An Identification Problem for First-Order Degenerate Differential Equations

We study a first-order identification problem in a Banach space. We discuss the nondegenerate and mainly the degenerate case. As a first step, suitable hypotheses on the involved closed linear operators are made in order to obtain unique solvability after reduction to a nondegenerate case; the general case is then handled with the help of new results on convolutions. Some applications to partial differential equations motivate this abstract approach.Communicated by I. GalliganiWork partially supported by MIUR (Ministero dell’ Istruzione, dell’ Università e dalla Ricerca), Project PRIN 2004011204 “Analisi Matematica nei Problemi Inversi,” and by the University of Bologna Funds for Selected Research Topics.     

Assessment of local influence on Cox’s proportional hazards model

The second order approach of local influence (see [15]) is developed and applied to Cox’s proportional hazards model, and compared with Cook's local influence approach (see [6] and [13]) which was used in this model. To study local influence, we perturb not only all cases simultaneously, but also cases individually to obtain “direction curvature” in directionl and “curvature” for single case. Some examples are used to illustrate these methods. This work is supported by the Youth Science Foundation of Peking University and a research grant from State Educational Committee     

On the ‘confidence bounds” of the ratio of the means of a bivariate normal distribution

Summary Although the “confidence bounds’ of the ratio of the means of a bivariate normal distribution given by R. A. Fisher in his bookStatistical Methods for Research Workers is not the confidence bounds in the strict sense of the words, it is shown in the present article that they can be regarded as confidence bounds in a certain subset of parameter space.     

Towards a new theory of confirmation

Any sequence of events can be “explained” by any of an infinite number of hypotheses. Popper describes the “logic of discovery” as a process of choosing from a hierarchy of hypotheses the first hypothesis which is not at variance with the observed facts. Blum and Blum formalized these hierarchies of hypotheses as hierarchies of infinite binary sequences and imposed on them certain decidability conditions. In this paper we also consider hierarchies of infinite binary sequences but we impose only the most elementary Bayesian considerations. We use the structure of such hierarchies to define “confirmation”. We then suggest a definition of probability based on the amount of confirmation a particular hypothesis (i.e. pattern) has received. We show that hypothesis confirmation alone is a sound basis for determining probabilities and in particular that Carnap’s logical and empirical criteria for determining probabilities are consequences of the confirmation criterion in appropriate limiting cases.     

Copulas: Tales and facts

“But he does not wear any clothes” said the little child in Hans Christian Andersen’s “The Emperor’s New Clothes.”Mikosch’s research is partially supported by the Danish Research Council (SNF) GrantNo 21-04-0400. This is a discussion paper which was initiated at the 4th InternationalConference on Extreme Value Analysis in Gothenburg, 15–19 August, 2005; see.     

Stochastic monotonicity of the MLE of exponential mean under different censoring schemes

In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE) of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the result for the exponential competing risks model with censoring.     

Spectral properties of some problems in mechanics of strongly inhomogeneous media

Spectral properties of the following three homogenized problems in mechanics of strongly inhomogeneous media are considered: the problem of “double porosity,” the problem of vibration of a mixture of two viscous compressible fluids, and the problem of vibration of a medium consisting of an elastic frame and a viscous fluid. Interesting results about the structure of spectra and the presence of so-called “spectral gaps” are obtained for each of these cases. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 17, Differential and Functional Differential Equations. Part 3, 2006.     

BOOTSTRAP CRITICAL POINT FOR CIRCULAR MEAN DIRECTION AND ITS APPLICATIONS

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Carleson Measures via BMO

We obtain new characterizations of Carleson measures via uniform boundedness of BMO norms of certain mass functions associated with the given measure in a natural way. This research was performed during M. Stessin’s visit to Korea University. He thanks the Mathematics Department of Korea University and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00012).     

Bootstrap and permutation tests in ANOVA for directional data

The problem of testing the null hypothesis of a common direction across several populations defined on the hypersphere arises frequently when we deal with directional data. We may consider the Analysis of Variance (ANOVA) for testing such hypotheses. However, for the Watson distribution, a commonly used distribution for modeling axial data, the ANOVA test is only valid for large concentrations. So we suggest to use alternative tests, such as bootstrap and permutation tests in ANOVA. Then, we investigate the performance of these tests for data from Watson populations defined on the hypersphere.     

Finding the Homology of Submanifolds with High Confidence from Random Samples

Recently there has been a lot of interest in geometrically motivated approaches to data analysis in high-dimensional spaces. We consider the case where data are drawn from sampling a probability distribution that has support on or near a submanifold of Euclidean space. We show how to “learn” the homology of the submanifold with high confidence. We discuss an algorithm to do this and provide learning-theoretic complexity bounds. Our bounds are obtained in terms of a condition number that limits the curvature and nearness to self-intersection of the submanifold. We are also able to treat the situation where the data are “noisy” and lie near rather than on the submanifold in question. The main results of this paper were first presented at a conference in honor of John Franks and Clark Robinson at Northwestern University in April 2003. These results were formally written as Technical Report No. TR-2004-08, Department of Computer Science, University of Chicago.     

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R~N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.     

Multiple comparisons of several homoscedastic multivariate populations

The limiting joint distribution of correlated Hotelling’s T ² statistics associated with multiple comparisons with a control in multivariate one-way layout model is a multivariate central nonsingular chi-square distribution with one-factorial correlation matrix, which has the distribution function expressed in a closed form as an integral of a product of noncentral chi-square distribution functions with respect to a central chi-square density function. For pairwise comparisons, it is a multivariate central singular chi-square distribution whose distribution function is generally intricate. To overcome the complexity of the (exact or asymptotic) distribution theory of -type statistics appeared in simultaneous confidence intervals of mean vectors, improved Bonferroni-type inequalities are applied to construct asymptotically conservative simultaneous confidence intervals for pairwise comparisons as well as comparisons with a control.     

S-matrix description of nonequilibrium finite-temperature systems

We consider the “inclusive” (“partial”) method for describing nonequilibrium dissipative systems at the early (kinetic) evolution stage, when the temperature distribution is nonuniform. We formulate the perturbation theory in terms of space-time-local temperature Green’s functions and derive the Liouville equation for the one-particle partition function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 368–380, December, 2006.     

The Pepsi Putnam Challenge

Opening a copy of The Mathematical Intelligencer you may ask yourself uneasily, “What is this anyway—a mathematical journal, or what?” Or you may ask, “Where am I?” Or even “Who am I?” This sense of disorientation is at its most acute when you open to Cohn Adam’s column. Relax. Breathe regularly. It’s mathematical, it’s a humor column, and it may even be hannless.     

An improvement of discrete Tardos fingerprinting codes

It has been proven that the code lengths of Tardos’s collusion-secure fingerprinting codes are of theoretically minimal order with respect to the number of adversarial users (pirates). However, the code lengths can be further reduced as some preceding studies have revealed. In this article we improve a recent discrete variant of Tardos’s codes, and give a security proof of our codes under an assumption weaker than the original Marking Assumption. Our analysis shows that our codes have significantly shorter lengths than Tardos’s codes. For example, when c = 8, our code length is about 4.94% of Tardos’s code in a practical setting and about 4.62% in a certain limit case. Our code lengths for large c are asymptotically about 5.35% of Tardos’s codes. A part of this work was presented at 17th Applied Algebra, Algebraic Algorithms, and Error Correcting Codes (AAECC-17), Bangalore, India, December 16–20, 2007.     

Accurate confidence intervals in regression analyses of non-normal data

A linear model in which random errors are distributed independently and identically according to an arbitrary continuous distribution is assumed. Second- and third-order accurate confidence intervals for regression parameters are constructed from Charlier differential series expansions of approximately pivotal quantities around Student’s t distribution. Simulation verifies that small sample performance of the intervals surpasses that of conventional asymptotic intervals and equals or surpasses that of bootstrap percentile-t and bootstrap percentile-|t| intervals under mild to marked departure from normality.     

When does management matter in a dog-eat-dog world: An “Interaction Value Analysis” model of organizational climate

Interaction Value Interaction Value Analysis (I.V.A.) models a network of rational actors who generate value by interacting with each other. This model can be used to understand human organizations. Since people form organizations to facilitate interactions between productive individuals, the value added by interaction is the contribution of the organization. This paper examines the result of varying the queuing discipline used in selecting among back-logged interaction requests. Previously developed I.V.A. models assumed a First-in-first-out (FIFO) discipline, but using other disciplines can better represent the “Climate” of an organization. I.V.A. identifies circumstances under which organizations that control members’ interaction choices outperform organizations where individuals choose their own interaction partners. Management can be said to “matter” when individual choices converge to a point where interactions generate a lower than optimal value. In previous I.V.A. models, relinquishing central control of interaction choices reduced the aggregate value by anything from 0% to 12%, depending on circumstances. This paper finds the difference between the two modes of organization to go as high as 47% if actors display preferences between interaction partners instead of treating all equally. A politically divided, dog-eat-dog, “Capitalist” climate follows one queuing discipline, which is found to generally increase the value that a strong control structure can add. A chummy, in-bred “Fraternal” climate gains from control in some circumstances (low interdependence or low differentiation), but not in others (high or medium interdependence and differentiation under low diversity, for example). These are compared to the previous version of I.V.A., in which the queuing discipline was FIFO and the climate deemed “Disciplined”. Previously published findings on Organizational Climate are duplicated and extended with a higher level of detail. Priority queuing in an I.V.A. model is thus a useful proxy for Organizational Climate, open to future validation because its detailed predictions can be confirmed or falsified by observation. Walid Nasrallah is currently Assistant Professor in the Engineering Management program at the American University of Beirut (AUB). He received his Ph.D. from the Construction Engineering and Management program at Stanford University in 2000 and his Master’s degree at MIT in 1989. Between the two, he occupied several positions in the construction and software engineering fields. His research interests today include simulation, decision theory, and the evolution of organizations in response to new technologies.     

Density problems connected with overconvergence

Due to Ostrowskii’s classical results on overconvergence of power series, there is an interdependence between the occurrence of gaps in the sequence of coefficients and the overconvergence phenomenon. The paper investigates the structure of the corresponding gaps and especially the density properties of gap intervals, as well as of “non-gap” intervals of overconvergent power series.