A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is
For NAS, Davis Drusvyatskiy (2019) showed that ρ-weakly convex functions admit finite-time computation, while Tian So (2021) provided the matching impossibility results of dimension-free finite-time complexity ... For GAS, our scheme removes the unrealistic subgradient selection oracle assumption in (Zhang et al., 2020, Assumption 1) and computes GAS with the same finite-time complexity. ... In contrast to the asymptotic regime, the finite-time complexity in the general "non"setting is still developing. ...arXiv:2112.09002v2 fatcat:7dlalqfemfhznpisxwcnyqkd74
From the theory of algorithmic information introduced by Chaitin  it is known that the more complex a system that is acting on a random binary input sequence the more it can deform the stochastic properties ... The level of complexity of the system is controlled via external parameters. The output response is the field of displacements observed at several positions on the body. ... He modeled a solid as a selection rule of a finite algorithmic complexity which acts on an incoming random sequence of particles in the surroundings. ...doi:10.1007/s11424-010-8465-2 fatcat:3qhipfjdyvcc7fb5tgjx474ima
For more complex shell geometry and more complex correlation function of the loads which are random both in time and space, numerical methods may be desirable. ... Olson and Lindberg (26) and Olson (25), developed a consistent finite element method for analyzing the random response of complex struc- tures. ...
We prove that typical random sequences of finite length fall short of the maximum Lempel-Ziv complexity, contrary to common belief. ... We discuss that, for a finite length, maximum Lempel-Ziv sequences can be built from a well defined generating algorithm, which makes them of low Kolmogorov-Chaitin complexity, quite the opposite to randomness ... It has been proved 14 that a finite random sequence with maximum KC complexity does not have the same number of zeros and ones. ...doi:10.1063/1.4808251 pmid:23822483 fatcat:v6n6k54rqrdnzarsvz6arkvau4
In particular, a large amount of work has focused on analyzing the variation of the complex envelope of the transmitted signal and on designing methods to minimize this variation. ... This shows that the properties of the OFDM signal will asymptotically approach those of a Gaussian random process over any finite time interval. ... ACKNOWLEDGMENT The authors are indebted to the editor and reviewers for feedback that both greatly streamlined the proofs of the original manuscript and improved the framing of the results of the paper ...doi:10.1109/tit.2010.2059550 fatcat:tlkqbsbpdnfp7cxutvzttj3gye
Research on the notions of information and randomness has drawn on methods and ideas from computability theory and cumputational complexity, as well as core mathematical subjects like measure theory and ... This report collects the material presented during the course of the seminar. ... The problem posed by Kolmogorov on a notion of randomness of finite objects remains unsolved. This is also the case for arbitrary countable objects. ...doi:10.4230/dagrep.2.1.19 dblp:journals/dagstuhl-reports/BecherBDM12 fatcat:bkapirz4vfgkzcexiutm33k74q
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample ... We also strengthen and elaborate on earlier results for the "Kolmogorov structure function" and "absolutely nonstochastic objects"-those objects for which the simplest models that summarize their relevant ... Levin for some enlightening discussions on Kolmogorov's "structure function." ...doi:10.1109/18.945257 fatcat:qe7s4mib4vff5eawevwxdrgwyu
We can define a particular complex valued random variable Z in the following way: | Z| =r with probability one, and arg Z is uniformly distributed on the interval |[—7, 7]. ... ON A CLASS OF RANDOM VARIABLES FRANK SPITZER 1. Introduction. ...
Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the description of the random variable involved plus the entropy it induces. ... We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. ... This difference parallels that between the Kolmogorov complexity of a single finite object and the entropy of a random variable. ...arXiv:1103.5985v1 fatcat:ptr7avn7bvdhbduxy3w7c3xcm4
In  Miller also gave a quantitative version of the first result: the 0'-randomness deficiency of a sequence ω equals lim inf [n - C (ω1 . . . ωn)] + O(1). ... that have infinitely many initial segments with O(1)-maximal plain complexity (among the strings of the same length). ... Introduction The connection between complexity and randomness is one of the basic ideas that motivated the development of algorithmic information theory and algorithmic randomness theory. ...arXiv:1310.5230v1 fatcat:2w26f2kpjjdr7hv3byvk3sqmh4
In  Miller also gave a quantitative version of the first result: the 0 ′randomness deficiency of a sequence ω equals lim infn[n − C (ω1 . . . ωn)] + O(1). ... sequences that have infinitely many initial segments with O(1)-maximal plain complexity (among the strings of the same length). ... Introduction The connection between complexity and randomness is one of the basic ideas that motivated the development of algorithmic information theory and algorithmic randomness theory. ...doi:10.1007/s00153-015-0430-2 fatcat:uzhs5w2u7zegpgy254t3hc3cza
In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. ... We also study randomness from the view point of arithmetic using the relativization to a complete Π^0_1-class. ... It will show that these two definitions of randomness have a duality, in other words, given a new notion of randomness in one of the above, then, one can automatically get the definition of the same notion ...arXiv:1310.3091v2 fatcat:g4af4x5edrhdjd4ctczezwprru
Finite State Incompressible Infinite Sequences 2 / 21 Motivation The incomputability of all descriptional complexities is an obstacle towards more "down-to-earth" applications of AIT (e.g. for practical ... Finite State Incompressible Infinite Sequences 2 / 21 Motivation The incomputability of all descriptional complexities is an obstacle towards more "down-to-earth" applications of AIT (e.g. for practical ... In particular, finite state complexities based on some exotic enumerations behave like the plain (Kolmogorov) complexity. ...doi:10.1016/j.ic.2015.11.003 fatcat:g3p6qls62nc6hl2mp4ahsntsuy
We introduce a method to estimate the complexity function of symbolic dynamical systems from a finite sequence of symbols. ... We test such complexity estimator on several symbolic dynamical systems whose complexity functions are known exactly. ... It was found that the complexity function for a finite string has a profile which is independent on how the string was produced [4, 5] . ...doi:10.1088/1751-8113/49/44/445601 fatcat:ihnsaxi5mnajfjj6jsvjsuhjdq
Physicalism would then be violated by the existence of oracles that produce certain kinds of noncomputable functions. ... necessity"-algorithmic rules and randomness. ... an earlier version of the manuscript. ...doi:10.1007/s10699-014-9349-z fatcat:juqvbuwpdnb6hh6scrri67azui
« Previous Showing results 1 — 15 out of 619,368 results