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.

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.

Active security in multiparty computation over black-box groups

Most previous work on unconditionally secure multiparty computation has focused on computing over a finite field (or ring). Multiparty computation over other algebraic structures has not received much attention, but is an interesting topic whose study may provide new and improved tools for certain applications. At CRYPTO 2007, Desmedt et al introduced a construction for a passive-secure multiparty multiplication protocol for black-box groups, reducing it to a certain graph coloring problem, leaving as an open problem to achieve security against active attacks. We present the first n-party protocol for unconditionally secure multiparty computation over a black-box group which is secure under an active attack model, tolerating any adversary structure Δ satisfying the Q 3 property (in which no union of three subsets from Δ covers the whole player set), which is known to be necessary for achieving security in the active setting. Our protocol uses Maurer’s Verifiable Secret Sharing (VSS) but preserves the essential simplicity of the graph-based approach of Desmedt et al, which avoids each shareholder having to rerun the full VSS protocol after each local computation. A corollary of our result is a new active-secure protocol for general multiparty computation of an arbitrary Boolean circuit.

On secure multi-party computation in black-box groups

We study the natural problem of secure n-party computation (in the passive, computationally unbounded attack model) of the n-product function f G (x 1,...,x n ) = x 1 ·x 2 ⋯ x n in an arbitrary finite group (G,·), where the input of party P i is x i  ∈ G for i = 1,...,n. For flexibility, we are interested in protocols for f G which require only black-box access to the group G (i.e. the only computations performed by players in the protocol are a group operation, a group inverse, or sampling a uniformly random group element). Our results are as follows. First, on the negative side, we show that if (G,·) is non-abelian and n ≥ 4, then no ⌈n/2⌉-private protocol for computing f G exists. Second, on the positive side, we initiate an approach for construction of black-box protocols for f G based on k-of-k threshold secret sharing schemes, which are efficiently implementable over any black-box group G. We reduce the problem of constructing such protocols to a combinatorial colouring problem in planar graphs. We then give two constructions for such graph colourings. Our first colouring construction gives a protocol with optimal collusion resistance t < n/2, but has exponential communication complexity O(n*2t+1^2/t) group elements (this construction easily extends to general adversary structures). Our second probabilistic colouring construction gives a protocol with (close to optimal) collusion resistance t < n/μ for a graph-related constant μ ≤ 2.948, and has efficient communication complexity O(n*t^2) group elements. Furthermore, we believe that our results can be improved by further study of the associated combinatorial problems.

A method to improve size estimates of walleye pollock (Theragra chalcogramma) Atka mackerel (Pleurogrammus monopterygius) consumed by pinnipeds: digestion correction factors applied to bones and otoliths recovered in scats

The lengths of otoliths and other skeletal structures recovered from the scats of pinnipeds, such as Steller sea lions (Eumetopias jubatus), correlate with body size and can be used to estimate the length of prey consumed. Unfortunately, otoliths are often found in too few scats or are too digested to usefully estimate prey size. Alternative diagnostic bones are frequently recovered, but few bone-size to prey-size correlations exist and bones are also reduced in size by various degrees owing to digestion. To prevent underestimates in prey sizes consumed techniques are required to account for the degree of digestion of alternative bones prior to estimating prey size. We developed a method (using defined criteria and photo-reference material) to assign the degree of digestion for key cranial structures of two prey species: walleye pollock (Theragra chalcogramma) and Atka mackerel (Pleurogrammus monopterygius). The method grades each structure into one of three condition categories; good, fair or poor. We also conducted feeding trials with captive Steller sea lions, feeding both fish species to determine the extent of erosion of each structure and to derive condition-specific digestion correction factors to reconstruct the original sizes of the structures consumed. In general, larger structures were relatively more digested than smaller ones. Mean size reduction varied between different types of structures (3.3−26.3%), but was not influenced by the size of the prey consumed. Results from the observations and experiments were combined to be able to reconstruct the size of prey consumed by sea lions and other pinnipeds. The proposed method has four steps: 1) measure the recovered structures and grade the extent of digestion by using defined criteria and photo-reference collection; 2) exclude structures graded in poor condition; 3) multiply measurements of structures in good and fair condition by their appropriate digestion correction factors to derive their original size; and 4) calculate the size of prey from allometric regressions relating corrected structure measurements to body lengths. This technique can be readily applied to piscivore dietary studies that use hard remains of fish.

No-Holdback allocation rules for continuous-time assemble-to-order systems

This paper analyzes a class of common-component allocation rules, termed no-holdback (NHB) rules, in continuous-review assemble-to-order (ATO) systems with positive lead times. The inventory of each component is replenished following an independent base-stock policy. In contrast to the usually assumed first-come-first-served (FCFS) component allocation rule in the literature, an NHB rule allocates a component to a product demand only if it will yield immediate fulfillment of that demand. We identify metrics as well as cost and product structures under which NHB rules outperform all other component allocation rules. For systems with certain product structures, we obtain key performance expressions and compare them to those under FCFS. For general product structures, we present performance bounds and approximations. Finally, we discuss the applicability of these results to more general ATO systems. © 2010 INFORMS.

Structure and solvation in ionic liquids

This Account describes experimental data used to understand the structure of ionic liquids and solute-solvent interactions of both molecular solutes and dissolved metal complexes. In general, the structures of the ionic liquids determined from experimental data show good agreement with both simulated structures and solid-state structures. For all ionic liquids studied, strong charge ordering is found leading to long-range order even in the presence of a solute. For dissolved metal complexes, the ionic liquid is not innocent and a clear dependence on the speciation is observed with variations in both the cation and anion.

Information theoretic measures of UHG graphs with low computational complexity

We introduce a novel graph class we call universal hierarchical graphs (UHG) whose topology can be found numerously in problems representing, e.g., temporal, spacial or general process structures of systems. For this graph class we show, that we can naturally assign two probability distributions, for nodes and for edges, which lead us directly to the definition of the entropy and joint entropy and, hence, mutual information establishing an information theory for this graph class. Furthermore, we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy. Also, we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples. (c) 2007 Elsevier Inc. All rights reserved.

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