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J. Jost

Publications and source records attributed to J. Jost.

At least 19 recordsLinked to original sources
arXiv2024

The MICADO first light imager for the ELT: off-axis performance of PSF reconstruction

The highest scientific return, for adaptive optics (AO) observations, is achieved with a reliable reconstruction of the PSF. This is especially true for MICADO@ELT. In this presentation, we will focus on extending the MICADO PSF reconstruction (PSF-R) method to the off-axis case. Specifically, a novel approach based on temporal-based tomography of AO telemetry data has been recently implemented. Results from the PSF-R of both simulated and real data show that, at half isoplanatic angle distances, a precision of about 10-15% is achievable in both Strehl ratio and full-width at half maximum, paving the way to extend the MICADO PSF-R tool also to the multi-conjugated AO case.

astro-ph.IM↗
arXiv2021

Minimal graphs of arbitrary codimension in Euclidean space with bounded 2-dilation

For any $\Lambda>0$, let $\mathcal{M}_{n,\Lambda}$ denote the space containing all locally Lipschitz minimal graphs of dimension $n$ and of arbitrary codimension $m$ in Euclidean space $\mathbb{R}^{n+m}$ with uniformly bounded 2-dilation $\Lambda$ of their graphic functions. In this paper, we show that this is a natural class to extend structural results known for codimension one. In particular, we prove that any tangent cone $C$ of $M\in\mathcal{M}_{n,\Lambda}$ at infinity has multiplicity one. This enables us to get a Neumann-Poincar$\mathrm{\acute{e}}$ inequality on stationary indecomposable components of $C$. A corollary is a Liouville theorem for $M$. For small $\Lambda>1$(we can take any $\Lambda<\sqrt{2}$), we prove that (i) for $n\leq7$, $M$ is flat; (2) for $n>8$ and a non-flat $M$, any tangent cone of $M$ at infinity is a multiplicity one quasi-cylindrical minimal cone in $\mathbb{R}^{n+m}$ whose singular set has dimension $\leq n-7$.

math.DG↗
arXiv2020

Periodic Strategies II: Generalizations and Extensions

At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.

cs.GT↗
arXiv2018

Periodic Strategies: A New Solution Concept and an Algorithm for NonTrivial Strategic Form Games

We introduce a new solution concept, called periodicity, for selecting optimal strategies in strategic form games. This periodicity solution concept yields new insight into non-trivial games. In mixed strategy strategic form games, periodic solutions yield values for the utility function of each player that are equal to the Nash equilibrium ones. In contrast to the Nash strategies, here the payoffs of each player are robust against what the opponent plays. Sometimes, periodicity strategies yield higher utilities, and sometimes the Nash strategies do, but often the utilities of these two strategies coincide. We formally define and study periodic strategies in two player perfect information strategic form games with pure strategies and we prove that every non-trivial finite game has at least one periodic strategy, with non-trivial meaning non-degenerate payoffs. In some classes of games where mixed strategies are used, we identify quantitative features. Particularly interesting are the implications for collective action games, since there the collective action strategy can be incorporated in a purely non-cooperative context. Moreover, we address the periodicity issue when the players have a continuum set of strategies available.

cs.GT↗
arXiv2017

Existence and non-existence of minimal graphs

We study the Dirichlet problem for minimal surface systems in arbitrary dimension and codimension via mean curvature flow, and obtain the existence of minimal graphs over arbitrary mean convex bounded $C^2$ domains for a large class of prescribed boundary data. This result can be seen as a natural generalization of the classical sharp criterion for solvability of the minimal surface equation by Jenkins-Serrin. In contrast, we also construct a class of prescribed boundary data on just mean convex domains for which the Dirichlet problem in codimension 2 is not solvable. Moreover, we study existence and the uniqueness of minimal graphs by perturbation.

math.DG↗
arXiv2015

Submanifolds with constant Jordan angles

To study the Lawson-Osserman's counterexample to the Bernstein problem for minimal submanifolds of higher codimension, a new geometric concept, submanifolds in Euclidean space with constant Jordan angles(CJA), is introduced. By exploring the second fundamental form of submanifolds with CJA, we can characterize the Lawson-Osserman's cone from the viewpoint of Jordan angles.

math.DG↗
arXiv2014

A spherical Bernstein theorem for minimal submanifolds of higher codimension

Combining the tools of geometric analysis with properties of Jordan angles and angle space distributions, we derive a spherical and a Euclidean Bernstein theorem for minimal submanifolds of arbitrary dimension and codimension, under the condition that the Gauss image is contained in some geometrically defined closed region of a Grassmannian manifold. The proof depends on the subharmoncity of an auxiliary function, the Codazzi equations and geometric measure theory.

math.DG↗
arXiv2013

Minimal graphic functions on manifolds of non-negative Ricci curvature

We study minimal graphic functions on complete Riemannian manifolds $\Si$ with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with such growth via splitting for tangent cones of $\Si$ at infinity. When, in contrast, we do not impose any growth restrictions for minimal graphic functions, we also obtain a Liouville type theorem under a certain non-radial Ricci curvature decay condition on $\Si$. In particular, the borderline for the Ricci curvature decay is sharp by our example in the last section.

math.DG↗
arXiv2011

The geometry of Grassmannian manifolds and Bernstein type theorems for higher codimension

We identify a region $\Bbb{W}_{\f{1}{3}}$ in a Grassmann manifold $\grs{n}{m}$, not covered by a usual matrix coordinate chart, with the following important property. For a complete $n-$submanifold in $\ir{n+m} \, (n\ge 3, m\ge2)$ with parallel mean curvature whose image under the Gauss map is contained in a compact subset $K\subset\Bbb{W}_{\f{1}{3}}\subset\grs{n}{m}$, we can construct strongly subharmonic functions and derive a priori estimates for the harmonic Gauss map. While we do not know yet how close our region is to being optimal in this respect, it is substantially larger than what could be achieved previously with other methods. Consequently, this enables us to obtain substantially stronger Bernstein type theorems in higher codimension than previously known.

math.DG↗
arXiv2010

The Gauss image of entire graphs of higher codimension and Bernstein type theorems

Under suitable conditions on the range of the Gauss map of a complete submanifold of Euclidean space with parallel mean curvature, we construct a strongly subharmonic function and derive a-priori estimates for the harmonic Gauss map. The required conditions here are more general than in previous work and they therefore enable us to improve substantially previous results for the Lawson-Osseman problem concerning the regularity of minimal submanifolds in higher codimension and to derive Bernstein type results.

math.DG↗
arXiv2007

Harmonic nets in metric spaces

We investigate harmonic maps from weighted graphs into metric spaces that locally admit unique centers of gravity, like Alexandrov spaces with upper curvature bounds. We prove an existence result by constructing an iterative geometric process that converges to such maps, called harmonic nets for short.

math.MG↗
arXiv2002

Evolving networks with distance preferences

We study evolving networks where new nodes when attached to the network form links with other nodes of preferred distances. A particular case is where always the shortest distances are selected (``make friends with the friends of your present friends''). We present simulation results for network parameters like the first eigenvalue of the graph Laplacian (synchronizability), clustering coefficients, average distances, and degree distributions for different distance preferences and compare with the parameter values for random and scale free networks. We find that for the shortest distance rule we obtain a power law degree distribution as in scale free networks, while the other parameters are significantly different, especially the clustering coefficient.

cond-mat.stat-mech↗
arXiv2001

Spectral Properties and Synchronization in Coupled Map Lattices

Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbor coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling.

nlin.CD↗
arXiv1997

Existence results for mean field equations

Let $Ω$ be an annulus. We prove that the mean field equation $-Δψ=\frac{e\sp{-βψ}}{\int\sbΩe\sp{-βψ}} $ admits a solution with zero boundary for $β\in (-16π,-8π)$. This is a supercritical case for the Moser-Trudinger inequality.

dg-ga↗