Two applications of Weil-Serre's explicit formula

We apply Weil-Serre's explicit formula to produce non-trivial estimates of exponential sums along a curve and of the dual distance of subfield subcodes of algebraic-geometric (AG-)codes. These bounds work while the number of rational points of a curve is large when compared to its genus thus the Weil-Bombieri bound for exponential sums being trivial.Partly supported by Russian Fundamental Research Foundation (project N 93-012-458) and by the grant MPN000 from the International Science FoundationThe author is deeply grateful to Mme Aurélia Lozingot for her help in typing of the present paper.     

An overview of robust Bayesian analysis

Summary Robust Bayesian analysis is the study of the sensitivity of Bayesian answers to uncertain inputs. This paper seeks to provide an overview of the subject, one that is accessible to statisticians outside the field. Recent developments in the area are also reviewed, though with very uneven emphasis. Carnegie Mellon University The research of Professor Kadane was supported in part by the following grants; ONR: N0004-89-J-1851, NSF: SES-9123370, DMS-9005858 and DMS-9302557. Professor Srinivasan was supported in part by NSF grants ATM-9108177 and DMS-9204380. Duke University CNR-IAMI and Duke University Read before the Spanish Statistical Society at a meeting organized by the Universidad Autónoma de Madrid on Friday, November 19, 1993 Research supported by the National Science Foundation, Grants DMS-8923071 and DMS 93-03556.     

Computation of the weight distribution of CRC codes

In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from some “representative” words. Thanks to MacWilliams’ Theorem, the computation of the weight distribution of the dual codes can be easily brought back to that of CRC codes. The author was partially supported by the Swiss National Science Foundation under Grant no. 113251.     

Character sum constructions of constrained error-correcting codes

We estimate parameters of constrained error-correcting codes constructed by means of additive and multiplicative characters. To get the bounds we derive estimates for some incomplete character sums.This work was supported in part by the Academy of Finland. The first-named author would also like to express his gratitude to the Department of Mathematics of the University of Turku for the hospitality during his visit in August, 1992.     

Empirical depth processes

We consider the asymptotics of two depth processes, the projection depth process and certain generalizations of the Tukey halfspace depth process, and give ntural conditions for the uniform convergence of these processes over certain subsets of ℝ^d. In general, these processes do not converge uniformly over ℝ ^d . Research partially supported by NSFC (No:10231030) and the EYTP of China. Research partially supported by NSF Grants DMS-0071976 and DMS-0134628.     

Bounds and constructions of asymmetric or unidirectional error-correcting codes

Binary block codes for correctingt symmetric, asymmetric and unidirectional errors are calledt-SyEC codes,t-AsEC codes andt-UEC codes respectively. Two tables with bounds on the cardinality of binary block codes for correcting asymmetric and unidirectional errors respectively are presented. They include many improvements over the existing literature. The lower bounds follow from explicit constructions, while the upper bounds are obtained by applying combinatorial arguments to the weight structure of such codes.The authors are with Department of Mathematics and Computing Science of Eindhoven University of Technology, The Netherlands. Part of this work was presented at the IEEE International Symposium on Information Theory, Budapest, 1991     

The h-p version of the finite element method

The paper is the first of the series of two which analyses the h-p version of the finite element method in two dimensions. It proves the basic approximation results which in part 2 will be generalized and applied in a computational setting. The main result is that the h-p version leads to an exponential rate of convergence when solving problems with piecewise analytic data.Supported by the NSF Grant DMS-8315216Partially supported by ONR Contract N00014-85-K-0169     

On the subsample bootstrap variance estimation

In this paper we further elaborate on the subsample bootstrap result of Politis and Romano. Combining the jackknife and bootstrap ideas we were able to establish a wide consistency for the subsample bootstrap variance estimator. This was confirmed by simulations. Research partly supported by NSF Grant No. DMS-93-00725     

On minimum distance bounds for abelian codes

This paper is an exposition of two methods of formulating a lower bound for the minimum distance of a code which is an ideal in an abelian group ring. The first, a generalization of the cyclic BCH (Bose-Chaudhuri-Hoquenghem) bound, was proposed by Camion [2]. The second method, presented by Jensen [4], allows the application of the BCH bound or any of its improvements by viewing an abelian code as a direct sum of concatenations of cyclic codes. This second method avoids the mathematical analysis required for a direct generalization of a cyclic bound to the abelian case. It can produce a lower bound that improves the generalized BCH bound. We present simple algorithms for 1) deriving the generalized BCH bound for an abelian code 2) determining direct sum decompositions of an abelian code to concatenated codes and 3) deriving a bound on an abelian code, viewed as a direct sum of concatenated codes, by applying the cyclic BCH bound to the inner and outer code of each concatenation. Finally, we point out the applicability of these methods to codes that are not ideals in abelian group rings.     

Exponential and bayesian conjugate families: Review and extensions

Summary The notion of a conjugate family of distributions plays a very important role in the Bayesian approach to parametric inference. One of the main features of such a family is that it is closed under sampling, but a conjugate family often provides prior distributions which are tractable in various other respects. This paper is concerned with the properties of conjugate families for exponential family models. Special attention is given to the class of natural exponential families having a quadratic variance function, for which the theory is particularly fruitful. Several classes of conjugate families have been considered in the literature and here we describe some of their most interesting features. Relationships between such classes are also discussed. Our aim is to provide a unified approach to the theory of conjugate families for exponential family likelihoods. An important aspect of the theory concerns reparameterisations of the exponential family under consideration. We briefly review the concept of a conjugate parameterisation, which provides further insight into many of the properties discussed throughout the paper. Finally, further implications of these results for Bayesian conjugate analysis of exponential families are investigated. Research partially funded by ONR Grant N00014-96-1-0192 Research funded by NSF Grant DMS 94.04408 and Texas ARP Grant 003658130     

Shubnikov-de Haas and high-field magnetoresistance effects in the A15 compound Nb3Sb

High-field magnetoresistance and Shubnikov-de Haas (SdH) effects were studied in the A15 compound Nb₃Sb in fields up to 215 kG. A change in the field dependence of the magnetoresistance for certain field directions above about 150 kG appears to signal the onset of magnetic breakdown. Five sets of SdH frequencies were observed, four of them closely corresponding to de Haas-van Alphen (dHvA) frequencies observed by Arko et al. The fifth frequency had an extremely large amplitude, about 20% of the backgroud magnetoresistance, and it is suggested that this also is due to magnetic breakdown. The results are compared with the ab initio band calculations of van Kessel et al., which can explain many of the observed features of the dHvA and SdH frequencies.Research performed at the Francis Bitter National Magnet Laboratory at MIT, which is supported by the NSF. This work has been supported by NSF Grants DMR-7810781 and DMR-7916187 (DJS and DL), the U.S. Department of Energy (AJA), and NSF Grant DMR 77-08469 (ZF).     

The h-p version of the finite element method

The paper is the second in the series of two analyzing the h-p version of the finite element method. It generalizes the results of the first part (Guo, Babuska 1986) and presents computational results.Supported by the NSF Grant DMS-8315216Partially supported by ONR Contract N00014-85-K-0169     

Understanding rapid theoretical change in particle physics: A month-by-month co-citation analysis

While co-citation analysis nas proved a powerful tool in the study of changes in intellectual foci in science, the technique has never been used to study very rapid changes in the theoretical structure of a scientific field. In this paper we present month-by-month co-citation analyses of key phases in the weak-electromagnetic unification research program within particle physics and show that these analyses capture and illuminate very rapid intellectual changes. These data provide yet another illustration of the utility of co-citation analysis for understanding the history of science.An earlier version of this paper was published inInformation Choices and Policies (Knowledge Industries Publications, Inc., White Plains, N. Y.: 1979), Vol. 16, Proceedings of the 42nd Annual Meeting of the American Society for Information Science. Knowledge Industries and the ASIS have kindly given permission to us to seek a wider audience. This work was made possible by NSF Grant GS-41697 to the Research Program on Social Analyses of Science Systems (SASS), Cornell University, Ithaca, New York and NSF Grant SOC76-84482 to Carleton College, Northfield, Minnesota.     

Hydrodynamic stability of an evolving vortex ring in a counterflow

The time-dependent motion of a vortex ring obeying the Hall-Vinen equations in a superfluid He counterflow is shown to be locally stable. Both the real and imaginary parts of the normal modes of oscillation scale as wave number squared.Work supported in part by the National Science Foundation through the Cornell materials Science Center, Grant Number DMR-76-81083, MSC Report Number 4027, and by the NSF, Grant Number DMR-77-18329.     

Semiparametric censorship model with covariates

In real applications, we may be confronted with the problem of informative censoring. Koziol-Green model is commonly used to model the possible information contained in the informative censoring. However the proportionality assumption cast by Koziol-Green model (see (1.2) below) is “too restrictive in that it limits the scope of the Cox model in practice” (see Subramanian, 2000). In this paper, we try to relax the proportionality condition of Koziol-Green model by modeling the censorship semiparametrically. It is shown that our suggested semiparametric censoring model is an applicable extension of the Koziol-Green model. Through a close connection with the logistic regression, our model assumptions are readily to be checked in paractice. We also propose estimation for both the regression parameter and the cumulative baseline hazard function which can incorporate the additional information contained in the semiparametric censorship model. Simulations and the analysis of a real dataset confirm the applicability of the suggested model and estimation. This research is partially supported by NSF Grant DMS-0772292     

Properties of melting 3He: Specific heat,entropy, latent heat,and temperature

A sequence of experiments has been performed to measure thermal properties of liquid and solid ³ He between the temperatures 1 and 25 mK at melting curve densities. A two-phase mixture of ³ He sample was self-cooled by the Pomeranchuk method. A heat pulse technique was used, combined with measurements of pressure and volume, to yield separate determinations of liquid and solid properties: the specific heat of liquid ³ He in the normal Fermi liquid and superfluid phases; the entropy of solid ³ He above and through a nuclear magnetic transition at 1.10 mK; and an absolute thermodynamic temperature scale based on measurement of latent heat of conversion of liquid to solid.Support for this work was obtained from the Research Corporation, the NSF through Grant no. DMR 75-15933, and the Materials Science Center of Cornell University, Grant no. GH 33637. Also, the work was supported by travel grants from the NATO Science Fellowship Programme and the Danish Natural Science Research Council.Work performed while on leave from Phys. Lab. I, H. C. ørsted Institute, Universitetsparken, Copenhagen, Denmark.     

Evaluation codes at singular points of algebraic differential equations

We use the special geometry of singular points of algebraic differential equations on the affine plane over finite fields to study the main features and parameters of error correcting codes giving by evaluating functions at sets of singular points. In particular, one gets new methods to construct codes with designed minimum distance. This work was partially supported by MCyT BFM2001-2251.     

Hall conductivity of a moving magnetic-field-induced spin-density wave

The influence of the motion of a magnetic-field-induced spin-density-wave (FISDW) on the quantum Hall effect in a quasi-one-dimensional conductor is studied theoretically. In the ideal case, when the pinning and the damping of the FISDW can be neglected, it is found that the counterflow of the FISDW precisely cancels the quantum Hall current, so that the resultant Hall conductivity is zero. In real systems, the Hall conductivity should vanish at the high frequencies where the dynamics of the FISDW is dominated by inertia, and the pinning and the damping can be neglected.This work was partially supported by the NSF Grant No. DMR 89-06958.