Explicit asymptotic velocity of the boundary between particles and antiparticles

On the real line initially there are infinite number of particles on the positive half-line., each having one of $K$ negative velocities $v_{1}^{(+)},...,v_{K}^{(+)}$. Similarly, there are infinite number of antiparticles on the negative half-line, each having one of $L$ positive velocities $v_{1}^{(-)},...,v_{L}^{(-)}$. Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of $\beta(t)$ - the coordinate of the last collision before $t$ between particle and antiparticle.Comment: 25 page

Translation-covariant Markovian master equation for a test particle in a quantum fluid

A recently proposed master equation in the Lindblad form is studied with respect to covariance properties and existence of a stationary solution. The master equation describes the interaction of a test particle with a quantum fluid, the so-called Rayleigh gas, and is characterized by the appearance of a two-point correlation function known as dynamic structure factor, which reflects symmetry and statistical mechanics properties of the fluid. In the case of a free gas all relevant physical parameters, such as fugacity, ratio between the masses, momentum transfer and energy transfer are put into evidence, giving an exact expansion of the dynamic structure factor. The limit in which these quantities are small is then considered. In particular in the Brownian limit a Fokker-Planck equation is obtained in which the corrections due to quantum statistics can be explicitly evaluated and are given in terms of the Bose function $g_0 (z)$ and the Fermi function $f_0 (z)$.Comment: 18 pages, revtex, no figures, to appear in J. Math. Phy

A fully-discrete scheme for systems of nonlinear Fokker-Planck-Kolmogorov equations

We consider a system of Fokker-Planck-Kolmogorov (FPK) equations, where the dependence of the coefficients is nonlinear and nonlocal in time with respect to the unknowns. We extend the numerical scheme proposed and studied recently by the authors for a single FPK equation of this type. We analyse the convergence of the scheme and we study its applicability in two examples. The first one concerns a population model involving two interacting species and the second one concerns two populations Mean Field Games

IgG4-Related Hashimoto's Thyroiditis - A New Variant of a Well Known Disease

Hashimoto's thyroiditis (HT) has been characterized for many years as a well-defined clinicopathologic entity, but is now considered a heterogeneous disease. IgG4-related HT is a new subtype characterized by thyroid inflammation rich in IgG4-positive plasma cells and marked fibrosis. It may be part of the systemic IgG4-related disease. We report a case of a 56-year-old Portuguese man who presented with a one-month history of progressive neck swelling and dysphagia. Laboratory testing revealed increased inflammatory parameters, subclinical hypothyroidism and very high levels of thyroid autoantibodies. Cervical ultrasound (US) demonstrated an enlarged and heterogeneous thyroid gland and two hypoechoic nodules. US-guided fine needle aspiration cytology was consistent with lymphocytic thyroiditis. The patient was submitted to total thyroidectomy and microscopic examination identified typical findings of HT, marked fibrosis limited within the thyroid capsule and lymphoplasmacytic infiltration, with >50 IgG4-positive plasma cells per high-power field and an IgG4/IgG ratio of >40%. After surgery, serum IgG4 concentration was high-normal. Symptoms relief and reduction in laboratory inflammatory parameters were noticed. Thyroid function is controlled with levothyroxine. To our knowledge we report the first case of IgG4-related HT in a non-Asian patient. We also perform a review of the literature regarding IgG4-related disease and IgG4-related HT. Our case highlights this new variant of the well known HT, and helps physicians in recognizing its main clinical features, allowing for proper diagnosis and treatment

Serial MR diffusion to predict treatment response in high-grade pediatric brain tumors: a comparison of regional and voxel-based diffusion change metrics

Background Assessment of treatment response by measuring tumor size is known to be a late and potentially confounded response index. Serial diffusion MRI has shown potential for allowing earlier and possibly more reliable response assessment in adult patients, with limited experience in clinical settings and in pediatric brain cancer. We present a retrospective study of clinical MRI data in children with high-grade brain tumors to assess and compare the values of several diffusion change metrics to predict treatment response. Methods Eighteen patients (age range, 1.9–20.6 years) with high-grade brain tumors and serial diffusion MRI (pre- and posttreatment interval range, 1–16 weeks posttreatment) were identified after obtaining parental consent. The following diffusion change metrics were compared with the clinical response status assessed at 6 months: (1) regional change in absolute and normalized apparent diffusivity coefficient (ADC), (2) voxel-based fractional volume of increased (fiADC) and decreased ADC (fdADC), and (3) a new metric based on the slope of the first principal component of functional diffusion maps (fDM). Results Responders (n = 12) differed significantly from nonresponders (n = 6) in all 3 diffusional change metrics demonstrating higher regional ADC increase, larger fiADC, and steeper slopes (P < .05). The slope method allowed the best response prediction (P < .01, η2 = 0.78) with a classification accuracy of 83% for a slope of 58° using receiver operating characteristic (ROC) analysis. Conclusions We demonstrate that diffusion change metrics are suitable response predictors for high-grade pediatric tumors, even in the presence of variable clinical diffusion imaging protocols

Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs

While all media can exhibit first-order conductivity describing current linearly proportional to electric field, $E$, the second-order conductivity, $\sigma^{(2)}$ , relating current to $E^2$, is nonzero only when inversion symmetry is broken. Second order nonlinear optical responses are powerful tools in basic research, as probes of symmetry breaking, and in optical technology as the basis for generating currents from far-infrared to X-ray wavelengths. The recent surge of interest in Weyl semimetals with acentric crystal structures has led to the discovery of a host of $\sigma^{(2)}$ -related phenomena in this class of materials, such as polarization-selective conversion of light to dc current (photogalvanic effects) and the observation of giant second-harmonic generation (SHG) efficiency in TaAs at photon energy 1.5 eV. Here, we present measurements of the SHG spectrum of TaAs revealing that the response at 1.5 eV corresponds to the high-energy tail of a resonance at 0.7 eV, at which point the second harmonic conductivity is approximately 200 times larger than seen in the standard candle nonlinear crystal, GaAs. This remarkably large SHG response provokes the question of ultimate limits on $\sigma^{(2)}$ , which we address by a new theorem relating frequency-integrated nonlinear response functions to the third cumulant (or "skewness") of the polarization distribution function in the ground state. This theorem provides considerable insight into the factors that lead to the largest possible second-order nonlinear response, specifically showing that the spectral weight is unbounded and potentially divergent when the possibility of next-neighbor hopping is included.Comment: 7 pages, 4 figure

Metrics and textural features of MRI diffusion to improve classification of pediatric posterior fossa tumors

BACKGROUND AND PURPOSE: Qualitative radiologic MR imaging review affords limited differentiation among types of pediatric posterior fossa brain tumors and cannot detect histologic or molecular subtypes, which could help to stratify treatment. This study aimed to improve current posterior fossa discrimination of histologic tumor type by using support vector machine classifiers on quantitative MR imaging features. MATERIALS AND METHODS: This retrospective study included preoperative MRI in 40 children with posterior fossa tumors (17 medulloblastomas, 16 pilocytic astrocytomas, and 7 ependymomas). Shape, histogram, and textural features were computed from contrast-enhanced T2WI and T1WI and diffusivity (ADC) maps. Combinations of features were used to train tumor-type-specific classifiers for medulloblastoma, pilocytic astrocytoma, and ependymoma types in separation and as a joint posterior fossa classifier. A tumor-subtype classifier was also produced for classic medulloblastoma. The performance of different classifiers was assessed and compared by using randomly selected subsets of training and test data. RESULTS: ADC histogram features (25th and 75th percentiles and skewness) yielded the best classification of tumor type (on average >95.8% of medulloblastomas, >96.9% of pilocytic astrocytomas, and >94.3% of ependymomas by using 8 training samples). The resulting joint posterior fossa classifier correctly assigned >91.4% of the posterior fossa tumors. For subtype classification, 89.4% of classic medulloblastomas were correctly classified on the basis of ADC texture features extracted from the Gray-Level Co-Occurence Matrix. CONCLUSIONS: Support vector machine–based classifiers using ADC histogram features yielded very good discrimination among pediatric posterior fossa tumor types, and ADC textural features show promise for further subtype discrimination. These findings suggest an added diagnostic value of quantitative feature analysis of diffusion MR imaging in pediatric neuro-oncology