Statistical mechanics of lossy compression using multilayer perceptrons

Statistical mechanics is applied to lossy compression using multilayer perceptrons for unbiased Boolean messages. We utilize a tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are monotonic. For compression using committee tree, a lower bound of achievable distortion becomes small as the number of hidden units K increases. However, it cannot reach the Shannon bound even where K -> infty. For a compression using a parity tree with K >= 2 hidden units, the rate distortion function, which is known as the theoretical limit for compression, is derived where the code length becomes infinity.Comment: 12 pages, 5 figure

D6 Family Symmetry and Cold Dark Matter at LHC

We consider a non-supersymmetric extension of the standard model with a family symmetry based on D6 Z2 Z2, where one of Z2's is exactly conserved. This Z2 forbids the tree-level neutrino masses and simultaneously ensures the stability of cold dark matter candidates. From the assumption that cold dark matter is fermionic we can single out the D6 singlet right-handed neutrino as the best cold dark mater candidate. We find that an inert charged Higgs with a mass between 300 and 750 GeV decays mostly into an electron (or a positron) with a large missing energy, where the missing energy is carried away by the cold dark matter candidate. This will be a clean signal at LHC.Comment: 20 pages, 7 figure

Statistical mechanics of lossy compression for non-monotonic multilayer perceptrons

A lossy data compression scheme for uniformly biased Boolean messages is investigated via statistical mechanics techniques. We utilize tree-like committee machine (committee tree) and tree-like parity machine (parity tree) whose transfer functions are non-monotonic. The scheme performance at the infinite code length limit is analyzed using the replica method. Both committee and parity treelike networks are shown to saturate the Shannon bound. The AT stability of the Replica Symmetric solution is analyzed, and the tuning of the non-monotonic transfer function is also discussed.Comment: 29 pages, 7 figure

Error correcting code using tree-like multilayer perceptron

An error correcting code using a tree-like multilayer perceptron is proposed. An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0 using a tree-like committee machine (committee tree) or a tree-like parity machine (parity tree). Based on these architectures, several schemes featuring monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by noise. The analytical performance of these schemes is investigated using the replica method of statistical mechanics. Under some specific conditions, some of the proposed schemes are shown to saturate the Shannon bound at the infinite codeword length limit. The influence of the monotonicity of the units on the performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise

Functional variants of DOG1 control seed chilling responses and variation in seasonal life-history strategies in Arabidopsis thaliana.

The seasonal timing of seed germination determines a plant's realized environmental niche, and is important for adaptation to climate. The timing of seasonal germination depends on patterns of seed dormancy release or induction by cold and interacts with flowering-time variation to construct different seasonal life histories. To characterize the genetic basis and climatic associations of natural variation in seed chilling responses and associated life-history syndromes, we selected 559 fully sequenced accessions of the model annual species Arabidopsis thaliana from across a wide climate range and scored each for seed germination across a range of 13 cold stratification treatments, as well as the timing of flowering and senescence. Germination strategies varied continuously along 2 major axes: 1) Overall germination fraction and 2) induction vs. release of dormancy by cold. Natural variation in seed responses to chilling was correlated with flowering time and senescence to create a range of seasonal life-history syndromes. Genome-wide association identified several loci associated with natural variation in seed chilling responses, including a known functional polymorphism in the self-binding domain of the candidate gene DOG1. A phylogeny of DOG1 haplotypes revealed ancient divergence of these functional variants associated with periods of Pleistocene climate change, and Gradient Forest analysis showed that allele turnover of candidate SNPs was significantly associated with climate gradients. These results provide evidence that A. thaliana's germination niche and correlated life-history syndromes are shaped by past climate cycles, as well as local adaptation to contemporary climate

Electroweak phase transition in a nonminimal supersymmetric model

The Higgs potential of the minimal nonminimal supersymmetric standard model (MNMSSM) is investigated within the context of electroweak phase transition. We investigate the allowed parameter space yielding correct electroweak phase transitoin employing a high temperature approximation. We devote to phenomenological consequences for the Higgs sector of the MNMSSM for electron-positron colliders. It is observed that a future $e^+ e^-$ linear collider with $\sqrt{s} = 1000$ GeV will be able to test the model with regard to electroweak baryogenesis.Comment: 28 pages, 5 tables, 12 figure

Structural phase transitions in multipole traps

A small number of laser-cooled ions trapped in a linear radiofrequency multipole trap forms a hollow tube structure. We have studied, by means of molecular dynamics simulations, the structural transition from a double ring to a single ring of ions. We show that the single-ring configuration has the advantage to inhibit the thermal transfer from the rf-excited radial components of the motion to the axial component, allowing to reach the Doppler limit temperature along the direction of the trap axis. Once cooled in this particular configuration, the ions experience an angular dependency of the confinement if the local adiabaticity parameter exceeds the empirical limit. Bunching of the ion structures can then be observed and an analytic expression is proposed to take into account for this behaviour

Future directions in kaonic atom physics

Recent progress and open problems in kaonic atom physics are presented. A connection between phenomenological deep potentials and the underlying $K^-N$ interaction is established as well as the need for a theory for multinucleon absorption of kaons. $K^-$ absorption at rest to specific $\Lambda$ hypernuclei states is briefly discussed.Comment: 6 pages, 3 figures, proceedings of the EXA2011 conference, to appear in Hyperfine Interaction

Self-control in Sparsely Coded Networks

A complete self-control mechanism is proposed in the dynamics of neural networks through the introduction of a time-dependent threshold, determined in function of both the noise and the pattern activity in the network. Especially for sparsely coded models this mechanism is shown to considerably improve the storage capacity, the basins of attraction and the mutual information content of the network.Comment: 4 pages, 6 Postscript figure