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- Jack Raymond, David Saad
- ArXiv
- 2007

Sparse Code Division Multiple Access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of non-zero elements, is presented and analysed using methods of statistical physics. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codesâ€¦ (More)

- Alexander Mozeika, David Saad, Jack Raymond
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2010

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in theâ€¦ (More)

- Jack Raymond, Sheir Yarkoni, Evgeny Andriyash
- Front. ICT
- 2016

Sampling from a Boltzmann distribution is NP-hard and so requires heuristic approaches. Quantum annealing is one promising candidate. The failure of annealing dynamics to equilibrate on practical time scales is a well understood limitation, but does not always prevent a heuristically useful distribution from being generated. In this paper, we evaluateâ€¦ (More)

- Toshiyuki Tanaka, Jack Raymond
- ArXiv
- 2010

- Jack Raymond
- 2008

- Alexander Mozeika, David Saad, Jack Raymond
- Physical review letters
- 2009

Computing circuits composed of noisy logical gates and their ability to represent arbitrary boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results onâ€¦ (More)

We study the typical case properties of the 1-in-3 satisfiability problem, the boolean satisfaction problem where a clause is satisfied by exactly one literal, in an enlarged random ensemble parametrized by average connectivity and probability of negation of a variable in a clause. Random 1-in-3 Satisfiability and Exact 3-Cover are special cases of thisâ€¦ (More)

- Toshiyuki Tanaka, Jack Raymond
- ISIT
- 2010

Compressed sensing of sparse sources can be improved by incorporating prior knowledge of the source. In this paper we demonstrate a method for optimal selection of weights in weighted l1 norm minimization for a noiseless reconstruction model, and show the improvements in compression that can be achieved.

- Jack Raymond, Martin R. Evans
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2006

We study a one-dimensional lattice flocking model incorporating all three of the flocking criteria proposed by Reynolds [Computer Graphics 21, 4 (1987)]: alignment, centering, and separation. The model generalizes that introduced by O. J. O'Loan and M. R. Evans [J. Phys. A. 32, L99 (1999)]. We motivate the dynamical rules by microscopic samplingâ€¦ (More)

- Adam Douglass, Andrew D. King, Jack Raymond
- SAT
- 2015

SAT filters are a novel and compact data structure that can be used to quickly query a word for membership in a fixed set. They have the potential to store more information in a fixed storage limit than a Bloom filter. Constructing a SAT filter requires sampling diverse solutions to randomly constructed constraint satisfaction instances, but there isâ€¦ (More)