Signed graphs for portfolio analysis in risk management

We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable.     

On isomorphic factorizations of circulant graphs

We investigate the conjecture that every circulant graph X admits a k‐isofactorization for every k dividing |E(X)|. We obtain partial results with an emphasis on small values of k. © 2006 Wiley Periodicals, Inc. J Combin Designs 14: 406–414, 2006     

Supersymmetry,vacuum statistics,and the fundamental theorem of algebra

I give an interpretation of the fundamental theorem of algebra based on supersymmetry and the Witten index. The argument gives a physical explanation of why a real polynomial of degreen need not haven real zeroes, while a complex polynomial of degreen must haven complex zeroes. This paper also addresses in a general and model-independent way the statistics of the perturbative ground states (the states which correspond to classical vacua) in supersymmetric theories with complex and with real superfields.     

Information recovery from black holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss. First Award in the 2006 Essay Competition of the Gravity Research Foundation.     

Critical branching in a highly fluctuating random medium

Summary A model of one-dimensional critical branching (superprocess) is constructed in a random medium fluctuating both in time and space. The medium describes a moving system of point catalysts, and branching occurs only in the presence of these catalysts. Although the medium has an infinite overall density, the clumping features of the branching model can be exhibited by rescaling time, space, and mass by an exactly calculated scaling power which is stronger than in the constant medium case. The main technique used is the asymptotic analysis of a generalized diffusion-reaction equation in the space-time random medium, which (given the medium) prescribes the evolution of the Laplace transition functional of the Markov branching process.     

A generalization of Connor's inequality to t-designs with automorphisms

In this paper the incidence algebra for t-designs with automorphisms and the fundamental theorem discovered in [4] are exploited to obtain a generalization of Connor's inequality.     

A simple approximation for the vibrational partition function of a hindered internal rotation

A simple formula is presented for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule. The formula gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.     

The evolution of the viscoelastic retardation spectrum during the development of an epoxy resin network

The evolution of the viscoelastic behavior of an epoxy resin at various stages of curing has been followed with the changes in the retardation spectrum. The creep J(t) and recoverable creep compliance J_r(t) curves of the neat epoxy resin Epon l00lF (Shell) were determined at temperatures between 30 and 77°C. The viscosity decreased over 8 orders of magnitude as the temperature was increased. Specimens with eight stages of network development were prepared by reacting all of the epoxy resin's oxirane rings with amine hydrogens from varying ratios of a monofunctional amine (methyl aniline) and a tetrafunctional amine 4,4′-diamino diphenyl sulfone (DDS). Preparations in which 25, 35, and 40% DDS were used did not result in a molecular network, so they were viscoelastic liquids. With 45% DDS, the product had a nascent network and was judged to be just beyond the point of incipient gelation. The remaining preparations from 0.50, 0.60, 0.70, and 1.0 DDS yielded tighter less compliant molecular networks. The creep and recoverable compliance curves were measured over a range of temperatures above the glass transition temperature, T_g. They were reduced to T_g, and retardation spectra L(ln τ) were calculated.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.