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This paper proposes a hierarchical Bayesian multitask learning model that is applicable to the general multi-task binary classification learning problem where the model assumes a shared sparsity structure across different tasks. We derive a computationally efficient inference algorithm based on variational inference to approximate the posterior distribution. We demonstrate the potential of the new approach on various synthetic datasets and for predicting human health status based on microbiome profile. Our analysis incorporates data pooled from multiple microbiome studies, along with a comprehensive comparison with other benchmark methods. Results in synthetic datasets show that the proposed approach has superior support recovery property when the underlying regression coefficients share a common sparsity structure across different tasks. Our experiments on microbiome classification demonstrate the utility of the method in extracting informative taxa while providing well-calibrated predictions with uncertainty quantification and achieving competitive performance in terms of prediction metrics. Notably, despite the heterogeneity of the pooled datasets (e.g., different experimental objectives, laboratory setups, sequencing equipment, patient demographics), our method delivers robust results.

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and description often rely on specific knowledge of the parent object and its automorphisms. In many cases, questions of reproducibility and comparison arise. Here we present a categorical framework that addresses these questions. We prove that every characteristic structure is the image of a functor equipped with a natural transformation. This shifts the local description in the parent object to a global one in the ambient category. Through constructions in representation theory, such as tensor products, we can combine characteristic structure across multiple categories. Our results are constructive, stated in the language of a constructive type theory, which facilitates implementations in theorem checkers., Comment: 47 pages

Active matter systems, composed of self-propelled agents that convert energy into directed motion, exhibit a wide range of emergent behaviors, such as motility-induced phase separation, flocking, and swarming. These phenomena, observed across natural and engineered systems, hold immense potential for applications in programmable materials, directed assembly, and micro-robotics. However, precisely controlling their macroscopic continuum fields, e.g., density or flux, remains a significant challenge due to the complexity of multibody interactions and correlated particle dynamics. To address this challenge, we present a framework that combines physics-informed machine learning with Model Predictive Control. Our approach learns a closure model for complex particle interactions while incorporating known physical principles, resulting in an accurate predictive model suitable for real-time control. By integrating this model into a Model Predictive Control framework, we enable systematic optimization of control actions that can guide the system toward desired macroscopic behaviors. Through two illustrative examples, we showcase the versatility of the framework. First, we control the spatial distribution of particles by splitting them into two groups and dynamically juggling their densities. Second, we simultaneously control both the number density and the mean flux, guiding the latter to follow a prescribed sinusoidal profile. These results highlight the framework's potential to systematically control complex dynamics in active matter systems and provide a foundation for broader applications in programmable and adaptive materials.

Quantum computing (QC) is expected to solve incredibly difficult problems, including finding optimal solutions to combinatorial optimization problems. However, to date, QC alone is still far to demonstrate this capability except on small-sized problems. Hybrid approaches where QC and classical computing work together have shown the most potential for solving real-world scale problems. This work aims to show that we can enhance a classical optimization algorithm with QC so that it can overcome this limitation. We present a new hybrid quantum-classical tabu search (HQTS) algorithm to solve the capacitated vehicle routing problem (CVRP). Based on our prior work, HQTS leverages QC for routing within a classical tabu search framework. The quantum component formulates the traveling salesman problem (TSP) for each route as a QUBO, solved using D-Wave's Advantage system. Experiments investigate the impact of quantum routing frequency and starting solution methods. While different starting solution methods, including quantum-based and classical heuristics methods, it shows minimal overall impact. HQTS achieved optimal or near-optimal solutions for several CVRP problems, outperforming other hybrid CVRP algorithms and significantly reducing the optimality gap compared to preliminary research. The experimental results demonstrate that more frequent quantum routing improves solution quality and runtime. The findings highlight the potential of integrating QC within meta-heuristic frameworks for complex optimization in vehicle routing problems.

We demonstrate that scalable neuromorphic hardware can implement the finite element method, which is a critical numerical method for engineering and scientific discovery. Our approach maps the sparse interactions between neighboring finite elements to small populations of neurons that dynamically update according to the governing physics of a desired problem description. We show that for the Poisson equation, which describes many physical systems such as gravitational and electrostatic fields, this cortical-inspired neural circuit can achieve comparable levels of numerical accuracy and scaling while enabling the use of inherently parallel and energy-efficient neuromorphic hardware. We demonstrate that this approach can be used on the Intel Loihi 2 platform and illustrate how this approach can be extended to nontrivial mesh geometries and dynamics., Comment: Pre-publication submission

We introduce a novel framework for developing fully-automated trading model algorithms. Unlike the traditional approach, which is grounded in analytical complexity favored by most quantitative analysts, we propose a paradigm shift that embraces real-world complexity. This approach leverages key concepts relating to self-organization, emergence, complex systems theory, scaling laws, and utilizes an event-based reframing of time. In closing, we describe an example algorithm that incorporates the outlined elements, called the Delta Engine., Comment: 6 pages

Federated learning is a computing paradigm that enhances privacy by enabling multiple parties to collaboratively train a machine learning model without revealing personal data. However, current research indicates that traditional federated learning platforms are unable to ensure privacy due to privacy leaks caused by the interchange of gradients. To achieve privacy-preserving federated learning, integrating secure aggregation mechanisms is essential. Unfortunately, existing solutions are vulnerable to recently demonstrated inference attacks such as the disaggregation attack. This paper proposes TAPFed, an approach for achieving privacy-preserving federated learning in the context of multiple decentralized aggregators with malicious actors. TAPFed uses a proposed threshold functional encryption scheme and allows for a certain number of malicious aggregators while maintaining security and privacy. We provide formal security and privacy analyses of TAPFed and compare it to various baselines through experimental evaluation. Our results show that TAPFed offers equivalent performance in terms of model quality compared to state-of-the-art approaches while reducing transmission overhead by 29%-45% across different model training scenarios. Most importantly, TAPFed can defend against recently demonstrated inference attacks caused by curious aggregators, which the majority of existing approaches are susceptible to., Comment: The paper has been published in IEEE TDSC

We present the first general stability results for nonlinear offset-free model predictive control (MPC). Despite over twenty years of active research, the offset-free MPC literature has not shaken the assumption of closed-loop stability for establishing offset-free performance. In this paper, we present a nonlinear offset-free MPC design that is robustly stable with respect to the tracking errors, and thus achieves offset-free performance, despite plant-model mismatch and persistent disturbances. Key features and assumptions of this design include quadratic costs, differentiability of the plant and model functions, constraint backoffs at steady state, and a robustly stable state and disturbance estimator. We first establish nominal stability and offset-free performance. Then, robustness to state and disturbance estimate errors and setpoint and disturbance changes is demonstrated. Finally, the results are extended to sufficiently small plant-model mismatch. The results are illustrated by numerical examples., Comment: 55 pages, 4 figures

We consider the asymptotic stability of MPC under plant-model mismatch, considering primarily models where the origin remains a steady state despite mismatch. Our results differ from prior results on the inherent robustness of MPC, which guarantee only convergence to a neighborhood of the origin, the size of which scales with the magnitude of the mismatch. For MPC with quadratic costs, continuous differentiability of the system dynamics is sufficient to demonstrate exponential stability of the closed-loop system despite mismatch. For MPC with general costs, a joint comparison function bound and scaling condition guarantee asymptotic stability despite mismatch. The results are illustrated in both algebraic and engineering examples. The tools developed to establish these results can address the stability of offset-free MPC, an open and interesting question in the MPC research literature., Comment: 42 pages, 9 figures

We present a series of equations that track the total realized and unrealized profits and losses at any time, incorporating the spread. The resulting formalism is ideally suited to evaluate the performance of trading model algorithms.

We explore the potential of gravitational waves (GWs) to probe the pre-BBN era of the early universe, focusing on the effects of energy injection. Specifically, we examine a hidden sector alongside the Standard Model that undergoes a strong first-order phase transition (FOPT), producing a GW signal. Once the phase transition has completed, energy injection initiates reheating in the hidden sector, which positions the hidden sector field so that additional phase transitions can occur. This can result in a total of three distinct phase transitions with a unique three-peak GW spectrum. Among these transitions, the first and third are of the standard type, while the intermediate second transition is inverted, moving from a broken to an unbroken phase. Using polynomial potentials as a framework, we derive analytical relations among the phase transition parameters and the resulting GW spectrum. Our results indicate that the second and third transitions generate GWs with higher amplitudes than the first, with a peak frequency ratio differing by up to an order of magnitude. This three-peak GW spectrum is detectable by upcoming facilities such as LISA, BBO, and UDECIGO. Notably, the phenomenon is robust across various potentials and model parameters, suggesting that hidden sector GWs provide a powerful tool for exploring new physics scenarios in the pre-BBN era.

Novel devices and novel computing paradigms are key for energy efficient, performant future computing systems. However, designing devices for new applications is often time consuming and tedious. Here, we investigate the design and optimization of spin orbit torque and spin transfer torque magnetic tunnel junction models as the probabilistic devices for true random number generation. We leverage reinforcement learning and evolutionary optimization to vary key device and material properties of the various device models for stochastic operation. Our AI guided codesign methods generated different candidate devices capable of generating stochastic samples for a desired probability distribution, while also minimizing energy usage for the devices.

In this study, we propose a novel approach to uncover subgroup-specific and subgroup-common latent factors addressing the challenges posed by the heterogeneity of neurological and mental disorders, which hinder disease understanding, treatment development, and outcome prediction. The proposed approach, sparse Group Factor Analysis (GFA) with regularised horseshoe priors, was implemented with probabilistic programming and can uncover associations (or latent factors) among multiple data modalities differentially expressed in sample subgroups. Synthetic data experiments showed the robustness of our sparse GFA by correctly inferring latent factors and model parameters. When applied to the Genetic Frontotemporal Dementia Initiative (GENFI) dataset, which comprises patients with frontotemporal dementia (FTD) with genetically defined subgroups, the sparse GFA identified latent disease factors differentially expressed across the subgroups, distinguishing between "subgroup-specific" latent factors within homogeneous groups and "subgroup common" latent factors shared across subgroups. The latent disease factors captured associations between brain structure and non-imaging variables (i.e., questionnaires assessing behaviour and disease severity) across the different genetic subgroups, offering insights into disease profiles. Importantly, two latent factors were more pronounced in the two more homogeneous FTD patient subgroups (progranulin (GRN) and microtubule-associated protein tau (MAPT) mutation), showcasing the method's ability to reveal subgroup-specific characteristics. These findings underscore the potential of sparse GFA for integrating multiple data modalities and identifying interpretable latent disease factors that can improve the characterization and stratification of patients with neurological and mental health disorders., Comment: 38 pages, 14 figures

We consider neural networks (NNs) where the final layer is down-scaled by a fixed hyperparameter $\gamma$. Recent work has identified $\gamma$ as controlling the strength of feature learning. As $\gamma$ increases, network evolution changes from "lazy" kernel dynamics to "rich" feature-learning dynamics, with a host of associated benefits including improved performance on common tasks. In this work, we conduct a thorough empirical investigation of the effect of scaling $\gamma$ across a variety of models and datasets in the online training setting. We first examine the interaction of $\gamma$ with the learning rate $\eta$, identifying several scaling regimes in the $\gamma$-$\eta$ plane which we explain theoretically using a simple model. We find that the optimal learning rate $\eta^*$ scales non-trivially with $\gamma$. In particular, $\eta^* \propto \gamma^2$ when $\gamma \ll 1$ and $\eta^* \propto \gamma^{2/L}$ when $\gamma \gg 1$ for a feed-forward network of depth $L$. Using this optimal learning rate scaling, we proceed with an empirical study of the under-explored "ultra-rich" $\gamma \gg 1$ regime. We find that networks in this regime display characteristic loss curves, starting with a long plateau followed by a drop-off, sometimes followed by one or more additional staircase steps. We find networks of different large $\gamma$ values optimize along similar trajectories up to a reparameterization of time. We further find that optimal online performance is often found at large $\gamma$ and could be missed if this hyperparameter is not tuned. Our findings indicate that analytical study of the large-$\gamma$ limit may yield useful insights into the dynamics of representation learning in performant models., Comment: 33 Pages, 38 figures, preprint text corrected

We prove a strong form of the hot spots conjecture for a class of domains in $\mathbb{R}^d$ which are a natural generalization of the lip domains of Atar and Burdzy [J. Amer. Math. Soc. 17 (2004), 243-265] in dimension two, as well as for a class of symmetric domains in $\mathbb{R}^d$ generalizing the domains studied by Jerison and Nadirashvili [J. Amer. Math. Soc. 13 (2000), 741-772]. Our method of proof is based on studying a vector-valued Laplace operator whose spectrum contains the spectrum of the Neumann Laplacian. This proof is essentially variational and does not require tools from stochastic analysis, nor does it use deformation arguments. In particular, it contains a new proof of the main result of Jerison and Nadirashvili.

A tensor consists of data, $t$, equipped with a multilinear product $\langle t|u_1,\ldots, u_{\ell}\rangle$, called a tensor contraction. Each vector $u_a$ comes from a space $U_a$ called an axis (or mode), the output $\langle t|u_1,\ldots, u_{\ell}\rangle$ lies in a base space $U_0$. In applications, axes often function as linear models of input parameters to a multiparameter process. The tensor then models the complex ways these parameters interact to produce a vector in the base which models outcomes. Thus some linear methods become accessible on a nonlinear problem. Many applications of tensors use decompositions $U_a=X_{a,1}\oplus \cdots \oplus X_{a,k_a}$ with a prescribed subset $\Delta$ of coordinates $(i_0,i_1,\ldots, i_{\ell})$, $1\leq i_a\leq k_a$, where \[ (i_0,i_1,\ldots, i_{\ell})\not\in \Delta \qquad \Longrightarrow \qquad \langle t|X_{1,i_1},\ldots, X_{\ell,i_{\ell}}\rangle \leq \sum_{j\neq i_0} X_{0,j}. \] We call $\Delta$ a cluster pattern and observe that these generalize familiar structures such as echelon forms, block diagonalization, orthogonal, eigen, and singular value decompositions, and clustering more broadly. This article introduces a class of efficiently computable cluster patterns that emerge from an underlying Lie theory of multilinear maps. The new family generalizes known cluster patterns such as Tucker decompositions and block diagonal decompositions but also includes decompositions that approximate curves and surfaces. The latter patterns can capture properties of data categories that do not decompose into the types of disjoint clustering for which existing methods are designed., Comment: 17 pages, 8 figures

The purpose of this note is to summarize the arguments required to derive the results appearing in robust minmax control of linear dynamical systems using a quadratic stage cost. The main results required in robust minmax control are Corollary 19 and Proposition 20. Moreover, the solution to the trust-region problem given in Proposition 15 and Lemma 16 may be of more general interest.

The concept of time mostly plays a subordinate role in finance and economics. The assumption is that time flows continuously and that time series data should be analyzed at regular, equidistant intervals. Nonetheless, already nearly 60 years ago, the concept of an event-based measure of time was first introduced. This paper expands on this theme by discussing the paradigm of intrinsic time, its origins, history, and modern applications. Departing from traditional, continuous measures of time, intrinsic time proposes an event-based, algorithmic framework that captures the dynamic and fluctuating nature of real-world phenomena more accurately. Unsuspected implications arise in general for complex systems and specifically for financial markets. For instance, novel structures and regularities are revealed, otherwise obscured by any analysis utilizing equidistant time intervals. Of particular interest is the emergence of a multiplicity of scaling laws, a hallmark signature of an underlying organizational principle in complex systems. Moreover, a central insight from this novel paradigm is the realization that universal time does not exist; instead, time is observer-dependent, shaped by the intrinsic activity unfolding within complex systems. This research opens up new avenues for economic modeling and forecasting, paving the way for a deeper understanding of the invisible forces that guide the evolution and emergence of market dynamics and financial systems. An exciting and rich landscape of possibilities emerges within the paradigm of intrinsic time., Comment: 12 pages, 1 figure

This paper addresses the identification of models for offset-free model predictive control (MPC), where LTI models are augmented with (fictitious) uncontrollable integrating modes, called integrating disturbances. The states and disturbances are typically estimated with a Kalman filter. The disturbance estimates effectively provide integral control, so the quality of the disturbance model (and resulting filter) directly influences the control performance. We implement eigenvalue constraints to protect against undesirable filter behavior (unstable or marginally stable modes, high-frequency oscillations). Specifically, we consider the class of linear matrix inequality (LMI) regions for eigenvalue constraints. These LMI regions are open sets by default, so we introduce a barrier function method to create tightened, but closed, eigenvalue constraints. To solve the resulting nonlinear semidefinite program, we approximate it as a nonlinear program using a Cholesky factorization method that exploits known sparsity structures of semidefinite optimization variables and matrix inequalities. The algorithm is applied to real-world data taken from two physical systems: first, a low-cost benchmark temperature microcontroller suitable for classroom laboratories, and second, an industrial-scale chemical reactor at Eastman Chemical's plant in Kingsport, TN., Comment: 21 pages, 14 figures

Feedback driven massive outflows play a crucial role in galaxy evolution by regulating star formation and influencing the dynamics of surrounding media. Extracting outflow properties from spectral lines is a notoriously difficult process for a number of reasons, including the possibility that a substantial fraction of the outflow is carried by dense gas in a very narrow range in velocity. This gas can hide in spectra with insufficient resolution. Empirically motivated analysis based on the Apparent Optical Depth method, commonly used in the literature, neglects the contribution of this gas, and may therefore underestimate the true gas column density. More complex semi-analytical line transfer (e.g., SALT) models, on the other hand, allow for the presence of this gas by modeling the radial density and velocity of the outflows as power laws. Here we compare the two approaches to quantify the uncertainties in the inferences of outflow properties based on 1-D "down-the-barrel" using the UV spectra of the CLASSY galaxy sample. We find that empirical modeling may significantly underestimate the column densities relative to SALT analysis, particularly in the optically thick regime. We use simulations to show that the main reason for this discrepancy is the presence of large amount of dense material at low velocities, which can be hidden by the finite spectral resolution of the data. The SALT models in turn could over-estimate the column densities if the assumed power laws of the density profiles strong are not a property of actual outflows., Comment: Accepted to the Astrophysical Journal

Superradiance provides a unique opportunity for investigating dark sectors as well as primordial black holes, which themselves are candidates for dark matter over a wide mass range. Using axion-like particles as an example, we show that line signals emerging from a superradiated axion cloud combined with black hole Hawking radiation in extragalactic and galactic halos, along with microlensing observations lead to complementary constraints on parameter space combinations including the axion-photon coupling, axion mass, black hole mass, and its dark matter fraction, $f_{\rm PBH}$. For the asteroid mass range $\sim10^{16}-10^{22}~{\rm g}$, where primordial black holes can provide the totality of dark matter, we demonstrate that ongoing and upcoming observations such as SXI, JWST, and AMEGO-X will be sensitive to possible line and continuum signals, respectively, providing probes of previously inaccessible regions of $f_{\rm PBH}$ parameter space. Further complementarity from a stochastic gravitational-wave background emerging from the black hole formation mechanism is also considered., Comment: 6+3 pages, 6 figures; v2: matches published version

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean $E_1$ topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic $E_1$ topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches., Comment: 34 pages, 12 figures, 4 tables

Users often struggle with decision-making between two options (A vs B), as it usually requires time-consuming research across multiple web pages. We propose STRUM-LLM that addresses this challenge by generating attributed, structured, and helpful contrastive summaries that highlight key differences between the two options. STRUM-LLM identifies helpful contrast: the specific attributes along which the two options differ significantly and which are most likely to influence the user's decision. Our technique is domain-agnostic, and does not require any human-labeled data or fixed attribute list as supervision. STRUM-LLM attributes all extractions back to the input sources along with textual evidence, and it does not have a limit on the length of input sources that it can process. STRUM-LLM Distilled has 100x more throughput than the models with comparable performance while being 10x smaller. In this paper, we provide extensive evaluations for our method and lay out future directions for our currently deployed system.

We examine diagonal combs, a recently identified class of infinite metric graphs whose properties depend on one parameter. These graphs exhibit a fascinating regime where they possess infinite volume while maintaining purely discrete spectrum for the Neumann Laplacian. In this regime, we establish polynomial upper and lower bounds on the $k$-th eigenvalue, revealing that the eigenvalues grow at a rate strictly slower than quadratic. However, once the diagonal combs transition to finite volume, their growth accelerates to a quadratic rate. Our methodology involves employing spectral geometric principles tailored for metric graphs, complemented by deriving estimates for the $k$-th eigenvalue on compact metric graphs., Comment: 10 pages, 1 figure

The passive retroreflector arrays placed on the moon by Apollo 11, 14 and 15 astronauts continue to produce valuable Earth-Moon range measurements that enable high-precision tests of gravitational physics, as well as studies of geo- and selenophysics. The optical throughput of these retroreflectors has declined since their deployment, with an additional signal loss at full moon when the reflectors experience direct solar illumination. We show that the loss in return rate can be attributed to the accumulation of a thin layer of lunar dust on the surfaces of the corner cube retroreflectors. First, a careful analysis of the optical link budget for the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) experiment reveals that the lunar return rate is 15--20 times smaller than predicted, a deficit that can be explained by a reflector dust covering fraction of ${\sim} 50$\%. Second, range measurements taken during a lunar eclipse indicate that the solar illumination of the retroreflectors degrades their throughput by an additional factor of ${\sim}15$. Finally, a numerical simulation of heat transfer in dust-coated reflectors is able to model the resulting thermal lensing effect, in which thermal gradients in the retroreflectors degrade their far-field diffraction pattern. A comparison of this simulation to eclipse measurements finds a dust coverage fraction of ${\sim}50$%. Taken together, the link analysis, eclipse observations and thermal modeling support the claim that the retroreflectors are obscured by lunar dust, with both link budget and simulation independently finding the dust fraction to be $\sim$50%.