Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Kent-Dobias, Jaron"'
Autor:
Kent-Dobias, Jaron
We consider the set of solutions to $M$ random polynomial equations whose $N$ variables are restricted to the $(N-1)$-sphere. Each equation has independent Gaussian coefficients and a target value $V_0$. When solutions exist, they form a manifold. We
Externí odkaz:
http://arxiv.org/abs/2409.12781
Autor:
Kent-Dobias, Jaron
Optimization seeks extremal points in a function. When there are superextensively many optima, optimization algorithms are liable to get stuck. Under these conditions, generic algorithms tend to find marginal optima, which have many nearly flat direc
Externí odkaz:
http://arxiv.org/abs/2407.02092
Autor:
Kent-Dobias, Jaron
Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors are a vani
Externí odkaz:
http://arxiv.org/abs/2407.02082
Publikováno v:
Phys. Rev. Research 6, 023235 (2024)
The planar grasshopper problem, originally introduced in (Goulko & Kent 2017 Proc. R. Soc. A 473, 20170494), is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this work we analyz
Externí odkaz:
http://arxiv.org/abs/2311.05023
Autor:
Kent-Dobias, Jaron
Publikováno v:
SciPost Phys. 16, 001 (2024)
The mixed spherical models were recently found to violate long-held assumptions about mean-field glassy dynamics. In particular, the threshold energy, where most stationary points are marginal and that in the simpler pure models attracts long-time dy
Externí odkaz:
http://arxiv.org/abs/2306.12779
Autor:
Kent-Dobias, Jaron
Publikováno v:
EPL 143, 61003 (2023)
A common measure of a function's complexity is the count of its stationary points. For complicated functions, this count grows exponentially with the volume and dimension of their domain. In practice, the count is averaged over a class of functions (
Externí odkaz:
http://arxiv.org/abs/2306.12752
Our community has a deep and sophisticated understanding of phase transitions and their universal scaling functions. We outline and advocate an ambitious program to use this understanding as an anchor for describing the surrounding phases. We explain
Externí odkaz:
http://arxiv.org/abs/2304.00105
Autor:
Kent-Dobias, Jaron
We describe evidence for logarithmic correlations within the paintings of Claude Monet.
Externí odkaz:
http://arxiv.org/abs/2209.01989
Autor:
Kent-Dobias, Jaron, Kurchan, Jorge
We derive the general solution for counting the stationary points of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with mult
Externí odkaz:
http://arxiv.org/abs/2207.06161
Autor:
Kent-Dobias, Jaron, Kurchan, Jorge
In this paper we follow up the study of 'complex complex landscapes,' rugged landscapes of many complex variables. Unlike real landscapes, the classification of saddles by index is trivial. Instead, the spectrum of fluctuations at stationary points d
Externí odkaz:
http://arxiv.org/abs/2204.06072