Publications related to Torsion tensor

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We explore the design and analysis of post-quantum cryptographic primitives with an emphasis on two angles. First, diversity of assumptions, by building and analysing cryptography that does not rely on structured lattices. Second, diversity of functionalities, focusing on various primitives that extend beyond standard encryption. Motivated by the rapid development of quantum computing and the consequent threat to classical public-key cryptography, we therefore consider two families of post-quantum assumpti

The states of a single photon in four-dimensional de Sitter (dS) spacetime form a Unitary Irreducible Representation (UIR) of SO(1,4), which we call the photon UIR. While in flat spacetime photons are intimately tied to gauge symmetry, we demonstrate that in de Sitter, photon states emerge generically in any quantum field theory, even without an underlying U(1) gauge field. We derive a Källén-Lehmann representation for antisymmetric tensor two-point functions and show that numerous composite operators const

Let R be a complete valuation ring of mixed characteristic (0, p) with algebraically closed fraction field K and residue field k. Let X/R be a smooth projective morphism. We show that if X k is stably rational, then H 3 K et (X K , ‫)ޚ‬ is torsion-free. The proof uses the integral p-adic Hodge theory of Bhatt, Morrow and Scholze and the study of differential forms in positive characteristic. We then apply this result to study the Noether problem for finite p-groups.

A better understanding of the physics of tokamak breakdown has the potential to ensure reliable operation and increase confidence in the startup scenarios of future tokamak devices. This article presents an experimental validation of 0D Townsend breakdown theory in a toroidal geometry using the TCV tokamak and two separate time-dependent 2D torodally-symmetric electromagnetic field reconstruction techniques. Breakdown parameters have been scanned along three experimental axes: neutral pressure, toroidal loo

Stability of discrete-time Lur'e systems is one of the classical problems within the literature. For nonlinearities characterised by slope restriction, Zames-Falb multipliers provide a sufficient condition for robust stability, which may also be necessary, as posited by the Carrasco conjecture. In this paper, we explore a novel class of non-parametric discrete-time Zames-Falb multipliers with an infinite impulse response. We begin by introducing a new class of discrete-time systems characterised as continuo

Our Ref.: 39418.EPF.P110PC Official file: tba December 20, 2024 - 51 - Abstract The present invention provides a system (100) for planning and/or providing control to neuro- modulation and/or neurostimulation and/or an actuator such as a brain computer interface (BCI) and/or providing a neural interface system, especially a brain-spinal-cord-interface sys- tem, the system (100) comprising: at least one input module (10) for brain signals (S), espe- cially raw brain signals (S); at least one pre-processing m

Increased focus has been recently given to the ion temperature Ti near the separatrix and in the scrape-off layer (SOL) due to its impact on plasma confinement, wall sputtering, heat fluxes, and edge turbulence. In current tokamaks, high pedestal collisionality often clamps pedestal top ion and electron temperatures together. However, thermal decoupling occurs in the SOL due to the different ion and electron masses, leading to T-i/T-e>1 at the separatrix and in the SOL. Despite consistently observing elevat

Soft robot are celebrated for their propensity to enable compliant and complex robot-environment interactions. Soft robotic manipulators, or slender continuum structure robots have the potential to exploit these interactions to enable new exploration and manipulation capabilities and safe human-robot interactions. However, the interactions, or perturbations by external forces cause the soft structure to deform in an infinite degree of freedom (DOF) space. To control such system, reduced order models are nee

State-of-the-art classifiers have been shown to be largely vulnerable to adversarial perturbations. One of the most effective strategies to improve robustness is adversarial training. In this paper, we investigate the effect of adversarial training on the geometry of the classification landscape and decision boundaries. We show in particular that adversarial training leads to a significant decrease in the curvature of the loss surface with respect to inputs, leading to a drastically more "linear" behaviour

Simultaneous and proportional control of a prosthetic hand and wrist is still a controversial issue, although giant steps have lately been made in this direction. In this paper, we study the application of a novel machine learning method to the problem, with the aim to potentially improve such control. Namely we apply different kernels for tensor Gaussian process regression to data obtained from an advanced, flexible tactile sensor applied on the skin, recording muscle bulging in the forearm. The sensor is

Divertor detachment is explored on the TCV tokamak in alternative magnetic geometries. Starting from typical TCV single-null shapes, the poloidal flux expansion at the outer strikepoint is varied by a factor of 10 to investigate the X-divertor characterist ...

Plasma blob dynamics on the high-field side in the proximity of a magnetic field null (X point) is investigated in TORPEX. A significant acceleration of the blobs towards the X point is observed. Close to the X point the blobs break apart. The E x B drifts ...

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed reference domain with random coefficients. Under suitable assumptions on the random mapping and the input data, in particular the so-called small data assumption, we prove the well-posedness of the problem. We assume then that the mapping depends affinely on

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely parametrized operators is crucial in order to enhance the online solution of reduced-order models (ROMs). However, in many cases such an affine decomposition is not readily available, and must be recovered through (often) intrusive procedures, such as the

This paper presents a method for verb phrase (VP) alignment in an English/French parallel corpus and its use for improving statistical machine translation (SMT) of verb tenses. The method starts from automatic word alignment performed with GIZA++, and relies on a POS tagger and a parser, in combination with several heuristics, in order to identify non-contiguous components of VPs, and to label the aligned VPs with their tense and voice on each side. This procedure is applied to the Europarl corpus, leading

Torsion tensor

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Post-Quantum Cryptography beyond Encryption: Design and Cryptanalysis

What is a photon in de Sitter spacetime?

Reduction modulo p of Noether’s problem

Electromagnetic Analysis of Breakdown Conditions and Experimental Validation of 0d Townsend Breakdown Theory on the Tcv Tokamak

Convex Characterisation of Frequency-Domain Discrete-Time Zames-Falb Multipliers

System for planning and/or providing neuromodulation and/or neurostimulation and method thereof

Separatrix Ion to Electron Temperature Ratio in the Tcv and Asdex Upgrade Tokamaks

Piecewise Affine Curvature model: a reduced-order model for soft robot-environment interaction beyond PCC

Robustness via curvature regularization, and vice versa

Improving hand and wrist activity detection using tactile sensors and tensor regression methods on Riemannian manifolds

Results from recent detachment experiments in alternative divertor configurations on TCV

X-Point Effect on Plasma Blob Dynamics

MATHICSE Technical Report : A posteriori error estimation for the steady Navier-Stokes equations in random domains

MATHICSE Technical Report : Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

English-French Verb Phrase Alignment in Europarl for Tense Translation Modeling