Stokes-vector evolution in a weakly anisotropic inhomogeneous medium

Equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of quasi-isotropic approximation of the geometrical optics method, which provides consequent asymptotic solution of Maxwell equations. Our equation generalizes previous results, obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable to describe normal modes conversion in the inhomogeneous media. Remarkably, evolution of the Stokes vector is described by the Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau-Lifshitz equation for spin precession in ferromegnetic systems. General theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.Comment: 16 pages, 3 figures, to appear in J. Opt. Soc. Am.

Current Fluctuations of the One Dimensional Symmetric Simple Exclusion Process with Step Initial Condition

For the symmetric simple exclusion process on an infinite line, we calculate exactly the fluctuations of the integrated current $Q_t$ during time $t$ through the origin when, in the initial condition, the sites are occupied with density $\rho_a$ on the negative axis and with density $\rho_b$ on the positive axis. All the cumulants of $Q_t$ grow like $\sqrt{t}$. In the range where $Q_t \sim \sqrt{t}$, the decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is non-Gaussian. Our results are obtained using the Bethe ansatz and several identities recently derived by Tracy and Widom for exclusion processes on the infinite line.Comment: 2 figure

Comparison of intraoperative radiotherapy as a boost vs. simultaneously integrated boosts after breast-conserving therapy for breast cancer

BackgroundCurrently, there are no data from randomized trials on the use of intraoperative radiotherapy (IORT) as a tumor bed boost in women at high risk of local recurrence. The aim of this retrospective analysis was to compare the toxicity and oncological outcome of IORT or simultaneous integrated boost (SIB) with conventional external beam radiotherapy (WBI) after breast conserving surgery (BCS).MethodsBetween 2009 and 2019, patients were treated with a single dose of 20 Gy IORT with 50 kV photons, followed by WBI 50 Gy in 25 or 40.05 in 15 fractions or WBI 50 Gy with SIB up to 58.80–61.60 Gy in 25–28 fractions. Toxicity was compared after propensity score matching. Overall survival (OS) and progression-free survival (PFS) were calculated using the Kaplan–Meier method.ResultsA 1:1 propensity-score matching resulted in an IORT + WBI and SIB + WBI cohort of 60 patients, respectively. The median follow-up for IORT + WBI was 43.5 vs. 32 months in the SIB + WBI cohort. Most women had a pT1c tumor: IORT group 33 (55%) vs. 31 (51.7%) SIB group (p = 0.972). The luminal-B immunophenotype was most frequently diagnosed in the IORT group 43 (71.6%) vs. 35 (58.3%) in the SIB group (p = 0.283). The most reported acute adverse event in both groups was radiodermatitis. In the IORT cohort, radiodermatitis was grade 1: 23 (38.3%), grade 2: 26 (43.3%), and grade 3: 6 (10%) vs. SIB cohort grade 1: 3 (5.1%), grade 2: 21 (35%), and grade 3: 7 (11.6%) without a meaningful difference (p = 0.309). Fatigue occurred more frequently in the IORT group (grade 1: 21.7% vs. 6.7%; p = 0.041). In addition, intramammary lymphedema grade 1 occurred significantly more often in the IORT group (11.7% vs. 1.7%; p = 0.026). Both groups showed comparable late toxicity. The 3- and 5-year local control (LC) rates were each 98% in the SIB group vs. 98% and 93% in the IORT group (LS: log rank p = 0.717).ConclusionTumor bed boost using IORT and SIB techniques after BCS shows excellent local control and comparable late toxicity, while IORT application exhibits a moderate increase in acute toxicity. These data should be validated by the expected publication of the prospective randomized TARGIT-B study

Conditional Intensity and Gibbsianness of Determinantal Point Processes

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $(\Sigma_{\lambda})$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.Comment: revised and extende

Infrared problem for the Nelson model on static space-times

We consider the Nelson model with variable coefficients and investigate the problem of existence of a ground state and the removal of the ultraviolet cutoff. Nelson models with variable coefficients arise when one replaces in the usual Nelson model the flat Minkowski metric by a static metric, allowing also the boson mass to depend on position. A physical example is obtained by quantizing the Klein-Gordon equation on a static space-time coupled with a non-relativistic particle. We investigate the existence of a ground state of the Hamiltonian in the presence of the infrared problem, i.e. assuming that the boson mass tends to 0 at infinity

Natural boundaries for the Smoluchowski equation and affiliated diffusion processes

The Schr\"{o}dinger problem of deducing the microscopic dynamics from the input-output statistics data is known to admit a solution in terms of Markov diffusions. The uniqueness of solution is found linked to the natural boundaries respected by the underlying random motion. By choosing a reference Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential and the field of local accelerations it induces. We generate the family of affiliated diffusions with the same local dynamics, but different inaccessible boundaries on finite, semi-infinite and infinite domains. For each diffusion process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet boundary data) Wiener path integration.As a by-product of the discussion, we give an overview of the problem of inaccessible boundaries for the diffusion and bring together (sometimes viewed from unexpected angles) results which are little known, and dispersed in publications from scarcely communicating areas of mathematics and physics.Comment: Latex file, Phys. Rev. E 49, 3815-3824, (1994

The maximum standardized uptake value in patients with recurrent or persistent prostate cancer after radical prostatectomy and PSMA-PET-guided salvage radiotherapy-a multicenter retrospective analysis

Purpose This study aims to evaluate the association of the maximum standardized uptake value (SUVmax) in positron-emission tomography targeting prostate-specific membrane antigen (PSMA-PET) prior to salvage radiotherapy (sRT) on biochemical recurrence free survival (BRFS) in a large multicenter cohort.Methods Patients who underwent (68) Ga-PSMA11-PET prior to sRT were enrolled in four high-volume centers in this retrospective multicenter study. Only patients with PET-positive local recurrence (LR) and/or nodal recurrence (NR) within the pelvis were included. Patients were treated with intensity-modulated-sRT to the prostatic fossa and elective lymphatics in case of nodal disease. Dose escalation was delivered to PET-positive LR and NR. Androgen deprivation therapy was administered at the discretion of the treating physician. LR and NR were manually delineated and SUVmax was extracted for LR and NR. Cox-regression was performed to analyze the impact of clinical parameters and the SUVmax-derived values on BRFS.Results Two hundred thirty-five patients with a median follow-up (FU) of 24 months were included in the final cohort. Two-year and 4-year BRFS for all patients were 68% and 56%. The presence of LR was associated with favorable BRFS (p = 0.016). Presence of NR was associated with unfavorable BRFS (p = 0.007). While there was a trend for SUVmax values >= median (p = 0.071), SUVmax values >= 75% quartile in LR were significantly associated with unfavorable BRFS (p = 0.022, HR: 2.1, 95%CI 1.1-4.6). SUVmax value in NR was not significantly associated with BRFS. SUVmax in LR stayed significant in multivariate analysis (p = 0.030). Sensitivity analysis with patients for who had a FU of > 12 months (n = 197) confirmed these results.Conclusion The non-invasive biomarker SUVmax can prognosticate outcome in patients undergoing sRT and recurrence confined to the prostatic fossa in PSMA-PET. Its addition might contribute to improve risk stratification of patients with recurrent PCa and to guide personalized treatment decisions in terms of treatment intensification or de-intensification. This article is part of the Topical Collection on Oncology-Genitourinary

PSMA-PET/CT-guided salvage radiotherapy in recurrent or persistent prostate cancer and PSA < 0.2 ng/ml.

PURPOSE The purpose of this retrospective, multicenter study was to assess efficacy of PSMA-PET/CT-guided salvage radiotherapy (sRT) in patients with recurrent or persistent PSA after primary surgery and PSA levels < 0.2 ng/ml. METHODS The study included patients from a pooled cohort (n = 1223) of 11 centers from 6 countries. Patients with PSA levels > 0.2 ng/ml prior to sRT or without sRT to the prostatic fossa were excluded. The primary study endpoint was biochemical recurrence-free survival (BRFS) and BR was defined as PSA nadir after sRT + 0.2 ng/ml. Cox regression analysis was performed to assess the impact of clinical parameters on BRFS. Recurrence patterns after sRT were analyzed. RESULTS The final cohort consisted of 273 patients; 78/273 (28.6%) and 48/273 (17.6%) patients had local or nodal recurrence on PET/CT. The most frequently applied sRT dose to the prostatic fossa was 66-70 Gy (n = 143/273, 52.4%). SRT to pelvic lymphatics was delivered in 87/273 (31.9%) patients and androgen deprivation therapy was given to 36/273 (13.2%) patients. After a median follow-up time of 31.1 months (IQR: 20-44), 60/273 (22%) patients had biochemical recurrence. The 2- and 3-year BRFS was 90.1% and 79.2%, respectively. The presence of seminal vesicle invasion in surgery (p = 0.019) and local recurrences in PET/CT (p = 0.039) had a significant impact on BR in multivariate analysis. In 16 patients, information on recurrence patterns on PSMA-PET/CT after sRT was available and one had recurrent disease inside the RT field. CONCLUSION This multicenter analysis suggests that implementation of PSMA-PET/CT imaging for sRT guidance might be of benefit for patients with very low PSA levels after surgery due to promising BRFS rates and a low number of relapses within the sRT field

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

The prognostic significance of a negative PSMA-PET scan prior to salvage radiotherapy following radical prostatectomy.

AIM The optimal management for early recurrent prostate cancer following radical prostatectomy (RP) in patients with negative prostate-specific membrane antigen positron-emission tomography (PSMA-PET) scan is an ongoing subject of debate. The aim of this study was to evaluate the outcome of salvage radiotherapy (SRT) in patients with biochemical recurrence with negative PSMA PET finding. METHODS This retrospective, multicenter (11 centers, 5 countries) analysis included patients who underwent SRT following biochemical recurrence (BR) of PC after RP without evidence of disease on PSMA-PET staging. Biochemical recurrence-free survival (bRFS), metastatic-free survival (MFS) and overall survival (OS) were assessed using Kaplan-Meier method. Multivariable Cox proportional hazards regression assessed predefined predictors of survival outcomes. RESULTS Three hundred patients were included, 253 (84.3%) received SRT to the prostate bed only, 46 (15.3%) additional elective pelvic nodal irradiation, respectively. Only 41 patients (13.7%) received concomitant androgen deprivation therapy (ADT). Median follow-up after SRT was 33 months (IQR: 20-46 months). Three-year bRFS, MFS, and OS following SRT were 73.9%, 87.8%, and 99.1%, respectively. Three-year bRFS was 77.5% and 48.3% for patients with PSA levels before PSMA-PET ≤ 0.5 ng/ml and > 0.5 ng/ml, respectively. Using univariate analysis, the International Society of Urological Pathology (ISUP) grade > 2 (p = 0.006), metastatic pelvic lymph nodes at surgery (p = 0.032), seminal vesicle involvement (p 0.5 ng/ml (p = 0.004), and lack of concomitant ADT (p = 0.023) were significantly associated with worse bRFS. On multivariate Cox proportional hazards, seminal vesicle infiltration (p = 0.007), ISUP score >2 (p = 0.048), and pre SRT PSA level > 0.5 ng/ml (p = 0.013) remained significantly associated with worse bRFS. CONCLUSION Favorable bRFS after SRT in patients with BR and negative PSMA-PET following RP was achieved. These data support the usage of early SRT for patients with negative PSMA-PET findings