On Normal Forms for Levi-flat hypersurfaces with an Isolated Line Singularity

We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for that a Levi-flat hypersurface with a complex line as singularity to be a pullback of a real-analytic curve in C via a holomorphic function.Comment: 9 pages, accepted to Arkiv f\"or Matemati

Inter-spikes-intervals exponential and gamma distributions study of neuron firing rate for SVITE motor control model on FPGA

This paper presents a statistical study on a neuro-inspired spike-based implementation of the Vector-Integration-To-End-Point motor controller (SVITE) and compares its deterministic neuron-model stream of spikes with a proposed modification that converts the model, and thus the controller, in a Poisson like spike stream distribution. A set of hardware pseudo-random numbers generators, based on a Linear Feedback Shift Register (LFSR), have been introduced in the neuron-model so that they reach a closer biological neuron behavior. To validate the new neuron-model behavior a comparison between the Inter-Spikes-Interval empirical data and the Exponential and Gamma distributions has been carried out using the Kolmogorov–Smirnoff test. An in-hardware validation of the controller has been performed in a Spartan6 FPGA to drive directly with spikes DC motors from robotics to study the behavior and viability of the modified controller with random components. The results show that the original deterministic spikes distribution of the controller blocks can be swapped with Poisson distributions using 30-bit LFSRs. The comparative between the usable controlling signals such as the trajectory and the speed profile using a deterministic and the new controller show a standard deviation of 11.53 spikes/s and 3.86 spikes/s respectively. These rates do not affect our system because, within Pulse Frequency Modulation, in order to drive the motors, time length can be fixed to spread the spikes. Tuning this value, the slow rates could be filtered by the motor. Therefore, this SVITE neuro-inspired controller can be integrated within complex neuromorphic architectures with Poisson-like neurons

Dos nuevas inscripciones de Isona, Pallars Jussà. Los Antonii de Aeso

Aeso, la actual Isona en el occidente de Cataluña, es el más septentrional de los municipios conocidos en la zona en el Alto Imperio, y es notoria la cantidad de inscripciones que del mismo conservamos. Presentamos dos nuevos documentos epigráficos inéditos. Ambos se refieren a miembros de la familia de los Antonii, una de las más importantes de la localidad. Añadiendo estos nuevos lementos, estudiamos el papel en el municipio de tal familia -varios miembros ocuparon cargos municipales y también en el ejército, alcanzando el orden ecuestre- y sus posibles parentescos externos.The Roman Aeso, today Isona, ist the last municipium known before reaching the Pyrenean mounts in N.W. of Catalonia, Spain, and it is notorious the quantity inscriptions kept. We present here two new epigraphycs documents. Both belong to the Antonii family one of the most important in the town. Through these new elements we study this family's role in the municipium, -sorne of its membres held municipals charges, al so in the army, reaching the ordo equester-, and its possible family relationships outside tbe town