Random matrix ensembles for PTPT-symmetric systems

Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and split-quaternionic versions of Hermitian matrices. We introduce two new random matrix ensembles of (a) Gaussian split-complex Hermitian, and (b) Gaussian split-quaternionic Hermitian matrices, of arbitrary sizes. They are related to the split signature versions of the complex and the quaternionic numbers, respectively. We conjecture that these ensembles represent universality classes for $PT$-symmetric matrices. For the case of $2\times2$ matrices we derive analytic expressions for the joint probability distributions of the eigenvalues, the one-level densities and the level spacings in the case of real eigenvalues.Comment: 9 pages, 3 figures, typos corrected, small changes, accepted for publication in Journal of Physics

Towards More Efficient Enhanced Sampling Methods To Study Phase Transitions

The most familiar phase transitions observed in nature are associated with a change in the state of matter (solid, liquid, and gas). In some rare cases this may involve the plasma phase. Such transitions are often referred to as first order phase transitions and often occur commonly such as during the melting of snow or freezing of lakes and rivers during winter. This project focuses on the most ubiquitous phase changes such as, liquid-solid and vapor-liquid as well as the less prevalent vapor-solid transitions. These types of phase transitions are also known as classical phase transitions. They usually involve symmetry breaking and can be identified by a singularity in the free energy or one of its derivatives. More modern classification of phase transitions relies on the order parameters as exemplified by the Landau\u27s theory. An order parameter is a quantity that takes a value of zero in the disordered phase and assumes finite values in the ordered phase. In the case of liquid-vapor transition, the order parameter is the density. The study of phase transitions is often complicated by the amount of time required by these phase changes and the presence of a high free energy barrier. Consequently, changes occurring close to coexistence are hard or even impossible to follow via conventional experimental techniques. Molecular simulation is therefore the method of choice to study these processes. Molecular simulations are numerical experiments carried out on model systems and have a number of advantages over traditional experiments. Simulations do not have any limitation as to the type of molecules or conditions under which they can be applied. Current simulation methods used to accomplish this task, such as the grand canonical and Gibbs ensemble Monte Carlo methods, employ the concept of particles insertion and deletion moves or requires the knowledge of at least one point at coexistence. These types of moves are extremely inefficient when dense fluids are involved and limit the accuracy of these methods. To circumvent these difficulties, non-Boltzmann sampling methods such as the umbrella sampling and Wang-Landau sampling techniques, have been employed to study these phase transitions. Vapor-solid and liquid-solid phase transitions were studied using a combination of hybrid Monte Carlo (HMC) and the umbrella sampling on a system of C60 molecules. The crystallization process occurs in two steps, nucleation and growth. The nucleation step is an activated process that involves a high free energy barrier. The free energy barrier is overcome through a series of HMC steps. The growth step on the other hand is studied by means of unconstrained molecular dynamics (MD). This study illustrates that the body centered cubic structure plays no role in the crystallization of C60. This is because only the face centered cubic and the hexagonal closed parked crystal structures were observed in both the nucleation and growth steps. In addition, the growth process is observed to follow a complex mechanism known as cross nucleation. The process of cross nucleation has also been observed in model fluids such as Lennard-Jones fluid and in the experimental study of D-mannitol. Hybrid Monte Carlo and configurational bias Monte Carlo (CBMC) were combined with the Wang-Landau (WL) sample method to study the vapor-liquid equilibria of Polycyclic aromatic hydrocarbons (PAHs) with four fused benzene rings and &alpha-olefins (C2 - C6 respectively. These studies are conducted in the isothermal-isobaric (NPT) ensemble to avoid the particle insertion and deletion moves that resulted in low acceptance rates in previous simulations. These studies led to the prediction of the critical temperatures, pressures and densities of both systems

An Analysis of Congressman Bennie Thompson’s Leadership in Advancing Equality and Democracy in America

This article analyzes Congressman Bennie Thompson’s leadership role in the fight for equality and justice for all Americans and his fight to maintain and sustain the democracy experiment in America. The analysis examines the political trajectory of the subject in question, casting light on their initial engagement and underlying motivations. Additionally, this article examines the strategies and initiatives utilized by Thompson. This study aims to assess the impact of Thompson’s leadership on advancing equity and democracy in the United States by thoroughly analyzing his policies, legislative achievements, and public advocacy. Finally, it looks at Thompson’s political career, casting light on the efficacy and significance of his efforts to advance a society characterized by justice and democracy

Two Years after the Fourth External Review: TDR Moves Forward with a New Vision and Strategy

summary:In the paper it is proved that a nontrivial direct product of lattice ordered groups is never affine complete

Clinical studies on seroprevalence of rubella virus in pregnant women of Cameroon regions.

A study was conducted to investigate the seroprevalence of the rubella virus amongst pregnant women and the relationship it has with the duration of pregnancy, premature delivery, and past history of abortion in pregnant women visiting the Yaoundé Gynecological, Obstetric and Pediatric Hospital (HGOPY). 211 pregnant women attending the prenatal consultation of mean age 27±5.99 years were randomly selected and screened for rubella IgG antibodies. 39.3% of them were in their third trimester of pregnancy while 25.6% and 35.1% were in their first and second trimester of pregnancy respectively. 11.73% of the women had a history of premature delivery and 40.3% had a history of at least one abortion. Spearman's correlation was calculated between antibody titre and age. 88.6% of pregnant women were seropositive while 9% (susceptible) were seronagative and 2.4% had equivocal results. The most susceptible women to rubella infection were in the age group 26-30 years while women in the age group 21-25 years band were the most seropositive. There was a strong correlation between the antibody titre and age (r=0.549

Se réconcilier avec son passé grâce à sa langue et affirmer son identité multiculturelle sur le plan international par les productions de sa langue : l’engagement et l’expérience de la Fondation AfricAvenir International et des Editions AfricAvenir depuis 1985

Résumé : Mon cher Tadadjeu, Me voici sur le sol de tes ancêtres, venu célébrer les fruits de tes efforts infatigables, le résultat de ton engagement sans faille, pendant tant de décennies, au Cameroun, en Afrique, dans le monde. Nos chemins se croisaient souvent, et nous marchions alors ensemble, aussi avec Neville Alexander, à qui je voudrais aussi rendre un hommage solennel. Ne me demandez pas de l’appeler Maurice, son nom du blanc, qui n’est pas son vrai nom. Mon cher Tadadjeu, je te parle en français, dans le sillon de ton trilinguisme intensif, mais un jour, un des miens viendra ici, à l’Université de Dschang, t’invoquer en langue duala, pendant que les traducteurs en yemba transmettront aux académiciens ici réunis le message envoyé depuis les profondeurs des eaux du Wouri. Ce jour-là, nous pourrons alors dire que nous sommes enfin sortis du génocide intellectuel et spirituel dans lequel nos peuples ont été engloutis depuis bientôt six siècles. Nous parler en nos langues, sans intermédiaire, sans interférence linguistique de l’Europe coloniale ou postcoloniale. Là, nous aurons commencé à nous parler vraiment, à transmettre les codes secrets africains qui ont besoin de nos langues pour s’enraciner et féconder profondément

Reference Values of CD4-Lymphocyte Counts in HIV Seronegative Pregnant Women in Buea, Cameroon

Pregnancy is a physiologically immunocompromised state, during which alterations in T-lymphocyte subsets may occur. Reference values for CD4 counts in pregnancy have not been established particularly in sub-Saharan populations. This study aimed at describing expected (‘normal’) values of CD4 counts in healthy HIV-negative pregnant women so these could serve as reference for assessing the progress of HIV disease in HIV-infected pregnant women. The study was conducted in antenatal clinics in the Buea Health District, Cameroon. All eligible women were interviewed using a standardized questionnaire. Whole blood samples collected were tested for HIV using Determine 1/2 and SD Bioline HIV-1/2 3.0 rapid tests. The CD4+ absolute counts were assessed using the Partec Cyflow Counter and the CD4 easy count kit. A total of 279 women were analysed. Their ages ranged from 15 to 47 years. A vast majority (95%) of participants were in the second or third trimester of gestation. Slightly less than half (43%) were primiparous. The CD4 cell count ranged from 321 to 1808 cells/μl . This distribution was approximately normal with a mean of 851cells/μl, a median of 831cells/μl , and a standard deviation of 254cells/μl . The expected (‘normal’) range, covering 95% of the sample was 438-1532 cells/μl. Participants with malaria parasitaemia tended to have a lower CD4 count (lower on average by 115 cells/μl,