The zero-removing property in some Hilbert spaces of entire functions arising in sampling theory

In the topic of sampling in reproducing kernel Hilbert spaces, sampling in Paley–Wiener spaces is the paradigmatic example. A natural generalization of Paley–Wiener spaces is obtained by substituting the Fourier kernel with an analytic Hilbert-space-valued kernel K. Thus we obtain a reproducing kernel Hilbert space HKHK of entire functions in which the Kramer property allows to prove a sampling theorem. A necessary and sufficient condition ensuring that this sampling formula can be written as a Lagrange-type interpolation series concerns the stability under removal of a finite number of zeros of the functions belonging to the space HKHK; this is the so-called zero-removing property. This work is devoted to the study of the zero-removing property in HKHK spaces, regardless of the Kramer property, revealing its connections with other mathematical fields

On the Distributional Fourier Duality and Its Applications

AbstractSampling theorems for bandlimited functions or distributions are obtained by exploiting the topological isomorphism between the space E′(R) of distributions of compact support on R and the Paley–Wiener spacePWof entire functions satisfying an estimate of the form |f(z)|≤A(1+|z|)NeB|Imz|for some constantsA,B,N≥0. We obtain sampling theorems forfinPWby expanding its Fourier transformTin a series converging in the topology of E′(R) and whose coefficients are samples taken fromf. By Fourier duality, we obtain a sampling theorem forfin the spacePW. These sampling expansions converge, in fact, uniformly on compact sets of C, since convergence in the topology ofPWimplies uniform convergence on compact sets of C. This procedure allows us to recover previous sampling theorems in a unified way. We also present further expansions of Paley–Wiener functions obtained by expanding their Fourier transform as a series involving Legendre or Hermite polynomials

Improving Dialogue Management: Quality Datasets vs Models

Task-oriented dialogue systems (TODS) have become crucial for users to interact with machines and computers using natural language. One of its key components is the dialogue manager, which guides the conversation towards a good goal for the user by providing the best possible response. Previous works have proposed rule-based systems (RBS), reinforcement learning (RL), and supervised learning (SL) as solutions for the correct dialogue management; in other words, select the best response given input by the user. However, this work argues that the leading cause of DMs not achieving maximum performance resides in the quality of the datasets rather than the models employed thus far; this means that dataset errors, like mislabeling, originate a large percentage of failures in dialogue management. We studied the main errors in the most widely used datasets, Multiwoz 2.1 and SGD, to demonstrate this hypothesis. To do this, we have designed a synthetic dialogue generator to fully control the amount and type of errors introduced in the dataset. Using this generator, we demonstrated that errors in the datasets contribute proportionally to the performance of the model

Convolution Systems on Discrete Abelian Groups as a Unifying Strategy in Sampling Theory

A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space H is proposed. This subspace is associated to a unitary representation of a countable discrete abelian group G on H. The samples are defined by means of a filtering process which generalizes the usual sampling settings. The multiply generated setting allows to consider some examples where the group G is non-abelian as, for instance, crystallographic groups. Finally, it is worth to mention that classical average or pointwise sampling in shift-invariant subspaces are particular examples included in the followed approach.This work has been supported by the grant MTM2017-84098-P from the Spanish Ministerio de Economía y Competitividad (MINECO).Publicad

Sampling Associated with a Unitary Representation of a Semi-Direct Product of Groups: A Filter Bank Approach

This article belongs to the Special Issue New trends on Symmetry and Topology in Quantum MechanicsAn abstract sampling theory associated with a unitary representation of a countable discrete non abelian group G, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples, the use of a filter bank formalism and the corresponding frame analysis allow for fixing the mathematical problem to be solved: the search of appropriate dual frames for l2(G). An example involving crystallographic groups illustrates the obtained results by using either average or pointwise samples.This research was funded by the grant MTM2017-84098-P from the Spanish Ministerio de Economía y Competitividad (MINECO)

Generalized sampling in U-invariant subspaces

In this work we carry out some results in sampling theory for U-invariant subspaces of a separable Hilbert space H, also called atomic subspaces. These spaces are a generalization of the well-known shift- invariant subspaces in L2 (R); here the space L2 (R) is replaced by H, and the shift operator by U. Having as data the samples of some related operators, we derive frame expansions allowing the recovery of the elements in Aa. Moreover, we include a frame perturbation-type result whenever the samples are affected with a jitter error

Knit product of finite groups and sampling

A finite sampling theory associated with a unitary representation of a finite non-abelian group G on a Hilbert space is established. The non-abelian group G is a knit product N⋈H of two finite subgroups N and H where at least N or H is abelian. Sampling formulas where the samples are indexed by either N or H are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space ℓ2(G) having a unitary invariance property; this is done by using matrix analysis techniques. An example involving dihedral groups illustrates the obtained sampling results

Montfort, obres hidràuliques disperses

Les comarques del Vinalopó tenen moltes obres hidràuliques de origen musulmá i de tradició cristiana que es mantenen en l'actualitat com el cas de Montfort d'Alacant

Monitoring the phenolic ripening of red grapes using a multisensor system based on metal-oxide nanoparticles

Producción CientíficaThe maturity of grapes is usually monitored by means of the sugar concentration. However, the assessment of other parameters such as the phenolic content is also important because the phenolic maturity has an important impact on the organoleptic characteristics of wines. In this work, voltammetric sensors able to detect phenols in red grapes have been developed. They are based on metal oxide nanoparticles (CeO2, NiO, and TiO2,) whose excellent electrocatalytic properties toward phenols allows obtaining sensors with detection limits in the range of 10−8 M and coefficients of variation lower than 7%. An electronic tongue constructed using a combination of the nanoparticle-based sensors is capable to monitor the phenolic maturity of red grapes from véraison to maturity. Principal Component Analysis (PCA) can be successfully used to discriminate samples according to the ripeness. Regression models performed using Partial Least Squares (PLS-1) have established good correlations between voltammetric data obtained with the electrochemical sensors and the Total Polyphenolic Index, the Brix degree and the Total Acidity, with correlation coefficients close to 1 and low number of latent variables. An advantage of this system is that the electronic tongue can be used for the simultaneous assessment of these three parameters which are the main factors used to monitor the maturity of grapes. Thus the electronic tongue based on metal oxide nanoparticles can be a valuable tool to monitor ripeness. These results demonstrate the exciting possible applications of metal oxide nanoparticles in the field of electronic tongues.Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (project AGL2015-67482- R)Junta de Castilla y Leon - Fondo Europeo de Desarrollo Regional (project VA011U16)Junta de Castilla y León (grant BOCYL-D-24112015-9