large annotated library of reef sounds, though modest compared to bird libraries at 2% of the sample count. Through testing few-shot transfer learning performance, we observe that pretraining on bird audio provides notably superior generalizability compared to pretraining on ReefSet or unrelated audio alone. However, our key findings show that cross-domain mixing which leverages bird, reef and unrelated audio during pretraining maximizes reef generalizability. SurfPerch, our pretrained network, provides a strong foundation for automated analysis of marine PAM data with minimal annotation and compute costs., Comment: 18 pages, 5 figures

Understanding the characteristics of swarming autonomous agents is critical for defense and security applications. This article presents a study on using supervised neural network time series classification (NN TSC) to predict key attributes and tactics of swarming autonomous agents for military contexts. Specifically, NN TSC is applied to infer two binary attributes - communication and proportional navigation - which combine to define four mutually exclusive swarm tactics. We identify a gap in literature on using NNs for swarm classification and demonstrate the effectiveness of NN TSC in rapidly deducing intelligence about attacking swarms to inform counter-maneuvers. Through simulated swarm-vs-swarm engagements, we evaluate NN TSC performance in terms of observation window requirements, noise robustness, and scalability to swarm size. Key findings show NNs can predict swarm behaviors with 97% accuracy using short observation windows of 20 time steps, while also demonstrating graceful degradation down to 80% accuracy under 50% noise, as well as excellent scalability to swarm sizes from 10 to 100 agents. These capabilities are promising for real-time decision-making support in defense scenarios by rapidly inferring insights about swarm behavior., Comment: Added funding acknowledgment and author bios

Functional Differential Equations (FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equation), and statistical physics. Despite their significance, computing solutions to FDEs remains a longstanding challenge in mathematical physics. In this paper we address this challenge by introducing new approximation theory and high-performance computational algorithms designed for solving FDEs on tensor manifolds. Our approach involves approximating FDEs using high-dimensional partial differential equations (PDEs), and then solving such high-dimensional PDEs on a low-rank tensor manifold leveraging high-performance parallel tensor algorithms. The effectiveness of the proposed approach is demonstrated through its application to the Burgers-Hopf FDE, which governs the characteristic functional of the stochastic solution to the Burgers equation evolving from a random initial state., Comment: 16 pages, 7 figures

Existing activity tracker datasets for human activity recognition are typically obtained by having participants perform predefined activities in an enclosed environment under supervision. This results in small datasets with a limited number of activities and heterogeneity, lacking the mixed and nuanced movements normally found in free-living scenarios. As such, models trained on laboratory-style datasets may not generalise out of sample. To address this problem, we introduce a new dataset involving wrist-worn accelerometers, wearable cameras, and sleep diaries, enabling data collection for over 24 hours in a free-living setting. The result is CAPTURE-24, a large activity tracker dataset collected in the wild from 151 participants, amounting to 3883 hours of accelerometer data, of which 2562 hours are annotated. CAPTURE-24 is two to three orders of magnitude larger than existing publicly available datasets, which is critical to developing accurate human activity recognition models.

In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions made by several collegues. The treatment is restricted to contractible spacetimes of globally hyperbolic nature in dimensions $d\ge 4$. In particular, we construct the classical M{\o}ller maps intertwining the configuration spaces of charged and uncharged fermions. In the last part, as a first step towards a quantization of the theory, we explore the combination of the classical M{\o}ller maps with Hadamard bidistributions and prove that they are involutive isomorphisms (algebraically and topologically) between suitable (formal) algebras of functionals (observables) over the configuration spaces of charged and uncharged Dirac fields.

In this paper, we explore the challenges inherent to Large Language Models (LLMs) like GPT-4, particularly their propensity for hallucinations, logic mistakes, and incorrect conclusions when tasked with answering complex questions. The capacity of LLMs to present erroneous answers in a coherent and semantically rigorous manner further complicates the detection of factual inaccuracies. This issue is especially pronounced in fields that require specialized expertise. Our work delves into these challenges, aiming to enhance the understanding and mitigation of such errors, thereby contributing to the improvement of LLM accuracy and reliability in scientific and other specialized domains. Our findings reveal a non-linear relationship between the context's relevancy and the answers' measured quality. In addition, we demonstrate that with the correct calibration, it is possible to automate the grading procedure -- a finding suggesting that, at least to some degree, the LLMs can be used to self-examine the quality of their own performance. Finally, we describe an experimental platform that can be seen as a proof-of-concept of the techniques described in this work., Comment: 11 pages, 6 figures, 4 tables, 3 pages of supplementary material

We have demonstrated three 4x2 hot electron bolometer (HEB) mixer arrays for operation at local oscillator (LO) frequencies of 1.46, 1.9 and 4.7 THz, respectively. They consist of spiral antenna coupled NbN HEB mixers combined with elliptical lenses. These are to date the highest pixel count arrays using a quasi-optical coupling scheme at supra-THz frequencies. At 1.4 THz, we measured an average double sideband mixer noise temperature of 330 K, a mixer conversion loss of 5.7 dB, and an optimum LO power of 210 nW. The array at 1.9 THz has an average mixer noise temperature of 420K, a conversion loss of 6.9 dB, and an optimum LO power of 190 nW. For the array at 4.7 THz, we obtained an average mixer noise temperature of 700 K, a conversion loss of 9.7 dB, and an optimum LO power of 240 nW. We found the arrays to be uniform regarding the mixer noise temperature with a standard deviation of 3-4%, the conversion loss with a standard deviation of 7-10%, and optimum LO power with a standard deviation of 5-6%. The noise bandwidth was also measured, being 3.5 GHz for the three arrays. These performances are comparable to previously reported values in the literature for single pixels and also other detector arrays. Our arrays meet the requirements of the Galactic/Extra-Galactic ULDB Spectroscopic Terahertz Observatory (GUSTO), a NASA balloon borne observatory, and are therefore scheduled to fly as part of the payload, which is expected to be launched in December 2023.

In this work we search for best practices in pre-processing of Electrocardiogram (ECG) signals in order to train better classifiers for the diagnosis of heart conditions. State of the art machine learning algorithms have achieved remarkable results in classification of some heart conditions using ECG data, yet there appears to be no consensus on pre-processing best practices. Is this lack of consensus due to different conditions and architectures requiring different processing steps for optimal performance? Is it possible that state of the art deep-learning models have rendered pre-processing unnecessary? In this work we apply down-sampling, normalization, and filtering functions to 3 different multi-label ECG datasets and measure their effects on 3 different high-performing time-series classifiers. We find that sampling rates as low as 50Hz can yield comparable results to the commonly used 500Hz. This is significant as smaller sampling rates will result in smaller datasets and models, which require less time and resources to train. Additionally, despite their common usage, we found min-max normalization to be slightly detrimental overall, and band-passing to make no measurable difference. We found the blind approach to pre-processing of ECGs for multi-label classification to be ineffective, with the exception of sample rate reduction which reliably reduces computational resources, but does not increase accuracy.

Atom arrangement plays a critical role in determining material properties. It is, therefore, essential for materials science and engineering to identify and characterize distinct atom configurations. Currently, crystal structures can be determined either by its static properties or by quantifying its structural evolution. Here we show how to classify an atom into phase solely by its speed dynamics. We model silicon crystals at different phase transition points and use a single atom speed trajectory to demonstrate that crystal-structure-independent Maxwell distribution of speed is generated by crystal-structure-dependent atom dynamics. As the classification accuracy of the method increases with trajectory length, we show that subtle difference in local atomic structures can be identified using sufficiently long trajectories. Thanks to symbolization of atom dynamics, the method is computationally efficient and suitable for an analysis of large datasets on the fly.

Video game development increasingly relies on using visual programming languages as the primary way to build video game features. The aim of using visual programming is to move game logic into the hands of game designers, who may not be as well versed in textual coding. In this paper, we empirically observe that there are more defect-inducing commits containing visual code than textual code in a AAA video game project codebase. This indicates that the existing textual code Just-in-Time (JIT) defect prediction models under evaluation by Electronic Arts (EA) may be ineffective as they do not account for changes in visual code. Thus, we focus our research on constructing visual code defect prediction models that encompass visual code metrics and evaluate the models against defect prediction models that use language agnostic features, and textual code metrics. We test our models using features extracted from the historical codebase of a AAA video game project, as well as the historical codebases of 70 open source projects that use textual and visual code. We find that defect prediction models have better performance overall in terms of the area under the ROC curve (AUC), and Mathews Correlation Coefficient (MCC) when incorporating visual code features for projects that contain more commits with visual code than textual code., Comment: ICSME 2023

Defects, or bugs, often form during software development. Identifying the root cause of defects is essential to improve code quality, evaluate testing methods, and support defect prediction. Examples of defect-inducing changes can be found using the SZZ algorithm to trace the textual history of defect-fixing changes back to the defect-inducing changes that they fix in line-based code. The line-based approach of the SZZ method is ineffective for visual code that represents source code graphically rather than textually. In this paper we adapt SZZ for visual code and present the "SZZ Visual Code" (SZZ-VC) algorithm, that finds changes in visual code based on the differences of graphical elements rather than differences of lines to detect defect-inducing changes. We validated the algorithm for an industry-made AAA video game and 20 music visual programming defects across 12 open source projects. Our results show that SZZ-VC is feasible for detecting defects in visual code for 3 different visual programming languages., Comment: ICSME 2023

We characterize learnability for quantum measurement classes by establishing matching necessary and sufficient conditions for their PAC learnability, along with corresponding sample complexity bounds, in the setting where the learner is given access only to prepared quantum states. We first probe the results from previous works on this setting. We show that the empirical risk defined in previous works and matching the definition in the classical theory fails to satisfy the uniform convergence property enjoyed in the classical setting for some learnable classes. Moreover, we show that VC dimension generalization upper bounds in previous work are frequently infinite, even for finite-dimensional POVM classes. To surmount the failure of the standard ERM to satisfy uniform convergence, we define a new learning rule -- denoised ERM. We show this to be a universal learning rule for POVM and probabilistically observed concept classes, and the condition for it to satisfy uniform convergence is finite fat shattering dimension of the class. We give quantitative sample complexity upper and lower bounds for learnability in terms of finite fat-shattering dimension and a notion of approximate finite partitionability into approximately jointly measurable subsets, which allow for sample reuse. We then show that finite fat shattering dimension implies finite coverability by approximately jointly measurable subsets, leading to our matching conditions. We also show that every measurement class defined on a finite-dimensional Hilbert space is PAC learnable. We illustrate our results on several example POVM classes., Comment: 33 pages

The dominant theories of rational choice assume logical omniscience. That is, they assume that when facing a decision problem, an agent can perform all relevant computations and determine the truth value of all relevant logical/mathematical claims. This assumption is unrealistic when, for example, we offer bets on remote digits of pi or when an agent faces a computationally intractable planning problem. Furthermore, the assumption of logical omniscience creates contradictions in cases where the environment can contain descriptions of the agent itself. Importantly, strategic interactions as studied in game theory are decision problems in which a rational agent is predicted by its environment (the other players). In this paper, we develop a theory of rational decision making that does not assume logical omniscience. We consider agents who repeatedly face decision problems (including ones like betting on digits of pi or games against other agents). The main contribution of this paper is to provide a sensible theory of rationality for such agents. Roughly, we require that a boundedly rational inductive agent tests each efficiently computable hypothesis infinitely often and follows those hypotheses that keep their promises of high rewards. We then prove that agents that are rational in this sense have other desirable properties. For example, they learn to value random and pseudo-random lotteries at their expected reward. Finally, we consider strategic interactions between different agents and prove a folk theorem for what strategies bounded rational inductive agents can converge to., Comment: In Proceedings TARK 2023, arXiv:2307.04005