arXiv subjects

Masoud Ataei

Publications and source records attributed to Masoud Ataei.

At least 19 recordsLinked to original sources

arXiv2026

Lehmer Transform

The Lehmer transform encodes a positive dataset as a single analytic curve, the ratio of its power sums at consecutive orders read as a function of the order. As the order sweeps the real line the curve generates every location statistic between the sample extremes, and its logarithm is the unit increment of the free energy of an exponentially tilted ensemble; the statistical theory of the curve flows from that identity. The slope of the curve is a Jeffreys divergence, the arithmetic-geometric gap is a relative entropy, and multiplicativity over independent factors makes deconvolution of multiplicative noise a pointwise division. A quantitative rigidity theorem locates the frontier of identifiability at geometric growth of the curve, with resonant log-periodic families of distinct laws sharing one curve beyond it. The empirical curve is an exact re-coordinatization of the order statistic, hence minimal sufficient, and its influence function, exact leading bias and limit theory are developed in full. At heavy tails the curve undergoes a phase transition whose two knees, one unit apart, sit at the tail index and its unit shift, a whole-sample diagnostic complementing threshold-based estimators.

math.ST↗

arXiv2026

Fractality of the Schr\"odinger Density for Rough Data

The observable of the Talbot effect is the intensity behind the grating: the density of the evolving field, not the field itself. Its fractality was previously known only for step data with rational jumps. We prove the general case. For arbitrary real data of bounded variation with at least one jump, the density of the free Schr\"odinger evolution on the torus is fractal at almost every time, with graph of upper box dimension exactly three halves. Its critical Sobolev mass diverges logarithmically, at a rate given in closed form by Wiener's jump statistic of the datum and independent of the positions and phases of the jumps. The same rate is halved along time traces and doubled for the Airy flow, so the critical mass probes the dispersion relation. Transported by the rank calculus of derangetropy operators, the theory equips every probability law with a quantum carpet: Gauss-sum revivals on quantile cells at rational times, a universal fractal at almost every other. The spectral growth rate of a single measured intensity profile returns the jump content of the grating, a prediction open to test in optical and matter-wave interferometry.

math-ph↗

arXiv2026

Derangetropy Operators

A derangetropy operator reweighs a probability density by a fixed profile of its own cumulative distribution function, acting through ranks alone. We prove that these operators are precisely the transformations of absolutely continuous laws equivariant under monotone changes of variable, and that they compose through interval maps, making their dynamics exactly solvable: iteration condenses every law onto its median with a universal Koenigs limit law, the continuous flow is solvable in closed form with the Cauchy family as invariant hyperbolic manifold, and balanced against diffusion the distribution function obeys an overdamped sine-Gordon equation whose unique steady law, the hyperbolic secant, is a globally stable kink. A variational principle selects the canonical kernel, the squared ground state of the Dirichlet Laplacian on the unit interval, whose update is a Bayesian posterior costing exactly one bit for every law, and a unitary lift equips each law with an isospectral Sturm-Liouville system and a quantum carpet: a strong law of large numbers for the critical Sobolev mass, with sharp constant given by Wiener's jump statistic, proves the fractality of the Schr\"odinger density for arbitrary real bounded-variation data with a jump, previously known only for rational step data. A lift to the dual of the Virasoro algebra, at central charge one, a normalization, identifies laws with disconjugate Hill potentials, tails with conformal weights, and the Cauchy family with the exceptional orbit. Randomized phases yield an exact sampler and a multiplicative chaos, log-correlated in the weakly tempered regime; in several dimensions, dependence stratifies into a conserved interaction, a torsion driven by maximal correlation, and a flat Sinkhorn transport.

math.PR↗

arXiv2026

Capture, Shield, or Neutralize: Engagement-Aware Pursuit-Evasion

This paper introduces a hierarchical control architecture for multi-agent adversarial environments, decoupling strategic task planning from rigorous safety assurance. The system formulates pursuit-evasion as a zero-sum receding-horizon game, solved via an iterative minimax \acl{mpc} scheme. This allows pursuers to anticipate and block evader trajectories using transverse velocity penalties rather than relying on reactive heuristic formations. To guarantee collision-free operation without compromising the convexity of the \acl{mpc}, a discrete-time \acl{cbf} operates as an inner-loop safety filter. Through simulated experiments, we demonstrate the framework's adaptability. By simply altering the weights of the shared zero-sum payoff and \acl{cbf} constraints, the swarm can fluidly switch from aggressive pursuit-evasion tactics to strict perimeter defense and area denial, demonstrating robust performance across varying rules of engagement without structural changes to the control logic. The source code is available: https://github.com/ananya-ac/pursuit-evasion-mpc-cbf.

eess.SY↗

arXiv2025

Worst-Case Distance-Aware Error Bounds for Neural Networks

Safety-critical applications of machine learning require uncertainty estimates that support reliable worst-case analysis. Neural networks (NNs) provide expressive function approximation, while Gaussian processes (GPs) offer principled probabilistic uncertainty, but both face limitations in this setting: most modern neural architectures lack tractable worst-case error bounds, and Gaussian processes become computationally expensive at scale. For uncertainty to be interpretable, a central requirement is distance-awareness: that is, uncertainty increases with the distance between a test input and the nearest relevant training data. We present a general framework for worst-case distance-aware error bounds for NNs that combine dense layers with spline-based components. Our approach establishes error bounds that are both distance-aware, reflecting proximity of a test point to its nearest training data, and worst-case, providing deterministic guarantees under known Lipschitz constraints rather than probabilistic assumptions. Our algorithm, K-DAREK (Distance-Aware Error for Kurkova-Kolmogorov Networks), provides efficient and interpretable uncertainty quantification for NNs. K-DAREK is about four times faster and ten times more computationally efficient than an ensemble of KANs, 8.6 times more scalable than GP, eliminates up to 8.2% error-bound violation rate observed in DAREK, and reduces the average collision rate from 1.8% to 1.1% in the multi-agent safe control experiment. On high-dimensional real-world regression tasks (e.g., Real Estate Valuation), K-DAREK preserves distance-aware error bounds and achieves zero coverage violations, addressing the overgeneralization and inducing-point-coverage limitations exhibited by SNGP and DUE, respectively.

cs.LG↗

arXiv2025

Statistical Geometry and Information Dynamics on Hyperspherical Surfaces

We study the statistical geometry of random chords on n-dimensional spheres by deriving explicit analytical expressions for the chord length distribution and its associated structural properties. A critical threshold emerges at dimension 19, marking the transition from curvature-dominated variability to high-dimensional concentration, where interpoint distances become nearly deterministic and probabilistic diversity collapses into geometric uniformity. We further derive a closed-form expression for the Fisher information, showing that it is inversely proportional to the square of the radius and varies non-monotonically with dimension. Notably, it attains a minimum at dimension 7, coinciding with the dimension at which the volume of the unit sphere is maximized. This reflects a unique regime of maximal spatial diffuseness and minimal inferential sensitivity, arising from the interplay between weakening curvature and still-latent concentration. The alignment between volumetric and statistical extrema reveals a deeper duality between geometry and information. We also analyze the characteristic function, which exhibits a dichotomy: in even dimensions, it takes rational-exponential form, while in odd dimensions it involves Bessel and Struve functions. This distinction reflects differences in harmonic structure and boundary regularity across dimensions. Together, these findings show how curvature and dimension jointly regulate statistical efficiency on hyperspherical domains, with implications for geometric inference and high-dimensional learning.

math.PR↗

arXiv2025

Inferring Grain Size Distributions from Magnetic Hysteresis in M-type Hexaferrites

We develop a stochastic-dynamic framework to infer latent grain size distribution from magnetic hysteresis data in M-type hexaferrite materials, offering an alternative to imaging-based characterization. A stochastic nucleation-growth process yields a Modified Lognormal Power-law grain size distribution. This is combined with Brown's relation to obtain a coercivity probability distribution, which is embedded within a dynamic magnetization model. A key feature is the joint estimation of microstructural parameters, including the critical grain radius, through inverse optimization of full hysteresis loops. Experimental validation on hydrothermally synthesized strontium hexaferrite subjected to nitrogen treatment and recalcination reveals interpretable trajectories of nucleation, growth, and structural memory encoded in the magnetic response.

cond-mat.mtrl-sci↗

arXiv2025

Multiscale Causal Analysis of Market Efficiency via News Uncertainty Networks and the Financial Chaos Index

This study evaluates the scale-dependent informational efficiency of stock markets using the Financial Chaos Index, a tensor-eigenvalue-based measure of realized volatility. Incorporating Granger causality and network-theoretic analysis across a range of economic, policy, and news-based uncertainty indices, we assess whether public information is efficiently incorporated into asset price fluctuations. Based on a 34-year time period from 1990 to 2023, at the daily frequency, the semi-strong form of the Efficient Market Hypothesis is rejected at the 1\% level of significance, indicating that asset price changes respond predictably to lagged news-based uncertainty. In contrast, at the monthly frequency, such predictive structure largely vanishes, supporting informational efficiency at coarser temporal resolutions. A structural analysis of the Granger causality network reveals that fiscal and monetary policy uncertainties act as core initiators of systemic volatility, while peripheral indices, such as those related to healthcare and consumer prices, serve as latent bridges that become activated under crisis conditions. These findings underscore the role of time-scale decomposition and structural asymmetries in diagnosing market inefficiencies and mapping the propagation of macro-financial uncertainty.

q-fin.ST↗

arXiv2025

Modeling Regime Structure and Informational Drivers of Stock Market Volatility via the Financial Chaos Index

This paper investigates the structural dynamics of stock market volatility through the Financial Chaos Index, a tensor- and eigenvalue-based measure designed to capture realized volatility via mutual fluctuations among asset prices. Motivated by empirical evidence of regime-dependent volatility behavior and perceptual time dilation during financial crises, we develop a regime-switching framework based on the Modified Lognormal Power-Law distribution. Analysis of the FCIX from January 1990 to December 2023 identifies three distinct market regimes, low-chaos, intermediate-chaos, and high-chaos, each characterized by differing levels of systemic stress, statistical dispersion and persistence characteristics. Building upon the segmented regime structure, we further examine the informational forces that shape forward-looking market expectations. Using sentiment-based predictors derived from the Equity Market Volatility tracker, we employ an elastic net regression model to forecast implied volatility, as proxied by the VIX index. Our findings indicate that shifts in macroeconomic, financial, policy, and geopolitical uncertainty exhibit strong predictive power for volatility dynamics across regimes. Together, these results offer a unified empirical perspective on how systemic uncertainty governs both the realized evolution of financial markets and the anticipatory behavior embedded in implied volatility measures.

q-fin.ST↗

arXiv2025

Generalized Derangetropy Functionals for Modeling Cyclical Information Flow

This paper introduces a framework for modeling cyclical and feedback-driven information flow through a generalized family of entropy-modulated transformations called derangetropy functionals. Unlike scalar and static entropy measures such as Shannon entropy, these functionals act directly on probability densities and provide a topographical representation of information structure across the support of the distribution. The framework captures periodic and self-referential aspects of information distribution and encodes them through functional operators governed by nonlinear differential equations. When applied recursively, these operators induce a spectral diffusion process governed by the heat equation, leading to convergence toward a Gaussian characteristic function. This convergence theorem provides a unified analytical foundation for describing the long-term dynamics of information under cyclic modulation. The proposed framework offers new tools for analyzing the temporal evolution of information in systems characterized by periodic structure, stochastic feedback, and delayed interaction, with applications in artificial neural networks, communication theory, and non-equilibrium statistical mechanics.

cs.IT↗

arXiv2025

Mathematical Programming Models for Exact and Interpretable Formulation of Neural Networks

This paper presents a unified mixed-integer programming framework for training sparse and interpretable neural networks. We develop exact formulations for both fully connected and convolutional architectures by modeling nonlinearities such as ReLU activations through binary variables and encoding structural sparsity via filter- and layer-level pruning constraints. The resulting models integrate parameter learning, architecture selection, and structural regularization within a single optimization problem, yielding globally optimal solutions with respect to a composite objective that balances prediction accuracy, weight sparsity, and architectural compactness. The mixed-integer programming formulation accommodates piecewise-linear operations, including max pooling and activation gating, and permits precise enforcement of logic-based or domain-specific constraints. By incorporating considerations of interpretability, sparsity, and verifiability directly into the training process, the proposed framework bridges a range of research areas including explainable artificial intelligence, symbolic reasoning, and formal verification.

cs.AI↗

arXiv2025

Efficient and Interpretable Neural Networks Using Complex Lehmer Transform

We propose an efficient and interpretable neural network with a novel activation function called the weighted Lehmer transform. This new activation function enables adaptive feature selection and extends to the complex domain, capturing phase-sensitive and hierarchical relationships within data. Notably, it provides greater interpretability and transparency compared to existing machine learning models, facilitating a deeper understanding of its functionality and decision-making processes. We analyze the mathematical properties of both real-valued and complex-valued Lehmer activation units and demonstrate their applications in modeling nonlinear interactions. Empirical evaluations demonstrate that our proposed neural network achieves competitive accuracy on benchmark datasets with significantly improved computational efficiency. A single layer of real-valued or complex-valued Lehmer activation units is shown to deliver state-of-the-art performance, balancing efficiency with interpretability.

cs.LG↗

arXiv2025

Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty

We develop a new class of distance-aware error bounds that tightly characterize the approximation error of spline neural networks. Our bottom-up approach analyzes the error bound of each neuron (a spline) and then extends it to the full network. We begin with error bounds for Newton's polynomial, generalize them to arbitrary splines under higher-order Lipschitz continuity, and extend the result to function compositions, the core of deep networks such as Kolmogorov-Arnold networks. By analyzing error propagation through composed spline layers, we obtain error bounds for the entire network. These bounds are deterministic, do not rely on sampling or probabilistic assumptions, and hold under mild regularity conditions. We evaluate our method on object shape estimation from sparse laser scans and safe navigation in unstructured environments. Our method is faster than the Gaussian process and Monte Carlo approaches, and our bounds reliably enclose the true error. We also develop a metric for the distance-awareness of an uncertainty estimator and show that distance-aware uncertainty for Kolmogorov networks (DAREK) is distance-aware in more regions than the baselines.

eess.SP↗

arXiv2024

Derangetropy in Probability Distributions and Information Dynamics

We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides deeper insights into information dynamics governed by differential equations and equilibrium states. Through combinatorial justifications and empirical analysis, we demonstrate the utility of derangetropy in depicting distribution behavior and evolution, providing a new tool for analyzing complex and hierarchical systems in information theory.

cs.IT↗

arXiv2024

Omobot: a low-cost mobile robot for autonomous search and fall detection

Detecting falls among the elderly and alerting their community responders can save countless lives. We design and develop a low-cost mobile robot that periodically searches the house for the person being monitored and sends an email to a set of designated responders if a fall is detected. In this project, we make three novel design decisions and contributions. First, our custom-designed low-cost robot has advanced features like omnidirectional wheels, the ability to run deep learning models, and autonomous wireless charging. Second, we improve the accuracy of fall detection for the YOLOv8-Pose-nano object detection network by 6% and YOLOv8-Pose-large by 12%. We do so by transforming the images captured from the robot viewpoint (camera height 0.15m from the ground) to a typical human viewpoint (1.5m above the ground) using a principally computed Homography matrix. This improves network accuracy because the training dataset MS-COCO on which YOLOv8-Pose is trained is captured from a human-height viewpoint. Lastly, we improve the robot controller by learning a model that predicts the robot velocity from the input signal to the motor controller.

cs.RO↗

arXiv2024

DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety

Uncertainty-aware controllers that guarantee safety are critical for safety critical applications. Among such controllers, Control Barrier Functions (CBFs) based approaches are popular because they are fast, yet safe. However, most such works depend on Gaussian Processes (GPs) or MC-Dropout for learning and uncertainty estimation, and both approaches come with drawbacks: GPs are non-parametric methods that are slow, while MC-Dropout does not capture aleatoric uncertainty. On the other hand, modern Bayesian learning algorithms have shown promise in uncertainty quantification. The application of modern Bayesian learning methods to CBF-based controllers has not yet been studied. We aim to fill this gap by surveying uncertainty quantification algorithms and evaluating them on CBF-based safe controllers. We find that model variance-based algorithms (for example, Deep ensembles, MC-dropout, etc.) and direct estimation-based algorithms (such as DEUP) have complementary strengths. Algorithms in the former category can only estimate uncertainty accurately out-of-domain, while those in the latter category can only do so in-domain. We combine the two approaches to obtain more accurate uncertainty estimates both in- and out-of-domain. As measured by the failure rate of a simulated robot, this results in a safer CBF-based robot controller.

cs.RO↗

arXiv2021

Theory and Applications of Financial Chaos Index

We develop a new stock market index that captures the chaos existing in the market by measuring the mutual changes of asset prices. This new index relies on a tensor-based embedding of the stock market information, which in turn frees it from the restrictive value- or capitalization-weighting assumptions that commonly underlie other various popular indexes. We show that our index is a robust estimator of the market volatility which enables us to characterize the market by performing the task of segmentation with a high degree of reliability. In addition, we analyze the dynamics and kinematics of the realized market volatility as compared to the implied volatility by introducing a time-dependent dynamical system model. Our computational results which pertain to the time period from January 1990 to December 2019 imply that there exist a bidirectional causal relation between the processes underlying the realized and implied volatility of the stock market within the given time period, where it is shown that the later has a stronger causal effect on the former as compared to the opposite. This result connotes that the implied volatility of the market plays a key role in characterization of the market's realized volatility.

q-fin.ST↗

arXiv2019

A Geometrical Branch-and-Price (GEOM-BP) Algorithm for Big Bin Packing Problems

Bin packing problem examines the minimum number of identical bins needed to pack a set of items of various weights. This problem arises in various areas of the artificial intelligence demanding derivation of the exact solutions in the shortest amount of time. Employing branch-and-bound and column generation techniques to derive the exact solutions to this problem, usually requires designation of problem-specific branching rules compatible with the nature of the polluted pricing sub-problem of column generation. In this work, we present a new approach to deal with the forbidden bins which handles two-dimensional knapsack problems. Furthermore, a set of diving criteria are introduced which emphasize the importance of the geometrical features of the bins. It is further shown that efficiency of the column generation technique could significantly get improved using an implicit sectional pricing scheme. The proposed algorithm outperforms the current state-of-the-art algorithms in number of the benchmark instances solved in less than one minute.

math.OC↗