Quantum Theory and Galois Fields

We discuss the motivation and main results of a quantum theory over a Galois field (GFQT). The goal of the paper is to describe main ideas of GFQT in a simplest possible way and to give clear and simple arguments that GFQT is a more natural quantum theory than the standard one. The paper has been prepared as a presentation to the ICSSUR' 2005 conference (Besancon, France, May 2-6, 2005).Comment: Latex, 24 pages, 1 figur

On Tractable Exponential Sums

We consider the problem of evaluating certain exponential sums. These sums take the form $\sum_{x_1,...,x_n \in Z_N} e^{f(x_1,...,x_n) {2 \pi i / N}}$, where each x_i is summed over a ring Z_N, and f(x_1,...,x_n) is a multivariate polynomial with integer coefficients. We show that the sum can be evaluated in polynomial time in n and log N when f is a quadratic polynomial. This is true even when the factorization of N is unknown. Previously, this was known for a prime modulus N. On the other hand, for very specific families of polynomials of degree \ge 3, we show the problem is #P-hard, even for any fixed prime or prime power modulus. This leads to a complexity dichotomy theorem - a complete classification of each problem to be either computable in polynomial time or #P-hard - for a class of exponential sums. These sums arise in the classifications of graph homomorphisms and some other counting CSP type problems, and these results lead to complexity dichotomy theorems. For the polynomial-time algorithm, Gauss sums form the basic building blocks. For the hardness results, we prove group-theoretic necessary conditions for tractability. These tests imply that the problem is #P-hard for even very restricted families of simple cubic polynomials over fixed modulus N

Final State Charge Exchange Interactions in the 12C(e,e′p)^{12}C(e,e'p) Reaction

The $^{12}C(e,e'p)$ reaction is analyzed in a model which explicitly includes final state interactions due to the coupling of the proton and neutron emission channels. We find that the effects of the final state interactions due to charge exchange reactions are important to get a good description of the symmetry properties of the recently measured Mainz spectral functions. We discuss the possible role the off-shell effects may play for the correct interpretation of spectral functions at large positive missing momenta.Comment: 9 pages Revtex, 4 figure

Principles And Practices Fostering Inclusive Excellence: Lessons From The Howard Hughes Medical Institute’s Capstone Institutions

Best-practices pedagogy in science, technology, engineering, and mathematics (STEM) aims for inclusive excellence that fosters student persistence. This paper describes principles of inclusivity across 11 primarily undergraduate institutions designated as Capstone Awardees in Howard Hughes Medical Institute’s (HHMI) 2012 competition. The Capstones represent a range of institutional missions, student profiles, and geographical locations. Each successfully directed activities toward persistence of STEM students, especially those from traditionally underrepresented groups, through a set of common elements: mentoring programs to build community; research experiences to strengthen scientific skill/identity; attention to quantitative skills; and outreach/bridge programs to broaden the student pool. This paper grounds these program elements in learning theory, emphasizing their essential principles with examples of how they were implemented within institutional contexts. We also describe common assessment approaches that in many cases informed programming and created traction for stakeholder buy-in. The lessons learned from our shared experiences in pursuit of inclusive excellence, including the resources housed on our companion website, can inform others’ efforts to increase access to and persistence in STEM in higher education

On the multiplicativity of quantum cat maps

The quantum mechanical propagators of the linear automorphisms of the two-torus (cat maps) determine a projective unitary representation of the theta group, known as Weil's representation. We prove that there exists an appropriate choice of phases in the propagators that defines a proper representation of the theta group. We also give explicit formulae for the propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page

Sexual exploitation in children: Nature, prevalence and distinguishing characteristics reported in young adulthood

The aim of this study was to explore the nature and extent of sexual exploitation in a university student sample, whilst being clear that sexual exploitation is sexual abuse. Overall, 47% of participants (96 out of 204) reported having been approached by an adult in a sexual manner when they were under the age of 16. The study predicted that a number of individual characteristics would increase a young person’s vulnerability for sexual exploitation. These included low self-esteem, external locus of control, social loneliness and insecure attachment. Results indicated lower levels of self-esteem among those who had been approached sexually, although it is not clear in terms of causality. There were no differences in scores for locus of control or loneliness. Relationship anxiety was significantly linked with children having engaged in sexual behaviours with an adult. The implications of these findings are discussed in terms of emerging individual characteristics relating to a risk of sexual exploitation

The Interpersonal Style and Complementarity Between Crisis Negotiators and Forensic Inpatients

Previous negotiation research has explored the interaction and communication between crisis negotiators and perpetrators. A crisis negotiator attempts to resolve a critical incident through negotiation with an individual, or group of persons in crisis. The purpose of this study was to establish the interpersonal style of crisis negotiators and complementarity of the interpersonal interaction between them and forensic inpatients. Crisis negotiators, clinical workers and students (n = 90) used the Check List of Interpersonal Transactions-Revised (CLOIT-R) to identify interpersonal style, along with eight vignettes detailing interpersonal styles. Crisis negotiators were most likely to have a friendly interpersonal style compared to the other non-trained groups. Complementarity theory was not exclusively supported as submissive individuals did not show optimistic judgments in working with dominant forensic inpatients and vice versa. Exploratory analysis revealed that dominant crisis negotiators were optimistic in working with forensic inpatients with a dominant interpersonal style. This study provides insight into the area of interpersonal complementarity of crisis negotiators and forensic inpatients. Whilst further research is required, a potential new finding was established, with significant ‘similarity’ found when dominant crisis negotiators are asked to work with dominant forensic inpatients

Bisabolane type sesquiterpenes from a marine Didiscus sponge

Two bisabolane type sesquiterpene phenols, (+)-curcuphenol (1) and (+)-curcudiol (2), were isolated from a Philippine marine sponge, Didiscus sp., in addition to b -sitosterol (3) and phenethylamine (4). The structures of the metabolites were established on the basis of spectral evidence (1D- and 2D NMR, [a]D, EIMS). (+)-Curcuphenol (1) showed cytotoxicity, which is indicative of a p53 independent mechanism