Models of discrete space and space-time that exhibit continuum-like behavior at large lengths could have profound implications for physics. They may help tame the infinities arising from quantizing gravity, and remove the need for the machinery of the real numbers; a construct with no direct observational support. However, despite many attempts to build discrete space, researchers have failed to produce even the simplest geometries.
View Article and Find Full Text PDFWe introduce a simple class of distribution networks that withstand damage by being repairable instead of redundant. Instead of asking how hard it is to disconnect nodes through damage, we ask how easy it is to reconnect nodes after damage. We prove that optimal networks on regular lattices have an expected cost of reconnection proportional to the lattice length, and that such networks have exactly three levels of structural hierarchy.
View Article and Find Full Text PDFBackground: Biological processes occur on a vast range of time scales, and many of them occur concurrently. As a result, system-wide measurements of gene expression have the potential to capture many of these processes simultaneously. The challenge however, is to separate these processes and time scales in the data.
View Article and Find Full Text PDFWhile genome-wide gene expression data are generated at an increasing rate, the repertoire of approaches for pattern discovery in these data is still limited. Identifying subtle patterns of interest in large amounts of data (tens of thousands of profiles) associated with a certain level of noise remains a challenge. A microarray time series was recently generated to study the transcriptional program of the mouse segmentation clock, a biological oscillator associated with the periodic formation of the segments of the body axis.
View Article and Find Full Text PDFDespite tremendous advances in the field of genomics, the amount and function of the large non-coding part of the genome in higher organisms remains poorly understood. Here we report an observation, made for 37 fully sequenced eukaryotic genomes, which indicates that eukaryotes require a certain minimum amount of non-coding DNA (ncDNA). This minimum increases quadratically with the amount of DNA located in exons.
View Article and Find Full Text PDFMotivation: We consider any collection of microarrays that can be ordered to form a progression; for example, as a function of time, severity of disease or dose of a stimulant. By plotting the expression level of each gene as a function of time, or severity, or dose, we form an expression series, or curve, for each gene. While most of these curves will exhibit random fluctuations, some will contain a pattern, and these are the genes that are most likely associated with the quantity used to order them.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
September 2003
We show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem. The probabilistic "traveling salesman" must decide on an a priori order in which to visit n cities (randomly distributed over a unit square) before learning that some cities can be omitted. We find the optimized average length of the pruned tour follows E(L(pruned))=sqrt[np](0.
View Article and Find Full Text PDFWe show how to simulate a system in thermal equilibrium when the energy cannot be evaluated exactly: the error distribution needs to be symmetric, but it does not need to be known. We also solve the Ceperley-Dewing version of this problem, where the error distribution is taken to be fully known. These underlying ideas give an effective optimization strategy for problems where the evaluation of each design can be sampled only statistically, including an application to protein folding.
View Article and Find Full Text PDFPhys Rev E Stat Nonlin Soft Matter Phys
September 2002
We consider the design of proteins to be simultaneously thermodynamically stable in multiple independent and correlated conformations. We first show that a protein can be trained to fold to multiple independent conformations and calculate its capacity. The number of configurations that it can remember is proportional to the logarithm of the number of amino acid species A, independent of chain length.
View Article and Find Full Text PDFAssembling fragments randomly sampled from along a sequence is the basis of whole-genome shotgun sequencing, a technique used to map the DNA of the human and other genomes. We calculate the probability that a random sequence can be recovered from a collection of overlapping fragments. We provide an exact solution for an infinite alphabet and in the case of constant overlaps.
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