Prediction logic: A method for empirical evaluation of formal theory†

This paper proposes an approach to data analysis that assists the investigator in discriminating among specific relations corresponding to alternative scientific predictions about qualitative variates.     

Asymptotic theory for the empirical Haezendonck–Goovaerts risk measure

Haezendonck–Goovaerts risk measures is a recently introduced class of risk measures which includes, as its minimal member, the Tail Value-at-Risk (T-VaR)—T-VaR arguably the most popular risk measure in global insurance regulation. In applications often one has to estimate the risk measure given a random sample from an unknown distribution. The distribution could either be truly unknown or could be the distribution of a complex function of economic and idiosyncratic variables with the complexity of the function rendering indeterminable its distribution. Hence statistical procedures for the estimation of Haezendonck–Goovaerts risk measures are a key requirement for their use in practice. A natural estimator of the Haezendonck–Goovaerts risk measure is the Haezendonck–Goovaerts risk measure of the empirical distribution, but its statistical properties have not yet been explored in detail. The main goal of this article is to both establish the strong consistency of this estimator and to derive weak convergence limits for this estimator. We also conduct a simulation study to lend insight into the sample sizes required for these asymptotic limits to take hold.     

More about λ-support iterations of (<λ)-complete forcing notions

This article continues Ros?anowski and Shelah (Int J Math Math Sci 28:63–82, 2001; Quaderni di Matematica 17:195–239, 2006; Israel J Math 159:109–174, 2007; 2011; Notre Dame J Formal Logic 52:113–147, 2011) and we introduce here a new property of (<λ)-strategically complete forcing notions which implies that their λ-support iterations do not collapse λ ⁺ (for a strongly inaccessible cardinal λ).     

Markov models of occupational mobility: Theoretical development and empirical support. Part 1: Careers†

This paper, consisting of two parts, presents an analysis of the current state of Markov model , building for intragenerational occupational mobility. Part One examines theories of careers and Part Two theories of continuously operative job systems. Stress is given to the empirical support of the models and to the cumulative development of theory. Among the paper's findings are that several models proposed to span both occupational and geographical mobility have used only migration data; that analytic development is more cumulative for career models; and that there exists a basic divergence of findings from tests of models of careers and continuously operative job systems. In Part One we focus on individual behavior or subaggregates (cohorts).     

Dynamic models of segregation†

Some segregation results from the practices of organizations, some from specialized communication systems, some from correlation with a variable that is non‐random; and some results from the interplay of individual choices. This is an abstract study of the interactive dynamics of discriminatory individual choices. One model is a simulation in which individual members of two recognizable groups distribute themselves in neighborhoods defined by reference to their own locations. A second model is analytic and deals with compartmented space. A final section applies the analytics to ‘neighborhood tipping.’ The systemic effects are found to be overwhelming: there is no simple correspondence of individual incentive to collective results. Exaggerated separation and patterning result from the dynamics of movement. Inferences about individual motives can usually not be drawn from aggregate patterns. Some unexpected phenomena, like density and vacancy, are generated. A general theory of ‘tipping’ begins to emerge.     

The structure of irreducible matrices †

Let A be an irreducible matrix with index of imprimitivity h is shown that there exists a permutation matrix P such that PAP^t is in a superdiagonal block form with k nonzero blocks if and only if k divides h It is also shown that a matrix in a superdiagonal block form without zero rows or columns is irreducible if and only if the product of the superdiagonal nonzero blocks is irreducible.     

Subpermanents of doubly stochastic matrices †

It is shown that if all subpermaneats of order k of an n × n doubly stochastic matrix are equal for some k ≤ n ? 2, then all the entries of the matrix must be equal to 1/n.     

The general and special superalgebras of formal vectorfields

The natural filtrations of the general algebra W and the special algebra S of formal vectorfields are proved to be invariant. Furthermore, the automorphism groups of W and S are proved to be isomorphic to the corresponding admissible automorphism groups of the base superalgebra U. Then the automorphisms of W or 5 can be induced by the continue automorphisms of U.     

Several Jordan-algebraic aspects of optimization†

We describe some concepts from the theory of Euclidean Jordan algebras and their use in optimization theory. This includes: primal-dual algorithms, optimality conditions, convexity of spectral functions, proof of some inequalities and a Jordan-algebraic version of Horn–Schur theorem     

Nonlinear filtering theory for coral/starfish and plant/herbivore interactions †

Several nonlinear filtering problems associated with specific 4 dimensional differential equation models of coral/starfish or chemically mediated plant/herbivore population dynamics are studied. Extensive use is made of H. Kunita's backward Stratonovich calculus and stochastic partial differential equations theory to obtain exact solution measures of the Zakai and Kushner equations. The hypoellipticity problem is solved positively, so that these measures all possess c^∞-densities. Thus, explicit formulas are obtained for the estimation of signal processes conditional on observational data. For example, biomass production/consumption processes are least squares estimated conditional on observations on the population dynamics of the producing and consuming units themselves.     

On the connectivity of social networks†

In the context of analyzing social structures through the use of graph theory, some binary matrix operations for valued graphs are presented. These operations are demonstrated in the analysis of social network data presented by Kapferer. Further examples of where the procedures should prove useful are suggested.     

On Fiber Coefficients of Fiber Cones †

Let (R,𝔪) be a Cohen–Macaulay local ring of dimension d > 0, I an 𝔪-primary ideal of R, and K an ideal containing I. When depth G(I) ≥ d ? 1, depth F_K(I) ≥ d ? 2, and r(I|K) < ∞, we calculate the fiber coefficients f_i(I). Under the above assumptions on depth G(I) and r(I|K), we give an upper bound for f₁(I), and also provide a characterization, in terms of f₁(I), of the condition depth F_K(I) ≥ d ? 2.     

Progress in physical concepts of string and superstring theory—thirty years of string theory

In this paper we discuss the evolution of physical concepts which led to the generation and development of string theories. The paper is conceived with the intention of summarizing and extending with new aspects the specific characteristics of strings which refer to the physical intuition and experiment. We hope to present new insights into the physics of strings and make it understandable from the point of view of a non-string theorist. Even if there exist some opinions that the (super)string theory appertains to the twenty-first or twenty-second century or that there are no concrete new predictions of string theory at low energies, we believe that string theory presents a rich field of research and a source of physical intuition not only for mathematicians but also for theoretical and experimental physicists. We offer as an example an atomic electron cloud which can also be interpreted in terms of a fixed point in a string theory We propose also an experiment to verify the fundamental hypotheses. Finally we deduce that the number of dimensions of spacetime must be infinite by virtue of the axiom of universality of motion.     

Extensions of Perron–Frobenius theory

The classical Perron–Frobenius theory asserts that, for two matrices $A$ and $B$ , if $0\le B \le A$ and $r(A)=r(B)$ with $A$ being irreducible, then $A=B$ . It has been extended to infinite-dimensional Banach lattices under certain additional conditions, including that $r(A)$ is a pole of the resolvent of $A$ . In this paper, we prove that the same result holds if $B$ is irreducible and $r(B)$ is a pole of the resolvent for $B$ . We also prove some other interesting extensions of the theorem for infinite-dimensional Banach lattices.