Generalized Erdos Numbers for network analysis

In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic

Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture

Geometry of the tracks left by a bicycle is closely related with the so-called Prytz planimeter and with linear fractional transformations of the complex plane. We describe these relations, along with the history of the problem, and give a proof of a conjecture made by Menzin in 1906.Comment: 20 pages, 18 figure

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform

Bayesian inference of a negative quantity from positive measurement results

In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements. Results are used to estimate the atom density shift in a caesium fountain clock. The comparison with the classical statistical analysis is also reported and the advantages of the Bayesian approach for the realization of the time unit are discussed.Comment: 10 pages, 4 figures, submitted to Metrologi

Wildlife Records from Mail Carriers in April

608 mail carriers kept records of game birds seen during the week of April 21 - 26. This was the eighth time that mail carriers have cooperated on a statewide basis. April counts were omitted in 1946 but comparisons are made below of 1945 and 1947 data. The mail carriers\u27 work provides an inexpensive method of getting extensive statewide observations, and informational bulletins returned to the carriers are of definite value as a public relations step. (Many ot the carriers send in long letters, in addition to the card form, and in a number of instances they have reported information useful to the law enforcement division in following up local game law violations.

Toward A More Perfect Union: The Road To Marriage Equality For Same-Sex Couples

The Author believes that civil unions have become synonymous with inequality. In this posture, the term inequality should be descriptive rather than subjective. She argues that civil unions relegate gay and lesbian couples to second-class status. However characterized or defined, civil unions are not marriages. Those two statuses are not equivalent; they are not equal. Within that framework, in order for any one person to decide where he or she stands on the issue of whether gay and lesbian couples should be entitled to marriage, civil unions, something else, or nothing, he or she must first understand why marriage matters to families and how the Goodridge case and others fit into the civil rights struggle to create equality for gays and lesbians as well as into other civil rights struggles. Section II of this Article describes several examples of how the exclusion from marriage has harmed families, and, therefore, why it matters to people, gay and non-gay alike. Section III describes the history of marriage as it has evolved for same-sex couples and its relationship to other civil rights struggles. Section IV describes the Goodridge case, its outcome, and aftermath. Finally, Section V takes up the question of whether civil unions are a legitimate station on the way to marriage rights or a misguided departure in a struggle for equality and concludes that civil unions are an unacceptable alternative