Bayesian online algorithms for learning in discrete Hidden Markov Models

We propose and analyze two different Bayesian online algorithms for learning in discrete Hidden Markov Models and compare their performance with the already known Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalization we draw learning curves in simplified situations for these algorithms and compare their performances.

Models of Alternating Renewal Process at Discrete Time

We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time that are translated negative binomial laws and the second class, suggested by Green is deduced from alternating renewal process in continuous time with sojourn time laws which are exponential laws with parameters α^0 and α^1 respectively.

Online learning in discrete hidden Markov models

We present and analyze three different online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare their performance with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of the generalization error we draw learning curves in simplified situations and compare the results. The performance for learning drifting concepts of one of the presented algorithms is analyzed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking based on our results is also presented. © 2006 American Institute of Physics.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Notes on the Solution of Dynamic Optimization Problems with Explicit Controls in Discrete-Time Economic Models

Йордан Йорданов, Андрей Василев - В работата се изследват методи за решаването на задачи на оптималното управление в дискретно време с безкраен хоризонт и явни управления. Дадена е обосновка на една процедура за решаване на такива задачи, базирана на множители на Лагранж, коята често се употребява в икономическата литература. Извеждени са необходимите условия за оптималност на базата на уравнения на Белман и са приведени достатъчни условия за оптималност при допускания, които често се използват в икономиката.

Surface velocity fields, digital elevation models, ice front positions and grounding line derived from remote sensing data at Dinsmoor-Bombardier-Edgeworth glacier system, Antarctic Peninsula (1992-2014)

The northern Antarctic Peninsula is one of the fastest changing regions on Earth. The disintegration of the Larsen-A Ice Shelf in 1995 caused tributary glaciers to adjust by speeding up, surface lowering, and overall increased ice-mass discharge. In this study, we investigate the temporal variation of these changes at the Dinsmoor-Bombardier-Edgeworth glacier system by analyzing dense time series from various spaceborne and airborne Earth observation missions. Precollapse ice shelf conditions and subsequent adjustments through 2014 were covered. Our results show a response of the glacier system some months after the breakup, reaching maximum surface velocities at the glacier front of up to 8.8 m/d in 1999 and a subsequent decrease to ~1.5 m/d in 2014. Using a dense time series of interferometrically derived TanDEM-X digital elevation models and photogrammetric data, an exponential function was fitted for the decrease in surface elevation. Elevation changes in areas below 1000 m a.s.l. amounted to at least 130±15 m130±15 m between 1995 and 2014, with change rates of ~3.15 m/a between 2003 and 2008. Current change rates (2010-2014) are in the range of 1.7 m/a. Mass imbalances were computed with different scenarios of boundary conditions. The most plausible results amount to -40.7±3.9 Gt-40.7±3.9 Gt. The contribution to sea level rise was estimated to be 18.8±1.8 Gt18.8±1.8 Gt, corresponding to a 0.052±0.005 mm0.052±0.005 mm sea level equivalent, for the period 1995-2014. Our analysis and scenario considerations revealed that major uncertainties still exist due to insufficiently accurate ice-thickness information. The second largest uncertainty in the computations was the glacier surface mass balance, which is still poorly known. Our time series analysis facilitates an improved comparison with GRACE data and as input to modeling of glacio-isostatic uplift in this region. The study contributed to a better understanding of how glacier systems adjust to ice shelf disintegration.

Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach

We summarise the properties and the fundamental mathematical results associated with basic models which describe coagulation and fragmentation processes in a deterministic manner and in which cluster size is a discrete quantity (an integer multiple of some basic unit size). In particular, we discuss Smoluchowski's equation for aggregation, the Becker-Döring model of simultaneous aggregation and fragmentation, and more general models involving coagulation and fragmentation.

Comparing simulation output accuracy of discrete event and agent based models: a quantitative approach

In our research we investigate the output accuracy of discrete event simulation models and agent based simulation models when studying human centric complex systems. In this paper we focus on human reactive behaviour as it is possible in both modelling approaches to implement human reactive behaviour in the model by using standard methods. As a case study we have chosen the retail sector, and here in particular the operations of the fitting room in the women wear department of a large UK department store. In our case study we looked at ways of determining the efficiency of implementing new management policies for the fitting room operation through modelling the reactive behaviour of staff and customers of the department. First, we have carried out a validation experiment in which we compared the results from our models to the performance of the real system. This experiment also allowed us to establish differences in output accuracy between the two modelling methods. In a second step a multi-scenario experiment was carried out to study the behaviour of the models when they are used for the purpose of operational improvement. Overall we have found that for our case study example both, discrete event simulation and agent based simulation have the same potential to support the investigation into the efficiency of implementing new management policies.

Inversion of ambient seismic noise HVSR to evaluate velocity and structural models of the Lower Tagus Basin, Portugal

During its history, several significant earthquakes have shaken the Lower Tagus Valley (Portugal). These earthquakes were destructive; some strong earthquakes were produced by large ruptures in offshore structures located southwest of the Portuguese coastline, and other moderate earthquakes were produced by local faults. In recent years, several studies have successfully obtained strong-ground motion syntheses for the Lower Tagus Valley using the finite difference method. To confirm the velocity model of this sedimentary basin obtained from geophysical and geological data, we analysed the ambient seismic noise measurements by applying the horizontal to vertical spectral ratio (HVSR) method. This study reveals the dependence of the frequency and amplitude of the low-frequency (HVSR) peaks (0.2–2 Hz) on the sediment thickness. We have obtained the depth of the Cenozoic basement along a profile transversal to the basin by the inversion of these ratios, imposing constraints from seismic reflection, boreholes, seismic sounding and gravimetric and magnetic potentials. This technique enables us to improve the existing three-dimensional model of the Lower Tagus Valley structure. The improved model will be decisive for the improvement of strong motion predictions in the earthquake hazard analysis of this highly populated basin. The methodology discussed can be applied to any other sedimentary basin.

Calibration of the maximum carboxylation velocity (Vcmax) using data mining techniques and ecophysiological data from the Brazilian Semiarid region, for use in Dynamic Global Vegetation Models.

The semiarid region of northeastern Brazil, the Caatinga, is extremely important due to its biodiversity and endemism. Measurements of plant physiology are crucial to the calibration of Dynamic Global Vegetation Models (DGVMs) that are currently used to simulate the responses of vegetation in face of global changes. In a field work realized in an area of preserved Caatinga forest located in Petrolina, Pernambuco, measurements of carbon assimilation (in response to light and CO2) were performed on 11 individuals of Poincianella microphylla, a native species that is abundant in this region. These data were used to calibrate the maximum carboxylation velocity (Vcmax) used in the INLAND model. The calibration techniques used were Multiple Linear Regression (MLR), and data mining techniques as the Classification And Regression Tree (CART) and K-MEANS. The results were compared to the UNCALIBRATED model. It was found that simulated Gross Primary Productivity (GPP) reached 72% of observed GPP when using the calibrated Vcmax values, whereas the UNCALIBRATED approach accounted for 42% of observed GPP. Thus, this work shows the benefits of calibrating DGVMs using field ecophysiological measurements, especially in areas where field data is scarce or non-existent, such as in the Caatinga

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.