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arXiv:2507.15567v3 Announce Type: replace-cross Abstract: In this second work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations in general relativity with twisted Dirichlet boundary conditions on a finite timelike boundary. The boundary conditions consist of specification of the pointwise conformal class of the boundary metric, together with a scalar density involving a combination of the ..
arXiv:2508.14836v4 Announce Type: replace-cross Abstract: The space discreteness hypothesis asserts that the nature of space at short distances is radically different from that at large distances. Based on the Bronstein inequality, here, we use a totally disconnected topological space $\mathcal{X}$ as a model for the space. However, we consider the time as a real variable. In this framework, the formalism of Dirac-von Neumann can be used. ....
arXiv:2509.02293v2 Announce Type: replace-cross Abstract: In quantum gravity, the gravitational path integral involves a sum over topologies, representing the joining and splitting of multiple universes. To account for topology change, one is led to allow the creation and annihilation of closed and open universes in a framework often called third quantization or universe field theory. We argue that since topology change in gravity is a rar....
arXiv:2509.04631v2 Announce Type: replace-cross Abstract: Transductive conformal prediction addresses the simultaneous prediction for multiple data points. Given a desired confidence level, the objective is to construct a prediction set that includes the true outcomes with the prescribed confidence. We demonstrate a fundamental trade-off between confidence and efficiency in transductive methods, where efficiency is measured by the size of ....
arXiv:2509.05563v2 Announce Type: replace-cross Abstract: High-dimensional compositional data pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data, conventional approaches often rely on log-ratio transformations that compromise interpretability and distort the data through ad hoc zero replacements. To address these issues, we introduce a geomet....
arXiv:2510.03745v2 Announce Type: replace-cross Abstract: Low-discrepancy points are designed to efficiently fill the space in a uniform manner. This uniformity is highly advantageous in many problems in science and engineering, including in numerical integration, computer vision, machine perception, computer graphics, machine learning, and simulation. Whereas most previous low-discrepancy constructions rely on abstract algebra and number ....
arXiv:2510.27507v2 Announce Type: replace-cross Abstract: We study the stability of ground states in the Edwards-Anderson Ising spin glass in dimensions two and higher against perturbations of a single coupling. After reviewing the concepts of critical droplets, flexibilities and metastates, we show that, in any dimension, a certain kind of critical droplet with space-filling (i.e., positive spatial density) boundary does not exist in grou....
arXiv:2511.02165v4 Announce Type: replace-cross Abstract: Strongly nonlinear dynamics, from fluid turbulence to quantum chromodynamics, have long constituted some of the most challenging problems in theoretical physics. This review describes a unified theoretical framework, the loop space calculus, which offers an analytical approach to these problems. The central idea is a shift in perspective from pointwise fields to integrated loop obse....
arXiv:2511.03734v2 Announce Type: replace-cross Abstract: The Koopman operator and extended dynamic mode decomposition (EDMD) as a data-driven technique for its approximation have attracted considerable attention as a key tool for modeling, analysis, and control of complex dynamical systems. However, extensions towards control-affine systems resulting in bilinear surrogate models are prone to demanding data requirements rendering their app....
arXiv:2511.07438v3 Announce Type: replace-cross Abstract: Cryo-electron microscopy (cryo-EM) is a powerful imaging technique for reconstructing three-dimensional molecular structures from noisy tomographic projection images of randomly oriented particles. We introduce a new data fusion framework, termed the method of double moments (MoDM), which reconstructs molecular structures from two instances of the second-order moment of projection i....
arXiv:2511.14490v2 Announce Type: replace-cross Abstract: This paper considers multi-view imaging in a sixth-generation (6G) integrated sensing and communication network, which consists of a transmit base-station (BS), multiple receive BSs connected to a central processing unit (CPU), and multiple extended targets. Our goal is to devise an effective multi-view imaging technique that can jointly leverage the targets' echo signals at all the....
arXiv:2512.03267v2 Announce Type: replace-cross Abstract: In financial and actuarial research, distortion and Haezendonck-Goovaerts risk measures are attractive due to their strong properties. They have so far been treated separately. In this paper, following a suggestion by Goovaerts, Linders, Van Weert, and Tank, we introduce and study a new class of risk measure that encompasses the distortion and Haezendonck-Goovaerts risk measures, ap..
Symmetries in Sorting - arxiv.org - 1 month ago - eng
arXiv:2512.07349v2 Announce Type: replace-cross Abstract: Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions, they are functions on lists that perform combinatorial operations on the representation of the input list. In this paper, we study sorting algori....
arXiv:2512.07476v3 Announce Type: replace-cross Abstract: Patterns are words with terminals and variables. The language of a pattern is the set of words obtained by uniformly substituting all variables with words that contain only terminals. In their original definition, patterns only allow for multiple distinct occurrences of some variables to be related by the equality relation, represented by using the same variable multiple times. In a..
arXiv:2512.07842v2 Announce Type: replace-cross Abstract: The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in cortical recordings to the underlying dynamics responsible for their emergence. We present an effort to characterize the neural activity from the cortex of a mouse during natural sleep....
arXiv:2601.15880v3 Announce Type: replace-cross Abstract: The Mann-Whitney effect is an effect measure for the order of two sample-specific outcome variables. It has the interpretation of a probability and also a connection to the area under the ROC curve. In the literature it has been considered for both ordinal and right-censored time-to-event outcomes. For both cases, the present paper introduces a distribution-free regression model tha....
arXiv:2601.16884v3 Announce Type: replace-cross Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures remains challenging due to highly nonconvex and often ill-conditioned optimization landscapes. In contrast, for relatively shallow networks, mos....
arXiv:2601.18115v2 Announce Type: replace-cross Abstract: We study the problem of learning a single neuron under standard squared loss in the presence of arbitrary label noise and group-level distributional shifts, for a broad family of covariate distributions. Our goal is to identify a ''best-fit'' neuron parameterized by $\mathbf{w}_*$ that performs well under the most challenging reweighting of the groups. Specifically, we address a Gro....
arXiv:2602.03670v2 Announce Type: replace-cross Abstract: Equilibrium Propagation (EP) is a physics-inspired learning algorithm that uses stationary states of a dynamical system both for inference and learning. In its original formulation it is limited to conservative systems, $\textit{i.e.}$ to dynamics which derive from an energy function. Given their applications, it is important to extend EP to non-conservative systems, $\textit{i.e.}$....
arXiv:2602.03970v3 Announce Type: replace-cross Abstract: We study the statistical behavior of reasoning probes in a stylized model of iterative computation inspired by neural algorithmic reasoning. The underlying computation is given by a looped Boolean circuit whose graph is a perfect $\nu$-ary tree ($\nu\ge 2$), with outputs recursively fed back as inputs across computation rounds. A probe observes a sampled subset of internal nodes and....
arXiv:2602.05970v2 Announce Type: replace-cross Abstract: Neural scaling laws relate loss to model size in large language models (LLMs), yet depth and width may contribute to performance differently, requiring more detailed studies. Here, we quantify how depth affects loss via analysis of LLMs and toy residual networks. We find loss scales inversely proportional to depth in LLMs, probably due to functionally similar layers reducing error t..
arXiv:2602.10120v2 Announce Type: replace-cross Abstract: We provide a numerical method for computing solutions to a free boundary problem arising from the equilibrium state of a floating drop. This numerical method is based on a Newton's method for the underlying nonlinear boundary value problems, and at each iterative step a Chebyshev spectral collocation method is employed. The problems considered here are those that can be described by..
arXiv:2602.19126v2 Announce Type: replace-cross Abstract: We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets. Starting from the classical equivalence between ridge-regularized RF training and Bayesian inference with Gaussian priors and likelihoods, we replace the single prior and likelihood with $\epsilon$- and $\et....
arXiv:2602.21120v2 Announce Type: replace-cross Abstract: Hamiltonians ${\cal H}^{a}_k$ of new integrable systems associated with the integer rays $(1,a)$ (commutative subalgebras) of Ding-Iohara-Miki (DIM) algebra in the $N$-body representation are closely related to commuting twisted Cherednik Hamiltonians $\mathfrak{C}_i^{(a)}$, ${\cal H}^{a}_k = \sum_{i=1}^N (\mathfrak{C}_i^{(a)})^k$. Moreover, symmetric combinations of eigenfunctions ..
arXiv:2603.00781v2 Announce Type: replace-cross Abstract: Areostationary Mars orbit (AMO) satellites will play an important role in future expeditions to the Martian surface due to their strength as navigation and communication satellites. Perturbative forces experienced by an AMOR satellite will cause it to drift from its nominal orbit, necessitating station keeping. This note presents a novel approach to AMO station keeping that bridges ....
arXiv:2603.14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime. Based on one-step generative transport, the method learns an amortized neural operator whose pushforward of a Gaussian source approximates the posterior distribution conditioned on each new observation. We show that white-noise sources are incompatible with the function-space limit, a....
arXiv:2603.24170v3 Announce Type: replace-cross Abstract: At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific approaches to tackle the 6/49 lottery: probabilistic methods and combinatorial designs. The mathematical models developed herein can be modified and ..
arXiv:2603.29400v2 Announce Type: replace-cross Abstract: State-of-the-art optical wireless positioning (OWP) commonly reaches centimeter-level accuracy by depending on dense multi-light-emitting diodes (LED) infrastructures, photodiode (PD) arrays, or image-sensor receivers, incurring hardware complexity and deployment cost. This paper introduces a single beam-steered LED, single-PD OWP architecture that achieves three-dimensional (3D) lo....
arXiv:2604.05324v2 Announce Type: replace-cross Abstract: Statistical evaluation aims to estimate the generalization performance of a model using held-out i.i.d. test data sampled from the ground-truth distribution. In supervised learning settings such as classification, performance metrics such as error rate are well-defined, and test error reliably approximates population error given sufficiently large datasets. In contrast, evaluation i....
arXiv:2604.05676v2 Announce Type: replace-cross Abstract: We establish a correspondence between vortex equations on flat Riemann surfaces and harmonic spinors on the Nappi--Witten space, the group manifold of a central extension of the Euclidean group $SE(2)$. Vortex configurations lift naturally to this setting, producing explicit solutions of a twisted Dirac equation. Using the conformal flatness of the Nappi--Witten metric, these soluti..
arXiv:2604.16701v2 Announce Type: replace-cross Abstract: Efficient classical simulation has matured to a critical component of the quantum computing stack, driving hardware validation, algorithm design, benchmarking, and the study of structured quantum dynamics. Lie-algebraic simulation ($\mathfrak{g}$-sim) offers a compelling approach: it represents Heisenberg-picture dynamics in the adjoint space whose dimension is set by the dynamical ....
arXiv:2604.23765v3 Announce Type: replace-cross Abstract: We analyze the universal approximation property of Kolmogorov-Arnold Networks (KANs) in terms of their edge functions. If these functions are all affine, then universality clearly fails. How many non-affine functions are needed, in addition to affine ones, to ensure universality? We show that a single one suffices. More precisely, we prove that deep KANs in which all edge functions ....
arXiv:2605.00958v2 Announce Type: replace-cross Abstract: We develop a mesoscopic formulation of equilibrium statistical mechanics based on coarse-grained occupation-number sectors of one-particle phase space. A mesoscopic partition function is constructed by averaging the microscopic Hamiltonian over configurations compatible with a given occupation profile. The construction converges to the canonical Gibbs partition function in the fine-..
arXiv:2605.07818v2 Announce Type: replace-cross Abstract: The expectation--maximization (EM) algorithm combines global monotonicity, local linear convergence, and strong practical robustness, but these features are usually analyzed separately. Global descent is nonlinear, whereas local convergence is governed by the spectrum of the linearized EM map. How these two levels fit into a single dynamical picture has remained less transparent. W....
arXiv:2605.07934v2 Announce Type: replace-cross Abstract: We present a comprehensive Lefschetz thimble analysis of the one-dimensional Salpeter equation under a strong electric field. By treating the non-local square-root operator within the framework of algebraic analysis, we construct the full solution space, which includes relativistic generalizations of the Airy Ai and Bi functions and their negative-energy counterparts. Through a dire..
arXiv:2605.09382v2 Announce Type: replace-cross Abstract: The Linear Assignment Problem is a fundamental combinatorial optimization task where classical exact solvers ensure optimality but suffer from an $\mathcal{O}(N^{3})$ bottleneck, while recent neural approximations struggle with scalability and exactness. We propose a learning-augmented framework that accelerates exact solvers by predicting dual variables to warm-start the search, ba....
arXiv:2605.14432v2 Announce Type: replace-cross Abstract: We study far-field discrimination between one and two incoherent point sources in the singular regime of weak and closely spaced emitters. Under ideal alignment, spatial-mode demultiplexing (SPADE) attains the quantum-optimal large-sample Stein exponent, but the finite-photon behavior near the one-source boundary and the effect of realistic imperfections remain less understood. Usin....
arXiv:2605.15746v5 Announce Type: replace-cross Abstract: Privacy-preserving cryptocurrency exchanges alter what the pricing mechanism observes about order flow. We derive the unique linear Kyle equilibrium when a committed Bayesian market maker observes order flow perturbed by independent Gaussian privacy noise. The price-impact coefficient and informed-trader strategy rescale by reciprocal factors of the privacy parameter (one down, one ....
arXiv:2605.17628v2 Announce Type: replace-cross Abstract: Cardinality-constrained portfolio selection is routinely cast as a quadratic unconstrained binary optimization (QUBO) and submitted to a quantum processing unit (QPU) for direct annealing. We show that this standard penalty encoding is the binding constraint for direct-QPU execution on current D-Wave Pegasus and Zephyr hardware. Expanding the exact cardinality penalty contributes a ....
arXiv:2605.19706v4 Announce Type: replace-cross Abstract: Standard quantum mechanics is an idealisation based on infinite-precision objects: point states, exact probabilities, and sharp measurements. Yet every real experiment has finite resolution, and for macroscopic systems we never have access to the microscopic state. Following Heisenberg's call for a theory built only on observable quantities, and von Neumann's insight that a complete....
arXiv:2605.19742v4 Announce Type: replace-cross Abstract: We derive a closed-form bid-ask spread and welfare decomposition for the Glosten-Milgrom 1985 sequential-trading model when the market maker observes the trade direction perturbed by a binary flip channel of probability $\eta$ -- a natural information-theoretic model of privacy mechanisms acting on the direction signal. Under a committed Bayesian market-maker pricing rule, the equil....
arXiv:2605.20232v2 Announce Type: replace-cross Abstract: In this letter, we reveal a universal, very simple extremum seeking natural feedback law and mechanism that governs, adapts, and generates in real-time, optimized lift variations for successful energy gain flight in presence of wind shear. The introduced law/mechanism, which is computationally minimal and needs only sensory information of the wind or local energy rate (i.e., model-f....
arXiv:2605.21357v2 Announce Type: replace-cross Abstract: The incompressible Navier-Stokes equations contain viscous dissipation but no thermal noise. I show, using a topological argument based on Poincar\'e's lemma, that the fluctuation-dissipation relation for the full nonlinear dynamics can be derived without the linearisation or structural assumptions that all previous derivations require. The nonlinear convective term is Hamiltonian (....
arXiv:2605.23947v2 Announce Type: replace-cross Abstract: We introduce FLUID (Fountain LiqUId Delivery), a protocol that uses fountain coding and receiver feedback for low-latency delivery of data blocks over lossy networks. Idealized Automatic Repeat reQuest (ARQ) protocols are bandwidth-optimal, but must deliver every packet in a block and therefore can require additional rounds under packet loss. FLUID uses a controlled amount of slack ....
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