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This paper studies decision-making in the face of two stochastically independent sources of uncertainty. It characterizes axiomatically a Subjective Expected Utility representation of preferences where subjective beliefs consist of a product probability measure. The two key axioms in this characterization both involve some behavioral notions of stochastic independence. Our result can be understood as a purely subjective version of the Anscombe and Aumann (Ann Math Stat 34:199–205, 1963) theorem that avoids the controversial use of exogenous probabilities by appealing to stochastic independence. We also obtain an extension to Choquet Expected Utility representations. [ABSTRACT FROM AUTHOR]

We derive an effective one-dimensional limit from a three-dimensional Kelvin–Voigt model for viscoelastic thin-walled beams, in which the elastic and the viscous stress tensor comply with a frame-indifference principle. The limiting system of equations comprises stretching, bending, and twisting both in the elastic and the viscous stress. It coincides with the model already identified via Friedrich and Kružík (Arch Ration Mech Anal 238:489–540, 2020) and Friedrich and Machill (Nonlinear Differ Equ Appl NoDEA 29, Article number: 11, 2022) by a successive dimension reduction, first from 3D to a 2D theory for von Kármán plates and then from 2D to a 1D theory for ribbons. In the present paper, we complement the previous analysis by showing that the limit can also be obtained by sending the height and width of the beam to zero simultaneously. Our arguments rely on the static Γ -convergence in Freddi et al. (Math Models Methods Appl Sci 23:743–775, 2013), on the abstract theory of metric gradient flows (Ambrosio et al. in Gradient flows in metric spaces and in the space of probability measures. Lectures mathematics, ETH Zürich, Birkhäuser, Basel, 2005), and on evolutionary Γ -convergence (Sandier and Serfaty in Commun Pure Appl Math 57:1627–1672, 2004). [ABSTRACT FROM AUTHOR]

This paper aims at studying the inelastic Boltzmann equation without Grad's angular cutoff assumption, where the well-posedness theory of the Cauchy problem is established for the Maxwellian molecules in a space of probability measure defined by Cannone and Karch [Commun. Pure Appl. Math. 63, 747–778 (2010)] via Fourier transform and the infinite energy solutions are not a priori excluded. The key strategy is to construct a brand new geometric relation of the inelastic collision mechanism to extend the result of Cannone and Karch from moderate singularity of the non-cutoff collision kernels to strong singularity and simultaneously handle more general restitution coefficients. Moreover, we extend the self-similar solution to the Boltzmann equation with infinite energy shown by Bobylev and Cercignani [J. Stat. Phys. 106, 1039–1071 (2002)] to the inelastic case by using a constructive approach, which is also proved to be the large-time asymptotic steady solution with the help of an asymptotic stability result in a certain sense. [ABSTRACT FROM AUTHOR]

In recent works L.C. Evans has noticed a strong analogy between Mather's theory of minimal measures in Lagrangian dynamic and the theory developed in the last years for the optimalmass transportation (or Monge–Kantorovich) problem. In this paper we start to investigate this analogy by proving that to each minimal measure it is possible to associate, in a natural way, a family of curves on the space of probability measures. These curves are absolutely continuous with respect to the metric structure related to the optimal mass transportation problem. Someminimality properties of such curves are also addressed. [ABSTRACT FROM AUTHOR]

Let X_1,X_2,\ldots be independent and identically distributed random variables in {\mathbb {C}} chosen from a probability measure \mu and define the random polynomial \begin{align*} P_n(z)=(z-X_1)\ldots (z-X_n)\,. \end{align*} We show that for any sequence k = k(n) satisfying k \leq \log n / (5 \log \log n), the zeros of the kth derivative of P_n are asymptotically distributed according to the same measure \mu. This extends work of Kabluchko, which proved the k = 1 case, as well as Byun, Lee and Reddy [Trans. Amer. Math. Soc. 375, pp. 6311–6335] who proved the fixed k case. [ABSTRACT FROM AUTHOR]

The contribution of this paper is threefold. First, a characterization theorem of the subhypotheses comprising the seasonal unit root hypothesis is presented that provides a precise formulation of the alternative hypotheses associated with regression-based seasonal unit root tests. Second, it proposes regression-based tests for the seasonal unit root hypothesis that allow a general seasonal aspect for the data and are similar both exactly and asymptotically with respect to initial values and seasonal drift parameters. Third, limiting distribution theory is given for these statistics where, in contrast to previous papers in the literature, in doing so it is not assumed that unit roots hold at all of the zero and seasonal frequencies. This is shown to alter the large-sample null distribution theory for regression t-statistics for unit roots at the complex frequencies, but interestingly to not affect the limiting null distributions of the regression t-statistics for unit roots at the zero and Nyquist frequencies and regression F-statistics for unit roots at the complex frequencies. Our results therefore have important implications for how tests of the seasonal unit root hypothesis should be conducted in practice. Associated simulation evidence on the size and power properties of the statistics presented in this paper is given that is consonant with the predictions from the large-sample theory. [ABSTRACT FROM AUTHOR]

This paper starts by indicating the analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, ) as presented in Huber (). There I argue contra Carnap (, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper consists in working out the claim that one can have Hempel’s cake and eat it too — in the sense that there is a logic of theory assessment that takes into account both of the two conflicting aspects of plausibility and informativeness. According to the semantics of this logic, α is an acceptable theory for evidence β if and only if α is both sufficiently plausible given β and sufficiently informative about β. This is spelt out in terms of ranking functions (Spohn, ) and shown to represent the syntactically specified notion of an assessment relation. The paper then compares these acceptability relations to explanatory and confirmatory consequence relations (Flach, ) as well as to nonmonotonic consequence relations (Kraus et al., ). It concludes by relating the plausibility-informativeness approach to Carnap’s positive relevance account, thereby shedding new light on Carnap’s analysis as well as solving another problem of confirmation theory. [ABSTRACT FROM AUTHOR]

In this paper we deal with continuous time Markov decision drift processes (CTMDP), which permit both controls affecting jump rates of the process and impulsive controls causing immediate transitions. Between two successive jump epochs the state of the process evolves according to a deterministic drift function. Given a CTMDP we construct a sequence of discrete time Markov decision drift processes (DTMDP) with decreasing distance between the successive decision epochs. Sufficient conditions are provided under which the law of the CTMDP controlled by a fixed policy is the limit (in the sense of weak convergence of probability measures) of the laws of the approximating DTMDP's controlled by fixed discrete time policies. The conditions concern both the parameters of the CTMDP and the relation between the discrete time and continuous time policies. An application to a maintenance replacement model is given. [ABSTRACT FROM AUTHOR]

The analysis of simulation data in the evaluation of competing alternatives presents a problem for the analyst using conventional statistical techniques. The assumptions of normality and common variances generally cause difficulties since many classes of simulation experiments typically violate both of these assumptions. In addition, the analyst is usually interested in comparing competing alternatives using environments that are as close to identical as possible. In these situations, blocking is desirable and can usually be accomplished by using common random number streams. This paper discusses a distribution free method based on Friedman's rank sums test that can be used to analyze simulation results exhibiting the above characteristics. [ABSTRACT FROM AUTHOR]

This paper continues the investigation of "Wasserstein-like" transportation distances for probability measures on discrete sets. We prove that the discrete transportation metrics WN on the d-dimensional discrete torus TNd with mesh size 1/N converge, when N → ∞ to the standard 2-Wasserstein distance W2 on the continuous torus in the sense of Gromov--Hausdorff. This is the first convergence result for the recently developed discrete transportation metrics W. The result shows the compatibility between these metrics and the well-established 2-Wasserstein metric. [ABSTRACT FROM AUTHOR]

In this paper, we study an ergodic theorem of a parabolic Andersen model driven by Lévy noise. Under the assumption that A = ( a( i, j)) is symmetric with respect to a σ-finite measure gp, we obtain the long-time convergence to an invariant probability measure ν starting from a bounded nonnegative A-harmonic function h based on self-duality property. Furthermore, under some mild conditions, we obtain the one to one correspondence between the bounded nonnegative A-harmonic functions and the extremal invariant probability measures with finite second moment of the nonnegative solution of the parabolic Anderson model driven by Lévy noise, which is an extension of the result of Y. Liu and F. X. Yang. [ABSTRACT FROM AUTHOR]

Let A be a commutative integral domain with quotient field L, and let R be a subdomain of A with quotient field K. Assuming that L is a Galois extension of K, Nagata required the condition for R to be normal when A is called a Galois extension of R (see p. 31, M. Nagata, Local Rings (Wiley, New York, 1962)). However in this paper, A is considered in the case that R is not necessarily assumed to be normal. We introduce the notion of cyclic Galois extensions of integral domains and investigate several properties of such ring extensions. In particular, we completely determine the seminormalization ${}^+_BA$ of A in an overdomain B such that both A ⊆B are cyclic Galois extensions of R. [ABSTRACT FROM AUTHOR]

In this paper, we characterize functions that simulate independent unbiased coin flips from independent coin flips of unknown bias. We call such functions randomizing. Our characterization of randomizing functions enables us to identify the functions that generate the largest average number of fair coin flips from a fixed number of biased coin flips. We show that these optimal functions are efficiently computable. Then we generalize the characterization, and we present a method to simulate an arbitrary rational probability distribution optimally (in terms of the average number of output digits) and efficiently (in terms of computational complexity) from outputs of many-faced dice of unknown distribution. We also study randomizing functions on exhaustive prefix-free sets. [ABSTRACT FROM AUTHOR]

We depart from an n-degree-of-freedom Hamiltonian formed by the sum of homogeneous polynomials in $n$ coordinates and n momenta with arbitrary coefficients. By extending formally an integral of the principal part of the system to the full Hamiltonian and truncating higher-order terms, we obtain a simplified Hamiltonian. This "normalization" procedure can be used to extract qualitative features of the departure system. In this paper we present the symbolic routines needed to achieve the normalization. The power and generality of the algorithm are exhibited through two examples. [ABSTRACT FROM AUTHOR]

The K-groups and the Bowen–Franks groups for subshifts are invariant under not only topological conjugacy but also flow equivalence. In this paper, the K-groups and the Bowen–Franks groups for the Dyck shift D2 with 4 brackets are calculated. The spectrum of D2 with bounded nonnegative eigenvectors is shown to be the singleton {3}. We then prove that a unique conformal probability measure on the right one-sided subshift XD2 exists. These results are extended to general Dyck shifts DN with 2N brackets. [ABSTRACT FROM AUTHOR]

The general concept of probabilistic argumentation systems PAS is restricted to the two types of variables: assumptions, which model the uncertain part of the knowledge, and propositions, which model the rest of the information. Here, we introduce a third kind into PAS: so‐called decision variables. This new kind allows to describe the decisions a user can make to react on some state of the system. Such a decision allows then possibly to reach a certain goal state of the system. Further, we present an algorithm, which exploits the special structure of PAS with decision variables. Some results related with this paper were published in (Anrig and Baziukaitė, 2003a). [ABSTRACT FROM AUTHOR]

This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials among polynomials in noncommuting variables. They also fit well into the framework of free probability. For the free Appell polynomials, a number of combinatorial and “diagram” formulas are proven, such as the formulas for their linearization coefficients. An explicit formula for their generating function is obtained. These polynomials are also martingales for free Lévy processes. For more general free Sheffer families, a necessary condition for pseudo-orthogonality is given. Another family investigated is that of the Kailath-Segall polynomials. These are multivariate polynomials, which share with the Appell polynomials nice combinatorial properties, but are always orthogonal. Their origins lie in the Fock space representations, or in the theory of multiple stochastic integrals. Diagram formulas are proven for these polynomials as well, even in the q-deformed case. [ABSTRACT FROM AUTHOR]

We show that for any even log-concave probability measure \mu on \mathbb {R}^n, any pair of symmetric convex sets K and L, and any \lambda \in [0,1], \begin{equation*} \mu ((1-\lambda) K+\lambda L)^{c_n}\geq (1-\lambda) \mu (K)^{c_n}+\lambda \mu (L)^{c_n}, \end{equation*} where c_n\geq n^{-4-o(1)}. This constitutes progress towards the dimensional Brunn-Minkowski conjecture (see Richard J. Gardner and Artem Zvavitch [Tran. Amer. Math. Soc. 362 (2010), pp. 5333–5353]; Andrea Colesanti, Galyna V. Livshyts, Arnaud Marsiglietti [J. Funct. Anal. 273 (2017), pp. 1120–1139]). Moreover, our bound improves for various special classes of log-concave measures. [ABSTRACT FROM AUTHOR]

Let A be an n × n matrix and let ∨ k A be its k-th symmetric tensor power. We express the normalized trace of ∨ k A as an integral of the k-th powers of the numerical values of A over the unit sphere S n of C n with respect to the rotation-invariant probability measure. Equivalently, this expression in turn can be interpreted as an integral representation for the (normalized) complete symmetric polynomials over C n . As applications, we present a new proof for the MacMahon Master Theorem in enumerative combinatorics. Then, our next application deals with a generalization of the work of Cuttler et al. in [Cuttler A, Greene C, Skandera M. Inequalities for symmetric means. Eur J Comb. 2011;32(6):745–761] concerning the monotonicity of products of complete symmetric polynomials. Finally, we give a solution to an open problem that was raised by Roven a and Temereanca in [Roventa I, Temereanca LE. A note on the positivity of the even degree complete homogeneous symmetric polynomials. Mediterr J Math. 2019;16(1):1–16]. [ABSTRACT FROM AUTHOR]

We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the compressible Euler system with linear damping. Our results are limited to the 1 space dimensional case but allow for initial data taken in a Wasserstein space of probability measures. We first consider the case of smooth nonlocal interaction potentials, not subject to any symmetry condition, and prove existence and uniqueness. The concept of solutions relies on a stickiness condition in case of collisions, in the spirit of previous works in the literature. The result uses concepts from classical Hilbert space theory of gradient flows (cf. Brezis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, 1973) and a trick used in Brenier et al. (J. Math. Pures Appl. 99(5):577–617, 2013). We then consider a large-time and large-damping scaled version of our system and prove convergence to solutions to the corresponding first order system. Finally, we consider the case of Newtonian potentials - subject to symmetry of the cross-interaction potentials - and external convex potentials. After showing existence in the sticky particles framework in the spirit of Brenier et al. (J. Math. Pures Appl. 99(5):577–617, 2013), we prove convergence for large times towards Dirac delta solutions for the two densities. All the results share a common technical framework in that solutions are considered in a Lagrangian framework, which allows to estimate the behavior of solutions via L 2 estimates of the pseudo-inverse variables corresponding to the two densities. In particular, due to this technique, the large-damping result holds under a rather weak condition on the initial data, which does not require well-prepared initial velocities. We complement the results with numerical simulations. [ABSTRACT FROM AUTHOR]

Using techniques developed by Kanigowski, Lemańczyk, and Radziwiłł [Fund. Math. 255 (2021), pp. 309–336], we verify Sarnak's conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider is called almost complete congruency classes (accc), the definition of which is motivated by the main result of Foreman, Gao, Hill, Silva, and Weiss [Isr. J. Math., To appear], which implies that when a rank-one subshift carries a unique nonatomic invariant probability measure, it is accc if it is measure-theoretically isomorphic to an odometer. The second class we consider consists of Katok's map and its generalizations. [ABSTRACT FROM AUTHOR]

Among probability measures on d-dimensional real projective space, one which maximizes the expected angle arccos (x | x | · y | y |) between independently drawn projective points x and y was conjectured to equidistribute its mass over the standard Euclidean basis { e 0 , e 1 , ... , e d } by Fejes Tóth (Acta Math Acad Sci Hung 10:13–19, 1959. https://doi.org/10.1007/BF02063286). If true, this conjecture evidently implies the same measure maximizes the expectation of arccos α (x | x | · y | y |) for any exponent α > 1 . The kernel arccos α (x | x | · y | y |) represents the objective of an infinite-dimensional quadratic program. We verify discrete and continuous versions of this milder conjecture in a non-empty range α > α Δ d ≥ 1 , and establish uniqueness of the resulting maximizer μ ^ up to rotation. We show μ ^ no longer maximizes when α < α Δ d . At the endpoint α = α Δ d of this range, we show another maximizer μ must also exist which is not a rotation of μ ^ . For the continuous version of the conjecture, an "Appendix A" provided by Bilyk et al in response to an earlier draft of this work combines with the present improvements to yield α Δ d < 2 . The original conjecture α Δ d = 1 remains open (unless d = 1 ). However, in the maximum possible range α > 1 , we show μ ^ and its rotations maximize the aforementioned expectation uniquely on a sufficiently small ball in the L ∞ -Kantorovich–Rubinstein–Wasserstein metric d ∞ from optimal transportation; the same is true for any measure μ which is mutually absolutely continuous with respect to μ ^ , but the size of the ball depends on α , d , and ‖ d μ ^ d μ ‖ ∞ . [ABSTRACT FROM AUTHOR]

We consider the classical point vortex model in the mean-field scaling regime, in which the velocity field experienced by a single point vortex is proportional to the average of the velocity fields generated by the remaining point vortices. We show that if at some time the associated sequence of empirical measures converges in a renormalized H ˙ - 1 sense to a probability measure with density ω 0 ∈ L ∞ (R 2) and having finite energy as the number of point vortices N → ∞ , then the sequence converges in the weak-* topology for measures to the unique solution ω of the 2D incompressible Euler equation with initial datum ω 0 , locally uniformly in time. In contrast to previous results Schochet (Commun Pure Appl Math 49:911–965, 1996), Jabin and Wang (Invent Math 214:523–591, 2018), Serfaty (Duke Math J 169:2887–2935, 2020), our theorem requires no regularity assumptions on the limiting vorticity ω , is at the level of conservation laws for the 2D Euler equation, and provides a quantitative rate of convergence. Our proof is based on a combination of the modulated-energy method of Serfaty (J Am Math Soc 30:713–768, 2017) and a novel mollification argument. We contend that our result is a mean-field convergence analogue of the famous theorem of Yudovich (USSR Comput Math Math Phys 3:1407–1456, 1963) for global well-posedness of 2D Euler with vorticity in the scaling-critical function space L ∞ (R 2) . [ABSTRACT FROM AUTHOR]

In this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems for classical logic and Girard's proofnets for linear logic. [ABSTRACT FROM AUTHOR]

A partition Cii? I of a Boolean algebrain a probability measure spaceis called a Reichenbachian common cause system for the correlated pairA,Bof events inif any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index setIis called the size of the common cause system. It is shown that given any correlation in, and given any finite sizen>2, the probability spacecan be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of sizenfor the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions ofcontains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated. [ABSTRACT FROM AUTHOR]

This paper proposes a solution to Challenge Problem 1 posed by Oberkampf et al. [Reliab. Engng Syst. Safety (this issue)] and focuses on questions of dependence or independence of variables. The specification of uncertainties is consistently reduced to sets of probability measures. For whatever interpretation, the results essentially depend on the choice of combination rule in defining the joint distributions. The approach adopted here is shown to be consistent with interval analysis, random sets and fuzzy sets, and admits a clear description of the influence of the concept of independence used. A MATLAB-tool has been developed that allows to compute the lower and upper probability distributions for all choices of framework and combination rule. [Copyright &y& Elsevier]

Abstract. In the late 1940s, A. N. Kolmogorov suggested a remarkably simple example of a transitive, but not ergodic, action of the group of all permutations of positive integers. It turned out that such examples arise, as a rule, in the theory of actions of non-locally compact groups, and for locally compact groups this phenomenon cannot happen. Kolmogorov's example also helps to give a correct definition of the decomposition into ergodic components and orbit partition for actions of general groups. [ABSTRACT FROM AUTHOR]

For Ivor Grattan-Guinness on the occasion of his retirement. The work of Augustus De Morgan on symbolic logic in the mid-nineteenth century is familiar to historians of logic and mathematics alike. What is less well known is his work on probability and, more specifically, the use of probabilistic ideas and methods in his logic. The majority of De Morgan's work on probability was undertaken around 1837 - 1838, with his earliest publications on logic appearing from 1839, a period which culminated with the publication of his Formal Logic in 1847. This article examines the overlap between his work on probability theory and logic during the earliest period of his interest in both. [ABSTRACT FROM AUTHOR]

The resource-bounded measures of complexity classes are shown to be robust with respect to certain changes in the underlying probability measure. Specifically, for any real number > 0, any uniformly polynomial-time computable sequence &fitilde; = (fi[sub0];fi[sub1];fi[sub2];:::) of real numbers (biases) fi[subi] 2 [ ;1 &idot; ], and for any complexity class C (such as P, NP, BPP, P/Poly, PH, PSPACE, etc.) that is closed under positive, polynomial-time, truth-table reductions with queries of at most linear length, it is shown that the following two conditions are equivalent. (1) C has p-measure 0 (respectively, measure 0 in E, measure 0 in E[sub2]) relative to the coin-toss probability measure given by the sequence &fitilde;. (2) C has p-measure 0 (respectively, measure 0 in E, measure 0 in E[sub2]) relative to the uniform probability measure.The proof introduces three techniques that may be useful in other contexts, namely, (i) the transformation of an e cient martingale for one probability measure into an e cient martingale for a \nearby" probability measure; (ii) the construction of a positive bias reduction, a truth-table reduction that encodes a positive, e cient, approximate simulation of one bias sequence by another; and (iii) the use of such a reduction to dilate an e cient martingale for the simulated probability measure into an e cient martingale for the simulating probability measure. Key words: complexity classes; martingales; resource-bounded measure [ABSTRACT FROM AUTHOR]

Although traditional and idempotent mathematics are "parallel", by an application of the category theory we show that objects obtained the similar rules over traditional and idempotent mathematics must not be "parallel". At first we establish for a compact metric space X the spaces P(X) of probability measures and I(X) idempotent probability measures are homeomorphic ("parallelism"). Then we construct an example which shows that the constructions P and I form distinguished functors from each other ("parallelism" negation). Further for a com-pact Hausdorff space X we establish that the hereditary normality of I3(X)\X implies the metrizability of X. [ABSTRACT FROM AUTHOR]

A multiple-choice item is called ideal if all its alternatives are equally attractive to every person who cannot answer the item correctly without guessing. This paper discusses reasons for attempting to construct ideal items, develops methods for testing whether items are ideal or at least more nearly ideal than other items, and presents examples of both ideal and nonideal items. [ABSTRACT FROM AUTHOR]

This paper describes certain quota sampling procedures and attempts to show that they are very close to traditional probability sampling. Quotas are shown to depend on availability for interviewing and evidence is presented to show that sex, age, and employment status are reasonable predictors of availability. Quota sampling methods are not unbiased but data are presented which suggest that the bias is generally of the order of 3 to 5 per cent. It is shown, however, that the cost differentials between these quota samples and call-back samples are small. The major advantage of this new procedure may well be the speed with which interviewing may be completed during crises such as the Kennedy assassination. [ABSTRACT FROM AUTHOR]

Background and objective: Markov micro-simulation models are being increasingly used in health economic evaluations. An important feature of the Markov micro-simulation model is its ability to consider transition probabilities of heterogeneous subgroups with different risk profiles. A survival analysis is generally performed to accurately estimate the transition probabilities associated with the risk profiles. This study aimed to apply a flexible parametric survival model (FPSM) to estimate individual transition probabilities. Materials and methods: The data were obtained from a cohort study investigating ischemic stroke outcomes in Western China. In total, 585 subjects were included in the analysis. To explore the goodness of fit of the FPSM, we compared the estimated hazard ratios and baseline cumulative hazards, both of which are necessary to the calculate individual transition probabilities, and the Markov micro-simulation models constructed using the FPSM and Cox model to determine the validity of the two Markov micro-simulation models and cost-effectiveness results. Results: The flexible parametric proportional hazards model produced hazard ratio and baseline cumulative hazard estimates that were similar to those obtained using the Cox proportional hazards model. The simulated cumulative incidence of recurrent ischemic stroke and 5-years cost-effectiveness of Incremental cost-effectiveness Ratios (ICERs) were also similar using the two approaches. A discrepancy in the results was evident between the 5-years cost-effectiveness and the 10-years cost-effectiveness of ICERs, which were approximately 0.9 million (China Yuan) and 0.5 million (China Yuan), respectively. Conclusions: The flexible parametric survival model represents a good approach for estimating individual transition probabilities for a Markov micro-simulation model. [ABSTRACT FROM AUTHOR]

The article examines the actions of F∞ whose II1 factors and orbit equivalence relations have prescribed fundamental group. A large family of S of subgroups of R+, containing R+ itself are exhibited. The first examples of II1 factors with separable predual having uncountable fundamental group different from R+. The ergodic measures and Hausdorff dimension are discussed.

We prove a domination theorem for operators on Köthe function spaces by probability measures which includes both the Maurey-Rosenthal domination theorem and the Pisier domination theorem as special cases. [ABSTRACT FROM AUTHOR]

For a lower semicontinuous convex function ƒ : R → R ∪ {+∞}, dom ƒ ⊆ R+, we give a definition and study properties of the ƒ-divergence of finitely additive set functions μ and υ given on a measurable space (Ω,F). If f is finite on (0,+ ∞) and μ and υ are probability measures, our definition is equivalent to the classical definition of the ƒ-divergence introduced by Csiszár. As an application, we obtain a result on attaining the minimum by the ƒ-divergence over a set Z of pairs of probability measures. [ABSTRACT FROM AUTHOR]

We consider the height process of a Lévy process with no negative jumps, and its associated continuous tree representation. Using Lévy snake tools developed by Le Gall-Le Jan and Duquesne-Le Gall, with an underlying Poisson process, we construct a fragmentation process, which in the stable case corresponds to the self-similar fragmentation described by Miermont. For the general fragmentation process we compute a family of dislocation measures as well as the law of the size of a tagged fragment. We also give a special Markov property for the snake which is of its own interest. [ABSTRACT FROM AUTHOR]

The article reports on the asymptotic results for a run and cumulative mixed shock model. It mentions that the models assume that the shocks arrive at different times wherein it cause damages of random magnitude and the system fails in a specific way. In the cumulative shock model, the system fails as the sum of the random damages surpasses the prefixed level. It also discusses the classic shock models, mixed shock models and others.

Let ( X, $${\mathfrak{S}}$$ ( X), $${\mathfrak{m}})$$ be a probability space with σ-algebra , $${\mathfrak{S}}$$ ( X) and probability measure $${\mathfrak{m}}.$$ The set V in $${\mathfrak{S}}$$ is called P-admissible, provided that for any positive integer n and positive-measure set V n ∈ $${\mathfrak{S}}$$ contained in V , there exists a Z n ∈ $${\mathfrak{S}}$$ such that Z n ⊂ V n and 0 < $${\mathfrak{m}}$$ ( Z n ) < 1/ n. Let T be an ergodic automorphism of ( X, $${\mathfrak{S}})$$ preserving $${\mathfrak{m}},$$ and A belong to the space of linear measurable symplectic cocycles $${\fancyscript G}$$ IC ( X, SL(2,ℝ)) := { A : X → SL(2,ℝ)| log ∥ A ±1( x)∥ ∈ $${\Bbb L}$$ 1( X, $${\mathfrak{m}}).$$ We prove that for any P–admissible set V and ε > 0, there exists a B ∈ $${\fancyscript G}$$ IC ( X, SL(2,ℝ)) such that max{∥ A( x) − B( x)∥, ∥ A −1( x) − B −1( x)∥} < ε for all x ∈ V, A( x) = B( x) for all x ∈ X \ V, and B has the simple Lyapunov spectrum over the system ( X, $${\mathfrak{m}},$$ T). [ABSTRACT FROM AUTHOR]

We study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffice for catching rabbits with such local visibility with high probability. We distinguish between reactive rabbits who move only when a hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G. [ABSTRACT FROM AUTHOR]

The structure of a self-similar group G naturally gives rise to a transformation which assigns to any probability measure μ on G and any vertex w in the action tree of the group a new probability measure μw. If the measure μ is self-similar in the sense that μw is a convex combination of μ and the δ-measure at the group identity, then the asymptotic entropy of the random walk (G, μ) vanishes; therefore, the random walk is Liouville and the group G is amenable. We construct self-similar measures on several classes of self-similar groups, including the Grigorchuk group of intermediate growth. [ABSTRACT FROM AUTHOR]

We introduce a new class of rules for resolving quasilinear social choice problems. These rules extend those of Green [9]. We call such rules multi-utilitarian rules. Each multi-utilitarian rule is associated with a probability measure over the set of weighted utilitarian rules, and is derived as the expectation of this probability. These rules are characterized by the axioms efficiency, translation invariance, transfer monotonicity, continuity, and additivity. By adding recursive invariance, we obtain a class of asymmetric rules generalizing those Green characterizes. A multi-utilitarian rule satisfying strict monotonicity has an associated probability measure with full support. [ABSTRACT FROM AUTHOR]

On the symbolic space endowed with a metric given by a Gibbs measure, it is shown that, for any invariant probability measure $\mu$ other than the given Gibbs measure, the set of $\mu$-generical points satisfies a ‘zero-infinity law’ (in particular, its Hausdorff and packing measure are infinite). This extends a result of R. Kaufman on Besicovitch–Eggleston sets, and applies to level sets of Birkhoff averages and certain subsets of self-similar sets. [ABSTRACT FROM AUTHOR]

The DT-operators are introduced, one for every pair (μ, c) consisting of a compactly supported Borel probability measure μ on the complex plane and a constant c > 0. These are operators on Hilbert space that are defined as limits in ,-moments of certain upper triangular random matrices. The DT-operators include Voiculescu's circular operator and elliptic deformations of it, as well as the circular free Poisson operators. We show that every DT-operator is strongly decomposable. We also show that a DT-operator generates a II[sub 1]-factor, whose isomorphism class depends only on the number and sizes of atoms of μ. Those DT-operators that are also R-diagonal are identified. For a quasi-nilpotent DT-operator T, we find the distribution of T[sup *]T and a recursion formula for general [sup *]-moments of T. [ABSTRACT FROM AUTHOR]

The application of nonparametric probability density function estimation for the purpose of data analysis is well established. More recently, such methods have been applied to fluid flow calculations since the density of the fluid plays a crucial role in determining the flow. Furthermore, when the calculations involve directional or axial data, the domain of interest falls on the surface of the sphere. Accurate and fast estimation of probability density functions is crucial for these calculations since the density estimation is performed at each iteration during the computation. In particular the values fn(X1),fn(X2),…,fn(Xn) of the density estimate at the sampled points Xi are needed to evolve the system. Usual nonparametric estimators make use of kernel functions to construct fn. We propose a special sequence of weight functions for nonparametric density estimation that is especially suitable for such applications. The resulting method has a computational advantage over kernel methods in certain situations and also parallelizes easily. Conditions for convergence turn out to be similar to those required for kernel-based methods. We also discuss experiments on different distributions and compare the computational efficiency of our method with kernel based estimators. [ABSTRACT FROM AUTHOR]

An iterative procedure is described as a generalization of Bayes' method of updating an a priori assignment over the power set of the frame of discernment using uncertain evidence. In the context of probability kinematics the law of commutativity holds and the convergence is well behaved. The probability assignments of each updating evidence is retained. A general assignment method is also discussed for combining evidences without reference to any prior. The methods described here can be used in the field of Artificial Intelligence for common-sense reasoning and more specifically for treating uncertainly in Expert Systems. They are also relevant for nonmonotonic reasoning, abduction, and learning theory. [ABSTRACT FROM AUTHOR]

Probabilistic knowledge is an important input to the analysis of many decisions, and may be required for long-range forecasting, classical decision analysis, influence diagrams, fault tree analysis, and expert systems. If objective probabilities cannot be calculated, it is vital that decision makers use the best available subjective measures of probability. Standard mathematical theory allows the analyst several choices in framing subjective probability assessments. When assessing cause-effect probabilities, the three choices are causal, diagnostic, and joint probabilities. Choosing among these is difficult in light of conflicting reports that, due to cognitive heuristics, probability judgment may be biased in various poorly understood ways. For example, it has been reported that, when judging causal probabilities, people are subject to the causal information bias, and thus upwardly revise their prior probabilities more than when judging diagnostic probabilities. On the other hand, it has also been reported that in some cases, people do not take proper account of new evidence, which results in under-revision of prior probabilities. Furthermore it has been reported that, when assessing joint probabilities, people are subject to the conjunction fallacy, and thus often judge a joint probability to be higher than one of the two corresponding marginal probabilities. Our research compares the relative effects of these biases in a laboratory setting: we present new empirical results comparing the test-retest reliabilities and under(over) revision rates of causal, diagnostic, and joint probabilities. Our results suggest that the tendency to both under-revise and over-revise prior probabilities is greatest when judging diagnostic probabilities, as opposed to either causal or joint probabilities. Furthermore our results suggest that joint probability judgment is more reliable than either causal or diagnostic probability judgment [ABSTRACT FROM AUTHOR]