Covering Problems for Partial Words and for Indeterminate Strings

We consider the problem of computing a shortest solid cover of an indeterminate string. An indeterminate string may contain non-solid symbols, each of which specifies a subset of the alphabet that could be present at the corresponding position. We also consider covering partial words, which are a special case of indeterminate strings where each non-solid symbol is a don't care symbol. We prove that indeterminate string covering problem and partial word covering problem are NP-complete for binary alphabet and show that both problems are fixed-parameter tractable with respect to $k$, the number of non-solid symbols. For the indeterminate string covering problem we obtain a $2^{O(k \log k)} + n k^{O(1)}$-time algorithm. For the partial word covering problem we obtain a $2^{O(\sqrt{k}\log k)} + nk^{O(1)}$-time algorithm. We prove that, unless the Exponential Time Hypothesis is false, no $2^{o(\sqrt{k})} n^{O(1)}$-time solution exists for either problem, which shows that our algorithm for this case is close to optimal. We also present an algorithm for both problems which is feasible in practice.Comment: full version (simplified and corrected); preliminary version appeared at ISAAC 2014; 14 pages, 4 figure

Circular pattern matching with k mismatches

The k-mismatch problem consists in computing the Hamming distance between a pattern P of length m and every length-m substring of a text T of length n, if this distance is no more than k. In many real-world applications, any cyclic shift of P is a relevant pattern, and thus one is interested in computing the minimal distance of every length-m substring of T and any cyclic shift of P. This is the circular pattern m

Renal Thrombotic Microangiopathy in Mice with Combined Deletion of Endocytic Recycling Regulators EHD3 and EHD4

Eps15 Homology Domain-containing 3 (EHD3), a member of the EHD protein family that regulates endocytic recycling, is the first protein reported to be specifically expressed in the glomerular endothelium in the kidney; therefore we generated Ehd3–/– mice and assessed renal development and pathology. Ehd3–/– animals showed no overt defects, and exhibited no proteinuria or glomerular pathology. However, as the expression of EHD4, a related family member, was elevated in the glomerular endothelium of Ehd3–/– mice and suggested functional compensation, we generated and analyzed Ehd3–/–; Ehd4–/– mice. These mice were smaller, possessed smaller and paler kidneys, were proteinuric and died between 3–24 weeks of age. Detailed analyses of Ehd3–/–; Ehd4–/– kidneys demonstrated thrombotic microangiopathy (TMA)-like glomerular lesions including thickening and duplication of glomerular basement membrane, endothelial swelling and loss of fenestrations. Other changes included segmental podocyte foot process effacement, mesangial interposition, and abnormal podocytic and mesangial marker expression. The glomerular lesions observed were strikingly similar to those seen in human pre-eclampsia and mouse models of reduced VEGF expression. As altered glomerular endothelial VEGFR2 expression and localization and increased apoptosis was observed in the absence of EHD3 and EHD4, we propose that EHD-mediated endocytic traffic of key surface receptors such as VEGFR2 is essential for physiological control of glomerular function. Furthermore, Ehd3–/–; Ehd4–/– mice provide a unique model to elucidate mechanisms of glomerular endothelial injury which is observed in a wide variety of human renal and extra-renal diseases

Research on Teaching and Learning Probability

This book summarizes the vast amount of research related to teaching and learning probability that has been conducted for more than 50 years in a variety of disciplines. It begins with a synthesis of the most important probability interpretations throughout history: intuitive, classical, frequentist, subjective, logical propensity and axiomatic views. It discusses their possible applications, philosophical problems, as well as their potential and the level of interest they enjoy at different educational levels. Next, the book describes the main features of probabilistic thinking and reasoning, including the contrast to classical logic, probability language features, the role of intuitions, as well as paradoxes and the relevance of modeling. It presents an analysis of the differences between conditioning and causation, the variability expression in data as a sum of random and causal variations, as well as those of probabilistic versus statistical thinking. This is followed by an analysis of probability’s role and main presence in school curricula and an outline of the central expectations in recent curricular guidelines at the primary, secondary and high school level in several countries. This book classifies and discusses in detail the three different research periods on students’ and people’s intuitions and difficulties concerning probability: early research focused on cognitive development, a period of heuristics and biases programs, and the current period marked by a multitude of foci, approaches and theoretical frameworks

Exponential-Size Model Property for PDL with Separating Parallel Composition

International audiencePropositional dynamic logic is extended with a parallel program having a separating semantic: the program (α || β) executes α and β on two substates of the current state. We prove that when the composition of two substates is deterministic, the logic has the exponential-size model property. The proof is by a piecewise filtration using an adaptation of the Fischer-Ladner closure. We conclude that the satisfiability of the logic is decidable in NEXPTIME