Concept

Lie theory

Publications associées (25)

Hybrid ground-state quantum algorithms based on neural Schrödinger forging

Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis stat ...

Amer Physical Soc2024

Touch and Closeness in Naturally Organized Activities

Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...

2024

An elementary treatment on the diffraction of crystalline structures

Gervais Chapuis

Although W. L. Bragg's law can be easily derived for beginners in the field of crystallography, its interpretation however seems to cause some difficulties which lies essentially in the relation between the concept of lattice planes and the unit cell const ...

2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

Acoustic Actuation Of Suspended Graphene For Linear Excitation Of 2D Nems

Luis Guillermo Villanueva Torrijo, Muhammad Faizan, Marsha Mary Parmar

In this paper, we present the fabrication of on-chip piezoelectric acoustic actuation for 2D materials. Acoustic actuation is achieved at device level through patterning of aluminum nitride (AlN) thin film at wafer scale. Two piezoelectric stacks consistin ...

IEEE2019

$A_1$-type subgroups containing regular unipotent elements

Donna Testerman

Let be a simple exceptional algebraic group of adjoint type over an algebraically closed field of characteristic and let be a subgroup of containing a regular unipotent element of . By a theorem of Testerman, is contained in a connected subgroup of of type ...

2019

On Sets Defining Few Ordinary Circles

Frank de Zeeuw

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least ordinary circles. Moreover, we determine the exact minimu ...

Springer2018

Diophantine properties of nilpotent Lie groups

A finitely generated subgroup F of a real Lie group G is said to be Diophantine if there is beta > 0 such that non-trivial elements in the word ball B-Gamma(n) centered at 1 is an element of F never approach the identity of G closer than broken vertical ba ...

London Mathematical Society, Cambridge2015

Density of rational points on del Pezzo surfaces of degree one

We state conditions under which the set S(k) of k-rational points on a del Pezzo surface S of degree 1 over an infinite field k of characteristic not equal to 2 or 3 is Zariski dense. For example, it suffices to require that the elliptic fibration S -> P-1 ...

Academic Press Inc Elsevier Science2014

Personalized neuroprosthetics

José del Rocio Millán Ruiz, Silvestro Micera, Grégoire Courtine, David Allenson Borton

Decades of technological developments have populated the field of neuroprosthetics with myriad replacement strategies, neuromodulation therapies, and rehabilitation procedures to improve the quality of life for individuals with neuromotor disorders. Despit ...

American Association for the Advancement of Science2013

On the irreducibility of symmetrizations of cross-characteristic representations of finite classical groups

Donna Testerman

Let W be a vector space over an algebraically closed field k. Let H be a quasisimple group of Lie type of characteristic p not equal char(k) acting irreducibly on W. Suppose also that G is a classical group with natural module W, chosen minimally with resp ...

2013

Extensions of Lie-Rinehart algebras and cotangent bundle reduction

Tudor Ratiu

Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...

Oxford University Press2013

Incommensurate crystallography without additional dimensions

Philippe Kocian

It is shown that the Euclidean group of translations, when treated as a Lie group, generates translations not only in Euclidean space but on any space, curved or not. Translations are then not necessarily vectors (straight lines); they can be any curve com ...

International Union of Crystallography2013

A Micro-Uav with the Capability of Direct Georeferencing

Jan Skaloud, Martin Rehak, Romain Mabillard

This paper presents the development of a low cost UAV (Unmanned Aerial Vehicle) with the capability of direct georeferencing. The advantage of such system lies in its high maneuverability, operation flexibility as well as capability to acquire image data w ...

ISPRS Archives2013

Invariant Higher-Order Variational Problems

Tudor Ratiu, François Gay-Balmaz

We investigate higher-order geometric k-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our approach formulat ...

2012

Stiffness tomography exploration of living and fixed macrophages

Giovanni Dietler, Sandor Kasas, Giovanni Longo, Charles Roduit, Bhaskar Saha, Andrea Volterra

Stiffness tomography is a new atomic force microscopy imaging technique that allows highlighting structures located underneath the surface of the sample. In this imaging mode, such structures are identified by investigating their mechanical properties. We ...

Wiley-Blackwell2012

Lie Group and Lie Algebra Variational Integrators for Flexible Beam and Plate in R3

François Marie Alain Demoures

The purpose of this thesis is to develop variational integrators synchronous or asynchronous, which can be used as tools to study complex structures composed of plates and beams subjected to large deformations and stress. We consider the geometrically exac ...

EPFL2012

Singular Reduction Of Dirac Structures

Tudor Ratiu, Madeleine Jotz

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about G-invariant vector fields and one-forms are shown. ...

2011

Dirac Group(oid)s and Their Homogeneous Spaces

Madeleine Jotz

A theorem of Drinfel'd (Drinfel'd (1993)) classifies the Poisson homogeneous spaces of a Poisson Lie group (G,πG) via a special class of Lagrangian subalgebras of the Drinfel'd double of its Lie bialgebra. This result is extended in Liu et al. (1998) to a ...

EPFL2011