The replica location problem and Chebyshev polynomials of the second kind

We study the optimal placement of replicas of data objects in a connected network with the topology of a straight-line segment. This special case of a NP-complete location problem has a remarkably attractive algebraic solution. The minimum cost problem gives rise to tridiagonal matrices that are both persymmetric and symmetric and these are used to prove the symmetry of the optimal solution. The eigenvalues and eigenvectors of these matrices are completely described by Chebyshev polynomials of the second kind to give a complete solution to the replica location problem. We denote the kth Chebyshev polynomials of the second kind by Uk. The Chebyshev identity U2m+1 = 2(x-1) × ((U0 + U1)2 + (U1+U2)2+ ⋯ +(Um-1 + Um)2) + 2(x+m)arises naturally in examining the norms of the eigenvectors that occur

Functors whose domain is a category of morphisms

Connected sequences of functors whose domain, is the category of morphisms of an arbitrary abelian category A and whose range category B is also abelian are compared with the composition functors of Eckmann and Hilton acting between the same categories Sequences of functors of both types are obtained from any half-exact functor A→B if A has enough injectives and projectives

Monte Carlo Algorithms for the Detection of Necessary Linear Matrix Inequality Constraints

We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor

A generalization of certain homological functors

By a natural process of relativization groups Extn(A, φ), πn(A, φ) are defined in any abelian category with sufficient injectives and projectives. Functoriality in φ i spro. ved and excision properties are established; and the groups are shown to behave well under suspension. The technique involves an interplay of different mapping-cone construction

A probabilistic method for detecting multivariate extreme outliers

Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem

A simulation study of the passenger check-in system at the Ottawa international airport

This work presents a simulation study of the check-in system at the Ottawa International Airport. Various data were collected and used to define the inputs to a simulation model. These include the current agents' working schedules, the passengers' arrival pattern distributions, the passengers' service time distributions, the historical flight load factor, the distributions of the types of passengers, and the flight schedule. The scenarios evaluated include changing the queue structure and considering alternate agents' working schedules. The performance measurement retained are the average waiting time in queues, the maximum waiting time in queues, the average queue length, the maximum queue length, and the distribution of passengers waiting times in queues. A linear programming (LP) model was developed to provide alternate agent working schedules that minimizes the total agent person hours and meets the passenger loads that vary throughout the day. A heuristic was used to incorporate breaks and lunches. The critical factor that impacts the check-in service performance proved to be the agents' working schedule. Sensitivity analysis on changes of passenger loads and service rates were performed and the findings are discussed

Statistical analysis of barefoot impressions

Comparison of the shapes of barefoot impressions from an individual with footprints or shoes linked to a crime may be useful as a means of including or excluding that individual as possibly being at the scene of a crime. The question of the distinguishability of a person's bare-foot print arises frequently. This study indicates that measurements taken from the outlines of inked footprint impressions show a great degree of variability between donors and a great degree