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Publication Sur la Réductibilité des Variétés des Lois d'Algèbres de Leibniz Complexes(Heldermann Verlag, 2007-06-26) Ancochea Bermúdez, José María; Margalef Bentabol, Juan; Sánchez Hernández, JonathanDans cette note, en utilisant les notions de déformation et contraction des lois d'algèbres de Lie et Leibniz, on montre que les variétés algébriques des lois d'algèbres de Leibniz complexes et de Leibniz nilpotentes de dimension supérieure ou égale à 3 sont réductibles.Publication Contractions of Low-Dimensional Nilpotent Jordan Algebras(Informa UK Limited, 2011-03-16) Margalef Bentabol, Juan; Ancochea Bermúdez, José María; Fresán, JavierIn this article, we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among their isomorphism classes. In particular, we prove that ... and ... are irreducible and that .... is the union of the Zariski closures of the orbits of two rigid Jordan algebras.Publication Evolution of the Cosmological Horizons in a Concordance Universe(IOP Publishing, 2012-12-21) Margalef Bentabol, Juan; Margalef Bentabol, Berta; Cepa, Jordi; Ministerio de Economía y Competitividad (España)The particle and event horizons are widely known and studied concepts, but the study of their properties, in particular their evolution, have only been done so far considering a single state equation in a decelerating universe. This paper is the first of two where we study this problem from a general point of view. Specifically, this paper is devoted to the study of the evolution of these cosmological horizons in an accelerated universe with two state equations, cosmological constant and dust. We have obtained simple expressions in terms of their respective recession velocities that generalize the previous results for one state equation only. With the equations of state considered, it is proved that both velocities remain always positive.Publication Evolution of the cosmological horizons in a universe with countably infinitely many state equations(IOP Publishing, 2013-02-08) Margalef Bentabol, Berta; Margalef Bentabol, Juan; Cepa, Jordi; Ministerio de Economía y Competitividad (España)This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider a general accelerated universe with countably infinitely many constant state equations, and we obtain simple expressions in terms of their respective recession velocities that generalize the previous results for one and two state equations. We also provide a qualitative study of the values of the horizons and their velocities at the origin of the universe and at the far future, and we prove that these values only depend on one dominant state equation. Finally, we compare both horizons and determine when one is larger than the other.Publication Bound and ground states of coupled 'NLS-KdV' equations with Hardy potential and critical power(Elsevier, 2023-08-25) Colorado Heras, Eduardo; López-Soriano, Rafael; Ortega García, Alejandro; Comunidad de Madrid; Ministerio de Economía y Competitividad (España)We consider the existence of bound and ground states for a family of nonlinear elliptic systems in RN, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equa-tions are coupled by what we call "Schrodinger-Korteweg-de Vries" non-symmetric terms, which arise in some phenomena of fluid mechanics. By means of variational methods, ground states are derived for several ranges of the positive coupling parameter nu. Moreover, by using min-max arguments, we seek bound states under some energy assumptions.Publication A stationary population model with an interior interface-type boundary(Elsevier, 2023-10-01) Álvarez Caudevilla, Pablo; Brandle Cerqueira, Cristina; Ministerio de Economía y Competitividad (España)We propose a stationary system that might be regarded as a migration model of some population abandoning their original place of abode and becoming part of another population, once they reach the interface boundary. To do so, we show a model where each population follows a logistic equation in their own environment while assuming spatial heterogeneities. Moreover, both populations are coupled through the common boundary, which acts as a permeable membrane on which their flow moves in and out. The main goal we face in this work will be to describe the precise interplay between the stationary solutions with respect to the parameters involved in the problem, in particular the growth rate of the populations and the coupling parameter involved on the boundary where the interchange of flux is taking place.Publication Auditable Asymmetric Password Authenticated Public Key Establishment(Springer, 2022-11) Faonio, Antonio; González Vasco, María Isabel; Soriente, Claudio; Truong, Hien Thi Thu; Ministerio de Economía y Competitividad (España)Non-interactive zero-knowledge (NIZK) arguments allow a prover to convince a verifier about the truthfulness of an N P-statement by sending just one message, without disclosing any additional information. In several practical scenarios, the Fiat-Shamir transform is used to convert an efficient constant-round public-coin honest-verifier zero-knowledge proof system into an efficient NIZK argument system. This approach is provably secure in the random oracle model, crucially requires the programmability of the random oracle and extraction works through rewinds. The works of Lindell [TCC 2015] and Ciampi et al. [TCC 2016] proposed efficient NIZK arguments with non-programmable random oracles along with a programmable common reference string. In this work we show an efficient NIZK argument with straight-line simulation and extraction that relies on features that alone are insufficient to construct NIZK arguments (regardless of efficiency). More specifically we consider the notion of quasi-polynomial time simulation proposed by Pass in [EUROCRYPT 2003] and combine it with simulation and extraction with non-programmable random oracles thus obtaining a NIZK argument of knowledge where neither the zero-knowledge simulator, nor the argument of knowledge extractor needs to program the random oracle. Still, both the simulator and the extractor are straightline. Our construction uses as a building block a modification of the Fischlin’s transform [CRYPTO 2005] and combines it with the concept of dense puzzles introduced by Baldimtsi et al. [ASIACRYPT 2016]. We also argue that our NIZK argument system inherits the efficiency features of Fischlin’s transform, which represents the main advantage of Fischlin’s protocol over existing schemes.Publication Group key exchange protocols withstanding ephemeral-key reveals(Institution of Engineering and Technology (IET), 2018-01) González Vasco, María Isabel; Pérez Del Pozo, Ángel Luis; Suarez Corona, Adriana; Ministerio de Economía y Competitividad (España)When a group key exchange protocol is executed, the session key is typically extracted from two types of secrets: long-term keys (for authentication) and freshly generated (often random) values. The leakage of this latter so-called ephemeral keys has been extensively analysed in the 2-party case, yet very few works are concerned with it in the group setting. The authors provide a generic group key exchange construction that is strongly secure, meaning that the attacker is allowed to learn both long-term and ephemeral keys (but not both from the same participant, as this would trivially disclose the session key). Their design can be seen as a compiler, in the sense that it builds on a 2-party key exchange protocol which is strongly secure and transforms it into a strongly secure group key exchange protocol by adding only one extra round of communication. When applied to an existing 2-party protocol from Bergsma et al., the result is a 2-round group key exchange protocol which is strongly secure in the standard model, thus yielding the first construction with this property.Publication Partitioned group password-based authenticated key exchange(Oxford Academic, 2017-12) Fiore, Dario; González Vasco, María Isabel; Soriente, ClaudioGroup Password-Based Authenticated Key Exchange (GPAKE) allows a group of users to establish a secret key, as long as all of them share the same password. However, in existing GPAKE protocols as soon as one user runs the protocol with a non-matching password, all the others abort and no key is established. In this paper we seek for a more flexible, yet secure, GPAKE and put forward the notion of partitioned GPAKE. Partitioned GPAKE tolerates users that run the protocol on different passwords. Through a protocol run, any subgroup of users that indeed share a password, establish a session key, factoring out the 'noise' of inputs by users holding different passwords. At the same time any two keys, each established by a different subgroup of users, are pair-wise independent if the corresponding subgroups hold different passwords. We also introduce the notion of password-privacy for partitioned GPAKE, which is a kind of affiliation hiding property, ensuring that an adversary should not be able to tell whether any given set of users share a password. Finally, we propose an efficient instantiation of partitioned GPAKE building on an unforgeable symmetric encryption scheme and a PAKE by Bellare et al. Our proposal is proven secure in the random oracle/ideal cipher model, and requires only two communication rounds.Publication A Key for John Doe: Modeling and Designing Anonymous Password-Authenticated Key Exchange Protocols(IEEE, 2021-05-01) González Vasco, María Isabel; Pérez Del Pozo, Angel; Soriente, Claudio; Ministerio de Economía y Competitividad (España)Anonymous Password-Authenticated Key Exchange (APAKE) can be seen as the hybrid offspring of standard key exchange and anonymous password authentication protocols. APAKE allows a client holding a low-entropy password to establish a session key with a server, provided that the client's password is in the server's set. Moreover, no information about the password input by the client or the set of valid passwords held by the server should leak to the other party-beyond whether the client's password lies or not in the server's password database. To the best of our knowledge, all APAKE proposals to date either assume client storage or force the client to remember the index assigned to its password in the server's database. Furthermore, earlier works either provide only informal definitions or fail in some sense to properly model the primitive. In this paper, we provide a formal security model for APAKE, capturing security and anonymity provisions for both clients and servers. In addition, we present two APAKE protocols that only require clients to remember a password and that attain our sought key secrecy and anonymity guarantees. Our first protocol leverages oblivious pseudo-random functions, while the second one builds upon a special type of identity-based encryption scheme.Publication Vibrational resonance: a study with high-order word-series averaging(Sciendo, 2016-01) Murua, A.; Sanz Serna, Jesús María; Ministerio de Economía y Competitividad (España)We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the technique applied here, the tasks of constructing the averaged system and the associated change of variables are divided into two parts. It is first necessary to build recursively a set of so-called word basis functions and, after that, all the required manipulations involve only scalar coefficients that are computed by means of simple recursions. As distinct from the situation with other approaches, with word-series, high-order averaged systems may be derived without having to compute the associated change of variables. In the system considered here, the construction of high-order averaged systems makes it possible to obtain very precise approximations to the true dynamics.Publication Remarks on a nonlinear nonlocal operator in Orlicz spaces(De Gruyter, 2019-05-22) Correa Velandia, Ernesto; Pablo Martínez, Arturo deWe study integral operators Lu(x)=∫RNpsi(u(x)−u(y))J(x−y)dy of the type of the fractional p-Laplacian operator, and the properties of the corresponding Orlicz and Sobolev-Orlicz spaces. In particular we show a Poincaré inequality and a Sobolev inequality, depending on the singularity at the origin of the kernel J considered, which may be very weak. Both inequalities lead to compact inclusions. We then use those properties to study the associated elliptic problem Lu=f in a bounded domain Omega, and boundary condition u≡0 on Omegac; both cases f=f(x) and f=f(u) are considred, including the generalized eigenvalue problem f(u)=lambdapsi(u).Publication Concurrent enhancement of percolation and synchronization in adaptive networks(Springer Nature, 2016-06-02) Eom, Young-Ho; Boccaletti, Stefano; Caldarelli, Guido; European Commission; Ministerio de Economía y Competitividad (España)Co-evolutionary adaptive mechanisms are not only ubiquitous in nature, but also beneficial for the functioning of a variety of systems. We here consider an adaptive network of oscillators with a stochastic, fitness-based, rule of connectivity, and show that it self-organizes from fragmented and incoherent states to connected and synchronized ones. The synchronization and percolation are associated to abrupt transitions, and they are concurrently (and significantly) enhanced as compared to the non-adaptive case. Finally we provide evidence that only partial adaptation is sufficient to determine these enhancements. Our study, therefore, indicates that inclusion of simple adaptive mechanisms can efficiently describe some emergent features of networked systems' collective behaviors, and suggests also self-organized ways to control synchronization and percolation in natural and social systems.Publication On the mathematical modelling of tumor-induced angiogenesis(American Institute of Mathematical Sciences (AIMS), 2017-02-01) López Bonilla, Luis Francisco; Capasso, Vincenzo; Álvaro Ballesteros, Mariano; Carretero Cerrajero, Manuel; Terragni, Filippo; Ministerio de Economía y Competitividad (España)An angiogenic system is taken as an example of extremely complex ones in the field of Life Sciences, from both analytical and computational points of view, due to the strong coupling between the kinetic parameters of the relevant branching-growth-anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. To reduce this complexity, for a conceptual stochastic model we have explored how to take advantage of the system intrinsic multiscale structure: one might describe the stochastic dynamics of the cells at the vessel tip at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. But the outcomes of relevant numerical simulations show that the proposed model, in presence of anastomosis, is not self-averaging, so that the "propagation of chaos" assumption cannot be applied to obtain a deterministic mean field approximation. On the other hand we have shown that ensemble averages over many realizations of the stochastic system may better correspond to a deterministic reaction-diffusion system.Publication The hyperbolicity constant of infinite circulant graphs(Walter de Gruyter GmbH, 2017-06-09) Rodríguez García, José Manuel; Sigarreta Almira, José María; Ministerio de Economía y Competitividad (España)If X is a geodesic metric space and x(1), x(2), x(3) is an element of X, a geodesic triangle T = {x(1), x(2), x(3)} is the union of the three geodesics [x(1)x(2)], [x(2)x(3)] and [x(3)x(1)] in X. The space X is delta-hyperbolic (in the Gromov sense) if any side of T is contained in a delta-neighborhood of the union of the two other sides, for every geodesic triangle T in X. Deciding whether or not a graph is hyperbolic is usually very difficult; therefore, it is interesting to find classes of graphs which are hyperbolic. A graph is circulant if it has a cyclic group of automorphisms that includes an automorphism taking any vertex to any other vertex. In this paper we prove that infinite circulant graphs and their complements are hyperbolic. Furthermore, we obtain several sharp inequalities for the hyperbolicity constant of a large class of infinite circulant graphs and the precise value of the hyperbolicity constant of many circulant graphs. Besides, we give sharp bounds for the hyperbolicity constant of the complement of every infinite circulant graph.Publication Sparse bilinear forms for Bochner Riesz multipliers and applications(London Mathematical Society, 2017-12-01) Benea, Cristina; Bernicot, Frederic; Luque, TeresaWe use the very recent approach developed by Lacey in [An elementary proof of the A2 Bound, Israel J. Math., to appear] and extended by Bernicot, Frey and Petermichl in [Sharp weighted norm estimates beyond Calderon-Zygmund theory, Anal. PDE 9 (2016) 1079-1113], in order to control Bochner-Riesz operators by a sparse bilinear form. In this way, new quantitative weighted estimates, as well as vector-valued inequalities are deduced.Publication Discrete locally finite full groups of Cantor set homeomorphisms(Wiley, 2021-08-01) Garrido Angulo, Alejandra; Reid, Colin D:This work is motivated by the problem of finding locally compact group topologies for piecewise full groups (a.k.a. topological full groups). We determine that any piecewise full group that is locally compact in the compact-open topology on the group of self-homeomorphisms of the Cantor set must be uniformly discrete, in a precise sense that we introduce here. Uniformly discrete groups of self-homeomorphisms of the Cantor set are in particular countable, locally finite, residually finite and discrete in the compact-open topology. The resulting piecewise full groups form a subclass of the ample groups introduced by Krieger. We determine the structure of these groups by means of their Bratteli diagrams and associated dimension ranges (K0 groups). We show through an example that not all uniformly discrete piecewise full groups are subgroups of the ‘obvious’ ones, namely piecewise full groups of finite groups.Publication Word series high-order averaging of highly oscillatory differential equations with delay(Sciendo, 2019-07) Sanz Serna, Jesús María; Zhu, Beibei; Ministerio de Economía y Competitividad (España)We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.Publication Genetic algorithms for the scheduling in additive manufacturing(Universitat Politècnica de València, 2020-07-18) Castillo Rivera, Salvador; Antón, J. de; Olmo, R. del; Pajares, J.; López Paredes, A.Genetic Algorithms (GAs) are introduced to tackle the packing problem. The scheduling in Additive Manufacturing (AM) is also dealt with to set up a managed market, called "Lonja3D". This will enable to determine an alternative tool through the combinatorial auctions, wherein the customers will be able to purchase the products at the best prices from the manufacturers. Moreover, the manufacturers will be able to optimize the production capacity and to decrease the operating costs in each case.Publication Understanding drivers when investing for impact: an experimental study(Springer Nature, 2020-05-06) De Amicis, Luisa; Binenti, Silvia; Maciel Cardoso, Felipe; Garcia Lazaro, Carlos; Sánchez, Angel; Moreno, Yamir; Ministerio de Economía y Competitividad (España); Ministerio de Ciencia, Innovación y Universidades (España)In the last decade, a global interest in impact investing-whose goal is to generate social and environmental benefits alongside economic returns-has rapidly grown. In this context, this paper explores the socio-demographic characteristics of investors who choose impact investment options over traditional investments, and on the drivers promoting such choices. More specifically, the study consists of an experiment-based research in which 602 participants (non-experts and experts in the financial sector) took part in a multiple-choice game involving different investment scenarios and incentive conditions. The findings show that both expert investors and female participants are more likely to choose impact investment options and that the tendency to invest in social funds increases with age. Neither external and centrally planned incentives, such as fiscal incentives, nor the educational level of participants show a significant influence on investment choices. By contrast, information about the actual social impact achieved by funds plays a role in promoting socially oriented decisions. In this regard, visual aids appear to be an effective means of promoting impact investment. These findings may be of interest to policymakers, social campaigners and investment practitioners themselves when designing strategies for raising interest in impact investing or norms to strengthen a conducive and enabling environment for social entrepreneurship more broadly.