Publications related to Topology

Topological Linear System Identification via Moderate Deviations Theory

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...

2021

Global Frobenius liftability I

Maciej Emilian Zdanowicz

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

EUROPEAN MATHEMATICAL SOC-EMS2021

Discretisation and continuity: The emergence of symbols in communication

Martin Alois Rohrmeier, Robert Lieck

Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and proso ...

2021

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

Wulfram Gerstner, Clément Hongler, Johanni Michael Brea, Francesco Spadaro, Berfin Simsek, Arthur Jacot

We study how permutation symmetries in overparameterized multi-layer neural networks generate `symmetry-induced' critical points. Assuming a network with

L

layers of minimal widths

r_1^*, \ldots, r_{L-1}^*

reaches a zero-loss minimum at $ r_1^*! \c ...

2021

On Topological Equivalence in Linear Quadratic Optimal Control

Daniel Kuhn, Wouter Jongeneel

Dynamical systems are topologically equivalent when their orbits can be mapped onto each other via a homeomorphic change of coordinates. We will show that in general, closed-loop systems resulting from Linear Quadratic Optimal Control problems are all topo ...

2021

Crossover between distinct symmetries in solid solutions of rare earth nickelates

Duncan Thomas Lindsay Alexander, Bernat Mundet, Jean-Marc Triscone

A strong coupling of the lattice to functional properties is observed in many transition metal oxide systems, such as the ABO(3) perovskites. In the quest for tailor-made materials, it is essential to be able to control the structural properties of the com ...

AIP Publishing2021

Sequential metric dimension for random graphs

Patrick Thiran, Gergely Odor

In the localization game on a graph, the goal is to find a fixed but unknown target node v* with the least number of distance queries possible. In the j-th step of the game, the player queries a single node v_j and receives, as an answer to their query, th ...

2021

Data-Driven Convergence Prediction of Astrobots Swarms

Denis Gillet, Jean-Paul Richard Kneib, Matin Macktoobian, Francesco Basciani

Astrobots are robotic artifacts whose swarms are used in astrophysical studies to generate the map of the observable universe. These swarms have to be coordinated with respect to various desired observations. Such coordination\footnote{\z{A coordination sa ...

2021

Turbulence in the scrape-off layer of double-null tokamak configurations

Carrie Fiona Beadle

Understanding the turbulent dynamics in the outermost region of the tokamak is essential to predict and control the heat and particle loads to the vessel wall, a crucial problem for the entire fusion program. In this thesis, the problem is approached via t ...

EPFL2021

Molecular Origin of the Asymmetric Photoluminescence Spectra of CsPbBr3 at Low Temperature

Ursula Röthlisberger, Ariadni Boziki, Mohammad Ibrahim Dar, Gwénolé Jean Jacopin

CsPbBr3 has received wide attention due to its superior emission yield and better thermal stability compared to other organic-inorganic lead halide perovskites. In this study, through an interplay of theory and experiments, we investigate the molecular ori ...

2021

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Topological Linear System Identification via Moderate Deviations Theory

Global Frobenius liftability I

Discretisation and continuity: The emergence of symbols in communication

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

On Topological Equivalence in Linear Quadratic Optimal Control

Crossover between distinct symmetries in solid solutions of rare earth nickelates

Sequential metric dimension for random graphs

Data-Driven Convergence Prediction of Astrobots Swarms

Turbulence in the scrape-off layer of double-null tokamak configurations

Molecular Origin of the Asymmetric Photoluminescence Spectra of CsPbBr3 at Low Temperature

Global Frobenius liftability I

Topological Linear System Identification via Moderate Deviations Theory

Data-Driven Convergence Prediction of Astrobots Swarms

Turbulence in the scrape-off layer of double-null tokamak configurations

Crossover between distinct symmetries in solid solutions of rare earth nickelates

Discretisation and continuity: The emergence of symbols in communication

Geometry of the Loss Landscape in Overparameterized Neural Networks: Symmetries and Invariances

On Topological Equivalence in Linear Quadratic Optimal Control

Sequential metric dimension for random graphs

Molecular Origin of the Asymmetric Photoluminescence Spectra of CsPbBr3 at Low Temperature