Cohomology of Artin groups of type tilde{A}_n, B_n and applications

We consider two natural embeddings between Artin groups: the group G_{tilde{A}_{n-1}} of type tilde{A}_{n-1} embeds into the group G_{B_n} of type B_n; G_{B_n} in turn embeds into the classical braid group Br_{n+1}:=G_{A_n} of type A_n. The cohomologies of these groups are related, by standard results, in a precise way. By using techniques developed in previous papers, we give precise formulas (sketching the proofs) for the cohomology of G_{B_n} with coefficients over the module Q[q^{+-1},t^{+-1}], where the action is (-q)-multiplication for the standard generators associated to the first n-1 nodes of the Dynkin diagram, while is (-t)-multiplication for the generator associated to the last node. As a corollary we obtain the rational cohomology for G_{tilde{A}_n} as well as the cohomology of Br_{n+1} with coefficients in the (n+1)-dimensional representation obtained by Tong, Yang and Ma. We stress the topological significance, recalling some constructions of explicit finite CW-complexes for orbit spaces of Artin groups. In case of groups of infinite type, we indicate the (few) variations to be done with respect to the finite type case. For affine groups, some of these orbit spaces are known to be K(pi,1) spaces (in particular, for type tilde{A}_n). We point out that the above cohomology of G_{B_n} gives (as a module over the monodromy operator) the rational cohomology of the fibre (analog to a Milnor fibre) of the natural fibration of K(G_{B_n},1) onto the 2-torus.Comment: This is the version published by Geometry & Topology Monographs on 22 February 200

Cohomology of affine Artin groups and applications

The result of this paper is the determination of the cohomology of Artin groups of type A_n, B_n and \tilde{A}_{n} with non-trivial local coefficients. The main result is an explicit computation of the cohomology of the Artin group of type B_n with coefficients over the module \Q[q^{\pm 1},t^{\pm 1}]. Here the first (n-1) standard generators of the group act by (-q)-multiplication, while the last one acts by (-t)-multiplication. The proof uses some technical results from previous papers plus computations over a suitable spectral sequence. The remaining cases follow from an application of Shapiro's lemma, by considering some well-known inclusions: we obtain the rational cohomology of the Artin group of affine type \tilde{A}_{n} as well as the cohomology of the classical braid group {Br}_{n} with coefficients in the n-dimensional representation presented in \cite{tong}. The topological counterpart is the explicit construction of finite CW-complexes endowed with a free action of the Artin groups, which are known to be K(\pi,1) spaces in some cases (including finite type groups). Particularly simple formulas for the Euler-characteristic of these orbit spaces are derived.Comment: 21 pages, 4 figure

Are We Using Autoencoders in a Wrong Way?

Autoencoders are certainly among the most studied and used Deep Learning models: the idea behind them is to train a model in order to reconstruct the same input data. The peculiarity of these models is to compress the information through a bottleneck, creating what is called Latent Space. Autoencoders are generally used for dimensionality reduction, anomaly detection and feature extraction. These models have been extensively studied and updated, given their high simplicity and power. Examples are (i) the Denoising Autoencoder, where the model is trained to reconstruct an image from a noisy one; (ii) Sparse Autoencoder, where the bottleneck is created by a regularization term in the loss function; (iii) Variational Autoencoder, where the latent space is used to generate new consistent data. In this article, we revisited the standard training for the undercomplete Autoencoder modifying the shape of the latent space without using any explicit regularization term in the loss function. We forced the model to reconstruct not the same observation in input, but another one sampled from the same class distribution. We also explored the behaviour of the latent space in the case of reconstruction of a random sample from the whole dataset

The K(\pi, 1) problem for the affine Artin group of type \widetilde{B}_n and its cohomology

In this paper we prove that the complement to the affine complex arrangement of type \widetilde{B}_n is a K(\pi, 1) space. We also compute the cohomology of the affine Artin group G of type \widetilde{B}_n with coefficients over several interesting local systems. In particular, we consider the module Q[q^{\pm 1}, t^{\pm 1}], where the first n-standard generators of G act by (-q)-multiplication while the last generator acts by (-t)-multiplication. Such representation generalizes the analog 1-parameter representation related to the bundle structure over the complement to the discriminant hypersurface, endowed with the monodromy action of the associated Milnor fibre. The cohomology of G with trivial coefficients is derived from the previous one.Comment: 21 page

Towards Seismic Design of Nonstructural Elements: Italian Code-Compliant Acceleration Floor Response Spectra

Seismic risk reduction of a building system, meant as primary building structure and nonstructural elements (NSEs) as a whole, must rely upon an adequate design of each of these two items. As far as NSEs are concerned, adequate seismic design means understanding of some basic principles and concepts that involve different actors, such as designers, manufacturers, installers, and directors of works. The current Italian Building Code, referred to as NTC18 hereinafter, defines each set of tasks and responsibilities in a sufficiently detailed manner, rendering now evident that achieving the desired performance level stems from a jointed contribution of all actors involved. Bearing in mind that seismic design is nothing else than proportioning properly seismic demand, in terms of acceleration and/or displacement, and the corresponding capacity, this paper gives a synthetic and informative overview on how to evaluate these two parameters. To shed some light on this, the concept of acceleration floor response spectrum (AFRS) is firstly brought in, along with basics of building structure-NSEs interaction, and is then deepened by means of calculation methods. Both the most rigorous method based on nonlinear dynamic simulations and the simplified analytical formulations provided by the NTC18 are briefly discussed and reviewed, trying to make them clearer even to readers with no structural/earthquake engineering background because, as a matter of fact, NSEs are often selected by architects and/or mechanical or electrical engineers. Lastly, a simple case study, representative of a European code-compliant five-storey masonry-infilled reinforced concrete frame building, is presented to examine differences between numerical and analytical AFRS and to quantify accuracy of different NTC18 procedures

Augmented Interaction Systems for Supporting Autistic Children. Evolution of a Multichannel Expressive Tool: The SEMI Project Feasibility Study

International audienceBackground: Over the past ten years, the authors have been designing, developing, and testing pervasive technology to support children with autism (ASD). Methods: In the present study, an integrated system based on multimedia and augmented interaction technologies have been tested on young subjects with ASD and dyspraxia in the age range of 6-10 years, in charge for rehabilitation treatments; a team of clinical psychologists has analyzed the results of the experimentation. The ten children involved in the project underwent an initial assessment of praxis skills and motor coordination. Subsequently, the subjects were subdivided into two subgroups: five children participated in the experimentation and five were evaluated as the control group (treatment as usual). Results: The evaluation showed an increased score in the several aspects considered, and particularly those related to motor coordination. An improvement in balancing tests and in hands-movement testing was found. Conclusion: The children involved in the sessions showed greater ability to self-control the movement as well as to select specific motor areas. The methods used seem to be promising to improve emotional and social skills too in a motivating and enjoyable climate. A high level of acceptance by professionals was observed and parents' feedback was also positive

Quantification of Epicardial Fat by Cardiac CT Imaging

The aim of this work is to introduce and design image processing methods for the quantitative analysis of epicardial fat by using cardiac CT imaging

A Preliminary Study on Non Contact Thermal Monitoring of Microwave Photonic Systems

Microwave photonic systems are more susceptible to thermal fluctuations due tothermo-optic effect. In order to stabilize the performance of photonic components, thermal monitoringis achieved by using thermistors placed at any arbitrary location along the component. This workpresents non contact thermography of a fully functional microwave photonic system. The temperatureprofile of printed circuit board (PCB) and photonic integrated circuit (PIC) is obtained using FlukeFLIR (A65) camera. We performed Otsu’s thresholding to segment heat centers located across PCB aswell as PIC. The infrared and visible cameras used in this work have different field of view, therefore,after applying morphological methods, we performed image registration to synchronize both visibleand thermal images. We demonstrate this method on the circuit board with active electrical/photonicelements and were able to observe thermal profile of these components