arXiv subjects

Javier Pérez

Publications and source records attributed to Javier Pérez.

18 recordsLinked to original sources

arXiv2026

Hybrid QKD-PQC Network Emulation through Automated and Scalable Cloud-Native Orchestration

The ongoing transition toward quantum-safe networking has motivated the development of hybrid network architectures integrating Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC). However, the experimental evaluation of hybrid QKD-PQC network architectures remains constrained by the high cost and limited accessibility of quantum hardware, as well as by the limited support for hybrid QKD-PQC networks in existing emulation platforms. Quditto is an open-source emulation platform originally designed for QKD networks that enables cost-effective and reproducible experimentation without requiring dedicated physical quantum infrastructure. Building on this foundation, this work presents Quditto as a hybrid QKD-PQC network emulation platform featuring automated and scalable cloud-native orchestration. The proposed platform introduces four principal contributions: a cloud-native orchestrator enabling fully automated infrastructure deployment across cloud and multi-cluster environments; an optimized provisioning workflow enabling large-scale quantum-safe network emulation; native integration of post-quantum nodes enabling unified emulation of hybrid QKD-PQC networks; and a secure key management module providing persistent and access-controlled storage of cryptographic material. Experimental validation demonstrates sublinear orchestration-time scaling with network size and successful end-to-end hybrid QKD-PQC key establishment on a representative spine-leaf deployment, thereby enabling the systematic evaluation of quantum-safe networking mechanisms in large-scale heterogeneous network environments.

cs.NI↗

arXiv2026

Phase behavior of thermoresponsive colloids drives re-entrant plasmon coupling

Plasmonic nanoparticles (NPs) integrated within thermoresponsive polymeric microgels provide a versatile platform for the realization of stimuli-responsive optical materials, where the microgel volume phase transition enables dynamic control of plasmon coupling. This study uncovers a counter-intuitive re-entrant behavior with increasing NP loading in which plasmon coupling initially strengthens and subsequently weakens beyond a critical NP-to-microgel number ratio. By combining light and X-ray scattering techniques with optical spectroscopy and electrophoretic mobility measurements, it is demonstrated that plasmon coupling is governed not only by the interparticle distance between NPs confined within individual microgels, but also by the colloidal stability of the hybrid complexes. At intermediate NP loadings, surface charge inhomogeneities induced by NP adsorption promote aggregation of microgel-NPs complexes, resulting in enhanced plasmon coupling. In contrast, when the complexes remain colloidally stable, coupling is dictated solely by NP organization within the corona of individual microgels. A quantitative relationship between plasmon coupling and interparticle distance reveals two distinct coupling regimes. This behavior is rationalized through a phase diagram linking colloidal stability to optical response. These findings identify colloidal stability as a key parameter for designing soft plasmonic systems with programmable optical properties.

cond-mat.soft↗

arXiv2025

Linking structure and optical properties of plasmonic nanoparticles on tunable spherical surfaces

The complexation of plasmonic nanoparticles (NPs) and thermoresponsive microgels is widely exploited for applications, but a microscopic description of the mechanisms governing the spatial organization of the NPs is still lacking. Combining small angle X-ray scattering, state-of-the-art simulations and a simple toy model, we uncover how the volume phase transition of microgels controls NP-NP interactions, establishing for the first time a microscopic link between plasmon coupling and NP local structure. Our study paves the way to experimentally investigate phase transitions on controlled curved surfaces at the nanoscale.

cond-mat.soft↗

arXiv2022

Perturbation theory of transfer function matrices

Zeros of rational transfer function matrices $R(λ)$ are the eigenvalues of associated polynomial system matrices $P(λ)$, under minimality conditions. In this paper we define a structured condition number for a simple eigenvalue $λ_0$ of a (locally) minimal polynomial system matrix $P(λ)$, which in turn is a simple zero $λ_0$ of its transfer function matrix $R(λ)$. Since any rational matrix can be written as the transfer function of a polynomial system matrix, our analysis yield a structured perturbation theory for simple zeros of rational matrices $R(λ)$. To capture all the zeros of $R(λ)$, regardless of whether they are poles or not, we consider the notion of root vectors. As corollaries of the main results, we pay particular attention to the special case of $λ_0$ being not a pole of $R(λ)$ since in this case the results get simpler and can be useful in practice. We also compare our structured condition number with Tisseur's unstructured condition number for eigenvalues of matrix polynomials, and show that the latter can be unboundedly larger. Finally, we corroborate our analysis by numerical experiments.

math.NA↗

arXiv2022

Reward-modulated learning using spiking neural networks for vehicle lateral control

This paper presents a vehicle lateral controller based on spiking neural networks capable of replicating the behavior of a model-based controller but with the additional ability to perform online adaptation. By making use of neural plasticity and thanks to reward modulation learning, neural connections are modified to adjust the response according to the committed error. Therefore, the error performs a similar role to dopamine in a biological system, modulating the learning process based on spiking time dependency. The connections are initially set to replicate behavior of the model-based controller. Online adaptation allows tuning connection parameters to improve controller performance. A path controller with a preview is used as a baseline controller to evaluate the performance of the proposed approach. Key performance indicators are obtained from simulation with a step response and a handling track with 20 curves of different radii.

eess.SY↗

arXiv2022

SAXS Investigation of Core-Shell Microgels with High Scattering Contrast Cores: Access to Structure Factor and Volume Fraction

To explore dense packings of soft colloids, scattering experiments are ideal to access the structure factor. However, for soft microgels determination of the structure factor is difficult because of the low contrast of the polymer network and potential microgel interpenetration and deformation that change the form factor contribution. Here, we employ small-angle X-ray scattering (SAXS) to study soft, thermoresponsive microgels with poly-N-isopropylacrylamide (PNIPAM) shells and gold nanoparticle cores. The scattering of the gold cores dominates the scattering patterns and allows precise determination of the microgel volume fraction over a broad range of concentrations. At high volume fractions we find distinct patterns with sharp Bragg peaks allowing extraction of the structure factor and characterization of the phases combined with UV-Vis spectroscopy. The unique scattering contrast of our core-shell microgels combined with SAXS opens up new ways to investigate dense packings of soft microgels including in situ studies of phase transitions.

cond-mat.soft↗

arXiv2020

Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis

In the framework of Polynomial Eigenvalue Problems, most of the matrix polynomials arising in applications are structured polynomials (namely (skew-)symmetric, (skew-)Hermitian, (anti-)palindromic, or alternating). The standard way to solve Polynomial Eigenvalue Problems is by means of linearizations. The most frequently used linearizations belong to general constructions, valid for all matrix polynomials of a fixed degree, known as {\em companion linearizations}. It is well known, however, that is not possible to construct companion linearizations that preserve any of the previous structures for matrix polynomials of even degree. This motivates the search for more general companion forms, in particular {\em companion $\ell$-ifications}. In this paper, we present, for the first time, a family of (generalized) companion $\ell$-ifications that preserve any of these structures, for matrix polynomials of degree $k=(2d+1)\ell$. We also show how to construct sparse $\ell$-ifications within this family. Finally, we prove that there are no structured companion quadratifications for quartic matrix polynomials.

math.NA↗

arXiv2020

Linearizations of rational matrices from general representations

We construct a new family of linearizations of rational matrices $R(λ)$ written in the general form $R(λ)= D(λ)+C(λ)A(λ)^{-1}B(λ)$, where $D(λ)$, $C(λ)$, $B(λ)$ and $A(λ)$ are polynomial matrices. Such representation always exists and are not unique. The new linearizations are constructed from linearizations of the polynomial matrices $D(λ)$ and $A(λ)$, where each of them can be represented in terms of any polynomial basis. In addition, we show how to recover eigenvectors, when $R(λ)$ is regular, and minimal bases and minimal indices, when $R(λ)$ is singular, from those of their linearizations in this family.

math.NA↗

arXiv2020

Linearizations for interpolation bases -- a comparison I

One strategy to solve a nonlinear eigenvalue problem $T(λ)x=0$ is to solve a polynomial eigenvalue problem (PEP) $P(λ)x=0$ that approximates the original problem through interpolation. Then, this PEP is usually solved by linearization. Most of the literature about linearizations assumes that $P(λ)$ is expressed in the monomial basis but, because of the polynomial approximation techniques, in this context, $P(λ)$ is expressed in a non-monomial basis. The bases used with most frequency are the Chebyshev basis, the Newton basis and the Lagrange basis. In this paper we construct a family of linearizations of $P(λ)$ that is easy to construct from the matrix coefficients of $P(λ)$ when this polynomial is expressed in any of those three bases. We also provide recovery formulas of eigenvectors (when $P(λ)$ is regular) and recovery formulas of minimal bases and minimal indices (when $P(λ)$ is singular). Our ultimate goal is to compare the numerical behavior of these linearizations, within the same family (to select the best one) and with the linearizations of other families based on the location of the eigenvalues with respect to the interpolation nodes.

math.NA↗

arXiv2019

A Spatial Concordance Correlation Coefficient with an Application to Image Analysis

In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to compare two spatial sequences along a 45-degree line. The proposed coefficient was explored for the bivariate Matérn and Wendland covariance functions. The asymptotic normality of a sample version of the spatial concordance coefficient for an increasing domain sampling framework was established for the Wendland covariance function. To work with large digital images, we developed a local approach for estimating the concordance that uses local spatial models on non-overlapping windows. Monte Carlo simulations were used to gain additional insights into the asymptotic properties for finite sample sizes. As an illustrative example, we applied this methodology to two similar images of a deciduous forest canopy. The images were recorded with different cameras but similar fields-of-view and within minutes of each other. Our analysis showed that the local approach helped to explain a percentage of the non-spatial concordance and to provided additional information about its decay as a function of the spatial lag.

stat.ME↗

arXiv2018

The conditioning of block Kronecker $\ell$-ifications of matrix polynomials

A strong $\ell$-ification of a matrix polynomial $P(λ)=\sum A_iλ^i$ of degree $d$ is a matrix polynomial $\mathcal{L}(λ)$ of degree $\ell$ having the same finite and infinite elementary divisors, and the same numbers of left and right minimal indices as $P(λ)$. Strong $\ell$-ifications can be used to transform the polynomial eigenvalue problem associated with $P(λ)$ into an equivalent polynomial eigenvalue problem associated with a larger matrix polynomial $\mathcal{L}(λ)$ of lower degree. Typically $\ell=1$ and, in this case, $\mathcal{L}(λ)$ receives the name of strong linearization. However, there exist some situations, e.g., the preservation of algebraic structures, in which it is more convenient to replace strong linearizations by other low degree matrix polynomials. In this work, we investigate the eigenvalue conditioning of $\ell$-ifications from a family of matrix polynomials recently identified and studied by Dopico, Pérez and Van Dooren, the so-called block Kronecker companion forms. We compare the conditioning of these $\ell$-ifications with that of the matrix polynomial $P(λ)$, and show that they are about as well conditioned as the original polynomial, provided we scale $P(λ)$ so that $\max\{\|A_i\|_2\}=1$, and the quantity $\min\{\|A_0\|_2,\|A_d\|_2\}$ is not too small. Moreover, under the scaling assumption $\max\{\|A_i\|_2\}=1$, we show that any block Kronecker companion form, regardless of its degree or block structure, is about as well-conditioned as the well-known Frobenius companion forms. Our theory is illustrated by numerical examples.

math.NA↗

arXiv2018

Block minimal bases $\ell$-ifications of matrix polynomials

The standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil, known as a strong linearization. This process transforms the problem into an equivalent generalized eigenvalue problem. However, there are some situations in which is more convenient to replace linearizations by other low degree matrix polynomials. This has motivated the idea of a strong $\ell$-ification of a matrix polynomial, which is a matrix polynomial of degree $\ell$ having the same finite and infinite elementary divisors, and the same numbers of left and right minimal indices as the original matrix polynomial. We present in this work a novel method for constructing strong $\ell$-ifications of matrix polynomials of size $m\times n$ and grade $d$ when $\ell< d$, and $\ell$ divides $nd$ or $md$. This method is based on a family called "strong block minimal bases matrix polynomials", and relies heavily on properties of dual minimal bases. We show how strong block minimal bases $\ell$-ifications can be constructed from the coefficients of a given matrix polynomial $P(λ)$. We also show that these $\ell$-ifications satisfy many desirable properties for numerical applications: they are strong $\ell$-ifications regardless of whether $P(λ)$ is regular or singular, the minimal indices of the $\ell$-ifications are related to those of $P(λ)$ via constant uniform shifts, and eigenvectors and minimal bases of $P(λ)$ can be recovered from those of any of the strong block minimal bases $\ell$-ifications. In the special case where $\ell$ divides $d$, we introduce a subfamily of strong block minimal bases matrix polynomials named "block Kronecker matrix polynomials", which is shown to be a fruitful source of companion $\ell$-ifications.

math.NA↗

arXiv2018

Automatic rational approximation and linearization of nonlinear eigenvalue problems

We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, Sète, and Trefethen to approximate the nonlinear eigenvalue problem by a rational eigenvalue problem and is embedded in the state space representation of a rational polynomial by Su and Bai. The advantage of the method, compared to related techniques such as NLEIGS and infinite Arnoldi, is the efficient computation by an automatic procedure. In addition, a set-valued approach is developed that allows building a low degree rational approximation of a nonlinear eigenvalue problem. The method perfectly fits the framework of the Compact rational Krylov methods (CORK and TS-CORK), allowing to efficiently solve large scale nonlinear eigenvalue problems. Numerical examples show that the presented framework is competitive with NLEIGS and usually produces smaller linearizations with the same accuracy but with less effort for the user.

math.NA↗

arXiv2017

Explicit block-structures for block-symmetric Fiedler-like pencils

In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(λ)$, regular and singular, with good properties. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fiedler pencils with repetition (GFPR) were constructed. In particular, one of the goals was to find in these families structured linearizations of structured matrix polynomials. For example, if a matrix polynomial $P(λ)$ is symmetric (Hermitian), it is convenient to use linearizations of $P(λ)$ that are also symmetric (Hermitian). Both the family of GFP and the family of GFPR contain block-symmetric linearizations of $P(λ)$, which are symmetric (Hermitian) when $P(λ)$ is. Now the objective is to determine which of those structured linearizations have the best numerical properties. The main obstacle for this study is the fact that these pencils are defined implicitly as products of so-called elementary matrices. In this paper we consider the family of block-minimal bases pencils, whose pencils are defined in terms of their block-structure, as a source of canonical forms for block-symmetric pencils. More precisely, we present four families of block-symmetric pencils which, under some generic nonsingularity conditions are block minimal bases pencils and strong linearizations of a matrix polynomial. We show that the block-symmetric GFP and GFPR, after some row and column permutations, belong to the union of these four families. Hence, these four families of pencils provide an alternative but explicit approach to the block-symmetric Fiedler-like pencils existing in the literature.

math.NA↗

arXiv2017

Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors

We introduce a new family of strong linearizations of matrix polynomials---which we call "block Kronecker pencils"---and perform a backward stability analysis of complete polynomial eigenproblems. These problems are solved by applying any backward stable algorithm to a block Kronecker pencil, such as the staircase algorithm for singular pencils or the QZ algorithm for regular pencils. This stability analysis allows us to identify those block Kronecker pencils that yield a computed complete eigenstructure which is exactly that of a slightly perturbed matrix polynomial. The global backward error analysis in this work presents for the first time the following key properties: it is a rigurous analysis valid for finite perturbations (i.e., it is not a first order analysis), it provides precise bounds, it is valid simultaneously for a large class of linearizations, and it establishes a framework that may be generalized to other classes of linearizations. These features are related to the fact that block Kronecker pencils are a particular case of the new family of "strong block minimal bases pencils", which are robust under certain perturbations and, so, include certain perturbations of block Kronecker pencils. We hope that this robustness property will allow us to extend the results in this paper to other contexts.

math.NA↗

arXiv2017

Mixed forward-backward stability of the two-level orthogonal Arnoldi method for quadratic problems

We revisit the numerical stability of the two-level orthogonal Arnoldi (TOAR) method for computing an orthonormal basis of a second--order Krylov subspace associated with two given matrices. We show that the computed basis is close (on certain subspace metric sense) to a basis for a second-order Krylov subspace associated with nearby coefficient matrices, provided that the norms of the given matrices are not too large or too small. Thus, the results in this work provide for the first time conditions that guarantee the numerical stability of the TOAR method in computing orthonormal bases of second-order Krylov subspaces. We also study scaling the quadratic problem for improving the numerical stability of the TOAR procedure when the norms of the matrices are too large or too small. We show that in many cases the TOAR procedure applied to scaled matrices is numerically stable when the scaling introduced by Fan, Lin and Van Dooren is used.

math.NA↗

arXiv2016

Structured backward error analysis of linearized structured polynomial eigenvalue problems

We introduce a new class of structured matrix polynomials, namely, the class of M_A-structured matrix polynomials, to provide a common framework for many classes of structured matrix polynomials that are important in applications: the classes of (skew-)symmetric, (anti-)palindromic, and alternating matrix polynomials. Then, we introduce the families of M_A-structured strong block minimal bases pencils and of M_A-structured block Kronecker pencils,, and show that any M_A-structured odd-degree matrix polynomial can be strongly linearized via an M_A-structured block Kronecker pencil. Finally, for the classes of (skew-)symmetric, (anti-)palindromic, and alternating odd-degree matrix polynomials, the M_A-structured framework allows us to perform a global and structured backward stability analysis of complete structured polynomial eigenproblems, regular or singular, solved by applying to an M_A-structured block Kronecker pencil a structurally backward stable algorithm that computes its complete eigenstructure, like the palindromic-QR algorithm or the structured versions of the staircase algorithm. This analysis allows us to identify those M_A-structured block Kronecker pencils that yield a computed complete eigenstructure which is the exact one of a slightly perturbed structured matrix polynomial.These pencils include (modulo permutations) the well-known block-tridiagonal and block-antitridiagonal structure-preserving linearizations. Our analysis incorporates structure to the recent (unstructured) backward error analysis performed for block Kronecker linearizations by Dopico, Lawrence, Pérez and Van Dooren, and share with it its key features, namely, it is a rigorous analysis valid for finite perturbations, i.e., it is not a first order analysis, it provides precise bounds, and it is valid simultaneously for a large class of structure-preserving strong linearizations.

math.NA↗

arXiv2016

A unified approach to Fiedler-like pencils via strong block minimal bases pencils

The standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix polynomial into a matrix pencil, transforming the problem into an equivalent generalized eigenvalue problem. Such pencils are known as linearizations. Many of the families of linearizations for matrix polynomials available in the literature are extensions of the so-called family of Fiedler pencils. These families are known as generalized Fiedler pencils, Fiedler pencils with repetition and generalized Fiedler pencils with repetition, or Fiedler-like pencils for simplicity. The goal of this work is to unify the Fiedler-like pencils approach with the more recent one based on strong block minimal bases pencils introduced in \cite{canonical}. To this end, we introduce a family of pencils that we have named extended block Kronecker pencils, whose members are, under some generic nonsingularity conditions, strong block minimal bases pencils, and show that, with the exception of the non proper generalized Fiedler pencils, all Fiedler-like pencils belong to this family modulo permutations. As a consequence of this result, we obtain a much simpler theory for Fiedler-like pencils than the one available so far. Moreover, we expect this unification to allow for further developments in the theory of Fiedler-like pencils such as global or local backward error analyses and eigenvalue conditioning analyses of polynomial eigenvalue problems solved via Fiedler-like linearizations.

math.NA↗