Supersymmetric Yang-Mills quantum mechanics in various dimensions

Recent analytical and numerical solutions of the above systems are reviewed. Discussed results include: a) exact construction of the supersymmetric vacua in two space-time dimensions, and b) precise numerical calculations of the coexisting continuous and discrete spectra in the four-dimensional system, together with the identification of dynamical supermultiplets and SUSY vacua. New construction of the gluinoless SO(9) singlet state, which is vastly different from the empty state, in the ten-dimensional model is also briefly summarized.Comment: Talk presented at the Eighth Workshop on Non-Perturbative QCD, Paris, June 2004; 8 pages, 4 figure

Zeta Functions on Kronecker Products of Graphs

Ihara introduced the zeta function of a p-adic matrix group in 1966 and the idea was generalized to finite graphs by Hashimoto in 1989. In her dissertation, Debra Czarneski explores the properties of graphs that are or are not determined by the zeta function. This paper defines a Kronecker product of finite graphs and explores th

A simple proof of Kaijser's unique ergodicity result for hidden Markov α\alpha-chains

According to a 1975 result of T. Kaijser, if some nonvanishing product of hidden Markov model (HMM) stepping matrices is subrectangular, and the underlying chain is aperiodic, the corresponding $\alpha$-chain has a unique invariant limiting measure $\lambda$. Here the $\alpha$-chain $\{\alpha_n\}=\{(\alpha_{ni})\}$ is given by $$\alpha_{ni}=P(X_n=i| Y_n,Y_{n-1},...),$$ where $\{(X_n,Y_n)\}$ is a finite state HMM with unobserved Markov chain component $\{X_n\}$ and observed output component $\{Y_n\}$. This defines $\{\alpha_n\}$ as a stochastic process taking values in the probability simplex. It is not hard to see that $\{\alpha_n\}$ is itself a Markov chain. The stepping matrices $M(y)=(M(y)_{ij})$ give the probability that $(X_n,Y_n)=(j,y)$, conditional on $X_{n-1}=i$. A matrix is said to be subrectangular if the locations of its nonzero entries forms a cartesian product of a set of row indices and a set of column indices. Kaijser's result is based on an application of the Furstenberg--Kesten theory to the random matrix products $M(Y_1)M(Y_2)... M(Y_n)$. In this paper we prove a slightly stronger form of Kaijser's theorem with a simpler argument, exploiting the theory of e chains.Comment: Published at http://dx.doi.org/10.1214/105051606000000367 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Maternal glucose and fatty acid kinetics and infant birth weight in obese women with type 2 diabetes

The objectives of this study were 1) to describe maternal glucose and lipid kinetics and 2) to examine the relationships with infant birth weight in obese women with pregestational type 2 diabetes during late pregnancy. Using stable isotope tracer methodology and mass spectrometry, maternal glucose and lipid kinetic rates during the basal condition were compared in three groups: lean women without diabetes (Lean, n = 25), obese women without diabetes (OB, n = 26), and obese women with pregestational type 2 diabetes (OB+DM, n = 28; total n = 79). Glucose and lipid kinetics during hyperinsulinemia were also measured in a subset of participants (n = 56). Relationships between maternal glucose and lipid kinetics during both conditions and infant birth weight were examined. Maternal endogenous glucose production (EGP) rate was higher in OB+DM than OB and Lean during hyperinsulinemia. Maternal insulin value at 50% palmitate R(a) suppression (IC50) for palmitate suppression with insulinemia was higher in OB+DM than OB and Lean. Maternal EGP per unit insulin and plasma free fatty acid concentration during hyperinsulinemia most strongly predicted infant birth weight. Our findings suggest maternal fatty acid and glucose kinetics are altered during late pregnancy and might suggest a mechanism for higher birth weight in obese women with pregestational diabetes

Comparison of Selected Thought Processes Used by Three- and Five-Year-Old Children

Family Relations and Child Developmen