A Vertex-Skipping property for almost-minimizers of the relative perimeter in convex sets

Given a convex domain $\Omega\subset \mathbb{R}^{3}$ and an almost-minimizer $E$ of the relative perimeter in $\Omega$, we prove that the closure of $\partial E \cap \Omega$ does not contain vertices of $\Omega$

The effect of X-ray dust-scattering on a bright burst from the magnetar 1E 1547.0-5408

A bright burst, followed by an X-ray tail lasting ~10 ks, was detected during an XMM-Newton observation of the magnetar 1E 1547.0-5408 carried out on 2009 February 3. The burst, also observed by SWIFT/BAT, had a spectrum well fit by the sum of two blackbodies with temperatures of ~4 keV and 10 keV and a fluence in the 0.3-150 keV energy range of ~1e-5 erg/cm2. The X-ray tail had a fluence of ~4e-8 erg/cm2. Thanks to the knowledge of the distances and relative optical depths of three dust clouds between us and 1E 1547.0-5408, we show that most of the X-rays in the tail can be explained by dust scattering of the burst emission, except for the first ~20-30 s. We point out that other X-ray tails observed after strong magnetar bursts may contain a non-negligible contribution due to dust scattering.Comment: 8 pages, 2 tables and 10 figures; accepted to publication in MNRA

Dendritic Computation through Exploiting Resistive Memory as both Delays and Weights

Biological neurons can detect complex spatio-temporal features in spiking patterns via their synapses spread across their dendritic branches. This is achieved by modulating the efficacy of the individual synapses, and by exploiting the temporal delays of their response to input spikes, depending on their position on the dendrite. Inspired by this mechanism, we propose a neuromorphic hardware architecture equipped with multiscale dendrites, each of which has synapses with tunable weight and delay elements. Weights and delays are both implemented using Resistive Random Access Memory (RRAM). We exploit the variability in the high resistance state of RRAM to implement a distribution of delays in the millisecond range for enabling spatio-temporal detection of sensory signals. We demonstrate the validity of the approach followed with a RRAM-aware simulation of a heartbeat anomaly detection task. In particular we show that, by incorporating delays directly into the network, the network's power and memory footprint can be reduced by up to 100x compared to equivalent state-of-the-art spiking recurrent networks with no delays

Self-organization of an inhomogeneous memristive hardware for sequence learning

Learning is a fundamental component of creating intelligent machines. Biological intelligence orchestrates synaptic and neuronal learning at multiple time scales to self-organize populations of neurons for solving complex tasks. Inspired by this, we design and experimentally demonstrate an adaptive hardware architecture Memristive Self-organizing Spiking Recurrent Neural Network (MEMSORN). MEMSORN incorporates resistive memory (RRAM) in its synapses and neurons which configure their state based on Hebbian and Homeostatic plasticity respectively. For the first time, we derive these plasticity rules directly from the statistical measurements of our fabricated RRAM-based neurons and synapses. These "technologically plausible” learning rules exploit the intrinsic variability of the devices and improve the accuracy of the network on a sequence learning task by 30%. Finally, we compare the performance of MEMSORN to a fully-randomly-set-up spiking recurrent network on the same task, showing that self-organization improves the accuracy by more than 15%. This work demonstrates the importance of the device-circuit-algorithm co-design approach for implementing brain-inspired computing hardware