DigitalUM :: Browsing by browse.metadata.contributordepartment "Matemáticas"

Browsing by browse.metadata.contributordepartment "Matemáticas"

Now showing 1 - 20 of 88

Open Access
A discrete approach to Zhang’s projection inequality
(Cambridge University Press. Canadian Mathematical Society, 2025-09-24) Alonso Gutiérrez, David; Lucas Marín, Eduardo; Martín Goñí, Javier; Matemáticas
In this paper we will provide a new proof of the fact that for any convex body K ⊆ Rn 2n n n nn∞rn−1voln(K ∩ (ren + K))dr ≤0(voln(K))n+1,(voln−1(P ⊥ (K)))nn where (ei)n denotes the canonical orthonormal basis in Rn, P ⊥ (K) denotes n the orthogonal projection of K onto the linear hyperplane orthogonal to en, and volk denotes the k-dimensional Lebesgue measure. This inequality was proved by Gardner and Zhang and it implies Zhang’s inequality. We will use our new approach to this inequality in order to prove discrete analogues of this inequality and of an equivalent version of it, where we will consider the lattice point enumerator measure instead of the Lebesgue measure, and show that from such discrete analogues we can recover the aforementioned inequality and, therefore, Zhang’s inequality.
Restricted
A general model for wildfire propagation with wind and slope
(Society for Industrial and Applied Mathematics, 2023-05-23) Javaloyes Victoria, Miguel Ángel; Pendás-Recondo, Enrique; Sánchez, Miguel; Matemáticas
A geometric model for the computation of the firefront of a forest wildfire which takes into account several effects (possibly time-dependent wind, anisotropies, and slope of the ground) is introduced. It relies on a general theoretical framework, which reduces the hyperbolic PDE system of any wave to an ODE in a Lorentz-Finsler framework. The wind induces a sort of double semielliptical fire growth, while the influence of the slope is modeled by means of a term which comes from the Matsumoto metric (i.e., the standard nonreversible Finsler metric that measures the time when going up and down a hill). These contributions make a significant difference from previous models because, now, the infinitesimal wavefronts are not restricted to be elliptical. Even though this is a technical complication, the wavefronts remain computable in real time. Some simulations of evolution are shown, paying special attention to possible crossovers of the fire.
Open Access
A generalization of the notion of helix
(Scientific and Technological Research Council of Turkey, 2023) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
In this paper we generalize the notion of helix in the three-dimensional Euclidean space, which we define as that curve $\alpha$ for which there is an $F$-constant vector field $W$ along $\alpha$ that forms a constant angle with a fixed direction $V$ (called an axis of the helix). We find the natural equation and the geometric integration of helices $\alpha$ where the $F$-constant vector field $W$ is orthogonal to its axis.
Open Access
A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding
(IEEE, 2021) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; Matemáticas
We study the problem of the computation of Groebner basis for the ideal of linear recurring relations of a doubly periodic array. We find a set of indexes such that, along with some conditions, guarantees that the set of polynomials obtained at the last iteration in the Berlekamp-Massey-Sakata algorithm is exactly a Groebner basis for the mentioned ideal. Then, we apply these results to improve locator decoding in abelian codes.
Open Access
A note on the theoretical support to compute dimension in Abelian codes
(2024) Bernal Buitrago, José Joaquín; Simón Pinero, Juan Jacobo; Matemáticas
In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.
Open Access
A programmable web platform for distributed access, analysis, and visualization of data
(Elsevier, 2023-10-26) Esquembre, Francisco; Chacón, Jesús; Saenz, Jacobo; Vega, Jesús; Dormido-Canto, Sebastián; Matemáticas
Daily work of Fusion Data Research (FDR) scientists faces three practical challenges: (i) getting access to vast amounts of validated, curated, and (ideally) annotated discharge data, (ii) applying a wide variety of standard, domain-specific, and home-made analysis and visualization software libraries and routines, and (iii) using fast, specialized, and not easy to obtain hardware and software installations. This paper introduces a novel web platform that addresses these three challenges in a federated way. Based on a client–server architecture, the new platform allows for easy use and exchange of curated data, validated analysis and visualization routines, and even networked hardware and software installations among the FDR community. This exchange goes beyond the mere use of a code repository, but facilitates the creation of an actual ready-to-use network of computers which can be used remotely to configure and perform data analysis. The network functions in a federated way, in which each member of the community contributes, using the same web platform, with its data, programming experience, and hardware and software availability. The platform is open source.
Open Access
A property that characterizes the Enneper surface and helix surfaces
(Springer, 2024-06-29) Lucas Saorín, Pascual; Otega Yagües, José Antonio; Matemáticas
The main goal of this paper is to show that helix surfaces and the Enneper surface are theonly surfaces in the 3-dimensional Euclidean space R3 whose isogonal lines are generalizedhelices and pseudo-geodesic lines.
Open Access
A refinement of Gorenstein flat dimension via the flat–cotorsion theory
(ScienceDirect, 2021-02-01) Christensen, Lars Winther; Estrada, Sergio; Liang, Li; Thompson, Peder; Wu, Dejun; Yang, Gang; Matemáticas
We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological di-mension without extra assumptions on the ring. Crucially, we show that it coincides with the Gorenstein flat dimension for complexes where the latter is finite, and for complexes over right coherent rings—the setting where the Gorenstein flat dimension is known to behave as expected.
Open Access
A supervised ML Biometric Continuous Authentication System for Industry 4.0
(IEEE, 2022-04-29) Espín López, Juan Manuel; Esquembre, Francisco; Martínez Pérez, Gregorio; Marín-Blázquez, Javier G.; Huertas Celdrán, Alberto; Matemáticas
Continuous authentication (CA) is a promis- ing approach to authenticate workers and avoid security breaches in the industry, especially in Industry 4.0, where most interaction between workers and devices takes place. However, introducing CA in industries raises unsolved questions regarding machine learning (ML) models: i) its precision and performance, ii) its robustness and iii) the issue about if or when to retrain the models. To answer these questions, this work explores these issues with a proposed supervised vs non-supervised ML-based CA sys- tem that uses sensors, applications statistics, or speaker data collected by the operator’s devices. Experiments show supervised models with Equal Error Rates of 7.28% using sensors data, 9.29% with statistics, and 0.31% with voice, a significant improvement of 71.97%, 62.14%, and 97.08%, respectively, over unsupervised models. Voice is the most robust dimension when adding new workers, with less than 2% of false acceptance rate even if workforce size is doubled.
Open Access
An intrinsical description of group codes
(Springer, 2009-01-06) Bernal Buitrago, José Joaquín; Río Mateos, Ángel del; Simón Pinero, Juan Jacobo; Matemáticas
A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism FG → Fn which maps G to the standard basis of Fn. Many classical linear codes have been shown to be group codes. In this paper we obtain a criterion to decide when a linear code is a group code in terms of its intrinsical properties in the ambient space Fn, which does not assume an “a priori” group algebra structure on Fn. As an application we provide a family of groups (including metacyclic groups) for which every two-sided group code is an abelian group code. It is well known that Reed-Solomon codes are cyclic and its parity check extensions are elementary abelian group codes. These two classes of codes are included in the class of Cauchy codes. Using our criterion we classify the Cauchy codes of some lengths which are left group codes and the possible group code structures on these codes.
Open Access
Apparent distance and a notion of BCH multivariate codes
(Institute of Electrical and Electronics Engineers, 2015) Bernal Buitrago, José Joaquín; Bueno Carreño, Diana H.; Simón Pinero, Juan Jacobo; Matemáticas
This paper is devoted to study two main problems: on the one hand, to compute the apparent distance of an abelian code and on the other hand, to give a notion of BCH multivariate code. To do this, we present an algorithm to compute the apparent distance of an abelian code, based on some manipulations of hypermatrices associated to its generating idempotent. Our method uses less computations than those given in [5] and [10]; furthermore, in the bivariate case, the order of the computations is reduced from exponential to linear. Then we use our techniques to develop a notion of BCH code in the multivariate case and we extend most of the classical results on BCH codes. Finally, we apply our method in two directions: we construct abelian codes from cyclic codes, multiplying their dimension and preserving their apparent distance; and we design abelian codes with maximum dimension with respect to a fixed apparent distance and a fixed length.
Restricted
Applications of cone structures to the anisotropic rheonomic Huygens’ principle
(Elsevier, 2021-08) Javaloyes Victoria, Miguel Ángel; Pendás-Recondo, Enrique; Sánchez, Miguel; Matemáticas
A general framework for the description of classic wave propagation is introduced. This relies on a cone structure C determined by an intrinsic space Σ of velocities of propagation (point, direction and time-dependent) and an observers’ vector field ∂/∂t whose integral curves provide both a Zermelo problem for the wave and an auxiliary Lorentz–Finsler metric G compatible with C. The PDE for the wavefront is reduced to the ODE for the t-parametrized cone geodesics of C. Particular cases include time-independence (∂/∂t is Killing for G), infinitesimally ellipsoidal propagation (G can be replaced by a Lorentz metric) or the case of a medium which moves with respect to ∂/∂t faster than the wave (the “strong wind” case of a sound wave), where a conic time-dependent Finsler metric emerges. The specific case of wildfire propagation is revisited.
Open Access
Balanced pairs, cotorsion triplets and quiver representations
(Cambridge University Press, 2019-08-13) Estrada, Sergio; Pérez, Marco A.; Zhu, Haiyan; Matemáticas
Balanced pairs appear naturally in the realm of relative homological algebra associated with the balance of right-derived functors of the Hom functor. Cotorsion triplets are a natural source of such pairs. In this paper, we study the connection between balanced pairs and cotorsion triplets by using recent quiver representation techniques. In doing so, we find a new characterization of abelian categories that have enough projectives and injectives in terms of the existence of complete hereditary cotorsion triplets. We also provide a short proof of the lack of balance for derived functors of Hom computed using flat resolutions, which extends the one given by Enochs in the commutative case.
Open Access
Brunn-Minkowski type inequalities for the lattice point enumerator
(Elsevier, 2020-08-26) Iglesias, David; Zvavitch, Artem ; Yepes Nicolás, Jesús; Matemáticas; Facultades de la UMU::Facultad de Matemáticas
Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator Gn(⋅) are provided. In particular, we show that Gn((1−λ)K+λL+(−1,1)^n)^{1/n}≥(1−λ)Gn(K)^{1/n}+λGn(L)^{1/n} for any non-empty bounded sets K,L⊂R^n and all λ∈(0,1). We also show that these new discrete versions imply the classical results, and discuss some links with other related inequalities.
Open Access
CGAPP: A continuous group authentication privacy-preserving platform for industrial scene
(Elsevier ltd., 2023-10-09) Espín López, Juan Manuel; Esquembre, Francisco; Martínez Pérez, Gregorio; Marín-Blázquez, Javier G.; Huertas Celdrán, Alberto; Matemáticas
In Industry 4.0, security begins with the workers’ authentication, which can be done individually or in groups. Recently, group authentication is gaining momentum, allowing users to authenticate as group members without the need to specify the particular individual. Continuous authentication and federated learning are promising techniques that might help group authentication by providing privacy, by its own design, and extra security compared to traditional methods based on passwords, tokens, or biometrics. However, these techniques have not previously been combined or evaluated for authenticating workers in Industry 4.0. Thus, this paper proposes a novel continuous group authentication privacy-preserving (CGAPP)platform that is suitable for the industry. The CGAPP platform incorporates statistical data from workers’ smartphones and employs federated learning-based outlier detection for group worker authentication while ensuring the privacy of personal data vectors. A series of experiments were performed to measure the framework’s suitability and address the following research questions: (i) What is the cost of using FL compared to full data access in industrial scenarios? (ii) How robust is federated learning against adversarial attacks, specifically, how much malicious data is required to deceive the model? and (iii) How much noise is required to disrupt the authentication system? The results demonstrate the effectiveness of the CGAPP platform in the industry since it provides factory safety while preserving privacy. This platform achieves an accuracy of 92%, comparable to the 96% obtained by traditional approaches in the literature that do not address privacy concerns. The platform’s robustness is tested against attacks in the second and third experiments, and various countermeasures are evaluated. While the CGAPP platform exhibits certain vulnerabilities to data injection attacks, straightforward countermeasures can alleviate them. Nevertheless, the system’s performance experiences a notable impact in the event of a data perturbation attack, and the countermeasures investigated are ineffective in addressing this issue.
Open Access
Characterizations of Ding Injective Complexes
(Springer, 2019-07-24) Yang, Gang; Estrada, Sergio; Matemáticas
Let R be a ring and X a chain complex of R-modules. It is proven that if each term is Ding injective in R-Mod for all i in Z , and there exists an integer k such that each ZiX is Ding injective in R-Mod for all i>=k , then X is Ding injective in Ch(R) . If R is a left coherent ring, then a chain complex X is Ding injective if and only if each term is Ding injective in R-Mod for all i in Z.
Open Access
Concircular helices and concircular surfaces in Euclidean 3-space R3
(Universidad de Hacettepe, 2023) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
In this paper we characterize concircular helices in R3 by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in R3 as a special family of ruled surfaces, and we show that M ⊂ R3 is a proper concircular surface if and only if either M is parallel to a conical surface or M is the normal surface to a spherical curve. Finally, we characterize the concircular helices as geodesics of concircular surfaces.
Open Access
Concircular hypersurfaces and concircular helices inspace forms
(Springer, 2023-08-23) Lucas Saorín, Pascual; Ortega Yagües, José Antonio; Matemáticas
In this paper, we find a full description of concircular hypersurfaces in spaceforms as a special family of ruled hypersurfaces. We also characterize concircularhelices in 3-dimensional space forms by means of a differential equation involving theconcircular factor and their curvature and torsion, and we show that the concircularhelices are precisely the geodesics of the concircular surfaces.
Open Access
Constructions of Abelian Codes multiplying dimension of cyclic codes
(Springer, 2020) Bernal Buitrago, José Joaquín; Bueno Carreño, Diana H.; Simón Pinero, Juan Jacobo; Matemáticas
In this note, we apply some techniques developed in [1]–[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of cyclic codes whose maximum BCH bound equals its minimum distance the obtained abelian code verifies the same property; that is, the strong apparent distance and the minimum distance coincide. We finally use this construction to multiply Reed-Solomon codes to abelian codes.
Open Access
Controlled and Secure Access to Promote the Industrial Internet of Things
(IEEE, 2018-08-29) Márquez, Marco A.; Herrera, Reyes S.; Mejías, Andrés; Esquembre, Francisco; Andújar, Jose M.; Matemáticas
Internet of Things (IoT) aims at facilitating access to all devices that are connected to the internet, both wired and wireless. This scenario can initially seem interesting. Nevertheless, it has a lack of privacy and danger of malicious interaction with the devices. Therefore, IoT, as it stands, is not suitable for companies to make their data and devices accessible through the internet, since they could find an untidy cloud, made up of devices without the necessary control of use. This paper proposes the use of the cloud computing advantages to develop a secure access global system based on a cloud. The company will decide the controlled access to the chosen devices and data, both by employees and external people. The developed system can be used from different scenarios such as: a public cloud; an Infrastructure as a Service (IaaS); and a private cloud. To illustrate the operation of the developed system, a representative network of heterogeneous multiprotocol devices has been designed.