Level density and level-spacing distributions of random, self-adjoint, non-Hermitian matrices

We investigate the level-density $\sigma(x)$ and level-spacing distribution $p(s)$ of random matrices $M=AF\neq M^{\dagger}$ where $F$ is a (diagonal) inner-product and $A$ is a random, real symmetric or complex Hermitian matrix with independent entries drawn from a probability distribution $q(x)$ with zero mean and finite higher moments. Although not Hermitian, the matrix $M$ is self-adjoint with respect to $F$ and thus has purely real eigenvalues. We find that the level density $\sigma_F(x)$ is independent of the underlying distribution $q(x)$, is solely characterized by $F$, and therefore generalizes Wigner's semicircle distribution $\sigma_W(x)$. We find that the level-spacing distributions $p(s)$ are independent of $q(x)$, are dependent upon the inner-product $F$ and whether $A$ is real or complex, and therefore generalize the Wigner's surmise for level spacing. Our results suggest $F$-dependent generalizations of the well-known Gaussian Orthogonal Ensemble (GOE) and Gaussian Unitary Ensemble (GUE) classes.Comment: 5 pages, 5 figures, revised tex

Marshall Space Flight Center Faculty Fellowship Program

The research projects conducted by the 2016 Faculty Fellows at NASA Marshall Space Flight Center included propulsion studies on propellant issues, and materials investigations involving plasma effects and friction stir welding. Spacecraft Systems research was conducted on wireless systems and 3D printing of avionics. Vehicle Systems studies were performed on controllers and spacecraft instruments. The Science and Technology group investigated additive construction applied to Mars and Lunar regolith, medical uses of 3D printing, and unique instrumentation, while the Test Laboratory measured pressure vessel leakage and crack growth rates

The unity and diversity of executive functions: A systematic review and re-analysis of latent variable studies.

Confirmatory factor analysis (CFA) has been frequently applied to executive function measurement since first used to identify a three-factor model of inhibition, updating, and shifting; however, subsequent CFAs have supported inconsistent models across the life span, ranging from unidimensional to nested-factor models (i.e., bifactor without inhibition). This systematic review summarized CFAs on performance-based tests of executive functions and reanalyzed summary data to identify best-fitting models. Eligible CFAs involved 46 samples (N = 9,756). The most frequently accepted models varied by age (i.e., preschool = one/two-factor; school-age = three-factor; adolescent/adult = three/nested-factor; older adult = two/three-factor), and most often included updating/working memory, inhibition, and shifting factors. A bootstrap reanalysis simulated 5,000 samples from 21 correlation matrices (11 child/adolescent; 10 adult) from studies including the three most common factors, fitting seven competing models. Model results were summarized as the mean percent accepted (i.e., average rate at which models converged and met fit thresholds: CFI ≥ .90/RMSEA ≤ .08) and mean percent selected (i.e., average rate at which a model showed superior fit to other models: ΔCFI ≥ .005/.010/ΔRMSEA ≤ -.010/-.015). No model consistently converged and met fit criteria in all samples. Among adult samples, the nested-factor was accepted (41-42%) and selected (8-30%) most often. Among child/adolescent samples, the unidimensional model was accepted (32-36%) and selected (21-53%) most often, with some support for two-factor models without a differentiated shifting factor. Results show some evidence for greater unidimensionality of executive function among child/adolescent samples and both unity and diversity among adult samples. However, low rates of model acceptance/selection suggest possible bias toward the publication of well-fitting but potentially nonreplicable models with underpowered samples. (PsycINFO Database Record (c) 2018 APA, all rights reserved)

Numerical approach to the Schrodinger equation in momentum space

The treatment of the time-independent Schrodinger equation in real-space is an indispensable part of introductory quantum mechanics. In contrast, the Schrodinger equation in momentum space is an integral equation that is not readily amenable to an analytical solution and is rarely taught. We present a numerical approach to the Schrodinger equation in momentum space. After a suitable discretization process, we obtain the Hamiltonian matrix and diagonalize it numerically. By considering a few examples, we show that this approach is ideal for exploring bound-states in a localized potential and complements the traditional (analytical or numerical) treatment of the Schrodinger equation in real-space.Comment: 14 pages, 4 figures, several changes and one figure correctio

Static Safety for an Actor Dedicated Process Calculus by Abstract Interpretation

The actor model eases the definition of concurrent programs with non uniform behaviors. Static analysis of such a model was previously done in a data-flow oriented way, with type systems. This approach was based on constraint set resolution and was not able to deal with precise properties for communications of behaviors. We present here a new approach, control-flow oriented, based on the abstract interpretation framework, able to deal with communication of behaviors. Within our new analyses, we are able to verify most of the previous properties we observed as well as new ones, principally based on occurrence counting

The effect of salts on the viscosity and wilt-inducing capacity of the capsular polysaccharide of Erwinia amylovora

Water solutions of the capsular polysaccharide (EPS) of Erwinia amylovora exhibit long flow times (t) in a kinematic viscometer. Addition of salts to the solutions greatly decreases the flow times. The salt-induced decrease in flow time is directly related to the ionic strength of the solution and independent of the ionic species present. The salt effect does not result from a change in the molecular weight of the EPS. Addition of NaCl, at concentrations sufficient to reduce the flow time, decreases or eliminates the capacity of EPS solution to cause wilt in the cut shoot assay. Treatment of EPS with either of two depolymerase phages decreases both t and the molecular weight of the EPS (from 100 × 106 D to less than 4 × 104 D). Such phage-produced fragments (ψdp) retain their capacity to cause wilt in the cut shoot assay but, like EPS, lose this ability in the presence of salts. Radiolabeled EPS and ψdp is retained at the end of the cut shoot when wilt occurs but is distributed throughout the shoot when wilt is inhibited by salt

A second order cone formulation of continuous CTA model

The final publication is available at link.springer.comIn this paper we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using l1 or l2 norm; with each measure having its advantages and disadvantages. Recently, in [4] a regularization of the l1 -CTA using Pseudo-Huber func- tion was introduced in an attempt to combine positive characteristics of both l1 -CTA and l2 -CTA. All three models can be solved using appro- priate versions of Interior-Point Methods (IPM). It is known that IPM in general works better on well structured problems such as conic op- timization problems, thus, reformulation of these CTA models as conic optimization problem may be advantageous. We present reformulation of Pseudo-Huber-CTA, and l1 -CTA as Second-Order Cone (SOC) op- timization problems and test the validity of the approach on the small example of two-dimensional tabular data set.Peer ReviewedPostprint (author's final draft

Candidate Coronagraphic Detections of Protoplanetary Disks around Four Young Stars

We present potential detections of H-band scattered light emission around four young star, selected from a total sample of 45 young stars observed with the CIAO coronagraph of the Subaru telescope. Two CTTS, CI Tau and DI Cep, and two WTTS, LkCa 14 and RXJ 0338.3+1020 were detected. In all four cases, the extended emission is within the area of the residual PSF halo, and is revealed only through careful data reduction. We compare the observed extended emission with simulations of the scattered light emission, to evaluate the plausibility and nature of the detected emission.Comment: 9 Figures, 40 page

Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes