Lower Bounds on the Bounded Coefficient Complexity of Bilinear Maps

We prove lower bounds of order $n\log n$ for both the problem to multiply polynomials of degree $n$, and to divide polynomials with remainder, in the model of bounded coefficient arithmetic circuits over the complex numbers. These lower bounds are optimal up to order of magnitude. The proof uses a recent idea of R. Raz [Proc. 34th STOC 2002] proposed for matrix multiplication. It reduces the linear problem to multiply a random circulant matrix with a vector to the bilinear problem of cyclic convolution. We treat the arising linear problem by extending J. Morgenstern's bound [J. ACM 20, pp. 305-306, 1973] in a unitarily invariant way. This establishes a new lower bound on the bounded coefficient complexity of linear forms in terms of the singular values of the corresponding matrix. In addition, we extend these lower bounds for linear and bilinear maps to a model of circuits that allows a restricted number of unbounded scalar multiplications.Comment: 19 page

Active learning in annotating micro-blogs dealing with e-reputation

Elections unleash strong political views on Twitter, but what do people really think about politics? Opinion and trend mining on micro blogs dealing with politics has recently attracted researchers in several fields including Information Retrieval and Machine Learning (ML). Since the performance of ML and Natural Language Processing (NLP) approaches are limited by the amount and quality of data available, one promising alternative for some tasks is the automatic propagation of expert annotations. This paper intends to develop a so-called active learning process for automatically annotating French language tweets that deal with the image (i.e., representation, web reputation) of politicians. Our main focus is on the methodology followed to build an original annotated dataset expressing opinion from two French politicians over time. We therefore review state of the art NLP-based ML algorithms to automatically annotate tweets using a manual initiation step as bootstrap. This paper focuses on key issues about active learning while building a large annotated data set from noise. This will be introduced by human annotators, abundance of data and the label distribution across data and entities. In turn, we show that Twitter characteristics such as the author's name or hashtags can be considered as the bearing point to not only improve automatic systems for Opinion Mining (OM) and Topic Classification but also to reduce noise in human annotations. However, a later thorough analysis shows that reducing noise might induce the loss of crucial information.Comment: Journal of Interdisciplinary Methodologies and Issues in Science - Vol 3 - Contextualisation digitale - 201

A methodology for producing reliable software, volume 1

An investigation into the areas having an impact on producing reliable software including automated verification tools, software modeling, testing techniques, structured programming, and management techniques is presented. This final report contains the results of this investigation, analysis of each technique, and the definition of a methodology for producing reliable software