Permanental Vectors

A permanental vector is a generalization of a vector with components that are squares of the components of a Gaussian vector, in the sense that the matrix that appears in the Laplace transform of the vector of Gaussian squares is not required to be either symmetric or positive definite. In addition the power of the determinant in the Laplace transform of the vector of Gaussian squares, which is -1/2, is allowed to be any number less than zero. It was not at all clear what vectors are permanental vectors. In this paper we characterize all permanental vectors in $R^{3}_{+}$ and give applications to permanental vectors in $R^{n}_{+}$ and to the study of permanental processes

Dynamic response of a spin-1/2 Kondo singlet

We present a study of spin 1/2 Kondo singlets in single electron transistors under a microwave frequency bias excitation. We compare time-averaged conductance $G$ to predicted universal response with respect to microwave frequency, oscillation amplitude and the Kondo temperature and find a non-adiabatic response when the microwave photon energy $hf$ is comparable to the Kondo temperature $k_B T_K$. We show that our measurements are qualitatively consistent with the predictions for the radiation-induced decoherence rate of the Kondo spin

Fixation for coarsening dynamics in 2D slabs

For the zero temperature limit of Ising Glauber Dynamics on 2D slabs the existence or nonexistence of vertices that do not fixate is determined as a function of slab thickness.Comment: 16 pages, 9 figure

Opening the Covenant: A Jewish Theology of Christianity

The Center for Catholic Studies and the Carl and Dorothy Bennett Center for Judaic Studies present the Sixth Annual Lecture in Jewish-Christian Engagement… featuring Dr. Michael S. Kogan, Professor of Religion, Montclair State University.https://digitalcommons.fairfield.edu/bennettcenter-posters/1299/thumbnail.jp

HIV-1 Accessory Protein Vpr: Relevance in the pathogenesis of HIV and potential for therapeutic intervention

The HIV protein, Vpr, is a multifunctional accessory protein critical for efficient viral infection of target CD4+ T cells and macrophages. Vpr is incorporated into virions and functions to transport the preintegration complex into the nucleus where the process of viral integration into the host genome is completed. This action is particularly important in macrophages, which as a result of their terminal differentiation and non-proliferative status, would be otherwise more refractory to HIV infection. Vpr has several other critical functions including activation of HIV-1 LTR transcription, cell-cycle arrest due to DCAF-1 binding, and both direct and indirect contributions to T-cell dysfunction. The interactions of Vpr with molecular pathways in the context of macrophages, on the other hand, support accumulation of a persistent reservoir of HIV infection in cells of the myeloid lineage. The role of Vpr in the virus life cycle, as well as its effects on immune cells, appears to play an important role in the immune pathogenesis of AIDS and the development of HIV induced end-organ disease. In view of the pivotal functions of Vpr in virus infection, replication, and persistence of infection, this protein represents an attractive target for therapeutic intervention

Operator Product Expansion in Logarithmic Conformal Field Theory

In logarithmic conformal field theory, primary fields come together with logarithmic partner fields on which the stress-energy tensor acts non-diagonally. Exploiting this fact and global conformal invariance of two- and three-point functions, operator product expansions of logarithmic operators in arbitrary rank logarithmic conformal field theory are investigated. Since the precise relationship between logarithmic operators and their primary partners is not yet sufficiently understood in all cases, the derivation of operator product expansion formulae is only possible under certain assumptions. The easiest cases are studied in this paper: firstly, where operator product expansions of two primaries only contain primary fields, secondly, where the primary fields are pre-logarithmic operators. Some comments on generalization towards more relaxed assumptions are made, in particular towards the case where logarithmic fields are not quasi-primary. We identify an algebraic structure generated by the zero modes of the fields, which proves useful in determining settings in which our approach can be successfully applied.Comment: 30+1 pages LaTeX2e. Version to be published. Major rework and extensio

Permanental processes

This is a survey of results about permanental processes, real valued positive processes which are a generalization of squares of Gaussian processes. In a certain sense the symmetric positive definite function that determines a Gaussian process is replaced by a function that is not necessarily symmetric nor positive definite, but that nevertheless determines a stochastic process. This is a new avenue of research with very many open problems.Comment: 31 page