20 papers · ranked by Valyu relevance
Markus Pettersen, Nicolai Haug, Joakim Bergli, Thomas M. Surowiec + 1 more
A fundamental challenge in neuroscience and AI is understanding how physical space is mapped into neural representations. While artificial neural networks can generate brain-like spatial representations, such as place and grid cells, their “black-box” nature makes it difficult to determine if these representations…
Zhaiming Shen, Lasse Rempe
We present an elementary and conceptual proof that the complex exponential map is chaotic when considered as a dynamical system on the complex plane. (This was conjectured by Fatou in 1926 and first proved by Misiurewicz 55 years later.) The only background required is a first undergraduate course in complex analysis.
Emmanuel Chevallier, Nicolas Guigui
This paper aims to describe a statistical model of wrapped densities for bi-invariant statistics on the group of rigid motions of a Euclidean space. Probability distributions on the group are constructed from distributions on tangent spaces and pushed to the group by the exponential map. We provide an expression of the…
Alexander Effland, Martin Rumpf, Florian Schäfer
The space of images can be equipped with a Riemannian metric measuring both the cost of transport of image intensities and the variation of image intensities along motion lines. The resulting metamorphosis model was introduced and analyzed in [19, 25] and a variational time discretization for the geodesic interpolation…
Karim Makki, Bhushan Borotikar, Marc Garétier, Sylvain Brochard + 2 more
'D. Ben Salem' 'François Rousseau'] Abstract The log Euclidean polyrigid registration framework provides a way to smoothly estimate and interpolate poly-rigid/affine transformations for which the invertibility is guaranteed. This powerful and flexible mathematical framework is currently being used to track the human…
Jacob Hinkle, Prasanna Muralidharan, P. Thomas Fletcher, Sarang Joshi
'Sarang Joshi'] In this paper we develop the theory of parametric polynomial regression in Riemannian manifolds and Lie groups. We show application of Riemannian polynomial regression to shape analysis in Kendall shape space. Results are presented, showing the power of polynomial regression on the classic rat skull…
András Domokos
This paper is the result of our efforts to understand the role of the chronological exponential [1] in the geometry of Lie groups, in general, and of semi-simple, compact Lie groups, in particular. We will try to find connections similar to those between the group exponential map and the Riemannian geometry of the Lie…
András Gilyén, Tamás Kiss, Igor Jex
State selective protocols, like entanglement purification, lead to an essentially non-linear quantum evolution, unusual in naturally occurring quantum processes. Sensitivity to initial states in quantum systems, stemming from such non-linear dynamics, is a promising perspective for applications. Here we demonstrate…
Daniele Mortari, David Anas
This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: a) complex mapping, b) projection mapping, and c) polynomial mapping. In that respect…
Takumi Takebayashi, Renato Miyagusuku, Koichi Ozaki, Sukhan Lee + 3 more
'Uwe D. Hanebeck' 'Florian Pfaff' 'Baochang Zhang'] Localization is fundamental to enable the use of autonomous mobile robots. In this work, we use magnetic-based localization. As Earth’s geomagnetic field is stable in time and is not affected by nonmagnetic materials, such as a large number of people in the robot’s…
Duncan Bossion, Sutirtha Chowdhury, Pengfei Huo
We present the rigorous theoretical framework of the generalized spin mapping representation for non- adiabatic dynamics. This formalism is based on the generators of the su(N) Lie algebra to represent N discrete electronic states, thus preserving the size of the original Hilbert space in the state representation. The…
Steven A. Frank
The universal law of generalization describes how animals discriminate between alternative sensory stimuli. On an appropriate perceptual scale, the probability of discrimination typically declines exponentially with the difference on the perceptual scale. Exceptions often follow a Gaussian probability pattern rather…
Florian Hutzler, Fabio Richlan, Michael Christian Leitner, Sarah Schuster + 2 more
'Sarah Schuster' 'Mario Braun' 'Stefan Hawelka'] Humans grossly underestimate exponential growth, but are at the same time overconfident in their (poor) judgement. The so-called ‘exponential growth bias' is of new relevance in the context of COVID-19, because it explains why humans have fundamental difficulties to…
Hans-Stefan Siller, Hans-Jürgen Elschenbroich, Gilbert Greefrath, Katrin Vorhölter
'Katrin Vorhölter'] Mathematical concepts are regularly used in media reports concerning the Covid-19 pandemic. These include growth models, which attempt to explain or predict the effectiveness of interventions and developments, as well as the reproductive factor. Our contribution has the aim of showing that basic…
Hans Strasburger
The retino-cortical visual pathway is retinotopically organized: Neighborhood relationships on the retina are preserved in the mapping to the cortex. Size relationships in that mapping are also highly regular: The size of a patch in the visual field that maps onto a cortical patch of fixed size, follows, along any…
Enahoro A. Owoloko, Pelumi E. Oguntunde, Adebowale O. Adejumo
In this article, the so called Transmuted Exponential (TE) distribution was applied to two real life datasets to assess its potential flexibility over some other generalized models. Various statistical properties of the TE distribution were also identified while the method of maximum likelihood estimation was used to…
harry gray
The matrix exponential method as implemented in MATLAB is demonstrated as a facile tool for solving the time-dependent concentrations of an arbitrary chemically reactive network modelled as a coupled linear system of first-order differential equations. The method is used to verify a 10 species network incorporating…
Dean Huang, Teresa Lo, Houra Merrikh, Paul A. Wiggins
Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing population, while the other captures cell cycle dynamics, either by time-lapse imaging of…
Charles Eads
This report describes and illustrates a set of automatable multicomponent exponential relaxation analysis protocols that are model-agnostic and suited to extracting information under circumstances when little prior knowledge about the underlying system is used. Methods are illustrated and mathematical and physical…
Joshua Horton, Simon Boothroyd, Pavan Behara, David Mobley + 1 more
The Lennard-Jones potential is the most widely-used function for the description of non-bonded interactions in transferable force fields for the condensed phase. This is not because it has an optimal functional form, but rather it is a legacy resulting from when computational expense was a major consideration and this…