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    Milestones: Supporting learners with complex additional support needs

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    CEC: Clinical Exchange Corner

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    UA10/1 CEC Newsletter

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    Newsletter created by and about the WKU Suzanne Vitale Clinical Education Complex

    Quantal-Classical Duality and the Semiclassical Trace Formula

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    We consider Hamiltonian systems which can be described both classically and quantum mechanically. Trace formulas establish links between the energy spectra of the quantum description and the spectrum of actions of periodic orbits in the classical description. This duality is investigated in the present paper. The duality holds for chaotic as well as for integrable systems. For billiards the quantal spectrum (eigenvalues of the Helmholtz equation) and the classical spectrum (lengths of periodic orbits) are two manifestations of the billiard's boundary. The trace formula expresses this link as a Fourier transform relation between the corresponding spectral densities. It follows that the two-point statistics are also simply related. The universal correlations of the quantal spectrum are well known, consequently one can deduce the classical universal correlations. An explicit expression for the scale of the classical correlations is derived and interpreted. This allows a further extension of the formalism to the case of complex billiard systems, and in particular to the most interesting case of diffusive system. The concept of classical correlations allows a better understanding of the so-called diagonal approximation and its breakdown. It also paves the way towards a semiclassical theory that is capable of global description of spectral statistics beyond the breaktime. An illustrative application is the derivation of the disorder-limited breaktime in case of a disordered chain, thus obtaining a semiclassical theory for localization. A numerical study of classical correlations in the case of the 3D Sinai billiard is presented. We gain a direct understanding of specific statistical properties of the classical spectrum, as well as their semiclassical manifestation in the quantal spectrum.Comment: 42 pages, 17 figure

    Complex Clause of Bahasa Indonesia From the Point of View of Systemic Functional Linguistic

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    This paper discusses the meaning of the complex clause by a series of processes that are combined in a logical of the two clauses. Complex clause can be combined through one of two logical-semantic relationships that is expansion or projection. Systemic Functional Linguistics approach is used to describe the five texts taken at random. The five texts are: (1) Gembala dan malaikat, (2) Pendahuluan, (3) Melakukan Studi Gender dalam Bahasa, (4) Korporasi, Kerja dan Kultur, dan (5) Gara-gara Dilarang Bertemu (1) Shepherd and angels, (2) Introduction, (3) Doing Gender in Language Studies, (4) Corporations, Employment and Culture, and (5) Due to Divorce, No Meet Pets. The analysis of the five texts is not opposed but complementary to one another. By using a qualitative descriptive method, it was found two types of logical-semantic relations: (1) Expansion, and (2) projection. Integrating through one of the logical-semantic relations: expansion or projection is realized through a system of mutual dependence or taxis that can be divided into paratactic and hypotactic. Key words: Clause complex, expansion, projectio

    Viral evolution under the pressure of an adaptive immune system - optimal mutation rates for viral escape

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    Based on a recent model of evolving viruses competing with an adapting immune system [1], we study the conditions under which a viral quasispecies can maximize its growth rate. The range of mutation rates that allows viruses to thrive is limited from above due to genomic information deterioration, and from below by insufficient sequence diversity, which leads to a quick eradication of the virus by the immune system. The mutation rate that optimally balances these two requirements depends to first order on the ratio of the inverse of the virus' growth rate and the time the immune system needs to develop a specific answer to an antigen. We find that a virus is most viable if it generates exactly one mutation within the time it takes for the immune system to adapt to a new viral epitope. Experimental viral mutation rates, in particular for HIV (human immunodeficiency virus), seem to suggest that many viruses have achieved their optimal mutation rate. [1] C.Kamp and S. Bornholdt, Phys. Rev. Lett., 88, 068104 (2002)Comment: 5 pages RevTeX including 3 figure

    Anomalous diffusion in a symbolic model

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    We address this work to investigate some statistical properties of symbolic sequences generated by a numerical procedure in which the symbols are repeated following a power law probability density. In this analysis, we consider that the sum of n symbols represents the position of a particle in erratic movement. This approach revealed a rich diffusive scenario characterized by non-Gaussian distributions and, depending on the power law exponent and also on the procedure used to build the walker, we may have superdiffusion, subdiffusion or usual diffusion. Additionally, we use the continuous-time random walk framework to compare with the numerical data, finding a good agreement. Because of its simplicity and flexibility, this model can be a candidate to describe real systems governed by power laws probabilities densities.Comment: Accepted for publication in Physica Script

    What Makes Complex Systems Complex?

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    This paper explores some of the factors that make complex systems complex. We first examine the history of complex systems. It was Aristotle’s insight that how elements are joined together helps determine the properties of the resulting whole. We find (a) that scientific reductionism does not provide a sufficient explanation; (b) that to understand complex systems, one must identify and trace energy flows; and (c) that disproportionate causality, including global tipping points, are all around us. Disproportionate causality results from the wide availability of energy stores. We discuss three categories of emergent phenomena—static, dynamic, and adaptive—and recommend retiring the term emergent, except perhaps as a synonym for creative. Finally, we find that virtually all communication is stigmergic

    Complex quotients by nonclosed groups and their stratifications

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    We define the notion of complex stratification by quasifolds and show that such spaces occur as complex quotients by certain nonclosed subgroups of tori associated to convex polytopes. The spaces thus obtained provide a natural generalization to the nonrational case of the notion of toric variety associated with a rational convex polytope.Comment: Research announcement. Updated version, shortened, exposition improved, 8 p
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