Implications of the Ganea Condition

Suppose the spaces X and X cross A have the same Lusternik-Schnirelmann category: cat(X cross A)= cat(X). Then there is a strict inequality cat(X cross (A halfsmash B)) < cat (X) + cat(A halfsmash B) for every space B, provided the connectivity of A is large enough (depending only on X). This is applied to give a partial verification of a conjecture of Iwase on the category of products of spaces with spheres.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-36.abs.htm

Deep Joint Entity Disambiguation with Local Neural Attention

We propose a novel deep learning model for joint document-level entity disambiguation, which leverages learned neural representations. Key components are entity embeddings, a neural attention mechanism over local context windows, and a differentiable joint inference stage for disambiguation. Our approach thereby combines benefits of deep learning with more traditional approaches such as graphical models and probabilistic mention-entity maps. Extensive experiments show that we are able to obtain competitive or state-of-the-art accuracy at moderate computational costs.Comment: Conference on Empirical Methods in Natural Language Processing (EMNLP) 2017 long pape

Management model of the correlation between the rate of tax pressure and the flow of Inland Revenue. The Laffer Curve

The adaptation to the Romanian macroeconomic realities of the theory according to which an increase in the tax pressure will not necessarily entail the corresponding increase of the Inland Revenue, but in exchange, the decrease of the tax pressure will create favorable conditions for the increase of the inland revenue, implies the creation of correlative models to support the idea and to provide a proper management at macroeconomic level. Such a model is the one using as statistic instrument the Laffer Curve starting from the concrete data of Romanian economy.Rate of tax pressure, normal range, prohibitive range, Inland Revenue, fiscal facilities

The product formula for Lusternik-Schnirelmann category

If C=C_\phi denotes the mapping cone of an essential phantom map \phi from the suspension of the Eilenberg-Mac Lane complex K=K(Z,5) to the 4-sphere S=S^4 we derive the following properties: (1) The LS category of the product of C with any n-sphere S^n is equal to 3; (2) The LS category of the product of C with itself is equal to 3, hence is strictly less than twice the LS category of C. These properties came to light in the course of an unsuccessful attempt to find, for each positive integer m, an example of a pair of 1-connected CW-complexes of finite type in the same Mislin (localization) genus with LS categories m and 2m. If \phi is such that its p-localizations are inessential for all primes p, then by the main result of [J. Roitberg, The Lusternik-Schnirelmann category of certain infinite CW-complexes, Topology 39 (2000), 95-101], the pair C_*, C where C_*= S wedge \Sigma ^2 K, provides such an example in the case m=1.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-25.abs.html Version 2: change of author's email addres