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A. González

Publications and source records attributed to A. González.

8 recordsLinked to original sources

Bounds on Frobenius dimension

In this article, we prove two types of results about the Frobenius dimension of associative algebras. First, we refine the known upper bound for the Frobenius dimension of a finite dimensional algebra in terms of its dimension as a vector space, and show that the only algebras reaching this bound are radical square zero algebras associated with single-vertex quivers. Second, we compute Frobenius dimension for low-dimensional algebras explicitly, and for truncated path algebras in terms of paths with no detours in their underlying quivers.

math.RA↗

The Equidistant Dimension of Graphs

A subset $S$ of vertices of a connected graph $G$ is a distance-equalizer set if for every two distinct vertices $x, y \in V (G) \setminus S$ there is a vertex $w \in S$ such that the distances from $x$ and $y$ to $w$ are the same. The equidistant dimension of $G$ is the minimum cardinality of a distance-equalizer set of G. This paper is devoted to introduce this parameter and explore its properties and applications to other mathematical problems, not necessarily in the context of graph theory. Concretely, we first establish some bounds concerning the order, the maximum degree, the clique number, and the independence number, and characterize all graphs attaining some extremal values. We then study the equidistant dimension of several families of graphs (complete and complete multipartite graphs, bistars, paths, cycles, and Johnson graphs), proving that, in the case of paths and cycles, this parameter is related with 3-AP-free sets. Subsequently, we show the usefulness of distance-equalizer sets for constructing doubly resolving sets.

math.CO↗

Spin-Seebeck effect and spin polarization in a multiple quantum dot molecule

In this work, we study the conductance and the thermoelectric properties of a quantum dot embedded between two metallic leads with a side-coupled triple quantum dot molecule under a magnetic field. We focus on the spin polarization and thermoelectric quantities. Our results show the possibility of design an efficient spin filter device besides a noticeable enhancement of the Seebeck coefficient driven by the asymmetry in the quantum dots energy levels and a tunable pure spin Seebeck effect is obtained. This behavior also holds in the interacting case, where a pure spin Seebeck effect can be obtained for fixed values of the embedded quantum dot energy level. Our findings could lead to the implementation of a new pure spin energy conversion and capable spin filter devices working with weak magnetic fields.

cond-mat.mes-hall↗

Proceedings of the third "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'16)

The third edition of the "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) took place in Aalborg, the 4th largest city in Denmark situated beautifully in the northern part of the country, from the 24th to 26th of August 2016. The workshop venue was at the Aalborg University campus. One implicit objective of this biennial workshop is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For this third edition, iTWIST'16 gathered about 50 international participants and features 8 invited talks, 12 oral presentations, and 12 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing (e.g., optics, computer vision, genomics, biomedical, digital communication, channel estimation, astronomy); Application of sparse models in non-convex/non-linear inverse problems (e.g., phase retrieval, blind deconvolution, self calibration); Approximate probabilistic inference for sparse problems; Sparse machine learning and inference; "Blind" inverse problems and dictionary learning; Optimization for sparse modelling; Information theory, geometry and randomness; Sparsity? What's next? (Discrete-valued signals; Union of low-dimensional spaces, Cosparsity, mixed/group norm, model-based, low-complexity models, ...); Matrix/manifold sensing/processing (graph, low-rank approximation, ...); Complexity/accuracy tradeoffs in numerical methods/optimization; Electronic/optical compressive sensors (hardware).

math.NA↗

First tests of the applicability of $γ$-ray imaging for background discrimination in time-of-flight neutron capture measurements

In this work we explore for the first time the applicability of using $γ$-ray imaging in neutron capture measurements to identify and suppress spatially localized background. For this aim, a pinhole gamma camera is assembled, tested and characterized in terms of energy and spatial performance. It consists of a monolithic CeBr$_3$ scintillating crystal coupled to a position-sensitive photomultiplier and readout through an integrated circuit AMIC2GR. The pinhole collimator is a massive carven block of lead. A series of dedicated measurements with calibrated sources and with a neutron beam incident on a $^{197}$Au sample have been carried out at n_TOF, achieving an enhancement of a factor of two in the signal-to-background ratio when selecting only those events coming from the direction of the sample.

physics.ins-det↗

VAMOS: a Pathfinder for the HAWC Gamma-Ray Observatory

VAMOS was a prototype detector built in 2011 at an altitude of 4100m a.s.l. in the state of Puebla, Mexico. The aim of VAMOS was to finalize the design, construction techniques and data acquisition system of the HAWC observatory. HAWC is an air-shower array currently under construction at the same site of VAMOS with the purpose to study the TeV sky. The VAMOS setup included six water Cherenkov detectors and two different data acquisition systems. It was in operation between October 2011 and May 2012 with an average live time of 30%. Besides the scientific verification purposes, the eight months of data were used to obtain the results presented in this paper: the detector response to the Forbush decrease of March 2012, and the analysis of possible emission, at energies above 30 GeV, for long gamma-ray bursts GRB111016B and GRB120328B.

astro-ph.IM↗

Hypergraphs for computing determining sets of Kneser graphs

A set of vertices $S$ is a \emph{determining set} of a graph $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The \emph{determining number} of $G$ is the minimum cardinality of a determining set of $G$. This paper studies determining sets of Kneser graphs from a hypergraph perspective. This new technique lets us compute the determining number of a wide range of Kneser graphs, concretely $K_{n:k}$ with $n\geq \frac{k(k+1)}{2}+1$. We also show its usefulness by giving shorter proofs of the characterization of all Kneser graphs with fixed determining number 2, 3 or 4, going even further to fixed determining number 5. We finally establish for which Kneser graphs $K_{n:k}$ the determining number is equal to $n-k$, answering a question posed by Boutin.

math.CO↗

Noisy kink in microtubules

We study the power spectrum of a class of noise effects generated by means of a digital-like disorder in the traveling variable of the conjectured Ginzburg-Landau-Montroll kink excitations moving along the walls of the microtubules. We have found a 1/f^α noise with α\in (1.82-2.04) on all the time scales we have considered

cond-mat.soft↗