arXiv subjects

Fredy Vides

Publications and source records attributed to Fredy Vides.

At least 19 recordsLinked to original sources

arXiv2026

Structured Stochastic Representations of Integrated Dynamic Strategies

Dynamic allocation decisions couple present resource use to evolving internal conditions, delayed returns, and future costs. We represent this interaction by four probability localizations linked through regime-indexed, graph-constrained column-stochastic operators. Pre-action state or context selects a locally affine model, while action-dependent changes update subsequent regimes, yielding a causal switched representation of nonlinear evolution. We characterize operator identifiability relative to the graph, the stochastic constraints, and the sampled embedding, separating coefficient recovery from predictive equivalence on the decision domain. Decision making is then formulated through implementable return--cost acceptability regions. Finite-horizon error propagation supplies conservative classification margins, and simultaneous intervals distinguish model-relative near-optimality from certified $\epsilon$-optimality over a declared finite policy class. Regime-indexed stochastic feedback is admitted when it satisfies the same certification test. Reproducible synthetic laboratories for personal preparation, supplier participation, and customer retention illustrate exact, operator-supplied, and noisy feedback cases. Multinomial experiments show improving recovery of the feedback function and fewer unresolved decisions with increasing sample size, while unrestricted off-policy recovery remains limited. The contribution is a structure-preserving representation--identification--decision workflow, not a domain-specific physiological or commercial calibration.

eess.SY↗

arXiv2026

Identifying Probability Localization Dynamics via Structured Stochastic Liftings

This work develops a discrete-time framework for identifying probability localization dynamics through finite stochastic representations adapted in space, time, memory, and state information. A compact dynamically relevant set is localized by a finite measurable partition, producing an observable probability state and a relational graph of admissible transitions. Structured stochastic liftings derived from Stochastically Structured Reservoir Computing (SSRC) give lossless polynomial representations of the observable state, while stochastic delay liftings add finite observable memory. These are distinguished from dynamically informed state-space enrichment: refinement of observational fibers containing states with the same present observation but different observable futures, yielding an exact obstruction-to-closure criterion. A route-network toy problem gives a minimal obstruction example, while four numerical laboratories (rotational phase dynamics, the chaotic logistic map, the Van der Pol oscillator, and a synthetic cyclic inventory system) show how spatial scale, temporal scale, polynomial degree, and delay depth interact. The logistic map isolates representation-induced memory in an otherwise Markovian chaotic system, using its exact invariant law as an ergodic benchmark and its zero-mass pseudospectrum to separate relaxation from transient amplification. An exact rotational cycle calibrates pseudospectra as a robustness diagnostic rather than a closure certificate. The inventory example gives a closure-driven enrichment procedure: residence-age hazards trigger age-refined states that improve predictive scores. These results motivate a minimal adequate representation: the least complex representation meeting predictive, structural, and identifiability requirements.

math.DS↗

arXiv2025

Stochastically Structured Reservoir Computers for Financial and Economic System Identification

This paper introduces a methodology for identifying and simulating financial and economic systems using stochastically structured reservoir computers (SSRCs). The framework combines structure-preserving embeddings with graph-informed coupling matrices to model inter-agent dynamics while enhancing interpretability. A constrained optimization scheme guarantees compliance with both stochastic and structural constraints. Two empirical case studies, a nonlinear stochastic dynamic model and regional inflation network dynamics, demonstrate the effectiveness of the approach in capturing complex nonlinear patterns and enabling interpretable predictive analysis under uncertainty.

math.OC↗

arXiv2023

Identifying Systems with Symmetries using Equivariant Autoregressive Reservoir Computers

The investigation reported in this document focuses on identifying systems with symmetries using equivariant autoregressive reservoir computers. General results in structured matrix approximation theory are presented, exploring a two-fold approach. Firstly, a comprehensive examination of generic symmetry-preserving nonlinear time delay embedding is conducted. This involves analyzing time series data sampled from an equivariant system under study. Secondly, sparse least-squares methods are applied to discern approximate representations of the output coupling matrices. These matrices play a critical role in determining the nonlinear autoregressive representation of an equivariant system. The structural characteristics of these matrices are dictated by the set of symmetries inherent in the system. The document outlines prototypical algorithms derived from the described techniques, offering insight into their practical applications. Emphasis is placed on the significant improvement on structured identification precision when compared to classical reservoir computing methods for the simulation of equivariant dynamical systems.

eess.SY↗

arXiv2023

Dynamic financial processes identification using sparse regressive reservoir computers

In this document, we present key findings in structured matrix approximation theory, with applications to the regressive representation of dynamic financial processes. Initially, we explore a comprehensive approach involving generic nonlinear time delay embedding for time series data extracted from a financial or economic system under examination. Subsequently, we employ sparse least-squares and structured matrix approximation methods to discern approximate representations of the output coupling matrices. These representations play a pivotal role in establishing the regressive models corresponding to the recursive structures inherent in a given financial system. The document further introduces prototypical algorithms that leverage the aforementioned techniques. These algorithms are demonstrated through applications in approximate identification and predictive simulation of dynamic financial and economic processes, encompassing scenarios that may or may not exhibit chaotic behavior.

eess.SY↗

arXiv2022

A Subspace Method for Time Series Anomaly Detection in Cyber-Physical Systems

Time series anomaly detection is an important process for system monitoring and model switching, among other applications in cyber-physical systems. In this document, we present a fast subspace method for time series anomaly detection, with a relatively low computational cost, that has been designed for anomaly detection in real sensor signals corresponding to dynamical systems. We also present some general results corresponding to the theoretical foundations of our method, together with a prototypical algorithm to for time series anomaly detection. Some numerical examples corresponding to applications of the prototypical algorithm are presented, and some computational tools based on the theory and algorithms presented in this paper, are provided.

eess.SY↗

arXiv2022

Quadratic pseudospectrum for identifying localized states

We examine the utility of the quadratic pseudospectrum in photonics and condensed matter. Specifically, the quadratic pseudospectrum represents a method for approaching systems with incompatible observables, as it both minimizes the "eigen-error" in the joint approximate spectrum of the incompatible observables and does not increase the system's computational complexity. Moreover, we derive an important estimate relating the Clifford and quadratic pseudospectra. Finally, we prove that the quadratic pseudospectrum is local, and derive the bounds on the errors that are incurred by truncating the system in the vicinity of where the pseudospectrum is being calculated.

quant-ph↗

arXiv2022

Computing Truncated Joint Approximate Eigenbases for Model Order Reduction

In this document, some elements of the theory and algorithmics corresponding to the existence and computability of approximate joint eigenpairs for finite collections of matrices with applications to model order reduction, are presented. More specifically, given a finite collection $X_1,\ldots,X_d$ of Hermitian matrices in $\mathbb{C}^{n\times n}$, a positive integer $r\ll n$, and a collection of complex numbers $\hat{x}_{j,k}\in \mathbb{C}$ for $1\leq j\leq d$, $1\leq k\leq r$. First, we study the computability of a set of $r$ vectors $w_1,\ldots,w_r\in \mathbb{C}^{n}$, such that $w_k=\arg\min_{w\in \mathbb{C}^n}\sum_{j=1}^d\|X_jw-\hat{x}_{j,k} w\|^2$ for each $1\leq k \leq r$, then we present a model order reduction procedure based on the truncated joint approximate eigenbases computed with the aforementioned techniques. Some prototypical algorithms together with some numerical examples are presented as well.

math.NA↗

arXiv2021

Computing Semilinear Sparse Models for Approximately Eventually Periodic Signals

Some elements of the theory and algorithmics corresponding to the computation of semilinear sparse models for discrete-time signals are presented. In this study, we will focus on approximately eventually periodic discrete-time signals, that is, signals that can exhibit an aperiodic behavior for an initial amount of time, and then become approximately periodic afterwards. The semilinear models considered in this study are obtained by combining sparse representation methods, linear autoregressive models and GRU neural network models, initially fitting each block model independently using some reference data corresponding to some signal under consideration, and then fitting some mixing parameters that are used to obtain a signal model consisting of a linear combination of the previously fitted blocks using the aforementioned reference data, computing sparse representations of some of the matrix parameters of the resulting model along the process. Some prototypical computational implementations are presented as well.

math.OC↗

arXiv2021

Sparse system identification by low-rank approximation

In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical methods are translated into algorithms that can be used for sparse model identification of discrete-time dynamical systems, based on structured data measured from the systems. The approximation of the state-transition operators that are determined primarily by matrices of parameters to be identified based on data measured from a given system, is approached by identifying conditions for the existence of low-rank approximations of submatrices of the trajectory matrices corresponding to the measured data, that can be used to compute approximate sparse representations of the matrices of parameters. One of the main advantages of the low-rank approximation approach presented in this document, concerns the parameter estimation for linear and nonlinear models where numerical or measurement noise could affect the estimates significantly. Prototypical algorithms based on the aforementioned techniques together with some applications to approximate identification and predictive simulation of time series models with symmetries and nonlinear structured dynamical systems in theoretical physics, fluid dynamics and weather forecasting are presented.

math.NA↗

arXiv2020

Computing Floquet Hamiltonians with Symmetries

Unitary matrices arise in many ways in physics, in particular as a time evolution operator. For a periodically driven system one frequently wishes to compute a Floquet Hamilonian that should be a Hermitian operator $H$ such that $e^{-iTH}=U(T)$ where $U(T)$ is the time evolution operator at time corresponding the period of the system. That is, we want $H$ to be equal to $-i$ times a matrix logarithm of $U(T)$. If the system has a symmetry, such as time reversal symmetry, one can expect $H$ to have a symmetry beyond being Hermitian. We discuss here practical numerical algorithms on computing matrix logarithms that have certain symmetries which can be used to compute Floquet Hamiltonians that have appropriate symmetries. Along the way, we prove some results on how a symmetry in the Floquet operator $U(T)$ can lead to a symmetry in a basis of Floquet eigenstates.

math.NA↗

arXiv2020

Universal Algebraic Controllers and System Identification

In this document, some structured operator approximation theoretical methods for system identification of nearly eventually periodic systems, are presented. Let $\mathbb{C}^{n\times m}$ denote the algebra of $n\times m$ complex matrices. Given $\varepsilon>0$, an arbitrary discrete-time dynamical system $(Σ,\mathcal{T})$ with state-space $Σ$ contained in the finite dimensional Hilbert space $\mathbb{C}^n$, whose state-transition map $\mathcal{T}:Σ\times ([0,\infty)\cap \mathbb{Z})\to Σ$ is unknown or partially known, and needs to be determined based on some sampled data in a finite set $\hatΣ=\{x_t\}_{1\leq t\leq m}\subset Σ$ according to the rule $\mathcal{T}(x_t,1)=x_{t+1}$ for each $1\leq t\leq m-1$, and given $x\in \hatΣ$. We study the solvability of the existence problems for two triples $(p,A,φ)$ and $(p,A_η,Φ)$ determined by a polynomial $p\in \mathbb{C}[z]$ with $°(p)\leq m$, a matrix root $A\in\mathbb{C}^{m\times m}$ and an approximate matrix root $A_η\in\mathbb{C}^{r\times r}$ of $p(z)=0$ with $r\leq m$, two completely positive linear multiplicative maps $φ:\mathbb{C}^{m\times m}\to \mathbb{C}^{n\times n}$ and $Φ:\mathbb{C}^{r\times r}\to \mathbb{C}^{n\times n}$, such that $\|\mathcal{T}(x,t)-φ(A^t)x\|\leq\varepsilon$ and $\|Φ(A_η^t)x-φ(A^t)x\|\leq\varepsilon$, for each integer $t\geq 1$ such that $\|\mathcal{T}(x,t)-y\|\leq \varepsilon$ for some $y\in \hatΣ$. Some numerical implementations of these techniques for the reduced-order predictive simulation of dynamical systems in continuum and quantum mechanics, are outlined.

math.NA↗

arXiv2019

On Cyclic Finite-State Approximation of Data-Driven Systems

In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix approximation problems that appear in the fields of system identification and model predictive control, for data-driven systems and processes. The research reported in this document is focused on finite-state approximation of data-driven systems. Some numerical implementations of the aforementioned techniques in the simulation and model predictive control of some generic data-driven systems, that are related to electrical signal transmission models, are outlined.

math.OC↗

arXiv2019

On Topologically Controlled Model Reduction for Discrete-Time Systems

In this document the author proves that several problems in data-driven numerical approximation of dynamical systems in $\mathbb{C}^n$, can be reduced to the computation of a family of constrained matrix representations of elements of the group algebra $\mathbb{C}[\mathbb{Z}/m]$ in $\mathbb{C}^{n\times n}$, factoring through the commutative algebra $Circ(m)$ of circulant matrices in $\mathbb{C}^{m\times m}$, for some integers $m\leq n$. The solvability of the previously described matrix representation problems is studied. Some connections of the aforementioned results, with numerical analysis of dynamical systems, are outlined, a prorotypical algorithm for the computation of the matrix representations, and some numerical implementations of the algorithm, will be presented.

math.OA↗

arXiv2018

On Uniform Connectivity of Algebraic Matrix Sets

In this document we study the uniform local path connectivity of sets of $m$-tuples of pairwise commuting normal matrices with some additional constraints. More specifically, given given $\varepsilon>0$, a fixed metric $\eth$ in ${M_n(\mathbb{C})}^m$ induced by the operator norm $\|\cdot\|$, any collection of $r$ non-constant multivariable polynomials $p_1(x_1,\ldots,x_m),\ldots,p_r(x_1,\ldots,x_m)$ over $\mathbb{C}$ with finite zero set $\mathbf{Z}(p_1,\ldots,p_r)\subset \mathbb{C}^m$, and any $m$-tuple $\mathbf{X}=(X_1,\ldots,X_m)$ in the set $\mathbb{ZD}_n^m(p_1,\ldots,p_r)\subseteq M_n^m(\mathbb{C})$, of pairwise commuting normal matrix contractions such that, $\|p_j(Y_1,\ldots,Y_m)\|=0$ for each $(Y_1,\ldots,Y_m)\in \mathbb{ZD}_n^m(p_1,\ldots,p_r)$ and each $1\leq j\leq r$. We prove the existence of paths between arbitrary $m$-tuples, that lie in the intersection of $\mathbb{ZD}_n^m(p_1,\ldots,p_r)$, and the $\delta$-ball $B_\eth(\mathbf{X},\delta)$ centered at $\mathbf{X}$ for some $\delta>0$, with respect to $\eth$. Two of the key features of these matrix paths is that $\delta$ can be chosen independent of $n$, and that they are contained in the intersection of $B_\eth(\mathbf{X},\varepsilon)$ and $\mathbb{ZD}_n^m(p_1,\ldots,p_r)$. Some connections with the approximation theory for matrix functions of several matrix variables, are studied as well.

math.NA↗

arXiv2017

Connecting Commuting Normal Matrices

In this document we study the local path connectivity of sets of $m$-tuples of commuting normal matrices with some additional geometric constraints in their joint spectra. In particular, given $\varepsilon>0$ and any fixed but arbitrary $m$-tuple $\mathbf{X}\in {M_n(\mathbb{C})}^m$ in the set of $m$-tuples of pairwise commuting normal matrix contractions, we prove the existence of paths between arbitrary $m$-tuples in the intersection of the previously mentioned sets of $m$-tuples in ${M_n(\mathbb{C})}^m$ and the $δ$-ball $B_ð(\mathbf{X},δ)$ centered at $\mathbf{X}$ for some $δ>0$, with respect to some suitable metric $ð$ in ${M_n(\mathbb{C})}^m$ induced by the operator norm. Two of the key features of these matrix paths is that $δ$ can be chosen independent of $n$, and that the paths stay in the intersection of $B_ð(\mathbf{X},\varepsilon)$, and the set pairwise commuting normal matrix contractions with some special geometric structure on their joint spectra. We apply these results to study the local connectivity properties of matrix $\ast$-representations of some universal commutative $C^\ast$-algebras. Some connections with the local connectivity properties of completely positive linear maps on matrix algebras are studied as well.

math.OA↗

arXiv2017

Dynamical Deformation of Toroidal Matrix Varieties

In this document we study the local connectivity of the sets whose elements are $m$-tuples of pairwise commuting normal matrix contractions. Given $\varepsilon>0$, we prove that there is $δ>0$ such that for any two $m$-tuples of pairwise commuting normal matrix contractions $\mathbf{X}:=(X_1,\ldots,X_m)$ and $\tilde{\mathbf{X}}:=(\tilde{X}_1,\ldots,\tilde{X}_m)$ that are $δ$-close with respect to some suitable distance $ð$ in $(\mathbb{C}^{n\times n})^m$, we can find a $m$-tuple of matrix paths (homotopies) connecting $\mathbf{X}$ to $\mathbf{\tilde{X}}$ relative to the intersection of some $\varepsilon,ð$-neighborhood of $\mathbf{X}$ with the set of $m$-tuples of pairwise commuting normal matrix contractions. One of the key features of these matrix homotopies is that $δ$ can be chosen independent of $n$. Some connections with topology and numerical matrix analysis will be outlined as well.

math.OA↗

arXiv2016

Local Deformation of Matrix Words

In this document we study some local deformation properties of matrix representations of the universal C$^*$-algebras denoted by $\mathbb{I}^{m}_\varepsilon[p_1,\ldots,p_m]$ and $\mathbb{S}^{m-1}_\varepsilon[p_1,\ldots,p_m]$, and that we call {\bf Semi-Soft Cubes} and {\bf Semi-Soft Spheres} respectively. We will use some C$^*$-algebraic technology to study the local deformation properties of matrix words in particular representations of Semi-Soft Cubes and Spheres, we will then use these results to study the local deformation properties of generic matrix equations on words. Some geometrical aspects of the local deformation of matrix words will be addressed, and some connections with matrix numerical analysis and computational physics will be outlined as well.

math.OA↗