相关论文: Complex Entropic Forms for Gradient Pattern Analys…
We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution,…
We introduce the Graded Transformer framework, a new class of sequence models that embeds algebraic inductive biases through grading transformations on vector spaces. Extending Graded Neural Networks (GNNs), we propose two architectures:…
We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even…
The Dynamical Graph Grammar (DGG) formalism can describe complex system dynamics with graphs that are mapped into a master equation. An exact stochastic simulation algorithm may be used, but it is slow for large systems. To overcome this…
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell…
We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for one-loop diagrams resulting from the exchange of both heavy and light fields,…
The general framework of Entropic Dynamics (ED) is used to construct non-relativistic models of relational quantum mechanics from well known inference principles -- probability, entropy and information geometry. Although only partially…
Topological entropy or spatial entropy is a way to measure the complexity of shift spaces. This study investigates the relationships between the spatial entropy and the various periodic entropies which are computed by skew-coordinated…
We propose entropic order parameters that capture the physics of generalized symmetries and phases in QFT's. We do it through an analysis of simple properties (additivity and Haag duality) of the net of operator algebras attached to…
Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP) / maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods…
Electrocardiogram (ECG) analysis plays a crucial role in diagnosing cardiovascular diseases, but accurate interpretation of these complex signals remains challenging. This paper introduces a novel multimodal framework(GAF-FusionNet) for ECG…
Empirical Mode Decomposition(EMD) is an adaptive data analysis technique for analyzing nonlinear and nonstationary data[1]. EMD decomposes the original data into a number of Intrinsic Mode Functions(IMFs)[1] for giving better physical…
L\'evy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. We propose an essentially asymptotically efficient estimation method for the system parameters of…
Uncertainty in past lifetime distributions and the timing of inactivity in systems and their components can be effectively measured using the fractional generalized cumulative past entropy (FGCPE) and its dynamic extension (DFGCPE),…
This paper presents a framework designed to tackle a range of planning problems arise in manipulation, which typically involve complex geometric-physical reasoning related to contact and dynamic constraints. We introduce the Contact Factor…
Graph-based analyses have gained a lot of relevance in the past years due to their high potential in describing complex systems by detailing the actors involved, their relations and their behaviours. Nevertheless, in scenarios where these…
This paper proposes an $SE_2(3)$ based extended Kalman filtering (EKF) framework for the inertial-integrated state estimation problem. The error representation using the straight difference of two vectors in the inertial navigation system…
This paper provides a generic framework of component analysis (CA) methods introducing a new expression for scatter matrices and Gram matrices, called Generalized Pairwise Expression (GPE). This expression is quite compact but highly…
We consider a lattice of weakly coupled expanding circle maps. We construct, via a cluster expansion of the Perron-Frobenius operator, an invariant measure for these infinite dimensional dynamical systems which exhibits space-time-chaos.
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…