Quotient Complexity of Regular Languages

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it "quotient complexity". The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations

Data Portraits and Intermediary Topics: Encouraging Exploration of Politically Diverse Profiles

In micro-blogging platforms, people connect and interact with others. However, due to cognitive biases, they tend to interact with like-minded people and read agreeable information only. Many efforts to make people connect with those who think differently have not worked well. In this paper, we hypothesize, first, that previous approaches have not worked because they have been direct -- they have tried to explicitly connect people with those having opposing views on sensitive issues. Second, that neither recommendation or presentation of information by themselves are enough to encourage behavioral change. We propose a platform that mixes a recommender algorithm and a visualization-based user interface to explore recommendations. It recommends politically diverse profiles in terms of distance of latent topics, and displays those recommendations in a visual representation of each user's personal content. We performed an "in the wild" evaluation of this platform, and found that people explored more recommendations when using a biased algorithm instead of ours. In line with our hypothesis, we also found that the mixture of our recommender algorithm and our user interface, allowed politically interested users to exhibit an unbiased exploration of the recommended profiles. Finally, our results contribute insights in two aspects: first, which individual differences are important when designing platforms aimed at behavioral change; and second, which algorithms and user interfaces should be mixed to help users avoid cognitive mechanisms that lead to biased behavior.Comment: 12 pages, 7 figures. To be presented at ACM Intelligent User Interfaces 201

Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation

Directed graphs (DG), interpreted as state transition diagrams, are traditionally used to represent finite-state automata (FSA). In the context of formal languages, both FSA and regular expressions (RE) are equivalent in that they accept and generate, respectively, type-3 (regular) languages. Based on our previous work, this paper analyzes effects of graph manipulations on corresponding RE. In this present, starting stage we assume that the DG under consideration contains no cycles. Graph manipulation is performed by deleting or inserting of nodes or arcs. Combined and/or multiple application of these basic operators enable a great variety of transformations of DG (and corresponding RE) that can be seen as mutants of the original DG (and corresponding RE). DG are popular for modeling complex systems; however they easily become intractable if the system under consideration is complex and/or large. In such situations, we propose to switch to corresponding RE in order to benefit from their compact format for modeling and algebraic operations for analysis. The results of the study are of great potential interest to mutation testing

5-(Prop-2-yn­yl)-5H-dibenzo[b,f]azepine

The asymmetric unit of the title compound, C17H13N, contains two independent butterfly-shaped mol­ecules. The seven-membered azepine rings both adopt a boat conformation. The dihedral angles between the benzene rings in the two mol­ecules are 46.95 (11) and 52.21 (11)°

Opto-mechanical measurement of micro-trap via nonlinear cavity enhanced Raman scattering spectrum

High-gain resonant nonlinear Raman scattering on trapped cold atoms within a high-fineness ring optical cavity is simply explained under a nonlinear opto-mechanical mechanism, and a proposal using it to detect frequency of micro-trap on atom chip is presented. The enhancement of scattering spectrum is due to a coherent Raman conversion between two different cavity modes mediated by collective vibrations of atoms through nonlinear opto-mechanical couplings. The physical conditions of this technique are roughly estimated on Rubidium atoms, and a simple quantum analysis as well as a multi-body semiclassical simulation on this nonlinear Raman process is conducted.Comment: 7 pages, 2 figure

Perturbed Timed Automata

We consider timed automata whose clocks are imperfect. For a given perturbation error 0 \u3c ε \u3c 1, the perturbed language of a timed automaton is obtained by letting its clocks change at a rate within the interval [1 - ε, 1 + ε]. We show that the perturbed language of a timed automaton with a single clock can be captured by a deterministic timed automaton. This leads to a decision procedure for the language inclusion problem for systems modeled as products of 1-clock automata with imperfect clocks. We also prove that determinization and decidability of language inclusion are not possible for multi-clock automata, even with perturbation

A Computational Assay of Estrogen Receptor alpha Antagonists Reveals the Key Common Structural Traits of Drugs Effectively Fighting Refractory Breast Cancers

Somatic mutations of the Estrogen Receptor alpha (ER alpha) occur with an up to 40% incidence in ER sensitive breast cancer (BC) patients undergoing prolonged endocrine treatments. These polymorphisms are implicated in acquired resistance, disease relapse, and increased mortality rates, hence representing a current major clinical challenge. Here, multi-microseconds (12.5 mu s) molecular dynamics simulations revealed that recurrent ER alpha. polymorphisms (i.e. L536Q, Y5375, Y537N, D538G) (mER alpha) are constitutively active in their apo form and that they prompt the selection of an agonist (active)-like conformation even upon antagonists binding. Interestingly, our simulations rationalize, for thefirst time, the efficacy profile of (pre)clinically used Selective Estrogen Receptor Modulators/Downregulators (SERMs/SERDs) against these variants, enlightening, at atomistic level of detail, the key common structural traits needed by drugs able to effectively fight refractory BC types. This knowledge represents a key advancement for mechanism-based therapeutics targeting resistant ER alpha isoforms, potentially allowing the community to move a step closer to 'precision medicine' calibrated on patients' genetic profiles and disease progression

Grounding Synchronous Deterministic Concurrency in Sequential Programming

In this report, we introduce an abstract interval domain I(D; P) and associated fixed point semantics for reasoning about concurrent and sequential variable accesses within a synchronous cycle-based model of computation. The interval domain captures must (lower bound) and cannot (upper bound) information to approximate the synchronisation status of variables consisting of a value status D and an init status P. We use this domain for a new behavioural definition of Berry’s causality analysis for Esterel. This gives a compact and uniform understanding of Esterel-style constructiveness for shared-memory multi-threaded programs. Using this new domain-theoretic characterisation we show that Berry’s constructive semantics is a conservative approximation of the recently proposed sequentially constructive (SC) model of computation. We prove that every Berry-constructive program is sequentially constructive, i.e., deterministic and deadlock-free under sequentially admissible scheduling. This gives, for the first time, a natural interpretation of Berry-constructiveness for main-stream imperative programming in terms of scheduling, where previous results were cast in terms of synchronous circuits. It also opens the door to a direct mapping of Esterel’s signal mechanism into boolean variables that can be set and reset arbitrarily within a tick. We illustrate the practical usefulness of this mapping by discussing how signal reincarnation is handled efficiently by this transformation, which is of complexity that is linear in progra