Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.

Demonstration of 10 Gbit/s transmission over 900 km SMF with <400 ns adaptation time using full-field EDC

This reported work significantly extends the reach of 10Gbit/s on-off keying singlemode fibre (SMF) transmission using full-field based electronic dispersion compensation (EDC) to 900 km. In addition, the EDC balances the complexity and the adaptation capability by employing a simple dispersive transmission line with static parameters for coarse dispersion compensation and 16-state maximum likelihood sequence estimation with Gaussian approximation based channel training for adaptive impairment trimming. Improved adaptation times of less than 400 ns for a bit error rate target of 10-3 over distances ranging from 0 to 900 km are reported.

Estimation of productivity in Korean electric power plants:a semiparametric smooth coefficient model

This paper analyzes the impact of load factor, facility and generator types on the productivity of Korean electric power plants. In order to capture important differences in the effect of load policy on power output, we use a semiparametric smooth coefficient (SPSC) model that allows us to model heterogeneous performances across power plants and over time by allowing underlying technologies to be heterogeneous. The SPSC model accommodates both continuous and discrete covariates. Various specification tests are conducted to assess the performance of the SPSC model. Using a unique generator level panel dataset spanning the period 1995-2006, we find that the impact of load factor, generator and facility types on power generation varies substantially in terms of magnitude and significance across different plant characteristics. The results have strong implications for generation policy in Korea as outlined in this study.

Pulse width modulation (PWM) method for power components estimation in power meters

The scope of this paper is to present the Pulse Width Modulation (PWM) based method for Active Power (AP) and Reactive Power (RP) measurements as can be applied in Power Meters. Necessarily, the main aim of the material presented is a twofold, first to present a realization methodology of the proposed algorithm, and second to verify the algorithm’s robustness and validity. The method takes advantage of the fact that frequencies present in a power line are of a specific fundamental frequency range (a range centred on the 50 Hz or 60 Hz) and that in case of the presence of harmonics the frequencies of those dominating in the power line spectrum can be specified on the basis of the fundamental. In contrast to a number of existing methods a time delay or shifting of the input signal is not required by the method presented and the time delay by n/2 of the Current signal with respect to the Voltage signal required by many of the existing measurement techniques, does not apply in the case of the PWM method as well.

Eye movement analysis in congenital nystagmus:concise parameters estimation

Along with other diseases that can affect binocular vision, reducing the visual quality of a subject, Congenital Nystagmus (CN) is of peculiar interest. CN is an ocular-motor disorder characterized by involuntary, conjugated ocular oscillations and, while identified more than forty years ago, its pathogenesis is still under investigation. This kind of nystagmus is termed congenital (or infantile) since it could be present at birth or it can arise in the first months of life. The majority of CN patients show a considerable decrease of their visual acuity: image fixation on the retina is disturbed by nystagmus continuous oscillations, mainly horizontal. However, the image of a given target can still be stable during short periods in which eye velocity slows down while the target image is placed onto the fovea (called foveation intervals). To quantify the extent of nystagmus, eye movement recordings are routinely employed, allowing physicians to extract and analyze nystagmus main features such as waveform shape, amplitude and frequency. Use of eye movement recording, opportunely processed, allows computing "estimated visual acuity" predictors, which are analytical functions that estimate expected visual acuity using signal features such as foveation time and foveation position variability. Hence, it is fundamental to develop robust and accurate methods to measure both those parameters in order to obtain reliable values from the predictors. In this chapter the current methods to record eye movements in subjects with congenital nystagmus will be discussed and the present techniques to accurately compute foveation time and eye position will be presented. This study aims to disclose new methodologies in congenital nystagmus eye movements analysis, in order to identify nystagmus cycles and to evaluate foveation time, reducing the influence of repositioning saccades and data noise on the critical parameters of the estimation functions. Use of those functions extends the information acquired with typical visual acuity measurement (e.g., Landolt C test) and could be a support for treatment planning or therapy monitoring. © 2010 by Nova Science Publishers, Inc. All rights reserved.

Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.

An algorithm for FHR estimation from foetal phonocardiographic signals

The long-term foetal surveillance is often to be recommended. Hence, the fully non-invasive acoustic recording, through maternal abdomen, represents a valuable alternative to the ultrasonic cardiotocography. Unfortunately, the recorded heart sound signal is heavily loaded by noise, thus the determination of the foetal heart rate raises serious signal processing issues. In this paper, we present a new algorithm for foetal heart rate estimation from foetal phonocardiographic recordings. A filtering is employed as a first step of the algorithm to reduce the background noise. A block for first heart sounds enhancing is then used to further reduce other components of foetal heart sound signals. A complex logic block, guided by a number of rules concerning foetal heart beat regularity, is proposed as a successive block, for the detection of most probable first heart sounds from several candidates. A final block is used for exact first heart sound timing and in turn foetal heart rate estimation. Filtering and enhancing blocks are actually implemented by means of different techniques, so that different processing paths are proposed. Furthermore, a reliability index is introduced to quantify the consistency of the estimated foetal heart rate and, based on statistic parameters; [,] a software quality index is designed to indicate the most reliable analysis procedure (that is, combining the best processing path and the most accurate time mark of the first heart sound, provides the lowest estimation errors). The algorithm performances have been tested on phonocardiographic signals recorded in a local gynaecology private practice from a sample group of about 50 pregnant women. Phonocardiographic signals have been recorded simultaneously to ultrasonic cardiotocographic signals in order to compare the two foetal heart rate series (the one estimated by our algorithm and the other provided by cardiotocographic device). Our results show that the proposed algorithm, in particular some analysis procedures, provides reliable foetal heart rate signals, very close to the reference cardiotocographic recordings. © 2010 Elsevier Ltd. All rights reserved.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

A quantum Jensen-Shannon graph kernel using discrete-time quantum walks

In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel.

Node centrality for continuous-time quantum walks

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a vertex to the influence that its initial phase has on the interference patterns that emerge during the quantum walk evolution. To this end, we make use of the quantum Jensen-Shannon divergence between two suitably defined quantum states. We investigate how the importance varies as we change the initial state of the walk and the Hamiltonian of the system. We find that, for a suitable combination of the two, the importance of a vertex is almost linearly correlated with its degree. Finally, we evaluate the proposed measure on two commonly used networks. © 2014 Springer-Verlag Berlin Heidelberg.

A quantum Jensen-Shannon graph kernel using the continuous-time quantum walk

In this paper, we use the quantum Jensen-Shannon divergence as a means to establish the similarity between a pair of graphs and to develop a novel graph kernel. In quantum theory, the quantum Jensen-Shannon divergence is defined as a distance measure between quantum states. In order to compute the quantum Jensen-Shannon divergence between a pair of graphs, we first need to associate a density operator with each of them. Hence, we decide to simulate the evolution of a continuous-time quantum walk on each graph and we propose a way to associate a suitable quantum state with it. With the density operator of this quantum state to hand, the graph kernel is defined as a function of the quantum Jensen-Shannon divergence between the graph density operators. We evaluate the performance of our kernel on several standard graph datasets from bioinformatics. We use the Principle Component Analysis (PCA) on the kernel matrix to embed the graphs into a feature space for classification. The experimental results demonstrate the effectiveness of the proposed approach. © 2013 Springer-Verlag.

A continuous-time quantum walk kernel for unattributed graphs

Kernel methods provide a way to apply a wide range of learning techniques to complex and structured data by shifting the representational problem from one of finding an embedding of the data to that of defining a positive semidefinite kernel. In this paper, we propose a novel kernel on unattributed graphs where the structure is characterized through the evolution of a continuous-time quantum walk. More precisely, given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic. With this new graph to hand, we compute the density operators of the quantum systems representing the evolutions of two suitably defined quantum walks. Finally, we define the kernel between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators. The experimental evaluation shows the effectiveness of the proposed approach. © 2013 Springer-Verlag.

Attributed graph similarity from the quantum Jensen-Shannon divergence

One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach. © 2013 Springer-Verlag.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Robust Estimation in Multitype Branching Processes Based on their Asymptotic Properties

2000 Mathematics Subject Classification: 60J80.