In the last lecture we discussed how distributional JL implies Gordon's theorem, and began our discussion of sparse JL. We wrote Πx 2 = σ T A T x A x σ and bounded the expression using Hanson-Wright in terms of the Frobenius norm. In this lecture we'll bound that Frobenius norm and then discuss applications to fast nearest neighbors. Note that we defined B x = A T x A x as the center of the pro...

This paper describes a corpus of Brazilian Portuguese texts built in view of the construction of an Anaphora Resolution system, which is part of a fully-fledged Natural Language Processing system (STRING). The ZAC corpus is aimed at the resolution of the so-called zero-anaphora, that is, an anaphora relation where the anaphoric expression (or anaphor) has been zeroed The paper briefly discusses...

(2) Let n be an ordinal number, T be an admissible connected term order of n, L be an addassociative right complementable right zeroed commutative associative well unital distributive Abelian field-like non degenerated non empty double loop structure, and f , p, g be polynomials of n, L. Suppose f reduces to g, p, T . Then there exists a monomial m of n, L such that g = f −m∗ p and HT(m∗ p,T ) ...

The oculomotor neural integrator is a brainstem nucleus that stores the short term memory of eye position during gaze holding. This neural integrator is believed to perform temporal integration of transient eye velocity input using positive feedback. Such models of integration are known to suffer from a fine-tuning problem [9] since changes in the amount of feedback by less than 10% can de-tune...

Knowledge of accuracy of numerical integration is important for composing an overall numerical error budget; in orbit determination and propagation for space surveillance, there is frequently a computation time-accuracy tradeoff that must be balanced. There are several techniques to assess the accuracy of a numerical integrator. In this paper we compare some of those techniques: comparison with...

Thomas Karcher Institute for Program Structures and Data Organization Karlsruhe Institute of Technology 76128 Karlsruhe, Germany [email protected] Christopher Guckes Institute for Program Structures and Data Organization Karlsruhe Institute of Technology 76128 Karlsruhe, Germany [email protected] Walter F. Tichy Institute for Program Structures and Data Organization Karlsruhe Institute...

Synapses play a critical role in memory, learning, and cognition. Their main functions include converting pre-synaptic voltage spikes to post-synaptic currents, as well scaling the input signal. Several brain-inspired architectures have been proposed emulate behavior of biological synapses. While these are useful explore properties nervous systems, challenge making biocompatible flexible circui...