Random matrices, random polynomials and Coulomb systems

It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special attention devoted to electrostatic analogies. We also discuss the joint probability density of the zeros of polynomials whose coefficients are complex Gaussian variables. This leads to a new two-dimensional solvable gas of interacting particles, with non-trivial interactions between particles.Comment: 8 pages, to appear in the Proceedings of the International Conference on Strongly Coupled Coulomb Systems, Saint-Malo, 199

Urn-based models for dependent credit risks and their calibration through EM algorithm

In this contribution we analyze two models for the joint probability of defaults of dependent credit risks that are based on a generalisation of Polya urn scheme. In particular we focus our attention on the problems related to the maximum likelihood estimation of the parameters involved, and to this purpose we introduce an approach based on the use of the Expectation-Maximization algorithm. We show how to implement it in this context, and then we analyze the results obtained, comparing them with results obtained by other approaches.

Out-Of-The_Money Monte Carlo Simulation Option Pricing: the join use of Importance Sampling and Descriptive Sampling

As in any Monte Carlo application, simulation option valuation produces imprecise estimates. In such an application, Descriptive Sampling (DS) has proven to be a powerful Variance Reduction Technique. However, this performance deteriorates as the probability of exercising an option decreases. In the case of out of the money options, the solution is to use Importance Sampling (IS). Following this track, the joint use of IS and DS is deserving of attention. Here, we evaluate and compare the benefits of using standard IS method with the joint use of IS and DS. We also investigate the influence of the problem dimensionality in the variance reduction achieved. Although the combination IS+DS showed gains over the standard IS implementation, the benefits in the case of out-of-the-money options were mainly due to the IS effect. On the other hand, the problem dimensionality did not affect the gains. Possible reasons for such results are discussed.

Modeling relation paths for knowledge base completion via joint adversarial training

Knowledge Base Completion (KBC), which aims at determining the missing relations between entity pairs, has received increasing attention in recent years. Most existing KBC methods focus on either embedding the Knowledge Base (KB) into a specific semantic space or leveraging the joint probability of Random Walks (RWs) on multi-hop paths. Only a few unified models take both semantic and path-related features into consideration with adequacy. In this paper, we propose a novel method to explore the intrinsic relationship between the single relation (i.e. 1-hop path) and multi-hop paths between paired entities. We use Hierarchical Attention Networks (HANs) to select important relations in multi-hop paths and encode them into low-dimensional vectors. By treating relations and multi-hop paths as two different input sources, we use a feature extractor, which is shared by two downstream components (i.e. relation classifier and source discriminator), to capture shared/similar information between them. By joint adversarial training, we encourage our model to extract features from the multi-hop paths which are representative for relation completion. We apply the trained model (except for the source discriminator) to several large-scale KBs for relation completion. Experimental results show that our method outperforms existing path information-based approaches. Since each sub-module of our model can be well interpreted, our model can be applied to a large number of relation learning tasks.Comment: Accepted by Knowledge-Based System

Statistical mechanics of neocortical interactions: EEG eigenfunctions of short-term memory

This paper focuses on how bottom-up neocortical models can be developed into eigenfunction expansions of probability distributions appropriate to describe short-term memory in the context of scalp EEG. The mathematics of eigenfunctions are similar to the top-down eigenfunctions developed by Nunez, albeit they have different physical manifestations. The bottom-up eigenfunctions are at the local mesocolumnar scale, whereas the top-down eigenfunctions are at the global regional scale. However, as described in several joint papers, our approaches have regions of substantial overlap, and future studies may expand top-down eigenfunctions into the bottom-up eigenfunctions, yielding a model of scalp EEG that is ultimately expressed in terms of columnar states of neocortical processing of attention and short-term memory.Comment: 5 PostScript page

Iso-entangled bases and joint measurements

While entanglement between distant parties has been extensively studied, entangled measurements have received relatively little attention despite their significance in understanding non-locality and their central role in quantum computation and networks. We present a systematic study of entangled measurements, providing a complete classification of all equivalence classes of iso-entangled bases for projective joint measurements on 2 qubits. The application of this classification to the triangular network reveals that the Elegant Joint Measurement, along with white noise, is the only measurement resulting in output permutation invariant probability distributions when the nodes are connected by Werner states. The paper concludes with a discussion of partial results in higher dimensions.Comment: 5 pages + appendice