Capacity Upper Bounds for Deletion-Type Channels

We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the classical deletion channel, we give a special attention to the Poisson-repeat channel introduced by Mitzenmacher and Drinea (IEEE Transactions on Information Theory, 2006). Our framework can be applied to obtain capacity upper bounds for any repetition distribution (the deletion and Poisson-repeat channels corresponding to the special cases of Bernoulli and Poisson distributions). Our techniques essentially reduce the task of proving capacity upper bounds to maximizing a univariate, real-valued, and often concave function over a bounded interval. We show the following: 1. The capacity of the binary deletion channel with deletion probability $d$ is at most $(1-d)\log\varphi$ for $d\geq 1/2$, and, assuming the capacity function is convex, is at most $1-d\log(4/\varphi)$ for $d<1/2$, where $\varphi=(1+\sqrt{5})/2$ is the golden ratio. This is the first nontrivial capacity upper bound for any value of $d$ outside the limiting case $d\to 0$ that is fully explicit and proved without computer assistance. 2. We derive the first set of capacity upper bounds for the Poisson-repeat channel. 3. We derive several novel upper bounds on the capacity of the deletion channel. All upper bounds are maximums of efficiently computable, and concave, univariate real functions over a bounded domain. In turn, we upper bound these functions in terms of explicit elementary and standard special functions, whose maximums can be found even more efficiently (and sometimes, analytically, for example for $d=1/2$). Along the way, we develop several new techniques of potentially independent interest in information theory, probability, and mathematical analysis.Comment: Minor edits, In Proceedings of 50th Annual ACM SIGACT Symposium on the Theory of Computing (STOC), 201

Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps

What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called fixed-template constraint satisfaction problems (CSPs) -- it has turned out that their complexity is captured by a certain specific form of symmetry. This paper explains an extension of this theory to a much broader class of computational problems, the promise CSPs, which includes relaxed versions of CSPs such as the problem of finding a 137-coloring of a 3-colorable graph

Epigenetic Characterization of the FMR1 Gene and Aberrant Neurodevelopment in Human Induced Pluripotent Stem Cell Models of Fragile X Syndrome

Fragile X syndrome (FXS) is the most common inherited cause of intellectual disability. In addition to cognitive deficits, FXS patients exhibit hyperactivity, attention deficits, social difficulties, anxiety, and other autistic-like behaviors. FXS is caused by an expanded CGG trinucleotide repeat in the 5′ untranslated region of the Fragile X Mental Retardation (FMR1) gene leading to epigenetic silencing and loss of expression of the Fragile X Mental Retardation protein (FMRP). Despite the known relationship between FMR1 CGG repeat expansion and FMR1 silencing, the epigenetic modifications observed at the FMR1 locus, and the consequences of the loss of FMRP on human neurodevelopment and neuronal function remain poorly understood. To address these limitations, we report on the generation of induced pluripotent stem cell (iPSC) lines from multiple patients with FXS and the characterization of their differentiation into post-mitotic neurons and glia. We show that clones from reprogrammed FXS patient fibroblast lines exhibit variation with respect to the predominant CGG-repeat length in the FMR1 gene. In two cases, iPSC clones contained predominant CGG-repeat lengths shorter than measured in corresponding input population of fibroblasts. In another instance, reprogramming a mosaic patient having both normal and pre-mutation length CGG repeats resulted in genetically matched iPSC clonal lines differing in FMR1 promoter CpG methylation and FMRP expression. Using this panel of patient-specific, FXS iPSC models, we demonstrate aberrant neuronal differentiation from FXS iPSCs that is directly correlated with epigenetic modification of the FMR1 gene and a loss of FMRP expression. Overall, these findings provide evidence for a key role for FMRP early in human neurodevelopment prior to synaptogenesis and have implications for modeling of FXS using iPSC technology. By revealing disease-associated cellular phenotypes in human neurons, these iPSC models will aid in the discovery of novel therapeutics for FXS and other autism-spectrum disorders sharing common pathophysiology.FRAXA Research FoundationHarvard Stem Cell Institute (seed grant)Stanley Medical Research InstituteNational Institute of Mental Health (U.S.) (grant #R33MH087896

Epigenetic regulation of mucin genes in human cancers

Mucins are high molecular weight glycoproteins that play important roles in diagnostic and prognostic prediction and in carcinogenesis and tumor invasion. Regulation of expression of mucin genes has been studied extensively, and signaling pathways, transcriptional regulators, and epigenetic modification in promoter regions have been described. Detection of the epigenetic status of cancer-related mucin genes is important for early diagnosis of cancer and for monitoring of tumor behavior and response to targeted therapy. Effects of micro-RNAs on mucin gene expression have also started to emerge. In this review, we discuss the current views on epigenetic mechanisms of regulation of mucin genes (MUC1, MUC2, MUC3A, MUC4, MUC5AC, MUC5B, MUC6, MUC16, and MUC17) and the possible clinical applications of this epigenetic information

Infiltration parameters for rangeland soils

Important to the management of rangelands is knowledge of the water intake properties of their soils and the effect of soil surface and canopy cover. Using a data base of rangeland infiltration runs covering a wide range of soil and cover conditions, a procedure incorporating the effects of soil properties, soil surface cover, and vegetative canopy on the Green-Ampt hydraulic conductivity parameter was developed. Test results indicate that the estimated Green-Ampt parameters provided good predictions of the mean final infiltration rates and volumes for a variety of soil-cover situations.This material was digitized as part of a cooperative project between the Society for Range Management and the University of Arizona Libraries.The Journal of Range Management archives are made available by the Society for Range Management and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform August 202

A Note on Determining Soil Properties for Soils Containing Rock Fragments

This material was digitized as part of a cooperative project between the Society for Range Management and the University of Arizona Libraries.The Journal of Range Management archives are made available by the Society for Range Management and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform August 202

Prediction of soil cover and soil rock for rangeland infiltration

Lane et al. (1987) found that the proportion of bare or covered ground surface under the canopy is important for modeling infiltration in rangeland soils. Using a total of 322 composite plant canopy cover and ground cover measurements collected in Idaho, Arizona, and Nevada, equations were developed for predicting the ground cover under plant canopy from standard resource surveys or remote sensing techniques which primarily measure ground cover outside plant canopy. Equations were developed for predicting (1) percent by weight of soil rock in the top 76 mm of soil from ground cover measurements made outside of plant canopy, and (2) surface rock cover outside plant canopy from soil texture.This material was digitized as part of a cooperative project between the Society for Range Management and the University of Arizona Libraries.The Journal of Range Management archives are made available by the Society for Range Management and the University of Arizona Libraries. Contact [email protected] for further information.Migrated from OJS platform August 202