A statistical sum associated with Young diagrams

We study the asymptotics of sums of powers of normalized dimensions of complex irreducible representations of the symmetric group as N. We calculate the limit Gibbs measure on the space of Young diagrams. The problem is connected with a one-dimensional model of statistical physics. In the appendix, written by A. M. Pass, numerical and graphical data about the free energy corresponding to the statistical studied are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 20–29, 1987.     

From regulatory life tables to stochastic mortality projections: The exponential decline model

Often in actuarial practice, mortality projections are obtained by letting age-specific death rates decline exponentially at their own rate. Many life tables used for annuity pricing are built in this way. The present paper adopts this point of view and proposes a simple and powerful mortality projection model in line with this elementary approach, based on the recently studied mortality improvement rates. Two main applications are considered. First, as most reference life tables produced by regulators are deterministic by nature, they can be made stochastic by superposing random departures from the assumed age-specific trend, with a volatility calibrated on market or portfolio data. This allows the actuary to account for the systematic longevity risk in solvency calculations. Second, the model can be fitted to historical data and used to produce longevity forecasts. A number of conservative and tractable approximations are derived to provide the actuary with reasonably accurate approximations for various relevant quantities, available at limited computational cost. Besides applications to stochastic mortality projection models, we also derive useful properties involving supermodular, directionally convex and stop-loss orders.     

A three-phase algorithm for the cell suppression problem in two-dimensional statistical tables

To obtain full cooperation from respondents, statistical offices must guarantee that confidential data will not be disclosed when their reports are published. For tabular data, cell suppression is one of the preferred techniques to control statistical disclosure. When suppressing only confidential values does not guarantee the desired data protection, it is also necessary to suppress the values in some non-confidential cells. The problem of finding an optimal set of complementary suppressions—the cell suppression problem (CSP)—is NP-hard. We present a three-phase algorithm for the CSP based on a binary relaxation derived from row and column protection conditions. To enforce violated single cell conditions, integer cuts are added to the CSP relaxation. The numerical results obtained in 1410 instances with up to more than 250?000 cells, which were generated to reproduce two classes of real-world data, indicate that the algorithm is quite effective for both classes of instances and that it outperforms state-of-the-art algorithms for one of them.     

Collegical Entrepreneurialism In Proactive Universities: Lessons From Europe

Abstract

Twenty years ago, when Change published the first survey on leadership in higher education, Clark Kerr was identified as the single most influential voice in higher education. He has remained a precise, creative thinker and writer on intellectual issues, on leadership, and otherwise. Virtually everyone who serves as a leader in higher education today owes something to Clark Kerr, to what he did and what he wrote. It was not only that he was ever on the cutting edge, that he fought the good fight in so many critical battles; unlike most other university presidents, he had the skill, the energy, and the desire to articulate what he was doing and reflect upon what it meant.

Clark Kerr lives the life of leadership. He took the risks, he fought good fights, he made mistakes (by his own admission), and writes about what he learned from them and would have done differently. It is with his words that we start this issue of Change, focused as it is on leadership. In our search for leadership, we've turned first to Clark Kerr to state its challenges.     

Erratum to: Hurwitz numbers from Feynman diagrams

Theoretical and Mathematical Physics - Erratum to https://doi.org/10.1134/S0040577920090068     

Combinatorial obstructions to the lifting of weaving diagrams

This paper deals with various connections of oriented matroids [3] and weaving diagrams of lines in space [9], [16], [27]. We encode the litability problem of a particular weaving diagramD onn lines by the realizability problem of a partial oriented matroid χ _D with2n elements in rank 4. We prove that the occurrence of a certain substructure inD implies that χD is noneuclidean in the sense of Edmonds, Fukuda, and Mandel [12], [14]. Using this criterion we construct an infinite class of minor-minimal noneuclidean oriented matroids in rank 4. Finally, we give an easy algebraic proof for the nonliftability of the alternating weaving diagram on a bipartite grid of 4×4 lines [16].     

Bifurcation diagrams and periodic solutions to nonlinear equations

Summary We consider a class of simple examples and investigate the connection between the solutions of the nonlinear wave equation and the solutions of the corresponding bifurcation problem.

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Zusammenfassung An einfachen Klassen von Beispielen wird der Zusammenhang untersucht zwischen den periodischen Lösungen nichtlinearer Wellengleichungen und den Lösungen des zugehörigen Verzweigungsproblems.

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Research supported in part by the European Research Office of the United States Army.     

Diophantine geometry over groups I: Makanin-Razborov diagrams

Manucsrit re?u le 4 janvier 2000.     

Optical solitons in communications: From integrability to controllability

A brief historical review and recent developments of theories and experiments of optical solitons in fibers are presented with particular emphasis on their integrability and controllability in real systems.     

Cycle expansions: From maps to turbulence

We present a derivation, a physical explanation and applications of cycle expansions in different dynamical systems, ranging from simple one-dimensional maps to turbulence in fluids. Cycle expansion is a newly devised powerful tool for computing averages of physical observables in nonlinear chaotic systems which combines many innovative ideas developed in dynamical systems, such as hyperbolicity, invariant manifolds, symbolic dynamics, measure theory and thermodynamic formalism. The concept of cycle expansion has a deep root in theoretical physics, bearing a close analogy to cumulant expansion in statistical physics and effective action functional in quantum field theory, the essence of which is to represent a physical system in a hierarchical way by utilizing certain multiplicative structures such that the dominant parts of physical observables are captured by compact, maneuverable objects while minor detailed variations are described by objects with a larger space and time scale. The technique has been successfully applied to many low-dimensional dynamical systems and much effort has recently been made to extend its use to spatially extended systems. For one-dimensional systems such as the Kuramoto–Sivashinsky equation, the method turns out to be very effective while for more complex real-world systems including the Navier–Stokes equation, the method is only starting to yield its first fruits and much more work is needed to enable practical computations. However, the experience and knowledge accumulated so far is already very useful to a large set of research problems. Several such applications are briefly described in what follows. As more research effort is devoted to the study of complex dynamics of nonlinear systems, cycle expansion will undergo a fast development and find wide applications.     

The propagation of updates to relational tables in a distributed database system

The problem of applying update operations to relational tables under the supervision of a distributed database management system is considered. A model describing the minimal cost propagation strategy of an update request to all copies of the relevant relation is offered, and takes the form of an integer linear program.A user request is issued at a given site in the network, specifying an amendment to the information comprising some particular logical data set, or relation. Replication of data admits the possibility of relations being duplicated, with several distinct copies disseminated amongst various processor sites; synchronization of replicated information to preserve its consistency commands that the alteration be applied uniformly to all. The update request must therefore be communicated to each site possessing a copy of the relation to which it refers.This task demands the utilization of limited system resources; data transmission channels convey the update signal between sites, and processors apply the operation to stored copies of the particular relation to be changed. The ultimate goal is therefore to choose from all possible update propagation strategies one that achieves the smallest total cost.The formulation initially attained by considering the role of an isolated processor in a valid strategy contains some constraints that are nonlinear. However, by introducing new decision variables and reconsidering the offending inequalities, the model can be transformed to realize an optimization program entirely linear in structure.     

Moral concepts: From thickness to response-dependence

The paper examines three tenets of Dancy's meta-ethics, finds them incompatible, and proposes a response-dependentist (or response-dispositional) solution. The first tenet is the central importance of thick concepts and properties. The second is that such concepts essentially involve response(s) of observers, which Dancy interprets in a way that fits the pattern of context-dependent resultance: thick concepts are well suited for the particularist grounding of moral theory. However, and this is the third tenet, in his earlier paper (1986) Dancy forcefully argues against response-dispositional accounts of moral concepts and properties. The present paper argues that an anti-dispositional view is incompatible with the first two points concerning thick concepts. If thick concepts and properties are paramount and ubiquitous in moral thought and reality, and if they are essentially tied to human responses, then anti-dispositionalism is false. Dancy himself avoids obvious contradiction by characterizing thick items (concepts) differently from the usual characterization of response-dependent items. Actions that satisfy thick concepts do so in virtue of meriting a determinate response. The (non-reductionist) response-dependentist usually puts it slightly differently: such actions satisfy a given moral concepts in virtue of eliciting a merited response. I have argued at length that this tenuous difference in formulation is too weak to support a relevant difference in rebus. If the argument is right, Dancy is implicitly committed to a kind of response-dependentism. Finally, the particularist should embrace thick concepts and properties, and reject anti-dispositionalism. However, this would bring back the analogy with color and other secondary qualities. Since there are ceteris paribus laws governing such properties, the analogy suggests that moral properties might also be best accounted for by a ceteris paribus, or hedged account, a compromise between traditional generalism and the particularism of Dancy's variety.     

Self-intersections in combinatorial topology: statistical structure

Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number of transversal self-intersection points of representatives of the class. We prove that if a class is chosen at random from among all classes of m letters, then for large m the distribution of the self-intersection number approaches the Gaussian distribution. The theorem was strongly suggested by a computer experiment with four million curves producing a very nearly Gaussian distribution.