arXiv subjects

Rafael Plaza

Publications and source records attributed to Rafael Plaza.

3 recordsLinked to original sources

arXiv2018

Compressed Sensing ECG using Restricted Boltzmann Machines

Recently, it has been shown that compressed sensing (CS) has the potential to lower energy consumption in wireless electrocardiogram (ECG) systems. By reducing the number of acquired measurements, the communication burden is decreased and energy is saved. In this paper, we aim at further reducing the number of necessary measurements to achieve faithful reconstruction by exploiting the representational power of restricted Boltzmann machines (RBMs) to model the probability distribution of the sparsity pattern of ECG signals. The motivation for using this approach is to capture the higher-order statistical dependencies between the coefficients of the ECG sparse representation, which in turn, leads to superior reconstruction accuracy and reduction in the number of measurements, as it is shown via experiments.

eess.SP↗

arXiv2018

Characterization of intersecting families of maximum size in $PSL(2,q)$

We consider the action of the $2$-dimensional projective special linear group $PSL(2,q)$ on the projective line $PG(1,q)$ over the finite field $\F_q$, where $q$ is an odd prime power. A subset $S$ of $PSL(2,q)$ is said to be an intersecting family if for any $g_1,g_2 \in S$, there exists an element $x\in PG(1,q)$ such that $x^{g_1}= x^{g_2}$. It is known that the maximum size of an intersecting family in $PSL(2,q)$ is $q(q-1)/2$. We prove that all intersecting families of maximum size are cosets of point stabilizers for all odd prime powers $q>3$.

math.CO↗

arXiv2017

Resilience of ranks of higher inclusion matrices

Let $n \geq r \geq s \geq 0$ be integers and $\mathcal{F}$ a family of $r$-subsets of $[n]$. Let $W_{r,s}^{\mathcal{F}}$ be the higher inclusion matrix of the subsets in ${\mathcal F}$ vs. the $s$-subsets of $[n]$. When $\mathcal{F}$ consists of all $r$-subsets of $[n]$, we shall simply write $W_{r,s}$ in place of $W_{r,s}^{\mathcal{F}}$. In this paper we prove that the rank of the higher inclusion matrix $W_{r,s}$ over an arbitrary field $K$ is resilient. That is, if the size of $\mathcal{F}$ is "close" to ${n \choose r}$ then $\mbox{rank}_{K}(W_{r,s}^{\mathcal{F}}) = \mbox{rank}_{K}(W_{r,s})$, where $K$ is an arbitrary field. Furthermore, we prove that the rank (over a field $K$) of the higher inclusion matrix of $r$-subspaces vs. $s$-subspaces of an $n$-dimensional vector space over $\mathbb{F}_q$ is also resilient if ${\rm char}(K)$ is coprime to $q$.

math.CO↗