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We provide an explicit computation of the topological $K$-theory groups $K_*(C_r^*(\mathbb{Z}^n\rtimes \mathbb{Z}/m))$ of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}Z/m$ with $m$ square-free. We want to highlight the fact that we are not impossing any conditions on the $\Z/m$-action on $\mathbb{Z}^n$. This generalizes previous computations of L\"uck-Davis and Langer-L\"uck., Comment: 10 pages. Comments are welcome

State of the art reinforcement learning methods sometimes encounter unsafe situations. Identifying when these situations occur is of interest both for post-hoc analysis and during deployment, where it might be advantageous to call out to a human overseer for help. Efforts to gauge the criticality of different points in time have been developed, but their accuracy is not well established due to a lack of ground truth, and they are not designed to be easily interpretable by end users. Therefore, we seek to define a criticality framework with both a quantifiable ground truth and a clear significance to users. We introduce true criticality as the expected drop in reward when an agent deviates from its policy for n consecutive random actions. We also introduce the concept of proxy criticality, a low-overhead metric that has a statistically monotonic relationship to true criticality. Safety margins make these interpretable, when defined as the number of random actions for which performance loss will not exceed some tolerance with high confidence. We demonstrate this approach in several environment-agent combinations; for an A3C agent in an Atari Beamrider environment, the lowest 5% of safety margins contain 47% of agent losses; i.e., supervising only 5% of decisions could potentially prevent roughly half of an agent's errors. This criticality framework measures the potential impacts of bad decisions, even before those decisions are made, allowing for more effective debugging and oversight of autonomous agents., Comment: 17 pages, 10 figures. This work has been submitted to the IEEE for possible publication

In this paper, we study a fully-decentralized multi-agent policy evaluation problem, which is an important sub-problem in cooperative multi-agent reinforcement learning, in the presence of up to $f$ faulty agents. In particular, we focus on the so-called Byzantine faulty model with model poisoning setting. In general, policy evaluation is to evaluate the value function of any given policy. In cooperative multi-agent system, the system-wide rewards are usually modeled as the uniform average of rewards from all agents. We investigate the multi-agent policy evaluation problem in the presence of Byzantine agents, particularly in the setting of heterogeneous local rewards. Ideally, the goal of the agents is to evaluate the accumulated system-wide rewards, which are uniform average of rewards of the normal agents for a given policy. It means that all agents agree upon common values (the consensus part) and furthermore, the consensus values are the value functions (the convergence part). However, we prove that this goal is not achievable. Instead, we consider a relaxed version of the problem, where the goal of the agents is to evaluate accumulated system-wide reward, which is an appropriately weighted average reward of the normal agents. We further prove that there is no correct algorithm that can guarantee that the total number of positive weights exceeds $|\mathcal{N}|-f $, where $|\mathcal{N}|$ is the number of normal agents. Towards the end, we propose a Byzantine-tolerant decentralized temporal difference algorithm that can guarantee asymptotic consensus under scalar function approximation. We then empirically test the effective of the proposed algorithm., Comment: To appear in Proceedings of the 22nd International Symposium on Modeling and Optimization in Mobile, Ad hoc, and Wireless Networks (WiOpt 2024)

Recent advancements in Large Language Models (LLMs) are transforming biology, computer science, and many other research fields, as well as impacting everyday life. While transformer-based technologies are currently being deployed in biology, no available agentic system has been developed to tackle bioinformatics workflows. We present a prototype Bioinformatics Retrieval Augmented Data (BRAD) digital assistant. BRAD is a chatbot and agentic system that integrates a suite of tools to handle bioinformatics tasks, from code execution to online search. We demonstrate its capabilities through (1) improved question-and-answering with retrieval augmented generation (RAG), (2) the ability to run complex software pipelines, and (3) the ability to organize and distribute tasks in agentic workflows. We use BRAD for automation, performing tasks ranging from gene enrichment and searching the archive to automatic code generation for running biomarker identification pipelines. BRAD is a step toward autonomous, self-driving labs for digital biology., Comment: 49 pages, 3 tables, 12 figures

In this paper we study some algebraic properties of the rack structure as well as the representation theory of it, following the ideas given by M. Elhamdadi and E. M. Moutuou in \cite{Elhamdadi}. We establish a correspondence between the irreducible strong representations of a finite and connected rack with the irreducible representation of its finite enveloping group which allows to use techniques of the latter topic in the other setting.

Selective fruit harvesting is a challenging manipulation problem due to occlusions and clutter arising from plant foliage. A harvesting gripper should i) have a small cross-section, to avoid collisions while approaching the fruit; ii) have a soft and compliant grasp to adapt to different fruit geometry and avoid bruising it; and iii) be capable of rigidly holding the fruit tightly enough to counteract detachment forces. Previous work on fruit harvesting has primarily focused on using grippers with a single actuation mode, either suction or fingers. In this paper we present a compact robotic gripper that combines the benefits of both. The gripper first uses an array of compliant suction cups to gently attach to the fruit. After attachment, telescoping cam-driven fingers deploy, sweeping obstacles away before pivoting inwards to provide a secure grip on the fruit for picking. We present and analyze the finger design for both ability to sweep clutter and maintain a tight grasp. Specifically, we use a motorized test bed to measure grasp strength for each actuation mode (suction, fingers, or both). We apply a tensile force at different angles (0{\deg}, 15{\deg}, 30{\deg} and 45{\deg}), and vary the point of contact between the fingers and the fruit. We observed that with both modes the grasp strength is approximately 40 N. We use an apple proxy to test the gripper's ability to obtain a grasp in the presence of occluding apples and leaves, achieving a grasp success rate over 96% (with an ideal controller). Finally, we validate our gripper in a commercial apple orchard., Comment: 8 pages, 9 figures

The emergence of intelligence in large language models (LLMs) has inspired investigations into their integration into automata learning. This paper introduces the probabilistic Minimally Adequate Teacher (pMAT) formulation, which leverages a probabilistic oracle that could give persistent errors randomly during answering the membership queries for deterministic finite automata (DFA) learning. Given the tendency of LLMs to produce hallucinatory content, we have developed techniques to improve answer accuracy and ensure the correctness of the learned automata. We propose the $\mathtt{Discrimination}$ prompt as well as the $\mathtt{Verification}$ prompt and explore their advantages over common prompts. Additionally, we compare DFA learning performance between the TTT algorithm and common active learning algorithms. To address the exponential number of persistent errors, we implement a dynamic query cache refinement algorithm that identifies and corrects conflicting queries by combining the active and passive learning algorithms. The empirical results demonstrate the robustness and efficiency of our approach, providing a theoretical foundation for automata learning with LLMs in the loop.

Weather disaster related emergency operations pose a great challenge to air mobility in both aircraft and airport operations, especially when the impact is gradually approaching. We propose an optimized framework for adjusting airport operational schedules for such pre-disaster scenarios. We first, aggregate operational data from multiple airports and then determine the optimal count of evacuation flights to maximize the impacted airport's outgoing capacity without impeding regular air traffic. We then propose a novel Neural Network (NN) accelerated Genetic Algorithm(GA) for evacuation planning. Our experiments show that integration yielded comparable results but with smaller computational overhead. We find that the utilization of a NN enhances the efficiency of a GA, facilitating more rapid convergence even when operating with a reduced population size. This effectiveness persists even when the model is trained on data from airports different from those under test., Comment: 7 pages, 8 figures, ITSC 2024

This survey paper delves into the emerging and critical area of symbolic knowledge distillation in Large Language Models (LLMs). As LLMs like Generative Pre-trained Transformer-3 (GPT-3) and Bidirectional Encoder Representations from Transformers (BERT) continue to expand in scale and complexity, the challenge of effectively harnessing their extensive knowledge becomes paramount. This survey concentrates on the process of distilling the intricate, often implicit knowledge contained within these models into a more symbolic, explicit form. This transformation is crucial for enhancing the interpretability, efficiency, and applicability of LLMs. We categorize the existing research based on methodologies and applications, focusing on how symbolic knowledge distillation can be used to improve the transparency and functionality of smaller, more efficient Artificial Intelligence (AI) models. The survey discusses the core challenges, including maintaining the depth of knowledge in a comprehensible format, and explores the various approaches and techniques that have been developed in this field. We identify gaps in current research and potential opportunities for future advancements. This survey aims to provide a comprehensive overview of symbolic knowledge distillation in LLMs, spotlighting its significance in the progression towards more accessible and efficient AI systems., Comment: 21 pages, 7 figures

Let $p>3$ be a prime number. In this note, we calculate explicitly the unitary dual and the matrix coefficients of the Engel group over the $p$-adic integers $\mathcal{B}_4(\mathbb{Z}_p)$. We use this information to calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it defines a globally hypoelliptic operator on $\mathcal{B}_4$., Comment: arXiv admin note: substantial text overlap with arXiv:2401.07146

AI-enabled capabilities are reaching the requisite level of maturity to be deployed in the real world, yet do not always make correct or safe decisions. One way of addressing these concerns is to leverage AI control systems alongside and in support of human decisions, relying on the AI control system in safe situations while calling on a human co-decider for critical situations. We extend a methodology for adversarial explanations (AE) to state-of-the-art reinforcement learning frameworks, including MuZero. Multiple improvements to the base agent architecture are proposed. We demonstrate how this technology has two applications: for intelligent decision tools and to enhance training / learning frameworks. In a decision support context, adversarial explanations help a user make the correct decision by highlighting those contextual factors that would need to change for a different AI-recommended decision. As another benefit of adversarial explanations, we show that the learned AI control system demonstrates robustness against adversarial tampering. Additionally, we supplement AE by introducing strategically similar autoencoders (SSAs) to help users identify and understand all salient factors being considered by the AI system. In a training / learning framework, this technology can improve both the AI's decisions and explanations through human interaction. Finally, to identify when AI decisions would most benefit from human oversight, we tie this combined system to our prior art on statistically verified analyses of the criticality of decisions at any point in time., Comment: 19 pages, 12 figures

Combinatorial Optimization (CO) addresses many important problems, including the challenging Maximum Independent Set (MIS) problem. Alongside exact and heuristic solvers, differentiable approaches have emerged, often using continuous relaxations of ReLU-based or quadratic objectives. Noting that an MIS in a graph is a Maximum Clique (MC) in its complement, we propose a new quadratic formulation for MIS by incorporating an MC term, improving convergence and exploration. We show that every maximal independent set corresponds to a local minimizer, derive conditions for the MIS size, and characterize stationary points. To solve our non-convex objective, we propose solving parallel multiple initializations using momentum-based gradient descent, complemented by an efficient MIS checking criterion derived from our theory. Therefore, we dub our method as parallelized Clique-Informed Quadratic Optimization for MIS (pCQO-MIS). Our experimental results demonstrate the effectiveness of the proposed method compared to exact, heuristic, sampling, and data-centric approaches. Notably, our method avoids the out-of-distribution tuning and reliance on (un)labeled data required by data-centric methods, while achieving superior MIS sizes and competitive runtime relative to their inference time. Additionally, a key advantage of pCQO-MIS is that, unlike exact and heuristic solvers, the runtime scales only with the number of nodes in the graph, not the number of edges.

This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it $N$-bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the $N$-bein behaves like a ``square root'' of the quantum geometric tensor. Using it, we present a quantum geometric tensor of two states that measures the possibility of moving from one state to another after two consecutive parameter variations. This new tensor determines the commutativity of such variations through its anti-symmetric part. In addition, we define a connection different from the Berry connection, and combining it with the $N$-bein allows us to introduce a notion of torsion and curvature \`{a} la Cartan that satisfies the Bianchi identities. Moreover, the torsion coincides with the anti-symmetric part of the two-state quantum geometric tensor previously mentioned, and thus, it is related to the commutativity of the parameter variations. We also describe our formalism using differential forms and discuss the possible physical interpretations of the new geometrical objects. Furthermore, we define different gauge invariants constructed from the geometrical quantities introduced in this work, resulting in new physical observables. Finally, we present two examples to illustrate these concepts: a harmonic oscillator and a generalized oscillator, both immersed in an electric field. We found that the new tensors quantify correlations between quantum states that were unavailable by other methods., Comment: 21 pages, 3 figures. Accepted version (Journal of Physics A: Mathematical and Theoretical)

Inverse reinforcement learning (IRL) is the problem of inferring a reward function from expert behavior. There are several approaches to IRL, but most are designed to learn a Markovian reward. However, a reward function might be non-Markovian, depending on more than just the current state, such as a reward machine (RM). Although there has been recent work on inferring RMs, it assumes access to the reward signal, absent in IRL. We propose a Bayesian IRL (BIRL) framework for inferring RMs directly from expert behavior, requiring significant changes to the standard framework. We define a new reward space, adapt the expert demonstration to include history, show how to compute the reward posterior, and propose a novel modification to simulated annealing to maximize this posterior. We demonstrate that our method performs well when optimizing according to its inferred reward and compares favorably to an existing method that learns exclusively binary non-Markovian rewards.

Jupiter's Grat Red Spot (GRS) is the largest and longest-lived vortex of all solar system planets but its lifetime is debated and its formation mechanism remains hidden. G. D. Cassini discovered in 1665 the presence of a dark oval at the GRS latitude, known as the "Permanent Spot" (PS) that was observed until 1713. We show from historical observations of its size evolution and motions that PS is unlikely to correspond to the current GRS, that was first observed in 1831. New numerical simulations rule out that the GRS formed by the merging of vortices or by a superstorm, but most likely formed from a flow disturbance between the two opposed Jovian zonal jets north and south of it. If so, the aearly GRS should have had a low tangential velocity so that its rotation velocity has increased over time as it shrunk.

Over the last ten years, the realm of Artificial Intelligence (AI) has experienced an explosion of revolutionary breakthroughs, transforming what seemed like a far-off dream into a reality that is now deeply embedded in our everyday lives. AI's widespread impact is revolutionizing virtually all aspects of human life, and software engineering (SE) is no exception. As we explore this changing landscape, we are faced with questions about what the future holds for SE and how AI will reshape the roles, duties, and methodologies within the field. The introduction of these groundbreaking technologies highlights the inevitable shift towards a new paradigm, suggesting a future where AI's capabilities may redefine the boundaries of SE, potentially even more than human input. In this paper, we aim at outlining the key elements that, based on our expertise, are vital for the smooth integration of AI into SE, all while preserving the intrinsic human creativity that has been the driving force behind the field. First, we provide a brief description of SE and AI evolution. Afterward, we delve into the intricate interplay between AI-driven automation and human innovation, exploring how these two components can work together to advance SE practices to new methods and standards.

This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and information retrieval. HDC employs high-dimensional vectors and efficient operators to encode and manipulate information, representing complex objects from atomic concepts. When one attempts to decode a hypervector that is the product (binding) of multiple hypervectors, the factorization becomes prohibitively costly with classical optimization-based methods and specialized recurrent networks, an inherent consequence of the binding operation. We propose HDQF, an innovative quantum computing approach, to address this challenge. By exploiting parallels between HDC and quantum computing and capitalizing on quantum algorithms' speedup capabilities, HDQF encodes potential factors as a quantum superposition using qubit states and bipolar vector representation. This yields a quadratic speedup over classical search methods and effectively mitigates Hypervector Factorization capacity issues., Comment: 8 pages, 7 figures

Background & Purpose: FLASH or ultra-high dose rate (UHDR) radiation therapy (RT) has gained attention in recent years for its ability to spare normal tissues relative to conventional dose rate (CDR) RT in various preclinical trials. However, clinical implementation of this promising treatment option has been limited because of the lack of availability of accelerators capable of delivering UHDR RT. We established a framework for the acceptance, commissioning, and periodic quality assurance (QA) of electron FLASH units and present an example of commissioning. Methods: A protocol for acceptance, commissioning, and QA of UHDR linear accelerators was established by combining and adapting standards and professional recommendations for standard linear accelerators based on the experience with UHDR at four clinical centers that use different UHDR devices. Non-standard dosimetric beam parameters considered included pulse width, pulse repetition frequency, dose per pulse, and instantaneous dose rate, together with recommendations on how to acquire these measurements. Results: The 6 and 9 MeV beams of an UHDR electron device were commissioned by using this developed protocol. Measurements were acquired with a combination of ion chambers, beam current transformers (BCTs), and dose rate independent passive dosimeters. The unit was calibrated according to the concept of redundant dosimetry using a reference setup. Conclusions: This study provides detailed recommendations for the acceptance testing, commissioning, and routine QA of low-energy electron UHDR linear accelerators. The proposed framework is not limited to any specific unit, making it applicable to all existing eFLASH units in the market. Through practical insights and theoretical discourse, this document establishes a benchmark for the commissioning of UHDR devices for clinical use., Comment: 22 Pages, 8 Figures

This paper presents Killkan, the first dataset for automatic speech recognition (ASR) in the Kichwa language, an indigenous language of Ecuador. Kichwa is an extremely low-resource endangered language, and there have been no resources before Killkan for Kichwa to be incorporated in applications of natural language processing. The dataset contains approximately 4 hours of audio with transcription, translation into Spanish, and morphosyntactic annotation in the format of Universal Dependencies. The audio data was retrieved from a publicly available radio program in Kichwa. This paper also provides corpus-linguistic analyses of the dataset with a special focus on the agglutinative morphology of Kichwa and frequent code-switching with Spanish. The experiments show that the dataset makes it possible to develop the first ASR system for Kichwa with reliable quality despite its small dataset size. This dataset, the ASR model, and the code used to develop them will be publicly available. Thus, our study positively showcases resource building and its applications for low-resource languages and their community., Comment: 11 pages, 9 tables, 3 figures, to be published in LREC-COLING 2024

This study uses advanced numerical methods to estimate the mean force potential (PMF) between charged, polarizable colloidal particles in dense electrolytes. We observe that when the Debye screening length, $\lambda_{\mathrm{D}}$, is below the hydrated ion size, the PMF shows discernible oscillations, contrasting with the expected decay in DLVO theory. Our findings provide evidence for the existence of anomalous underscreening in electrostatically stabilized suspensions, potentially having significant implications for our understanding of colloidal stability and the forces that govern the behavior of concentrated charged soft matter systems beyond DLVO theory.

Three-dimensional data registration is an established yet challenging problem that is key in many different applications, such as mapping the environment for autonomous vehicles, and modeling objects and people for avatar creation, among many others. Registration refers to the process of mapping multiple data into the same coordinate system by means of matching correspondences and transformation estimation. Novel proposals exploit the benefits of deep learning architectures for this purpose, as they learn the best features for the data, providing better matches and hence results. However, the state of the art is usually focused on cases of relatively small transformations, although in certain applications and in a real and practical environment, large transformations are very common. In this paper, we present ReLaTo (Registration for Large Transformations), an architecture that faces the cases where large transformations happen while maintaining good performance for local transformations. This proposal uses a novel Softmax pooling layer to find correspondences in a bilateral consensus manner between two point sets, sampling the most confident matches. These matches are used to estimate a coarse and global registration using weighted Singular Value Decomposition (SVD). A target-guided denoising step is then applied to both the obtained matches and latent features, estimating the final fine registration considering the local geometry. All these steps are carried out following an end-to-end approach, which has been shown to improve 10 state-of-the-art registration methods in two datasets commonly used for this task (ModelNet40 and KITTI), especially in the case of large transformations.

We provide an explicit computation of the cohomology groups (with untwisted coefficients) of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ free of squares, by means of formulas that only depend on $n$, $m$ and the action of $\mathbb{Z}/m$ on $\mathbb{Z}^n$. We want to highlight the fact that we are not impossing any conditions on the $\mathbb{Z}/m$-action on $\mathbb{Z}^n$, and as far as we know our formulas are the first in the literature in this generality. This generalizes previous computations of L\"uck-Davis and Adem-Ge-Pan-Petrosyan. In order to show that our formulas are usable, we develop a concrete example of the form $\mathbb{Z}^5\rtimes \mathbb{Z}/6$ where its cohomology groups are described in full detail.

Task-oriented object detection aims to find objects suitable for accomplishing specific tasks. As a challenging task, it requires simultaneous visual data processing and reasoning under ambiguous semantics. Recent solutions are mainly all-in-one models. However, the object detection backbones are pre-trained without text supervision. Thus, to incorporate task requirements, their intricate models undergo extensive learning on a highly imbalanced and scarce dataset, resulting in capped performance, laborious training, and poor generalizability. In contrast, we propose TaskCLIP, a more natural two-stage design composed of general object detection and task-guided object selection. Particularly for the latter, we resort to the recently successful large Vision-Language Models (VLMs) as our backbone, which provides rich semantic knowledge and a uniform embedding space for images and texts. Nevertheless, the naive application of VLMs leads to sub-optimal quality, due to the misalignment between embeddings of object images and their visual attributes, which are mainly adjective phrases. To this end, we design a transformer-based aligner after the pre-trained VLMs to re-calibrate both embeddings. Finally, we employ a trainable score function to post-process the VLM matching results for object selection. Experimental results demonstrate that our TaskCLIP outperforms the state-of-the-art DETR-based model TOIST by 3.5% and only requires a single NVIDIA RTX 4090 for both training and inference.

We propose two versions of radiative linear seesaw models, where electrically charged scalars and vector-like leptons generate the Dirac neutrino mass submatrix at one and two loop levels. In these models, the SM charged lepton masses are generated from a one loop level radiative seesaw mechanism mediated by charged exotic vector-like leptons and electrically neutral scalars running in the loops. These models can successfully accommodate the current amount of dark matter and baryon asymmetries observed in the Universe, as well as the muon anomalous magnetic moment., Comment: 25 pages, v2 contains enlarged discussion

Reinforcement Learning (RL) has made significant strides in enabling artificial agents to learn diverse behaviors. However, learning an effective policy often requires a large number of environment interactions. To mitigate sample complexity issues, recent approaches have used high-level task specifications, such as Linear Temporal Logic (LTL$_f$) formulas or Reward Machines (RM), to guide the learning progress of the agent. In this work, we propose a novel approach, called Logical Specifications-guided Dynamic Task Sampling (LSTS), that learns a set of RL policies to guide an agent from an initial state to a goal state based on a high-level task specification, while minimizing the number of environmental interactions. Unlike previous work, LSTS does not assume information about the environment dynamics or the Reward Machine, and dynamically samples promising tasks that lead to successful goal policies. We evaluate LSTS on a gridworld and show that it achieves improved time-to-threshold performance on complex sequential decision-making problems compared to state-of-the-art RM and Automaton-guided RL baselines, such as Q-Learning for Reward Machines and Compositional RL from logical Specifications (DIRL). Moreover, we demonstrate that our method outperforms RM and Automaton-guided RL baselines in terms of sample-efficiency, both in a partially observable robotic task and in a continuous control robotic manipulation task.

Double-core-hole (DCH) states in isolated water and heavy water molecules, resulting from the sequential absorption of two x-ray photons, have been investigated. A comparison of the subsequent Auger emission spectra from the two isotopes provides direct evidence of ultrafast nuclear motion during the 1.5 fs lifetime of these DCH states. Our numerical results align well with the experimental data, providing for various DCH states an in-depth study of the dynamics responsible of the observed isotope effect.

Our work addresses the problem of egocentric human pose estimation from downwards-facing cameras on head-mounted devices (HMD). This presents a challenging scenario, as parts of the body often fall outside of the image or are occluded. Previous solutions minimize this problem by using fish-eye camera lenses to capture a wider view, but these can present hardware design issues. They also predict 2D heat-maps per joint and lift them to 3D space to deal with self-occlusions, but this requires large network architectures which are impractical to deploy on resource-constrained HMDs. We predict pose from images captured with conventional rectilinear camera lenses. This resolves hardware design issues, but means body parts are often out of frame. As such, we directly regress probabilistic joint rotations represented as matrix Fisher distributions for a parameterized body model. This allows us to quantify pose uncertainties and explain out-of-frame or occluded joints. This also removes the need to compute 2D heat-maps and allows for simplified DNN architectures which require less compute. Given the lack of egocentric datasets using rectilinear camera lenses, we introduce the SynthEgo dataset, a synthetic dataset with 60K stereo images containing high diversity of pose, shape, clothing and skin tone. Our approach achieves state-of-the-art results for this challenging configuration, reducing mean per-joint position error by 23% overall and 58% for the lower body. Our architecture also has eight times fewer parameters and runs twice as fast as the current state-of-the-art. Experiments show that training on our synthetic dataset leads to good generalization to real world images without fine-tuning., Comment: Accepted in 3DV 2024

Let $p>2$ be a prime number. In this short note, we calculate explicitly the unitary dual and the matrix coefficients of the Heisenberg group over the $p$-adic integers. As an application, we consider directional Vladimirov-Taibleson derivatives, and some polynomials in these operators. In particular, we calculate explicitly the spectrum of the Vladimirov sub-Laplacian, and show how it provides a non-trivial example of a sub-elliptic operator on compact graded $p$-adic Lie groups.

We develop a computational method for modeling electrostatic interactions of arbitrarily-shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion electrolytes and nonionic solvents. Our method computes the nonuniform polarization charge distribution induced in a colloidal particle by both externally applied electric fields and local electric fields arising from other charged objects in the dispersion. This leads to expressions for electrostatic energies, forces, and torques that enable efficient molecular dynamics and Brownian dynamics simulations of colloidal dispersions in electrolytes, which can be harnessed to accurately predict structural and transport properties. We describe an implementation in which colloidal particles are modeled as rigid composites of small spherical beads that tessellate the surface of the particle. The electrostatics calculations are accelerated using a spectrally-accurate particle-mesh-Ewald technique implemented on a graphics processing unit (GPU) and regularized such that the electrostatic calculations are well-defined even for overlapping bodies. We demonstrate the effectiveness of this approach through a series of calculations, including the induced dipole moments and forces for one, two, and lattices of spherical colloids in an electric field; the induced dipole moment and torque for anisotropic particles in an electric field; the equilibrium distribution of ions in the double layer around charged colloids; the dynamics of charged colloids; and ions in the double layer around a polarizable colloid exposed to an electric field.

Neurosymbolic artificial intelligence (AI) is an emerging branch of AI that combines the strengths of symbolic AI and sub-symbolic AI. A major drawback of sub-symbolic AI is that it acts as a "black box", meaning that predictions are difficult to explain, making the testing & evaluation (T&E) and validation & verification (V&V) processes of a system that uses sub-symbolic AI a challenge. Since neurosymbolic AI combines the advantages of both symbolic and sub-symbolic AI, this survey explores how neurosymbolic applications can ease the V&V process. This survey considers two taxonomies of neurosymbolic AI, evaluates them, and analyzes which algorithms are commonly used as the symbolic and sub-symbolic components in current applications. Additionally, an overview of current techniques for the T&E and V&V processes of these components is provided. Furthermore, it is investigated how the symbolic part is used for T&E and V&V purposes in current neurosymbolic applications. Our research shows that neurosymbolic AI as great potential to ease the T&E and V&V processes of sub-symbolic AI by leveraging the possibilities of symbolic AI. Additionally, the applicability of current T&E and V&V methods to neurosymbolic AI is assessed, and how different neurosymbolic architectures can impact these methods is explored. It is found that current T&E and V&V techniques are partly sufficient to test, evaluate, verify, or validate the symbolic and sub-symbolic part of neurosymbolic applications independently, while some of them use approaches where current T&E and V&V methods are not applicable by default, and adjustments or even new approaches are needed. Our research shows that there is great potential in using symbolic AI to test, evaluate, verify, or validate the predictions of a sub-symbolic model, making neurosymbolic AI an interesting research direction for safe, secure, and trustworthy AI., Comment: 16 pages, 8 figures

We present a modular approach to \emph{reinforcement learning} (RL) in environments consisting of simpler components evolving in parallel. A monolithic view of such modular environments may be prohibitively large to learn, or may require unrealizable communication between the components in the form of a centralized controller. Our proposed approach is based on the assume-guarantee paradigm where the optimal control for the individual components is synthesized in isolation by making \emph{assumptions} about the behaviors of neighboring components, and providing \emph{guarantees} about their own behavior. We express these \emph{assume-guarantee contracts} as regular languages and provide automatic translations to scalar rewards to be used in RL. By combining local probabilities of satisfaction for each component, we provide a lower bound on the probability of satisfaction of the complete system. By solving a Markov game for each component, RL can produce a controller for each component that maximizes this lower bound. The controller utilizes the information it receives through communication, observations, and any knowledge of a coarse model of other agents. We experimentally demonstrate the efficiency of the proposed approach on a variety of case studies., Comment: This is the extended version of the paper accepted in the SRRAI Special Track at the Conference on Artificial Intelligence (AAAI-24)

In this work, we discuss the determination of the distance to the Large Magellanic Cloud (LMC) using the Leavitt Law, utilizing the public catalog of Classical Cepheid Variable stars from the observational project OGLE-IV (The Optical Gravitational Lensing Experiment Collection of Variable Stars), consisting of 4709 stars in the Large Magellanic Cloud. To determine the pulsation period of Cepheid Variable stars, we employ the computational algorithm \textit{Lomb-Scargle periodogram} modified for our data. Additionally, with the calculation of the period, we can derive a period-luminosity relation for Cepheid Variables in the Large Magellanic Cloud and, using an independent calibration distance, deduce their distance moduli. We also discuss some general theoretical concepts of the physical mechanism behind the oscillation of variable stars., Comment: in Portuguese language