Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Procedimento MIXED do SAS® para análise de modelos mistos

O modelo misto consiste numa importante classe de modelos que tem sido tradicionalmente analisada por meio de procedimentos da análise de variância. Nos modelos mistos, três aspectos são fundamentais: estimação e testes de hipóteses dos efeitos fixos, predição dos efeitos aleatórios e estimação dos componentes de variância. Na análise de modelos lineares mistos desbalanceados, a estimação dos componentes de variância é de fundamental importância e depende da estrutura de covariâncias e dos métodos de estimação utilizados. Nesse contexto, este artigo pretende apresentar os principais métodos de estimação e de análise utilizados no estudo de modelos lineares mistos com estruturas gerais de covariâncias nos efeitos aleatórios, disponíveis no procedimento MIXED, do SAS (Statistical Analysis System).

The Representation of Motherhood in Polish Cinema

The project aimed to analyse representations of motherhood in Polish cinema as a special case of a more general system within the representation of women. It concentrated on the image of the Polish Mother created during the 19th century in Polish culture under the influence of specific political, social and religious factors. Ms. Ostrowska's initial hypothesis was that this symbolic image became one of the most stable elements in Polish cinema and as her research revealed, it was valuable for the preservation of national identity but nevertheless a fiercely constraining model for Polish femininity. In order to fully understand the nature of this persistent image it was initially necessary to related it to broader contexts and issues in representation. These included the image of the Polish Mother within general mythological structures (using the notion of myth in the Barthesian sense). Following her initial research Ms. Ostrowska felt that it was most appropriate to view the myth of the Polish Mother as a dominant ideological structure in the discourse of motherhood within Polish culture. An analysis of the myth of the Polish Mother can provide an insight into how Polish society sees itself at different periods in time and how a national identity was constructed in relation to particular ideological demands stemming from concrete historical and political situations. The analysis of the film version of this myth also revealed some aspects of the national character of Polish cinema. There the image of woman has become enshrined as the "eternal feminine", with virtues which are inevitably derived directly from Catholicism, particularly in relation to the networks of meanings around the central figure of Mary, Mother of God. In 19th century Poland these were linked with patriotic values and images of woman became part of the defence of the very idea of Poland and Polishness. After World War Two, this religious-political image system was adapted to the demands of the new communist ideology. The possibility of manipulating the ideological dimensions of the myth of the Polish Mother is due to the very nature of the image, which as a symbol of civil religion had been able to function independently of any particular state or church institution. Although in communist ideology the stress was on the patriotic aspect of the myth, its pronounced religious aspect was also transmitted, consciously or not, in the denotation process, this being of great significance in the viewer's response to the female character. This appropriation of elements derived from the national patriotic tradition into the discourse of communist ideology was a very efficient strategy to establish the illusion of continuity in national existence, which was supposed to convince society of the rightness of the new political situation. The analysis of films made in the post-war period showed the persistence of this discourse on motherhood in a range of cinematic texts regardless of the changing political situation. Ms. Ostrowska claims that the stability of this discursive formation is to a certain extent the result of the mythological aspect of the mother figure. This mythological structure also belongs to the ideology of Romanticism which in general continues to prevail in Polish cultural discourse as a meta-language of national community. The analysis of the films confirmed the hypothesis of the Polish Mother as a myth-sign whose signifier is stable whereas the signified depends on the specific historical conditions in which it is set. Therefore in the famous propaganda documentary Kobiety naszych dni (Women of Our Days, 1951) by Jan Zelnik, and in other films made after the October 1956 "thaw" it functions as an "empty sign. She concludes that it would be difficult to deny that the myth of the Polish Mother has offered Polish women a special role in national life, granting them a high moral position in the social, hierarchy. However the processes of idealisation involved have resulted in a deprivation of her subjectivity and the right to decide about her own life. This idealisation also served to strengthen traditional patriarchal structures through this set of female obligations to the mother land. In Polish ideology it is not a man who demands sacrifice from a woman but the motherland, which, deprived of the institutions of male power for nearly 150 years, had functioned as a feminine structure. That is why oppressive aspects of the myth have been obscured for so long. While Polish women were doubtless able to accept the constrictions because of their sense of national duty and any misgivings were overridden by the argument of the cause, it is important to recognise that the strength of these constructions, compounded by the ways in which they spoke of and continue to speak of a certain perfection, make them persist into contemporary Poland. Poland is however no longer embattled and the signs that made these meanings are potentially empty. This space for meaning will be and is already being contested and increasingly colonised by current western models of femininity. Ms. Ostrowska's final question is whether this will help to prevent a possible resentful victimisation of the silent and noble Polish Mother.

A hybrid method in combining treatment effects from matched and unmatched studies

In the biomedical studies, the general data structures have been the matched (paired) and unmatched designs. Recently, many researchers are interested in Meta-Analysis to obtain a better understanding from several clinical data of a medical treatment. The hybrid design, which is combined two data structures, may create the fundamental question for statistical methods and the challenges for statistical inferences. The applied methods are depending on the underlying distribution. If the outcomes are normally distributed, we would use the classic paired and two independent sample T-tests on the matched and unmatched cases. If not, we can apply Wilcoxon signed rank and rank sum test on each case. ^ To assess an overall treatment effect on a hybrid design, we can apply the inverse variance weight method used in Meta-Analysis. On the nonparametric case, we can use a test statistic which is combined on two Wilcoxon test statistics. However, these two test statistics are not in same scale. We propose the Hybrid Test Statistic based on the Hodges-Lehmann estimates of the treatment effects, which are medians in the same scale.^ To compare the proposed method, we use the classic meta-analysis T-test statistic on the combined the estimates of the treatment effects from two T-test statistics. Theoretically, the efficiency of two unbiased estimators of a parameter is the ratio of their variances. With the concept of Asymptotic Relative Efficiency (ARE) developed by Pitman, we show ARE of the hybrid test statistic relative to classic meta-analysis T-test statistic using the Hodges-Lemann estimators associated with two test statistics.^ From several simulation studies, we calculate the empirical type I error rate and power of the test statistics. The proposed statistic would provide effective tool to evaluate and understand the treatment effect in various public health studies as well as clinical trials.^

Variance-balanced designs under interference for dependent observations

It is shown that variance-balanced designs can be obtained from Type I orthogonal arrays for many general models with two kinds of treatment effects, including ones for interference, with general dependence structures. These designs can be used to obtain optimal and efficient designs. Some examples and design comparisons are given. (C) 2002 Elsevier B.V. All rights reserved.

Dynamics and topographic organization of recursive self-organizing maps

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographicmaps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizingmap (SOM) for processing sequential data, recursive SOM (RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data. © 2006 Massachusetts Institute of Technology.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.

On Distributed Oblivious Transfer

The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshkoff and Lubomir Tschakaloff , Sofia, July, 2006. The material in this paper was presented in part at INDOCRYPT 2002

Sediment and pore water data of five cores from the continental slope off Uruguay

Assessing frequency and extent of mass movement at continental margins is crucial to evaluate risks for offshore constructions and coastal areas. A multidisciplinary approach including geophysical, sedimentological, geotechnical, and geochemical methods was applied to investigate multistage mass transport deposits (MTDs) off Uruguay, on top of which no surficial hemipelagic drape was detected based on echosounder data. Nonsteady state pore water conditions are evidenced by a distinct gradient change in the sulfate (SO4**2-) profile at 2.8 m depth. A sharp sedimentological contact at 2.43 m coincides with an abrupt downward increase in shear strength from approx. 10 to >20 kPa. This boundary is interpreted as a paleosurface (and top of an older MTD) that has recently been covered by a sediment package during a younger landslide event. This youngest MTD supposedly originated from an upslope position and carried its initial pore water signature downward. The kink in the SO4**2- profile approx. 35 cm below the sedimentological and geotechnical contact indicates that bioirrigation affected the paleosurface before deposition of the youngest MTD. Based on modeling of the diffusive re-equilibration of SO4**2- the age of the most recent MTD is estimated to be <30 years. The mass movement was possibly related to an earthquake in 1988 (approx. 70 km southwest of the core location). Probabilistic slope stability back analysis of general landslide structures in the study area reveals that slope failure initiation requires additional ground accelerations. Therefore, we consider the earthquake as a reasonable trigger if additional weakening processes (e.g., erosion by previous retrogressive failure events or excess pore pressures) preconditioned the slope for failure. Our study reveals the necessity of multidisciplinary approaches to accurately recognize and date recent slope failures in complex settings such as the investigated area.

General electromagnetic simulation tool to predict the microwave nonlinear response of planar, arbitrarily-shaped HTS structures

This work describes a simulation tool being developed at UPC to predict the microwave nonlinear behavior of planar superconducting structures with very few restrictions on the geometry of the planar layout. The software is intended to be applicable to most structures used in planar HTS circuits, including line, patch, and quasi-lumped microstrip resonators. The tool combines Method of Moments (MoM) algorithms for general electromagnetic simulation with Harmonic Balance algorithms to take into account the nonlinearities in the HTS material. The Method of Moments code is based on discretization of the Electric Field Integral Equation in Rao, Wilton and Glisson Basis Functions. The multilayer dyadic Green's function is used with Sommerfeld integral formulation. The Harmonic Balance algorithm has been adapted to this application where the nonlinearity is distributed and where compatibility with the MoM algorithm is required. Tests of the algorithm in TM010 disk resonators agree with closed-form equations for both the fundamental and third-order intermodulation currents. Simulations of hairpin resonators show good qualitative agreement with previously published results, but it is found that a finer meshing would be necessary to get correct quantitative results. Possible improvements are suggested.

General structures of Hamiltonian hierarchies

Three dimensional exactly solvable quantum potentials for which an extra term of form 1/r(2) has been added are shown to maintain their functional form which allows the construction of the Hamiltonian hierarchy and the determination of the spectra of eigenvalues and eigenfunctions within the Supersymmetric Quantum Mechanics formalism. For the specific cases of the harmonic oscillator and the Coulomb potentials, known as pseudo-harmonic oscillator and pseudo-Coulomb potentials, it is shown here that the inclusion of the new term corresponds to rescaling the angular momentum and it is responsible for maintaining their exact solvability.

A method for revealing phase space structures of general time dependent dynamical systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a “heuristic argument” that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper “side-by-side” comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field (“time averages”) are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.