6,072 research outputs found

    Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions

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    We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language XX or language YY, while the second model incorporates a third state XY, representing individuals that use both languages (bilinguals). We analyze the models on complex networks and two-dimensional square lattices by analytical and numerical methods, and show that they exhibit a transition from one-language dominance to language coexistence. We find that the coexistence of languages is more difficult to maintain in the Bilinguals model, where the presence of bilinguals in use facilitates the ultimate dominance of one of the two languages. A stability analysis reveals that the coexistence is more unlikely to happen in poorly-connected than in fully connected networks, and that the dominance of only one language is enhanced as the connectivity decreases. This dominance effect is even stronger in a two-dimensional space, where domain coarsening tends to drive the system towards language consensus.Comment: 30 pages, 11 figure

    Modeling two-language competition dynamics

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    During the last decade, much attention has been paid to language competition in the complex systems community, that is, how the fractions of speakers of several competing languages evolve in time. In this paper we review recent advances in this direction and focus on three aspects. First we consider the shift from two-state models to three state models that include the possibility of bilingual individuals. The understanding of the role played by bilingualism is essential in sociolinguistics. In particular, the question addressed is whether bilingualism facilitates the coexistence of languages. Second, we will analyze the effect of social interaction networks and physical barriers. Finally, we will show how to analyze the issue of bilingualism from a game theoretical perspective.Comment: 15 pages, 5 figures; published in the Special Issue of Advances in Complex Systems "Language Dynamics

    Homogenous Ensemble Phonotactic Language Recognition Based on SVM Supervector Reconstruction

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    Currently, acoustic spoken language recognition (SLR) and phonotactic SLR systems are widely used language recognition systems. To achieve better performance, researchers combine multiple subsystems with the results often much better than a single SLR system. Phonotactic SLR subsystems may vary in the acoustic features vectors or include multiple language-specific phone recognizers and different acoustic models. These methods achieve good performance but usually compute at high computational cost. In this paper, a new diversification for phonotactic language recognition systems is proposed using vector space models by support vector machine (SVM) supervector reconstruction (SSR). In this architecture, the subsystems share the same feature extraction, decoding, and N-gram counting preprocessing steps, but model in a different vector space by using the SSR algorithm without significant additional computation. We term this a homogeneous ensemble phonotactic language recognition (HEPLR) system. The system integrates three different SVM supervector reconstruction algorithms, including relative SVM supervector reconstruction, functional SVM supervector reconstruction, and perturbing SVM supervector reconstruction. All of the algorithms are incorporated using a linear discriminant analysis-maximum mutual information (LDA-MMI) backend for improving language recognition evaluation (LRE) accuracy. Evaluated on the National Institute of Standards and Technology (NIST) LRE 2009 task, the proposed HEPLR system achieves better performance than a baseline phone recognition-vector space modeling (PR-VSM) system with minimal extra computational cost. The performance of the HEPLR system yields 1.39%, 3.63%, and 14.79% equal error rate (EER), representing 6.06%, 10.15%, and 10.53% relative improvements over the baseline system, respectively, for the 30-, 10-, and 3-s test conditions

    Convolution, Separation and Concurrency

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    A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these constructions, the most prominent ones being separation logics, where convolution is separating conjunction in an assertion quantale; interval logics, where convolution is the chop operation; and stream interval functions, where convolution is used for analysing the trajectories of dynamical or real-time systems. A Hoare logic is constructed in a generic fashion on the power series quantale, which applies to each of these examples. In many cases, commutative notions of convolution have natural interpretations as concurrency operations.Comment: 39 page

    Quantum logic is undecidable

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    We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature (,,0,1)(\lor,\perp,0,1), where `\perp' is the orthogonality relation. Our main result is that already its quasi-identities are undecidable: there is no algorithm to decide whether an implication between equations and orthogonality relations implies another equation. This is a corollary of a recent result of Slofstra in combinatorial group theory. It follows upon reinterpreting that result in terms of the hypergraph approach to quantum contextuality, for which it constitutes a proof of the inverse sandwich conjecture. It can also be interpreted as stating that a certain quantum satisfiability problem is undecidable.Comment: 11 pages. v3: improved exposition. v4: minor clarification

    On the Parity Problem in One-Dimensional Cellular Automata

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    We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices. We are interested in determining the minimal neighbourhood that allows the problem to be solvable for any initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can possibly solve the parity problem from arbitrary initial configurations. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and we formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

    Computation of conserved densities for systems of nonlinear differential-difference equations

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    A new method for the computation of conserved densities of nonlinear differential-difference equations is applied to Toda lattices and discretizations of the Korteweg-de Vries and nonlinear Schrodinger equations. The algorithm, which can be implemented in computer algebra languages such as Mathematica, can be used as an indicator of integrability.Comment: submitted to Phys. Lett A, 10 pages, late
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