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Over the last decade the gradient flow formalism became an important tool for lattice simulations of Quantum Chromodynamics. It offers remarkable renormalization properties which pave the way for cross-fertilization between perturbative and…

Many image-based perception tasks can be formulated as detecting, associating and tracking semantic keypoints, e.g., human body pose estimation and tracking. In this work, we present a general framework that jointly detects and forms…

This paper reveals that a common and central role, played in many error bound (EB) conditions and a variety of gradient-type methods, is a residual measure operator. On one hand, by linking this operator with other optimality measures, we…

Gradient pattern analysis (GPA) is a well-established technique for measuring gradient bilateral asymmetries of a square numerical lattice. This paper introduces an improved version of GPA designed for galaxy morphometry. We show the…

A new complexity measure named as Lattice Complexity is presented for finite symbolic sequences. This measure is based on the symbolic dynamics of one-dimensional iterative maps and Lempel-Ziv Complexity. To make Lattice Complexity…

The GEFF - the Gradient Expansion Formalism Factory - is a new Python package designed to study gauge-field production during inflation. The package provides a framework to implement and use the gradient expansion formalism (GEF), a…

The rapid evolution of network services demands new paradigms for studying and designing networks. In order to understand the underlying mechanisms that provide network functions, we propose a framework which enables the functional analysis…

Static timing analysis is a crucial stage in the VLSI design flow that verifies the timing correctness of circuits. Timing analysis depends on the placement and routing of the design, but at the same time, placement and routing efficiency…

When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…

A method for classification of complex time series using coarse-grained entropy rates (CER's) is presented. The CER's, which are computed from information-theoretic functionals -- redundancies, are relative measures of regularity and…

A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…

Three quantitative measures of the spatiotemporal behavior of the coupled map lattices: reduced density matrix, reduced wave function, and an analog of particle number, have been introduced. They provide a quantitative meaning to the…

In a recent methodological paper, we showed how to learn chaotic dynamics along with the state trajectory from sequentially acquired observations, using local ensemble Kalman filters. Here, we more systematically investigate the possibility…

We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…

Modern machine learning approaches often prioritize performance at the cost of increased complexity, computational demands, and reduced interpretability. This paper introduces a novel framework that challenges this trend by reinterpreting…

In diagnosing neurological disorders from electroencephalography (EEG) data, foundation models such as Transformers have been employed to capture temporal dynamics. Additionally, Graph Neural Networks (GNNs) are critical for representing…

We introduce MoTIF, a mode-structured tensor framework for multi-parametric approximation, super-resolution, and temporal forecasting of high-dimensional unsteady systems. The methodology leverages High-Order Singular Value Decomposition…

This paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms. Leveraging these generalized entropies yields MD \& GEG…

Fine-grained action segmentation and recognition is an important yet challenging task. Given a long, untrimmed sequence of kinematic data, the task is to classify the action at each time frame and segment the time series into the correct…

The emergence of organized multiscale patterns resulting from convection is ubiquitous, observed throughout different cloud types. The reproduction of such patterns by general circulation models remains a challenge due to the complex nature…