Search results for "Mathematica"
showing 10 items of 7971 documents
A quantum particle in a box with moving walls
2013
We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.
Non-Markovianity and Coherence of a Moving Qubit inside a Leaky Cavity
2017
Non-Markovian features of a system evolution, stemming from memory effects, may be utilized to transfer, storage, and revive basic quantum properties of the system states. It is well known that an atom qubit undergoes non-Markovian dynamics in high quality cavities. We here consider the qubit-cavity interaction in the case when the qubit is in motion inside a leaky cavity. We show that, owing to the inhibition of the decay rate, the coherence of the traveling qubit remains closer to its initial value as time goes by compared to that of a qubit at rest. We also demonstrate that quantum coherence is preserved more efficiently for larger qubit velocities. This is true independently of the evol…
A decision support system methodology for forecasting of time series based on soft computing
2006
Exponential procedures are widely used as forecasting techniques for inventory control and business planning. A number of modifications to the generalized exponential smoothing (Holt-Winters) approach to forecasting univariate time series is presented, which have been adapted into a tool for decision support systems. This methodology unifies the phases of estimation and model selection into just one optimization framework which permits the identification of robust solutions. This procedure may provide forecasts from different versions of exponential smoothing by fitting the updated formulas of Holt-Winters and selects the best method using a fuzzy multicriteria approach. The elements of the…
Adaptive Modifications of Hypotheses After an Interim Analysis
2001
It is investigated how one can modify hypotheses in a trial after an interim analysis such that the type I error rate is controlled. If only a global statement is desired, a solution was given by Bauer (1989). For a general multiple testing problem, Kieser, Bauer and Lehmacher (1999) and Bauer and Kieser (1999) gave solutions, by means of which the initial set of hypotheses can be reduced after the interim analysis. The same techniques can be applied to obtain more flexible strategies, as changing weights of hypotheses, changing an a priori order, or even including new hypotheses. It is emphasized that the application of these methods requires very careful planning of a trial as well as a c…
Volatility in Financial Markets: Stochastic Models and Empirical Results
2002
We investigate the historical volatility of the 100 most capitalized stocks traded in US equity markets. An empirical probability density function (pdf) of volatility is obtained and compared with the theoretical predictions of a lognormal model and of the Hull and White model. The lognormal model well describes the pdf in the region of low values of volatility whereas the Hull and White model better approximates the empirical pdf for large values of volatility. Both models fails in describing the empirical pdf over a moderately large volatility range.
Geometric Entropies of Mixing (EOM)
2005
Trigonometric and trigonometric-algebraic entropies are introduced. Regularity increases the entropy and the maximal entropy is shown to result when a regular $n$-gon is inscribed in a circle. A regular $n$-gon circumscribing a circle gives the largest entropy reduction, or the smallest change in entropy from the state of maximum entropy which occurs in the asymptotic infinite $n$ limit. EOM are shown to correspond to minimum perimeter and maximum area in the theory of convex bodies, and can be used in the prediction of new inequalities for convex sets. These expressions are shown to be related to the phase functions obtained from the WKB approximation for Bessel and Hermite functions.
Heavy-tailed targets and (ab)normal asymptotics in diffusive motion
2010
We investigate temporal behavior of probability density functions (pdfs) of paradigmatic jump-type and continuous processes that, under confining regimes, share common heavy-tailed asymptotic (target) pdfs. Namely, we have shown that under suitable confinement conditions, the ordinary Fokker-Planck equation may generate non-Gaussian heavy-tailed pdfs (like e.g. Cauchy or more general L\'evy stable distribution) in its long time asymptotics. For diffusion-type processes, our main focus is on their transient regimes and specifically the crossover features, when initially infinite number of the pdf moments drops down to a few or none at all. The time-dependence of the variance (if in existence…
Testing for local structure in spatiotemporal point pattern data
2017
The detection of clustering structure in a point pattern is one of the main focuses of attention in spatiotemporal data mining. Indeed, statistical tools for clustering detection and identification of individual events belonging to clusters are welcome in epidemiology and seismology. Local second-order characteristics provide information on how an event relates to nearby events. In this work, we extend local indicators of spatial association (known as LISA functions) to the spatiotemporal context (which will be then called LISTA functions). These functions are then used to build local tests of clustering to analyse differences in local spatiotemporal structures. We present a simulation stud…
Building up adjusted indicators of students' evaluation of university courses using generalized item response models
2012
This article advances a proposal for building up adjusted composite indicators of the quality of university courses from students’ assessments. The flexible framework of Generalized Item Response Models is adopted here for controlling the sources of heterogeneity in the data structure that make evaluations across courses not directly comparable. Specifically, it allows us to: jointly model students’ ratings to the set of items which define the quality of university courses; explicitly consider the dimensionality of the items composing the evaluation form; evaluate and remove the effect of potential confounding factors which may affect students’ evaluation; model the intra-cluster variabilit…
Spatial moving average risk smoothing
2013
This paper introduces spatial moving average risk smoothing (SMARS) as a new way of carrying out disease mapping. This proposal applies the moving average ideas of time series theory to the spatial domain, making use of a spatial moving average process of unknown order to define dependence on the risk of a disease occurring. Correlation of the risks for different locations will be a function of m values (m being unknown), providing a rich class of correlation functions that may be reproduced by SMARS. Moreover, the distance (in terms of neighborhoods) that should be covered for two units to be found to make the correlation of their risks 0 is a quantity to be fitted by the model. This way, …