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

Movements of hatchery-reared lingcod released on rocky reefs in Puget Sound

Abstract Fourteen sub-adult hatchery-reared lingcod (Ophiodon elongatus) were released onto reefs in South Puget Sound, Washington, USA to evaluate their movement behavior. Acoustic telemetry revealed variation in movement among individuals that was related to body size. Larger lingcod tended to leave the release reef sooner than smaller lingcod. Four lingcod left the reefs less than 10 days after release, while three lingcod left between one and 4 months after release. Seven lingcod remained at the release reefs for the entire 5-month study, though they did make apparent short-term (&lt; 24 h duration) excursions away from the reefs. Data suggest that the frequency and duration of excursions increase with age and size in both wild and hatchery lingcod. Movement data from these hatchery lingcod and previously published studies on wild lingcod are compared

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

Aberrant methylation of the Adenomatous Polyposis Coli (APC) gene promoter is associated with the inflammatory breast cancer phenotype

Aberrant methylation of the adenomatous polyposis coli (APC) gene promoter occurs in about 40% of breast tumours and has been correlated with reduced APC protein levels. To what extent epigenetic alterations of the APC gene may differ according to specific breast cancer phenotypes, remains to be elucidated. Our aim was to explore the role of APC methylation in the inflammatory breast cancer (IBC) phenotype. The status of APC gene promoter hypermethylation was investigated in DNA from normal breast tissues, IBC and non-IBC by both conventional and real-time quantitative methylation-specific PCR (MSP). APC methylation levels were compared with APC mRNA and protein levels. Hypermethylation of the APC gene promoter was present in 71% of IBC samples (n=21) and 43% of non-IBC samples (n=30) by conventional MSP (P=0.047). The APC gene also showed an increased frequency of high methylation levels in IBC (in 74% of cases, n=19) vs non-IBC (in 46% of cases, n=35) using a qMSP assay (P=0.048). We observed no significant association between APC methylation levels by qMSP and APC mRNA or protein expression levels. In conclusion, for the first time, we report the association of aberrant methylation of the APC gene promoter with the IBC phenotype, which might be of biological and clinical importance

Natural History and Outcome of Hepatic Vascular Malformations in a Large Cohort of Patients with Hereditary Hemorrhagic Teleangiectasia

BACKGROUND: Hereditary hemorrhagic telangiectasia is a genetic disease characterized by teleangiectasias involving virtually every organ. There are limited data in the literature regarding the natural history of liver vascular malformations in hemorrhagic telangiectasia and their associated morbidity and mortality. AIM: This prospective cohort study sought to assess the outcome of liver involvement in hereditary hemorrhagic telangiectasia patients. METHODS: We analyzed 16 years of surveillance data from a tertiary hereditary hemorrhagic telangiectasia referral center in Italy. We considered for inclusion in this study 502 consecutive Italian patients at risk of hereditary hemorrhagic telangiectasia who presented at the hereditary hemorrhagic telangiectasia referral center and underwent a multidisciplinary screening protocol for the diagnosis of hereditary hemorrhagic telangiectasia. Of the 502 individuals assessed in the center, 154 had hepatic vascular malformations and were the subject of the study; 198 patients with hereditary hemorrhagic telangiectasia and without hepatic vascular malformations were the controls. Additionally, we report the response to treatment of patients with complicated hepatic vascular malformations. RESULTS: The 154 patients were included and followed for a median period of 44 months (range 12-181); of these, eight (5.2%) died from VM-related complications and 39 (25.3%) experienced complications. The average incidence rates of death and complications were 1.1 and 3.6 per 100 person-years, respectively. The median overall survival and event-free survival after diagnosis were 175 and 90 months, respectively. The rate of complete response to therapy was 63%. CONCLUSIONS: This study shows that substantial morbidity and mortality are associated with liver vascular malformations in hereditary hemorrhagic telangiectasia patients