Non Symmetric Dirichlet Forms on Semifinite von Neumann Algebras

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.Comment: 32 pages, plain TeX, Preprint Roma TOR VERGATA Nr.9-93-May 9

Exchange option pricing under stochastic volatility: a correlation expansion

Efficient valuation of exchange options with random volatilities while challenging at analytical level, has strong practical implications: in this paper we present a new approach to the problem which allows for extensions of previous known results. We undertake a route based on a multi-asset generalization of a methodology developed in Antonelli and Scarlatti (Finan Stoch 13:269–303, 2009) to handle simple European one-asset derivatives with volatility paths described by Ito’s diffusive equations. Our method seems to adapt rather smoothly to the evaluation of Exchange options involving correlations among all the financial quantities that specify the model and it is based on expanding and approximating the theoretical evaluation formula with respect to correlation parameters. It applies to a whole range of models and does not require any particular distributional property. In order to test the quality of our approximation numerical simulations are provided in the last part of the paper

Random Time Forward Starting Options

We introduce a natural generalization of the forward-starting options, first discussed by M. Rubinstein. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options {\bf Random Time Forward Starting (RTFS)}. We show that, under an appropriate "martingale preserving" hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence between the random time and the assets' prices. Practical implementations of the pricing methodologies are also provided. Finally a credit value adjustment formula for these OTC options is computed for the unilateral counterparty credit risk.Comment: 19 pages, 1 figur

Dispersive estimates for Schr\"odinger operators with point interactions in R3\mathbb{R}^3

The study of dispersive properties of Schr\"odinger operators with point interactions is a fundamental tool for understanding the behavior of many body quantum systems interacting with very short range potential, whose dynamics can be approximated by non linear Schr\"odinger equations with singular interactions. In this work we proved that, in the case of one point interaction in $\mathbb{R}^3$, the perturbed Laplacian satisfies the same $L^p-L^q$ estimates of the free Laplacian in the smaller regime $q\in[2,3)$. These estimates are implied by a recent result concerning the $L^p$ boundedness of the wave operators for the perturbed Laplacian. Our approach, however, is more direct and relatively simple, and could potentially be useful to prove optimal weighted estimates also in the regime $q\geq 3$.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201

HIV-1 with Multiple CCR5/CXCR4 Chimeric Receptor Use Is Predictive of Immunological Failure in Infected Children

BACKGROUND: HIV-1 R5 viruses are characterized by a large phenotypic variation, that is reflected by the mode of coreceptor use. The ability of R5 HIV-1 to infect target cells expressing chimeric receptors between CCR5 and CXCR4 (R5(broad) viruses), was shown to correlate with disease stage in HIV-1 infected adults. Here, we ask the question whether phenotypic variation of R5 viruses could play a role also in mother-to-child transmission (MTCT) of HIV-1 and pediatric disease progression. METHODOLOGY/PRINCIPAL FINDINGS: Viral isolates obtained from a total of 59 HIV-1 seropositive women (24 transmitting and 35 non transmitting) and 28 infected newborn children, were used to infect U87.CD4 cells expressing wild type or six different CCR5/CXCR4 chimeric receptors. HIV-1 isolates obtained from newborn infants had predominantly R5(narrow) phenotype (n = 20), but R5(broad) and R5X4 viruses were also found in seven and one case, respectively. The presence of R5(broad) and R5X4 phenotypes correlated significantly with a severe decline of the CD4+ T cells (CDC stage 3) or death within 2 years of age. Forty-three percent of the maternal R5 isolates displayed an R5(broad) phenotype, however, the presence of the R5(broad) virus was not predictive for MTCT of HIV-1. Of interest, while only 1 of 5 mothers with an R5X4 virus transmitted the dualtropic virus, 5 of 6 mothers carrying R5(broad) viruses transmitted viruses with a similar broad chimeric coreceptor usage. Thus, the maternal R5(broad) phenotype was largely preserved during transmission and could be predictive of the phenotype of the newborn's viral variant. CONCLUSIONS/SIGNIFICANCE: Our results show that R5(broad) viruses are not hampered in transmission. When transmitted, immunological failure occurs earlier than in children infected with HIV-1 of R5(narrow) phenotype. We believe that this finding is of utmost relevance for therapeutic interventions in pediatric HIV-1 infectio

2d frustrated Ising model with four phases

In this paper we consider a 2d random Ising system on a square lattice with nearest neighbour interactions. The disorder is short range correlated and asymmetry between the vertical and the horizontal direction is admitted. More precisely, the vertical bonds are supposed to be non random while the horizontal bonds alternate: one row of all non random horizontal bonds is followed by one row where they are independent dichotomic random variables. We solve the model using an approximate approach that replace the quenched average with an annealed average under the constraint that the number of frustrated plaquettes is keep fixed and equals that of the true system. The surprising fact is that for some choices of the parameters of the model there are three second order phase transitions separating four different phases: antiferromagnetic, glassy-like, ferromagnetic and paramagnetic.Comment: 17 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to Physical Review

Women for science and science for women: Gaps, challenges and opportunities towards optimizing pre-exposure prophylaxis for HIV-1 prevention

Preventing new HIV infections remains a global challenge. Young women continue to bear a disproportionate burden of infection. Oral pre-exposure prophylaxis (PrEP), offers a novel women-initiated prevention technology and PrEP trials completed to date underscore the importance of their inclusion early in trials evaluating new HIV PrEP technologies. Data from completed topical and systemic PrEP trials highlight the role of gender specific physiological and social factors that impact PrEP uptake, adherence and efficacy. Here we review the past and current developments of HIV-1 prevention options for women with special focus on PrEP considering the diverse factors that can impact PrEP efficacy. Furthermore, we highlight the importance of inclusion of female scientists, clinicians, and community advocates in scientific efforts to further improve HIV prevention strategies

HIV-1 co-receptor usage:influence on mother-to-child transmission and pediatric infection

Viral CCR5 usage is not a predictive marker of mother to child transmission (MTCT) of HIV-1. CXCR4-using viral variants are little represented in pregnant women, have an increased although not significant risk of transmission and can be eventually also detected in the neonates. Genetic polymorphisms are more frequently of relevance in the child than in the mother. However, specific tissues as the placenta or the intestine, which are involved in the prevalent routes of infection in MTCT, may play an important role of selective barriers