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Uncomputably Noisy Ergodic Limits
2012
Notre Dame Journal of Formal Logic
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function needs to be to approximate the limit to within a given epsilon. ...
V'yugin has shown that there are a computable shift-invariant measure on Cantor space and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages A_n ...
Intuitively, h k is a "noisy" function of complexity k. ...
doi:10.1215/00294527-1716757
fatcat:td7nm6j5njhrpnv5n7zkqnf32u
Uncomputably Noisy Ergodic Limits
2018
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function needs to be to approximate the limit to within a given ε. ...
V'yugin has shown that there are a computable shift-invariant measure on 2N and a simple function f such that there is no computable bound on the rate of convergence of the ergodic averages Anf. ...
Intuitively, h k is a "noisy" function of complexity k. ...
doi:10.1184/r1/6493031
fatcat:kx2io5g4mvfjzlnp2sqb2tvbcq
Cold dynamics in cellular automata: a tutorial
2022
Natural Computing
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2022 pre-print arXiv:2206.08139v1 fatcat:sn7giwmvunczhpdh42wugnopiu
A rich zoo of properties is presented and discussed: nilpotency and asymptotic, generic or mu-variants, unique ergodicity, convergence, bounded-changeness, freezingness. ...
Besides dynamical considerations, we also focus on computational aspects: we show how such 'cold cellular automata' can still compute under their dynamical constraint, and what are their computational limitation ...
It appears that in many cases the resulting noisy CA is ergodic [52] as a probabilistic CA. In fact, proving that a particular noisy CA is not ergodic turns out to be difficult. ...
doi:10.1007/s11047-022-09886-2
fatcat:e4ppv36pgbfgpdn46df54ivb7u
Signatures of infinity: Nonergodicity and resource scaling in prediction, complexity, and learning
2015
Physical Review E
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We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. ...
We draw out consequences for the resource divergences that delineate the structural hierarchy of ergodic processes and for processes that are themselves hierarchical. ...
All these are uncomputable, though, even if one is given a generative model. ...
doi:10.1103/physreve.91.050106
pmid:26066103
fatcat:zbfuofbzxjd5vcjsuxhpr6ayvy
Signatures of Infinity: Nonergodicity and Resource Scaling in Prediction, Complexity, and Learning
[article]
2015
arXiv
pre-print
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We introduce a simple analysis of the structural complexity of infinite-memory processes built from random samples of stationary, ergodic finite-memory component processes. ...
We draw out consequences for the resource divergences that delineate the structural hierarchy of ergodic processes and for processes that are themselves hierarchical. ...
All these are uncomputable, though, even if one is given a generative model. ...
arXiv:1504.00386v1
fatcat:3cicfswlijdyjjwf4txyk76u6a
Ensemble Inference Methods for Models With Noisy and Expensive Likelihoods
[article]
2022
arXiv
pre-print
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However, model complexity often leads to parameter-to-data maps which are expensive to evaluate and are only available through noisy approximations. ...
The objective evaluations (blue circles) are noisy leading to rapid fluctuations around a visible convex objective function (defined by the, in practice uncomputable, infinite time-average limit.) ...
For ergodic, mixing dynamical systems a central limit theorem may sometimes be proven to hold [2] , or empirically observed, for data drawn at random from the invariant measure. ...
arXiv:2104.03384v2
fatcat:xskk7dxnm5dttb4x42ab45edee
On the Theoretical Properties of the Exchange Algorithm
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:2005.09235v3 fatcat:jl3wxjjrn5e6bil3pgup7xcolmOther Versions
or 'Does the exchange algorithm admit a Central Limit Theorem?' have not been answered yet. ...
We compare the exchange algorithm with the original Metropolis--Hastings algorithm and provide both necessary and sufficient conditions for the geometric ergodicity of the exchange algorithm. ...
of a Markov chain Central Limit Theorem (CLT). ...
arXiv:2005.09235v4
fatcat:bzbcwknmwrg2ncviqt7ta6duq4
Multiuser MIMO Achievable Rates With Downlink Training and Channel State Feedback
2010
IEEE Transactions on Information Theory
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter ...
These results, as ours, rely on the behavior of the noisy prediction error for small .
C. ...
Section III develops bounds on the ergodic rates achievable by the baseline scheme. ...
doi:10.1109/tit.2010.2046225
fatcat:aks2ndmqzbbcxhwibswhtvpcni
Symbolic Dynamics for Discrete Adaptive Games
[article]
2003
arXiv
pre-print
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The transients are, however, bad news for methods based on either ergodic or thermodynamic limits. ...
The proofs of these assertions are somewhat complicated results from ergodic theory, well-summarized in Ref. [32] .
D. ...
arXiv:cond-mat/0207407v2
fatcat:g7ldqi2ncvh2fmdtzsgaasf6je
Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization
[article]
2020
arXiv
pre-print
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However, today, our ability to evaluate quantum heuristics through experimentation is limited since the only available quantum computers are small and noisy [1] . ...
The idea is motivated by the search of configuration space in the classically non-ergodic phase associated with hard optimization problems. ...
arXiv:2007.07391v2
fatcat:vd4yv7w2mzapbnatgkrf3r23ie
Separation Theorems for Phase-Incoherent Multiple-User Channels
[article]
2011
arXiv
pre-print
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In all cases, the input signals are assumed to undergo non-ergodic phase shifts due to the channel. ...
We now further upper bound C n (θ) and then take the limit and intersection. ...
In many systems, it is difficult to know phase shifts at the transmitter side due to the delay and resource limits in feedback transmission. ...
arXiv:1110.3062v1
fatcat:nhoftq7jj5gdzmd6ndz3yvhjdy
Lempel-Ziv complexity analysis of one dimensional cellular automata
2015
Chaos
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2015 pre-print arXiv:1511.08657v1 fatcat:u2nksyt7hvh77e6ckkkncvphnm
Lempel-Ziv complexity carries a number of practical advantages while avoiding the uncomputable nature of Kolmogorov randomness. ...
As Kolmogorov randomness is uncomputable, a practical alternative to equation (12) is needed. ...
The approach avoids the limitations in system size, inherent in using compression software and allows to analyze large systems. ...
doi:10.1063/1.4936876
pmid:26723145
fatcat:q6q3vqy2anbzzbazon54tl7dg4
An Algorithmic Approach to Emergence
[article]
2022
arXiv
pre-print
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Because algorithmic complexity is uncomputable, so is the structure function. ...
They are expressed in terms of models that distillate the structures from the apparently noisy boundary conditions. ...
arXiv:2205.12997v1
fatcat:d5t3hpjvurbtbk62vhz7wg2h5i
Exact Complexity: The Spectral Decomposition of Intrinsic Computation
[article]
2013
arXiv
pre-print
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Note that W 1 = |1 π W |, which is always the case for an ergodic process. ...
Note that W 1 = |1 π W |, again, since the timelike subprocess is ergodic. ...
arXiv:1309.3792v1
fatcat:ev24dje3gbfr5huf6zbltpaggi
Optimal high-level descriptions of dynamical systems
[article]
2015
arXiv
pre-print
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Furthermore, AIC is formally uncomputable, so one has to settle for results concerning asymptotic behavior. ...
Indeed, even if we allowed an infinitely expandable RAM, such a cost would be uncomputable, in general. ...
arXiv:1409.7403v2
fatcat:tsilyydsgbeifevfscsfxxikry
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