Search results for "Applied Mathematics"
showing 10 items of 4379 documents
Minimality via second variation for microphase separation of diblock copolymer melts
2017
Abstract We consider a non-local isoperimetric problem arising as the sharp interface limit of the Ohta–Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the problem. Moreover, we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the L 1 {L^{1}} -topology.
Adaptive Number Knowledge in Secondary School Students: Profiles and Antecedents
2019
Cited By :1 Export Date: 10 February 2021 Correspondence Address: McMullen, J.; Department of Teacher EducationFinland; email: jake.mcmullen@utu.fi The present study aims to examine inter-individual differences in adaptive number knowledge in secondary school students. Adaptive number knowledge is defined as a well-connected network of knowledge of numerical characteristics and arithmetic relations. Substantial and relevant qualitative differences in the strategies and expression of adaptive number knowledge have been found in primary school students still in the process of learning arithmetic. We present a study involving 879 seventh-grade students that examines the structure of individual…
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan
1992
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic orbit.
On the stability of some controlled Markov chains and its applications to stochastic approximation with Markovian dynamic
2015
We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading to the proof of the desired stability property. Of particular interest is the fact that the approach applies even in situations where the two components of the process present a time-scale separation, w…
Coupled conditional backward sampling particle filter
2020
The conditional particle filter (CPF) is a promising algorithm for general hidden Markov model smoothing. Empirical evidence suggests that the variant of CPF with backward sampling (CBPF) performs well even with long time series. Previous theoretical results have not been able to demonstrate the improvement brought by backward sampling, whereas we provide rates showing that CBPF can remain effective with a fixed number of particles independent of the time horizon. Our result is based on analysis of a new coupling of two CBPFs, the coupled conditional backward sampling particle filter (CCBPF). We show that CCBPF has good stability properties in the sense that with fixed number of particles, …
Uncertainty quantification on a spatial Markov-chain model for the progression of skin cancer
2019
AbstractA spatial Markov-chain model is formulated for the progression of skin cancer. The model is based on the division of the computational domain into nodal points, that can be in a binary state: either in ‘cancer state’ or in ‘non-cancer state’. The model assigns probabilities for the non-reversible transition from ‘non-cancer’ state to the ‘cancer state’ that depend on the states of the neighbouring nodes. The likelihood of transition further depends on the life burden intensity of the UV-rays that the skin is exposed to. The probabilistic nature of the process and the uncertainty in the input data is assessed by the use of Monte Carlo simulations. A good fit between experiments on mi…
From Feynman–Kac formulae to numerical stochastic homogenization in electrical impedance tomography
2016
In this paper, we use the theory of symmetric Dirichlet forms to derive Feynman–Kac formulae for the forward problem of electrical impedance tomography with possibly anisotropic, merely measurable conductivities corresponding to different electrode models on bounded Lipschitz domains. Subsequently, we employ these Feynman–Kac formulae to rigorously justify stochastic homogenization in the case of a stochastic boundary value problem arising from an inverse anomaly detection problem. Motivated by this theoretical result, we prove an estimate for the speed of convergence of the projected mean-square displacement of the underlying process which may serve as the theoretical foundation for the de…
Formulations and exact algorithms for the distance-constrained generalized directed rural postman problem
2017
[EN] The generalized directed rural postman problem is an arc routing problem with many interesting real-life applications, such as routing for meter reading. In this application, a vehicle with a receiver travels through a series of neighborhoods. If the vehicle gets closer than a certain distance to a meter, the receiver is able to record the gas, water, or electricity consumption. Therefore, the vehicle does not need to traverse every street, but only a few, to get close enough to each meter. We study an extension of this problem in which a fleet of vehicles is available. Given the characteristics of the mentioned application, the vehicles have no capacities but there is a maximum distan…
STABILITY OF A STOCHASTICALLY PERTURBED MODEL OF INTRACELLULAR SINGLE-STRANDED RNA VIRUS REPLICATION
2019
Compared to the replication of double-stranded RNA and DNA viruses, the replication of single-stranded viruses requires the production of a number of intermediate strands that serve as templates for the synthesis of genomic-sense strands. Two theoretical extreme mechanisms for replication for such single-stranded viruses have been proposed; one extreme being represented by the so-called linear stamping machine and the opposite extreme by the exponential growth. Of course, real systems are more complex and examples have been described in which a combination of such extreme mechanisms can also occur: a fraction of the produced progeny resulting from a stamping-machine type of replication that…
Adaptive and Creative Problem-Projects in the Teaching of Science. Description of the Methodology and Appreciation of the Students Involved
2019
En este artículo se describe la metodología que se ha denominado Aprendizaje Basadoen Problemas-Proyectos Adaptativos y Creativos (ABPac), utilizando como ejemplo algunos de losproyectos realizados en el centro concertado Jesús-María de Burgos durante diez años, entre 2006y 2016, con alumnos de Secundaria Obligatoria y Bachillerato. Esta metodología sugiere una aten-ción a la diversidad del alumnado considerando sus necesidades e inquietudes. Además, se analizacuantitativamente el resultado de la encuesta de percepción realizada a 73 individuos involucradosen esta metodología cuando ya ha transcurrido un tiempo de madurez y se encuentran finalizandosus carreras o con estas ya finalizadas. L…