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Computing Periodic Orbits and their Bifurcations with Automatic Differentiation
Automatic Differentiation Computing Periodic Orbits
2015/8/25
This paper examines algorithms for computing periodic orbits of dynamical systems. Our
goal is to explore the limits of accuracy that are attainable for these calculations within
the pragmatic conte...
Periodic Orbits of Vector Fields: Computational Challenges
Computational Challenges Vector Fields
2015/8/25
Simulation of vector elds is ubiquitous: examples occur in every discipline of
science and engineering. Periodic orbits are frequently encountered as trajectories.
We use solutions of initial value...
Singularly perturbed systems of ordinary di erential equations arise in many
biological, physical and chemical systems. We present an example of a singu-
larly perturbed system of ordinary di erenti...
The Set of Solutions of Random XORSAT Formulae
random constraint satisfaction problem clustering of solutions phase transition random graph local weak convergence belief propagation
2015/8/21
The XOR-satisfiability (XORSAT) problem requires finding an assignment of n Boolean variables that satisfy m exclusive OR (XOR) clauses, whereby each clause constrains a subset of the variables. We co...
Counting good truth assignments of random k-SAT formulae
Random k-SAT Correlation Decay Uniqueness Gibbs Distribution
2015/8/21
We present a deterministic approximation algorithm to compute logarithm of the number of ‘good’ truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by ‘good’ we m...
The asymptotic error floor of LDPC ensembles under BP decoding
Binary no memory random elements the noise
2015/8/21
We consider communication over binary memoryless symmetric channels using random elements from irregular low density parity check code (LDPC) ensembles, and belief propagation (BP) decoding. Under the...
Reconstruction for models on random graphs
Random variables algorithms the random sequence diagram
2015/8/21
Consider a collection of random variables attached to the vertices of a graph. The reconstruction problem requires to estimate one of them given ‘far away’ observations. Several theoretical results (a...
Computing the threshold shift for general channels
Threshold the probability curve noise the binary
2015/8/21
The ‘threshold’ of a code ensemble can be defined as the noise level at which the block error probability curve crosses 1/2. For ensembles of low-density parity check codes used over the binary erasur...
Learning Low Rank Matrices from O(n) Entries
Random items matrix reconstruction matrix the stochastic matrix
2015/8/21
How many random entries of an n × nα, rank r matrix are necessary to reconstruct the matrix within an accuracy δ? We address this question in the case of a random matrix with bounded rank, whereby the...
We present a simple and efficient algorithm for randomly generating simple graphs without small cycles. These graphs can be used to design high performance Low-Density Parity-Check (LDPC) codes. ...
Which graphical models are difficult to learn?
Ising model binary markov random field markov random
2015/8/21
We consider the problem of learning the structure of Ising models (pairwise binary Markov random fields) from i.i.d. samples. While several methods have been proposed to accomplish this task, their re...
Boosting search by rare events
Random search algorithm combination nonequilibrium random random algorithm
2015/8/21
Randomized search algorithms for hard combinatorial problems exhibit a large variability of per- formances. We study the different types of rare events which occur in such out-of-equilibrium stochasti...
Gibbs states and the set of solutions of random constraint satisfaction problems
Gibbs random constraints the solution
2015/8/21
Gibbs states and the set of solutions of random constraint satisfaction problems.
Estimating Random Variables from Random Sparse Observations
Discrete random variable random function decoupling principle
2015/8/21
Let X1, . . . ,Xn be a collection of iid discrete random variables, and Y1, . . . , Ym a set of noisy observations of such variables. Assume each observation Ya to be a random function of some a rando...
FINITE-LENGTH SCALING FOR ITERATIVELY DECODED LDPC ENSEMBLES
low-density parity-check codes iterative decoding density evolution binary erasure channel finite-length analysis error probability curve
2015/8/21
In this paper we investigate the behavior of iteratively decoded low-density paritycheck codes over the binary erasure channel in the so-called “waterfall region.” We show that the performance curves ...