From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using ``Feynman brackets.'' We show that Poincar\'e's magnetic angular momentum and Dirac magnetic monopole are the consequences of the structure of the Lorentz Lie algebra defined by the Feynman's brackets. Then, we extend these ideas to the dual momentum space by considering noncommutative quantum mechanics. In this context, we show that the noncommutativity of the coordinates is responsible for a new effect called the spin Hall effect. We also show its relation with the Berry phase notion. As a practical application, we found an unusual spin-orbit contribution of a nonrelativistic particle that could be experimentally tested. Another practical application is the Berry phase effect on the propagation of light in inhomogeneous media.Comment: Presented at the 3rd Feynman Festival (Collage Park, Maryland, U.S.A., August 2006

Tilted Euler characteristic densities for Central Limit random fields, with application to "bubbles"

Local increases in the mean of a random field are detected (conservatively) by thresholding a field of test statistics at a level $u$ chosen to control the tail probability or $p$-value of its maximum. This $p$-value is approximated by the expected Euler characteristic (EC) of the excursion set of the test statistic field above $u$, denoted $\mathbb{E}\varphi(A_u)$. Under isotropy, one can use the expansion $\mathbb{E}\varphi(A_u)=\sum_k\mathcal{V}_k\rho_k(u)$, where $\mathcal{V}_k$ is an intrinsic volume of the parameter space and $\rho_k$ is an EC density of the field. EC densities are available for a number of processes, mainly those constructed from (multivariate) Gaussian fields via smooth functions. Using saddlepoint methods, we derive an expansion for $\rho_k(u)$ for fields which are only approximately Gaussian, but for which higher-order cumulants are available. We focus on linear combinations of $n$ independent non-Gaussian fields, whence a Central Limit theorem is in force. The threshold $u$ is allowed to grow with the sample size $n$, in which case our expression has a smaller relative asymptotic error than the Gaussian EC density. Several illustrative examples including an application to "bubbles" data accompany the theory.Comment: Published in at http://dx.doi.org/10.1214/07-AOS549 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Appearance of Gauge Fields and Forces beyond the adiabatic approximation

We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix valued quantum Hamiltonians. The results are illustrated by several physical relevant examples

Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution

A generalized Peierls substitution which takes into account a Berry phase term must be considered for the semiclassical treatment of electrons in a magnetic field. This substitution turns out to be an essential element for the correct determination of the semiclassical equations of motion as well as for the semiclassical Bohr-Sommerfeld quantization condition for energy levels. A general expression for the cross-sectional area is derived and used as an illustration for the calculation of the energy levels of Bloch and Dirac electrons

Affinity and dose of TCR engagement yield proportional enhancer and gene activity in CD4+ T cells.

Affinity and dose of T cell receptor (TCR) interaction with antigens govern the magnitude of CD4+ T cell responses, but questions remain regarding the quantitative translation of TCR engagement into downstream signals. We find that while the response of mouse CD4+ T cells to antigenic stimulation is bimodal, activated cells exhibit analog responses proportional to signal strength. Gene expression output reflects TCR signal strength, providing a signature of T cell activation. Expression changes rely on a pre-established enhancer landscape and quantitative acetylation at AP-1 binding sites. Finally, we show that graded expression of activation genes depends on ERK pathway activation, suggesting that an ERK-AP-1 axis plays an important role in translating TCR signal strength into proportional activation of enhancers and genes essential for T cell function

Designed binary mixtures for subcritical organic Rankine cycles based on multiobjective optimization

The use of binary zeotropic mixtures as working fluids applied to Organic Rankine Cycles (ORCs) is investigated in this paper. In total, six (6) hydrocarbons and (2) hydrofluorocarbons are considered, leading to twenty-eight (28) possible binary combinations. The mixtures were tested with a basic Rankine cycle while using the heat source temperature as independent variable, which assumed six different values, ranging from 80 °C to 180 °C, in steps of 20 °C. The simulations aimed to identify the ideal mixtures that maximized the net power and exergetic efficiency, and minimized the heat exchanger’s global conductance for a given temperature of the heat source. The optimization process relied on a genetic algorithm and the selection of the best mixtures, on a non-dominated sorting method (NDS), which returned Pareto fronts gathering the best solutions. While no one specific ideal mixture was identified, the results showed that the range of the so-called ideal mixtures narrows as the heat source temperature increases, with mixtures including fluids like R245fa and pentane being good options, whereas at low temperature, a larger number of fluid mixtures perform well. Finally, a scale analysis is proposed and shows that the maximal net power varies linearly with a Number of Transfer Units (NTU) factor while its slope depends on the heat source temperature. The latter analysis is compared with the results obtained with the Pareto front and NDS, showing that both sets of results agree well while correlated by a single constant for the entire temperature range covered in the present study

Addressing the Fertility Needs of HIV-Seropositive Males

An increasing number of serodiscordant couples are utilizing advanced reproductive technologies to address their reproductive needs. Recent literature has demonstrated that it is not only technically possible but also safe to utilize sperm-washing techniques to allow for the creation of embryos, thereby preventing both horizontal and vertical transmission of HIV. This article addresses the strengths and weakness of various reproductive techniques and discusses our experience at Columbia University (NY, USA), the location of the largest HIV-focused fertility program in the USA

Diagnostic Value of Lingual Tonsillectomy in Unknown Primary Head and Neck Carcinoma Identification After a Negative Clinical Workup and Positron Emission Tomography-Computed Tomography

Objective: Diagnostic rates of unknown primary head and neck carcinoma (UPHNC) using lingual tonsillectomy (LT) are highly variable. This study sought to determine the diagnostic value of LT in UPHNC identification using strict inclusion criteria and definitions to produce a more accurate estimate of diagnosis rate. Methods: In this retrospective chart review, records of patients who underwent LT for UPHNC were reviewed. Inclusion criteria included absence of suspicious findings on physical exam and positron emission tomography-computed tomography as well as negative biopsies after panendoscopy and palatine tonsillectomy. Following inclusion criteria, 16 patients were reviewed. A systematic literature review on LT for the workup of CUP was also performed. Results: LT was performed using transoral robotic surgery (TORS), transoral laser microsurgery (TLM), or transoral microsurgery with cautery (TMC). Following LT, primary tumor was identified in 4 patients out of 16. Detection rate by technique was 1/6, 2/7, and 1/3 for TORS, TLM, and TMC respectively. Postoperative bleeding occurred in three patients (19%); however, this was not related to the LT. Following literature review, 12 studies were identified; however, only 3 had enough data to compare against. All three studies had a cohort with suspicious findings on clinical exam. A total of 34 patients had a negative workup, with no suspicious findings on clinical exam and subsequently received an LT. Conclusion: This study suggests that LT should be considered initially in the diagnostic algorithm for UPHNC. This study can increase the patient size in this cohort by approximately 47%