On the automorphisms group of the asymptotic pants complex of an infinite surface of genus zero

The braided Thompson group $\mathcal B$ is an asymptotic mapping class group of a sphere punctured along the standard Cantor set, endowed with a rigid structure. Inspired from the case of finite type surfaces we consider a Hatcher-Thurston cell complex whose vertices are asymptotically trivial pants decompositions. We prove that the automorphism group $\hat{\mathcal B^{\frac{1}{2}}}$ of this complex is also an asymptotic mapping class group in a weaker sense. Moreover $\hat{\mathcal B^{\frac{1}{2}}}$ is obtained by $\mathcal B$ by first adding new elements called half-twists and further completing it.Comment: revised version,17p., 13 figure

Geophysical investigation of the Pb-Zn deposit of Lontzen-Poppelsberg, Belgium

The drillhole information from the Lontzen-Poppelsberg site has demonstrated three orebodies and has allowed the estimation of the extension of the lodes, their dip, and the location at the ground surface. The localisation of the lodes makes them excellent targets for further exploration with geophysics. This deposit is classified as a Mississippi Valley Type (MVT) deposit. It consists mainly of Pb-Zn-Fe sulphides that display contrasting values in resistivity, chargeability, density, and magnetic susceptibility, with regards to the sedimentary host rocks. The dipole-dipole direct current (DC) resistivity and induce polarization (IP) profiles have been collected and inverted to successfully delineate the Pb-Zn mineralization and the geological structures. Short-spacing EM34 electromagnetic conductivity data were collected mainly on the top of Poppelsberg East lode and have revealed a conductive body matching with the geologically modelled mineralization. Gravity profiles have been carried out perpendicularly to the lode orientation; they show a strong structural anomaly. High resolution ground magnetic data were collected over the study area, but they showed no anomaly over the ore deposits. The geophysical inversion results are complementary to the model based on drill information, and allow us to refine the delineation of the mineralization. The identification of the geophysical signatures of this deposit permits targeting new possible mineralization in the area

Aubry sets for weakly coupled systems of Hamilton--Jacobi equations

We introduce a notion of Aubry set for weakly coupled systems of Hamilton--Jacobi equations on the torus and characterize it as the region where the obstruction to the existence of globally strict critical subsolutions concentrates. As in the case of a single equation, we prove the existence of critical subsolutions which are strict and smooth outside the Aubry set. This allows us to derive in a simple way a comparison result among critical sub and supersolutions with respect to their boundary data on the Aubry set, showing in particular that the latter is a uniqueness set for the critical system. We also highlight some rigidity phenomena taking place on the Aubry set.Comment: 35 pages v.2 the introduction has been rewritten and shortened. Some proofs simplified. Corrections and references added. Corollary 5.3 added stating antisymmetry of the Ma\~n\'e matrix on points of the Aubry set. Section 6 contains a new example

Detection of nonlinearity in a dynamic system using deformation modes obtained from the Wavelet Transfrom of measured responses

An efficient approach to Structural Health Monitoring of dynamical systems based on the Wavelet Transform (WT) and the concept of subspace angle is presented. The objective is to propose a detection method that is sensitive to the onset of nonlinear behaviour in a dynamic system. For this purpose, instantaneous frequencies are identified first from output-only vibration signals using the Wavelet Transform. Time varying deformation shapes are then extracted by analyzing the whole measurement data set on the structure. From this information, different dynamic states of the structure may be detected by inspecting time variations of ‘modal’ features. The experimental structure considered here as application example is a clamped beam with a geometric nonlinearity. Detection of nonlinearity is carried out by means of the concept of subspace angles between instantaneous deformation modes extracted from measurement data using the continuous Wavelet Transform. The method consists in controlling the angular coherence between active subspaces of the current and reference states respectively. The proposed technique, which shows a good sensitivity to small changes in the dynamic behaviour of the structure, may also be used for damage detection

Enhanced EEG-Based Mental State Classification : A novel approach to eliminate data leakage and improve training optimization for Machine Learning

In this paper, we explore prior research and introduce a new methodology for classifying mental state levels based on EEG signals utilizing machine learning (ML). Our method proposes an optimized training method by introducing a validation set and a refined standardization process to rectify data leakage shortcomings observed in preceding studies. Furthermore, we establish novel benchmark figures for various models, including random forest and deep neural networks.Comment: 5 pages, 2 figures, 1 tabl

Mechanistic insights into the metabolization of S-Sulfocysteine by CHO cells using a multi-omics approach

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Efficient Lattice-Based Blind Signatures via Gaussian One-Time Signatures

Lattice-based blind signature schemes have been receiving some recent attention lately. Earlier efficient 3-round schemes (Asiacrypt 2010, Financial Cryptography 2020) were recently shown to have mistakes in their proofs, and fixing them turned out to be extremely inefficient and limited the number of signatures that a signer could send to less than a dozen (Crypto 2020). In this work we propose a round-optimal, 2-round lattice-based blind signature scheme which produces signatures of length 150KB. The running time of the signing protocol is linear in the maximum number signatures that can be given out, and this limits the number of signatures that can be signed per public key. Nevertheless, the scheme is still quite efficient when the number of signatures is limited to a few dozen thousand, and appears to currently be the most efficient lattice-based candidate