BIRD, BCAM's Institutional Repository DataThe BIRD digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://bird.bcamath.org:802019-07-12T17:03:19Z2019-07-12T17:03:19ZConductance-Based Refractory Density Approach for a Population of Bursting NeuronsChizhov A.Campillo F.Desroches M.Guillamon ARodrigues S.http://hdl.handle.net/20.500.11824/9932019-07-12T01:00:11Z2019-01-01T00:00:00ZConductance-Based Refractory Density Approach for a Population of Bursting Neurons
Chizhov A.; Campillo F.; Desroches M.; Guillamon A; Rodrigues S.
The conductance-based refractory density (CBRD) approach is a parsimonious mathematical-computational framework for modeling interact- ing populations of regular spiking neurons, which, however, has not been yet extended for a population of bursting neurons. The canonical CBRD method allows to describe the firing activity of a statistical ensemble of uncoupled Hodgkin-Huxley-like neurons (differentiated by noise) and has demonstrated its validity against experimental data. The present manuscript generalises the CBRD for a population of bursting neurons; however, in this pilot computational study we consider the simplest setting in which each individual neuron is governed by a piecewise linear bursting dynamics. The resulting popula- tion model makes use of slow-fast analysis, which leads to a novel method- ology that combines CBRD with the theory of multiple timescale dynamics. The main prospect is that it opens novel avenues for mathematical explo- rations, as well as, the derivation of more sophisticated population activity from Hodgkin-Huxley-like bursting neurons, which will allow to capture the activity of synchronised bursting activity in hyper-excitable brain states (e.g. onset of epilepsy).
2019-01-01T00:00:00ZA Lê-Greuel type formula for the image Milnor numberNuño-Ballesteros J.J.Pallarés Torres I.http://hdl.handle.net/20.500.11824/9922019-07-12T01:00:12Z2019-02-01T00:00:00ZA Lê-Greuel type formula for the image Milnor number
Nuño-Ballesteros J.J.; Pallarés Torres I.
Let $f\colon (\mathbb{C}^n,0)\to (\mathbb{C}^{n+1},0)$ be a corank 1 finitely determined map germ. For a generic linear form $p\colon (\mathbb{C}^{n+1},0)\to(\mathbb{C},0)$ we denote by $g\colon (\mathbb{C}^{n-1},0)\to (\mathbb{C}^{n},0)$ the transverse slice of $f$ with respect to $p$. We prove that the sum of the image Milnor numbers $\mu_I(f)+\mu_I(g)$ is equal to the number of critical points of $p|_{X_s}\colon X_s\to\mathbb{C}$ on all the strata of $X_s$, where $X_s$ is the disentanglement of $f$ (i.e., the image of a stabilisation $f_s$ of $f$).
2019-02-01T00:00:00ZA Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operatorCassano B.Pizzichillo F.Vega L.http://hdl.handle.net/20.500.11824/9912019-07-04T01:00:09Z2019-06-01T00:00:00ZA Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator
Cassano B.; Pizzichillo F.; Vega L.
We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials $\mathbf V$ of Coulomb type: we characterise its eigenvalues in terms of the Birman—Schwinger principle and we bound its discrete spectrum from below, showing that the ground-state energy is reached if and only if $\mathbf V$ verifies some rigidity conditions. In the particular case of an electrostatic potential, these imply that $\mathbf V$ is the Coulomb potential.
2019-06-01T00:00:00ZExamples of varieties with index one on C1 fieldsDan A.Kaur I.http://hdl.handle.net/20.500.11824/9902019-07-03T01:00:09Z2019-04-16T00:00:00ZExamples of varieties with index one on C1 fields
Dan A.; Kaur I.
Let K be the fraction field of a Henselian discrete valuation ring with algebraically closed residue field k. In this article we give a sufficient criterion for a projective variety over such a field to have index 1.
2019-04-16T00:00:00Z