Related papers: Exponential bases, Paley-Wiener spaces and applica…
We investigate the possibility of constructing exponentially localized composite Wannier bases, or equivalently smooth periodic Bloch frames, for 3-dimensional time-reversal symmetric topological insulators, both of bosonic and of fermionic…
We address polarization coherence in terms of correlations of Stokes variables. We develop an scalar polarization mutual coherence function that allows us to define a polarization coherence time. We find a suitable spectral polarization…
Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope…
A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…
We study the exciton states in the symmetrically biased dice model, the electronic structures of which have an isolated flat band between two dispersive bands. At 1/3 or 2/3 filling, the model describes a two-dimensional semiconductor with…
We prove that Wigner functions contain a symplectic connection. The latter covariantises the symplectic exterior derivative on phase space. We analyse the role played by this connection and introduce the notion of local symplectic…
Bayesian networks have been used extensively in diagnostic tasks such as medicine, where they represent the dependency relations between a set of symptoms and a set of diseases. A criticism of this type of knowledge representation is that…
In this work we provide a mathematical framework to describe the periodically time variant (PTV) linear systems. We study their frequency-domain features to estimate the output bandwidth, a necessary value to obtain a suitable digital…
We present a different symplectic point of view in the definition of weighted modulation spaces $M^{p,q}_m(\mathbb{R}^d)$ and weighted Wiener amalgam spaces $W(\mathcal{F} L^p_{m_1},L^q_{m_2})(\mathbb{R}^d)$. All of the classical…
A signal space approach is presented to study the Nyquist sampling, number of degrees of freedom and reconstruction of an electromagnetic field under arbitrary scattering conditions. Conventional signal processing tools, such as the…
Fulling, King, Wybourne and Cummings (FKWC) have proposed to expand systematically the Riemann polynomials encountered in the context of field theories in curved spacetime on standard bases constructed from group theoretical considerations.…
Surface plasmons are usually described as surface waves with either a complex wavevector or a complex frequency. When discussing their merits in terms of field confinment or enhancement of the local density of states, controversies…
This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_\theta^{\alpha}$ of order $\alpha$ and skewness…
A $\phi$-exponential distribution is a generalization of an exponential distribution associated to functions $\phi$ in an appropriate class, and the space of $\phi$-exponential distributions has a dually flat structure. We study features of…
Vector space models have become popular in distributional semantics, despite the challenges they face in capturing various semantic phenomena. We propose a novel probabilistic framework which draws on both formal semantics and recent…
It has been shown that Paley-Wiener functions may be recovered from their values on a complete interpolating sequence. This paper explores the same phenomenon, and gives a sufficient condition on a function $\phi(x)$, called an…
We present a second quantization description of frequency-based continuous variables quantum computation in the subspace of single photons. For this, we define frequency and time operators using the free field Hamiltonian and its Fourier…
Variational Autoencoders (VAEs) provide a flexible and scalable framework for non-linear dimensionality reduction. However, in application domains such as genomics where data sets are typically tabular and high-dimensional, a black-box…
Inspired by the works of \cite{baz2} and \cite{kian}, this study develops an abstract framework for analyzing differential equations with space-dependent fractional time derivatives and bounded operators. Within this framework, we establish…
Asymptotic time evolution of a wave packet describing a non-relativistic particle incident on a potential barrier is considered, using the Wigner phase-space distribution. The distortion of the trasmitted wave packet is determined by two…