881 resultados para exponential-convexity
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Software product lines (SPL) are diverse systems that are developed using a dual engineering process: (a)family engineering defines the commonality and variability among all members of the SPL, and (b) application engineering derives specific products based on the common foundation combined with a variable selection of features. The number of derivable products in an SPL can thus be exponential in the number of features. This inherent complexity poses two main challenges when it comes to modelling: Firstly, the formalism used for modelling SPLs needs to be modular and scalable. Secondly, it should ensure that all products behave correctly by providing the ability to analyse and verify complex models efficiently. In this paper we propose to integrate an established modelling formalism (Petri nets) with the domain of software product line engineering. To this end we extend Petri nets to Feature Nets. While Petri nets provide a framework for formally modelling and verifying single software systems, Feature Nets offer the same sort of benefits for software product lines. We show how SPLs can be modelled in an incremental, modular fashion using Feature Nets, provide a Feature Nets variant that supports modelling dynamic SPLs, and propose an analysis method for SPL modelled as Feature Nets. By facilitating the construction of a single model that includes the various behaviours exhibited by the products in an SPL, we make a significant step towards efficient and practical quality assurance methods for software product lines.
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Dissertação de mestrado integrado em Engenharia Civil
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Dissertação de mestrado em Património e Turismo Cultural
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Dissertação de mestrado em Comunicação, Arte e Cultura
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Dissertação de mestrado em Applied Biochemistry (área de especialização em Biomedicine)
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Here we describe the results of some computational explorations in Thompson's group F. We describe experiments to estimate the cogrowth of F with respect to its standard finite generating set, designed to address the subtle and difficult question whether or not Thompson's group is amenable. We also describe experiments to estimate the exponential growth rate of F and the rate of escape of symmetric random walks with respect to the standard generating set.
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An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.
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We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.
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In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.
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The metropolitan spatial structure displays various patterns, sometimes monocentricity and sometimes multicentricity, which seems much more complicated than the exponential density function used in classic works such as Clark (1961), Muth (1969) or Mills (1973) among others, can effectively represent. It seems that a more flexible density function,such as cubic spline function (Anderson (1982), Zheng (1991), etc.) to describe the density-accessibility relationship is needed. Also, accessibility, the fundamental determinant of density variations, is only partly captured by the inclusion of distance to the city centre as an explanatory variable. Steen (1986) has proposed to correct that miss-especification by including an additional gradient for distance to the nearest transportation axis. In identifying the determinants of urban spatial structure in the context of inter-urban systems, some of the variables proposed by Muth (1969), Mills (1973) and Alperovich (1983) such as city age or population, make no sense in the case of a single urban system. All three criticism to the exponential density function and its determinants apply for the Barcelona Metropolitan Region, a polycentric conurbation structured on well defined transportation axes.
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The presence of subcentres cannot be captured by an exponential function. Cubic spline functions seem more appropriate to depict the polycentricity pattern of modern urban systems. Using data from Barcelona Metropolitan Region, two possible population subcentre delimitation procedures are discussed. One, taking an estimated derivative equal to zero, the other, a density gradient equal to zero. It is argued that, in using a cubic spline function, a delimitation strategy based on derivatives is more appropriate than one based on gradients because the estimated density can be negative in sections with very low densities and few observations, leading to sudden changes in estimated gradients. It is also argued that using as a criteria for subcentre delimitation a second derivative with value zero allow us to capture a more restricted subcentre area than using as a criteria a first derivative zero. This methodology can also be used for intermediate ring delimitation.
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The Whitehead minimization problem consists in finding a minimum size element in the automorphic orbit of a word, a cyclic word or a finitely generated subgroup in a finite rank free group. We give the first fully polynomial algorithm to solve this problem, that is, an algorithm that is polynomial both in the length of the input word and in the rank of the free group. Earlier algorithms had an exponential dependency in the rank of the free group. It follows that the primitivity problem – to decide whether a word is an element of some basis of the free group – and the free factor problem can also be solved in polynomial time.
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Els bacteris són la forma dominant de vida del planeta: poden sobreviure en medis molt adversos, i en alguns casos poden generar substàncies que quan les ingerim ens són tòxiques. La seva presència en els aliments fa que la microbiologia predictiva sigui un camp imprescindible en la microbiologia dels aliments per garantir la seguretat alimentària. Un cultiu bacterià pot passar per quatre fases de creixement: latència, exponencial, estacionària i de mort. En aquest treball s’ha avançat en la comprensió dels fenòmens intrínsecs a la fase de latència, que és de gran interès en l’àmbit de la microbiologia predictiva. Aquest estudi, realitzat al llarg de quatre anys, s’ha abordat des de la metodologia Individual-based Modelling (IbM) amb el simulador INDISIM (INDividual DIScrete SIMulation), que ha estat millorat per poder fer-ho. INDISIM ha permès estudiar dues causes de la fase de latència de forma separada, i abordar l’estudi del comportament del cultiu des d’una perspectiva mesoscòpica. S’ha vist que la fase de latència ha de ser estudiada com un procés dinàmic, i no definida per un paràmetre. L’estudi de l’evolució de variables com la distribució de propietats individuals entre la població (per exemple, la distribució de masses) o la velocitat de creixement, han permès distingir dues etapes en la fase de latència, inicial i de transició, i aprofundir en la comprensió del que passa a nivell cel•lular. S’han observat experimentalment amb citometria de flux diversos resultats previstos per les simulacions. La coincidència entre simulacions i experiments no és trivial ni casual: el sistema estudiat és un sistema complex, i per tant la coincidència del comportament al llarg del temps de diversos paràmetres interrelacionats és un aval a la metodologia emprada en les simulacions. Es pot afirmar, doncs, que s’ha verificat experimentalment la bondat de la metodologia INDISIM.
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BACKGROUND: Waddlia chondrophila (W. chondrophila) is an emerging abortifacient organism which has been identified in the placentae of humans and cattle. The organism is a member of the order Chlamydiales, and shares many similarities at the genome level and in growth studies with other well-characterised zoonotic chlamydial abortifacients, such as Chlamydia abortus (C. abortus). This study investigates the growth of the organism and its effects upon pro-inflammatory cytokine expression in a ruminant placental cell line which we have previously utilised in a model of C. abortus pathogenicity. METHODOLOGY/PRINCIPAL FINDINGS: Using qPCR, fluorescent immunocytochemistry and electron microscopy, we characterised the infection and growth of W. chondrophila within the ovine trophoblast AH-1 cell line. Inclusions were visible from 6 h post-infection (p.i.) and exponential growth of the organism could be observed over a 60 h time-course, with significant levels of host cell lysis being observed only after 36 h p.i. Expression of CXCL8, TNF-α, IL-1α and IL-1β were determined 24 h p.i. A statistically significant response in the expression of CXCL8, TNF-α and IL-1β could be observed following active infection with W. chondrophila. However a significant increase in IL-1β expression was also observed following the exposure of cells to UV-killed organisms, indicating the stimulation of multiple innate recognition pathways. CONCLUSIONS/SIGNIFICANCE: W. chondrophila infects and grows in the ruminant trophoblast AH-1 cell line exhibiting a complete chlamydial replicative cycle. Infection of the trophoblasts resulted in the expression of pro-inflammatory cytokines in a dose-dependent manner similar to that observed with C. abortus in previous studies, suggesting similarities in the pathogenesis of infection between the two organisms.
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In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.