-- In order to improve children speech therapy, we develop a Fuzzy Expert System based on a speech therapy guide. This guide, write in natural language, was formalized using fuzzy logic paradigm. In this manner we obtain a knowledge base with over 150 rules and 19 linguistic variables. All these researches, including expert system validation, are part of TERAPERS project (financed by the National Agency for Scientific Research, Romania). I. INTRODUCTION The main objectives of speech therapy expert system develop by our team are [1]: - personalized therapy (the therapy must be in according with child's problems level, context and possibilities); - speech therapist assistant (the expert system offer some suggestion regarding what exercises are better for a specific moment and from a specific child); - (self) teaching (when system's conclusion is different that speech therapist's conclusion the last one must have the knowledge base change possibility).

In this paper we present architecture of a fuzzy expert system used for therapy of dyslalic children. With fuzzy approach we can create a better model for speech therapist decisions. A software interface was developed for validation of the system. The main objectives of this task are: personalized therapy (the therapy must be in according with child's problems level, context and possibilities), speech therapist assistant (the expert system offer some suggestion regarding what exercises are better for a specific moment and from a specific child), (self) teaching (when system's conclusion is different that speech therapist's conclusion the last one must have the knowledge base change possibility). Keywords: fuzzy expert systems, speech therapy 1. Introduction In this article we refer to LOGOMON system developed in TERAPERS project by the authors.

When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f (n). n is re-inserted in the OPEN list with the f -cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain- and heuristic- specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

In many real world elections, agents are not required to rank all candidates. We study three of the most common methods used to modify voting rules to deal with such partial votes. These methods modify scoring rules (like the Borda count), elimination style rules (like single transferable vote) and rules based on the tournament graph (like Copeland) respectively. We argue that with an elimination style voting rule like single transferable vote, partial voting does not change the situations where strategic voting is possible. However, with scoring rules and rules based on the tournament graph, partial voting can increase the situations where strategic voting is possible. As a consequence, the computational complexity of computing a strategic vote can change. For example, with Borda count, the complexity of computing a strategic vote can decrease or stay the same depending on how we score partial votes.

INCE the appearance of the seminal paper [1], NMF has become a popular data decomposition technique due to succesful applications in a still growing number of fields where data are nonnegative, such as pixel intensities in computer vision, amplitude spectra in audio signal analysis and EEG signal analysis, term counts in document clustering problems, and item ratings in collaborative filtering. NMF aims at decompositions, where, and are all nonnegative matrices. Throughout this paper will be regarded as a collection of data samples organized columnwise, as a dictionary of features organized columnwise, and as matrix of coefficients when is projected onto the dictionary. Under assumptions of linearity and nonnegativity, when underlying dimensionality is lower than dimensionality of the original space of the data, dimensionality reduction of the data can effectively be achieved this way. Although the decomposition is nonunique in general, NMF is able to produce strictly additive decompositions perceived as part-based by adding additional bias in the model [1], [2]. To this end, different sparsity promoting regularizers have been proposed for divergence-based NMF [3]. Also, to include higher order data descriptions, many other variants have been developed, e.g.

We give some lectures on the work on formal logic of Jacques Herbrand, and sketch his life and his influence on automated theorem proving. The intended audience ranges from students interested in logic over historians to logicians. Besides the well-known correction of Herbrand's False Lemma by Goedel and Dreben, we also present the hardly known unpublished correction of Heijenoort and its consequences on Herbrand's Modus Ponens Elimination. Besides Herbrand's Fundamental Theorem and its relation to the Loewenheim-Skolem-Theorem, we carefully investigate Herbrand's notion of intuitionism in connection with his notion of falsehood in an infinite domain. We sketch Herbrand's two proofs of the consistency of arithmetic and his notion of a recursive function, and last but not least, present the correct original text of his unification algorithm with a new translation.

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed estimator performs more efficiently than a traditional approach. The method consists of three steps: (1) a classical Least Squares Estimate (LSE), (2) the support is recovered through a Linear Programming (LP) optimization problem which can be computed using a soft-thresholding step, (3) a de-biasing step using a LSE on the estimated support set. The main contribution of this note is a formal derivation of an associated ORACLE property of the final estimate. That is, when the number of samples is large enough, the estimate is shown to equal the LSE based on the support of the {\em true} parameters.

We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded, data-adaptive matrix. As a result of this adaptivity, the convex banding estimator enjoys theoretical optimality properties not attained by previous banding or tapered estimators. In particular, our convex banding estimator is minimax rate adaptive in Frobenius and operator norms, up to log factors, over commonly-studied classes of covariance matrices, and over more general classes. Furthermore, it correctly recovers the bandwidth when the true covariance is exactly banded. Our convex formulation admits a simple and efficient algorithm. Empirical studies demonstrate its practical effectiveness and illustrate that our exactly-banded estimator works well even when the true covariance matrix is only close to a banded matrix, confirming our theoretical results. Our method compares favorably with all existing methods, in terms of accuracy and speed. We illustrate the practical merits of the convex banding estimator by showing that it can be used to improve the performance of discriminant analysis for classifying sound recordings.

We consider the problem of learning soft assignments of $N$ items to $K$ categories given two sources of information: an item-category similarity matrix, which encourages items to be assigned to categories they are similar to (and to not be assigned to categories they are dissimilar to), and an item-item similarity matrix, which encourages similar items to have similar assignments. We propose a simple quadratic programming model that captures this intuition. We give necessary conditions for its solution to be unique, define an out-of-sample mapping, and derive a simple, effective training algorithm based on the alternating direction method of multipliers. The model predicts reasonable assignments from even a few similarity values, and can be seen as a generalization of semisupervised learning. It is particularly useful when items naturally belong to multiple categories, as for example when annotating documents with keywords or pictures with tags, with partially tagged items, or when the categories have complex interrelations (e.g. hierarchical) that are unknown.

In many circumstances where multiple agents need to make a joint decision, voting is used to aggregate the agents' preferences. Each agent's vote carries a weight, and if the sum of the weights of the agents in favor of some outcome is larger than or equal to a given quota, then this outcome is decided upon. The distribution of weights leads to a certain distribution of power. Several `power indices' have been proposed to measure such power. In the so-called inverse problem, we are given a target distribution of power, and are asked to come up with a game in the form of a quota, plus an assignment of weights to the players whose power distribution is as close as possible to the target distribution (according to some specied distance measure). Here we study solution approaches for the larger class of voting game design (VGD) problems, one of which is the inverse problem. In the general VGD problem, the goal is to find a voting game (with a given number of players) that optimizes some function over these games. In the inverse problem, for example, we look for a weighted voting game that minimizes the distance between the distribution of power among the players and a given target distribution of power (according to a given distance measure). Our goal is to find algorithms that solve voting game design problems exactly, and we approach this goal by enumerating all games in the class of games of interest. We first present a doubly exponential algorithm for enumerating the set of simple games. We then improve on this algorithm for the class of weighted voting games and obtain a quadratic exponential (i.e., 2^O(n^2)) algorithm for enumerating them. We show that this improved algorithm runs in output-polynomial time, making it the fastest possible enumeration algorithm up to a polynomial factor. Finally, we propose an exact anytime-algorithm that runs in exponential time for the power index weighted voting game design problem (the `inverse problem'). We implement this algorithm to find a weighted voting game with a normalized Banzhaf power distribution closest to a target power index, and perform experiments to obtain some insights about the set of weighted voting games. We remark that our algorithm is applicable to optimizing any exponential-time computable function, the distance of the normalized Banzhaf index to a target power index is merely taken as an example.