Local rigidity for actions of Kazhdan groups on non commutative LpL_p-spaces

Given a discrete group $\Gamma$, a finite factor $\mathcal N$ and a real number $p\in [1, +\infty)$ with $p\neq 2,$ we are concerned with the rigidity of actions of $\Gamma$ by linear isometries on the $L_p$-spaces $L_p(\mathcal N)$ associated to $\mathcal N$. More precisely, we show that, when $\Gamma$ and $\mathcal N$ have both Property (T) and under some natural ergodicity condition, such an action $\pi$ is locally rigid in the group $G$ of linear isometries of $L_p(\mathcal N)$, that is, every sufficiently small perturbation of $\pi$ is conjugate to $\pi$ under $G$. As a consequence, when $\Gamma$ is an ICC Kazhdan group, the action of $\Gamma$ on its von Neumann algebra ${\mathcal N}(\Gamma)$, given by conjugation, is locally rigid in the isometry group of $L_p({\mathcal N}(\Gamma)).$Comment: 20 page

Алгоритм определения оптимального числа волокон используемых при внутритканевой фотодинамической терапии рака молочной железы на основании диффузионного уравнения

It is essential in interstitial Photodynamic therapy (iPDT) treatment planning to ensure a homogeneous distribution within a tumor volume using cylindrical diffusing fibers while keeping the surrounding tissue intact. Light distribution is simulated through two algorithms based on the diffusion equation assuming diffusers as light sources. The first algorithm analyzes the diffusion equation and studies the effects of different variables (optical properties, delivered power, diffuser length, and position). Next, optical properties of breast were applied to estimate the volume that receives accepted light dose from one diffuser. In the second algorithm, multiple diffusers were simulated in order to find the relation between the volume and the number of required diffusers which are needed to cover cubical or cylindrical volume with sufficient light dose. Throughout this study, real values of optical properties, clinical laser power, and treatment time were considered to evaluate sufficient light doses. This study is in agreement with previous works in that optical properties are the major factors influencing light distribution in iPDT. It is shown that for a homogeneous phantom mimicking breast cancer and cubical or cylindrical shape, the number of required fibers N equal W×L or D2 respectively.При планировании внутритканевой фотодинамической терапии (iPDT ) с использованием цилиндрических диффузных волокон важно обеспечить однородное распределение света по всему объему опухоли, сохранив при этом целостность окружающей ткани. Авторы данной статьи смоделировали распределение света с помощью двух алгоритмов, основанных на уравнении диффузии, в которых в качестве источников света используются цилиндрические диффузоры. Первый алгоритм анализирует уравнение диффузии и изучает влияние различных переменных (оптических свойств источника, применяемой мощности, длины диффузора и его положения). Затем были использованы параметры оптических свойств молочной железы для оценки объема, который рассчитывает световую дозу от одного диффузора. Во втором алгоритме было смоделировано несколько рассеивателей для нахожде ния соотношения между объемом и количеством рассеивателей, необходимых для покрытия кубического или цилиндрического объема достаточной световой дозой. На протяжении всего этого исследования рассматривались реальные значения оптических свойств, клинической мощности лазера и времени лечения для оценки достаточных световых доз. Это исследование согласуется с предыдущими работами в том, что оптические свойства являются основными факторами, влияющими на распределение света при iPDT. Показано, что, для однородного фантома, имитирующего рак молочной железы, кубической или цилиндрической формы, количество требуемых волокон N равно W×L или D2 , соответственно

Effets des graines torréfiées de Vigna unguiculata (niébé) comme source de protéines, dans l’alimentation des poules locales en ponte au Burkina Faso, sur leurs performances zootechniques et la rentabilité économique des régimes

L’étude avait pour but d’évaluer les effets de l’incorporation des graines torréfiées de niébé dans l’alimentation de la poule locale en ponte, sur ses performances zootechniques et économique. Six coqs et soixante poules de race locale de 7,5 mois d’âge ont été répartis en six lots, par tirage aléatoire. Deux régimes alimentaires aux mêmes contraintes nutritionnelles dont un témoin et un régime expérimental comportant 8% de graines torréfiées de niébé ont été préparés. La ponte, les caractéristiques des oeufs, les consommations et les mortalités sont suivies hebdomadairement pendant 24 semaines. L’éclosion des oeufs a été suivie durant 03 semaines. La marge brute induite par chaque régime a été évaluée à la fin de l’essai. Au terme de l’étude, les taux de ponte, d’éclosions et l’indice de consommation ont été respectivement de 30,52%, 58,70% et 8,37% pour le régime expérimental, contre 29,67%, 53,81% et 8,52% pour le témoin. Les marges brutes ont été de 4807,82 FCFA pour le régime expérimental et de 4818,89 FCFA pour le témoin. Cependant, aucune différence significative n’est observée entre les paramètres mesurés (P>0,05). Ceci suggère que les graines torréfiées de niébé peuvent être incorporées dans l’alimentation des poules locales en ponte, comme source de protéines.Mots clés : Poule locale en ponte, graines de Vigna unguiculata, source de protéines, performances zootechniques, rentabilité économique

Les métastases ovariennes d’origine biliaire: 2 cas avec revue de la littérature

Les ovaires constituent un site fréquent de métastases. L'origine gastrique prédomine. Les métastases ovariennes d'origine biliaire sont rarement rapportées dans la littérature. Les auteurs rapportent deux cas de   métastases ovariennes d'origine vésiculaire chez des patientes âgées respectivement de 63 et 40 ans. Le diagnostic de ces métastases ovariennes était concomitant avec le cancer d'origine dans le premier cas, et a survenu à distance de l'atteinte initiale dans le deuxième cas. Le diagnostic est suggéré sur les données radiologiques et confirmé histologiquement. Les métastases ovariennes d'origine biliaire sont rarement rapportées dans la littérature. L'atteinte ovarienne pose un problème de diagnostic différentiel avec une atteinte ovarienne primitive surtout si l'atteinte ovarienne précède les manifestations biliaires. L'imagerie joue un rôle important et oriente sur le caractère secondaire de l'atteinte ovarienne

Skull metastasis of hepatocellular carcinoma in normal liver: Case report

Background: So far hepatocellular carcinoma (HCC) is the most common liver malignant tumour; it is rarely encountered on a healthy liver (9). The metastasis from HCC cancer are seen in lymph nodes (16%–40%) and lungs (34%–70%), (1,3,4,5,7,8), bone metastasis is unusual and some locations stay rare among them the skull (2,4,5). We report here a case of a patient operated in our department for skull metastasis. That patient was followed for hepatocellular carcinoma in digestive surgery department. Case presentation: The patient is a 57 years old male presenting HCC on healthy liver, the patient was referred to our department by digestive surgery colleagues to manage a parietal subcutaneous mass; brain CT scans were performed objectified a calvarial osteolytic process. We remove the tumour and we put a cranioplasty using surgical cement, later the histological studies were in favour of secondary location of hepatocellular carcinoma. Conclusion: Skull metastasis from hepatocellular carcinoma is rare, reporting such cases strengthen the idea of evoking HCC metastasis in the differential diagnosis of cranial subcutaneous mass

Electromagnetic corrections in the anomaly sector

Chiral perturbation theory in the anomaly sector for $N_f=2$ is extended to include dynamical photons, thereby allowing a complete treatment of isospin breaking. A minimal set of independent chiral lagrangian terms is determined and the divergence structure is worked out. There are contributions from irreducible and also from reducible one-loop graphs, a feature of ChPT at order larger than four. The generating functional is non-anomalous at order $e^2p^4$, but not necessarily at higher order in $e^2$. Practical applications to $\gamma\pi\to\pi\pi$ and to the $\pi^0\to2\gamma$ amplitudes are considered. In the latter case, a complete discussion of the corrections beyond current algebra is presented including quark mass as well as electromagnetic effects.Comment: 26 pages, 3 figure

A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications

International audienceWe state a kinetic formulation of weak entropy solutions of a general multidimensional scalar conservation law with initial and boundary conditions. We first associate with any weak entropy solution a entropy defect measure; the analysis of this measure at the boundary of the domain relies on the study of weak entropy sub and supersolutions and implies the introduction of the notion of sided boundary defect measures. As a first application, we prove that any weak entropy subsolution of the initial-boundary value problem is bounded above by any weak entropy supersolution (Comparison Theorem). We next study a BGK-like kinetic model that approximates the scalar conservation law. We prove that such a model converges by adapting the proof of the Comparison Theorem

Predictive Modeling of Breast Cancer Diagnosis Using Neural Networks:A Kaggle Dataset Analysis

Breast cancer remains a significant health concern worldwide, necessitating the development of effective diagnostic tools. In this study, we employ a neural network-based approach to analyze the Wisconsin Breast Cancer dataset, sourced from Kaggle, comprising 570 samples and 30 features. Our proposed model features six layers (1 input, 1 hidden, 1 output), and through rigorous training and validation, we achieve a remarkable accuracy rate of 99.57% and an average error of 0.000170 as shown in the image below. Furthermore, our investigation identifies the most influential features in breast cancer diagnosis, shedding light on the key determinants of malignancy. Notably, we find that factors such as fractal dimension_se, symmetry worst, compactness_worst, symmetry_se, and smoothness_se play pivotal roles in distinguishing between benign and malignant cases. This research contributes to the ongoing efforts to enhance breast cancer diagnosis, providing valuable insights into feature importance and showcasing the potential of neural networks in medical applications. Our findings have implications for improving early detection and treatment strategies, ultimately contributing to improved patient outcomes