Noise-Induced Stabilization of Planar Flows I

We show that the complex-valued ODE \begin{equation*} \dot z_t = a_{n+1} z^{n+1} + a_n z^n+\cdots+a_0, \end{equation*} which necessarily has trajectories along which the dynamics blows up in finite time, can be stabilized by the addition of an arbitrarily small elliptic, additive Brownian stochastic term. We also show that the stochastic perturbation has a unique invariant measure which is heavy-tailed yet is uniformly, exponentially attracting. The methods turn on the construction of Lyapunov functions. The techniques used in the construction are general and can likely be used in other settings where a Lyapunov function is needed. This is a two-part paper. This paper, Part I, focuses on general Lyapunov methods as applied to a special, simplified version of the problem. Part II of this paper extends the main results to the general setting.Comment: Part one of a two part pape

A Door in the Illinois Brick Wall - A Functional Equivalent to the Cost-Plus Contract Exception

In Mid-West Paper Products Co. v. Continental Group, Inc., I the Third Circuit took the position that it would not extend the exception beyond the limited circumstances recognized by the Supreme Court. Accordingly, the court held that the use of passing-on theory is impermissible unless its proponent can show preexisting, fixed-quantity, cost-plus contracts at every level of the distribution chain, with the result that he absorbed the illegal overcharge in its entirety. In In re Beef Industry Antitrust Litigation, however, the Fifth Circuit declared that if the exception is confined to cases involving literal cost-plus contracts, then it is a narrow one indeed. Rejecting such a rigid construction, the court held that the exception is also applicable when allegations of rigid formula pricing by middlemen and structural in elasticity of short term supplies compel recognition of a functional equivalent of the cost-plus contract.\u27 This Recent Development examines the conflict between the circuits in light of the principles underlying the Hanover Shoe--Illinois Brick rule to determine the feasibility and implications of recognizing a functional equivalent to the cost-plus exception

Assessment of ambient assisted living systems for patients with mild cognitive impairment

According to the World Health Organization, about 50 million people worldwide suffer from dementia. Ten million new cases added every year. Mild Cognitive Impairment (MCI) affects more than 15% of the population aged 65. Technological solutions, such as smart home technology with ubiquitous computing devices, 24/7 telemedical observation and support can alleviate the growing problem and lower pressure on the healthcare system. This approach is also preferable for homecare patients in distant and rural areas. MCI patients are mostly home-based. Ambient Assisted Living (AAL) systems provide tools for automatic registration of vital signs and other medically and socially important information. AAL system for MCI patients is a logical answer to the problem. At the same time, many of the proposed AAL systems are proprietary, technically complicated and have a high price tag for implementation and service. Also, some proposed technical solutions not entirely reflect the opinion of healthcare stakeholders. The current study was proposed as a way to bridge the possible differences in the positions. An online anonymous questionnaire for healthcare professionals was created to prove or disprove the number of interconnected hypotheses about the necessity and feasibility of AAL system for MCI patients. The main focus was made on the hypotheses: "There is necessity of AAL systems for the healthcare" and "AAL systems are capable of providing assistance for patients with Mild Cognitive Impairment". The questionnaire was presented to more than three hundred potential respondents. Around a hundred and twenty agreed to fill it, and sixty completed the whole questionnaire. Results were analyzed to produce some directions guideline for future technical applications of AAL systems for MCI patients and future research. Descriptive statistics show support for the implementation of general AAL and variants for MCI patients. Comparative analysis of ordinal data for specific groups of respondents is done with help of non-parametric tests. Mann–Whitney–Wilcoxon test and Kruskal-Wallis test are applied. Table questions results are analyzed with chisquare for frequency tables. Group analysis demonstrated relative positive uniformity in of responses in the support of AAL of MCI patients.Segundo a Organização Mundial da Saúde, cerca de 50 milhões de pessoas em todo o mundo sofrem de demência. Dez milhões de novos casos adicionados a cada ano. O comprometimento cognitivo leve (MCI) afeta mais de 15% da população com 65 anos. Soluções tecnológicas, como tecnologia de casa inteligente com dispositivos de computação onipresentes, observação e suporte telemédico 24 horas por dia, 7 dias por semana, podem aliviar o problema crescente e diminuir a pressão sobre o sistema de saúde. Essa abordagem também é preferível para pacientes de cuidados domiciliares em áreas distantes e rurais. Os pacientes com CCL são, em sua maioria, domiciliares. Os sistemas Ambient Assisted Living (AAL) fornecem ferramentas para registro automático de sinais vitais e outras informações médicas e socialmente importantes. O sistema AAL para pacientes com MCI é uma resposta lógica para o problema. Ao mesmo tempo, muitos dos sistemas AAL propostos são proprietários, tecnicamente complicados e têm um alto preço para implementação e serviço. Além disso, algumas soluções técnicas propostas não refletem inteiramente a opinião das partes interessadas na área da saúde. O presente estudo foi proposto como forma de colmatar as possíveis diferenças nas posições. Um questionário anônimo online para profissionais de saúde foi criado para comprovar ou refutar o número de hipóteses interligadas sobre a necessidade e viabilidade do sistema AAL para pacientes com CCL. O foco principal foi feito nas hipóteses: "Há necessidade de sistemas de AAL para a saúde" e "Os sistemas de AAL são capazes de prestar assistência a pacientes com Comprometimento Cognitivo Leve". O questionário foi apresentado a mais de trezentos respondentes potenciais. Cerca de cento e vinte concordaram em preenchê-lo e sessenta preencheram todo o questionário. Os resultados foram analisados para produzir algumas diretrizes para futuras aplicações técnicas de sistemas AAL para pacientes com MCI e pesquisas futuras. Estatísticas descritivas mostram suporte para a implementação de AAL geral e variantes para pacientes com CCL. A análise comparativa de dados ordinais para grupos específicos de respondentes é feita com a ajuda de testes não paramétricos. Aplicam-se os testes de Mann-Whitney-Wilcoxon e Kruskal-Wallis. Os resultados das questões da tabela são analisados com qui-quadrado para tabelas de frequência. A análise do grupo demonstrou relativa uniformidade positiva nas respostas no suporte de AAL de pacientes com CCL.Selon l'Organisation mondiale de la santé, environ 50 millions de personnes dans le monde souffrent de démence. Dix millions de nouveaux cas ajoutés chaque année. Les troubles cognitifs légers (MCI) touchent plus de 15 % de la population âgée de 65 ans. Les solutions technologiques, telles que la technologie de la maison intelligente avec des appareils informatiques omniprésents, l'observation et le soutien télémédicaux 24 heures sur 24, 7 jours sur 7, peuvent atténuer le problème croissant et réduire la pression sur le système de santé. Cette approche est également préférable pour les patients en soins à domicile dans les régions éloignées et rurales. Les patients MCI sont pour la plupart à domicile. Les systèmes Ambient Assisted Living (AAL) fournissent des outils pour l'enregistrement automatique des signes vitaux et d'autres informations importantes sur le plan médical et social. Le système AAL pour les patients MCI est une réponse logique au problème. Dans le même temps, bon nombre des systèmes AAL proposés sont propriétaires, techniquement compliqués et ont un prix élevé pour la mise en oeuvre et le service. De plus, certaines solutions techniques proposées ne reflètent pas entièrement l'opinion des acteurs de santé. L'étude actuelle a été proposée comme un moyen de combler les différences possible dans les positions. Un questionnaire anonyme en ligne destiné aux professionnels de la santé a été créé pour prouver ou réfuter le nombre d'hypothèses interconnectées sur la nécessité et la faisabilité du système AAL pour les patients MCI. L'accent a été mis principalement sur les hypothèses: "Il existe une nécessité de systèmes AAL pour les soins de santé" et "Les systèmes AAL sont capables de fournir une assistance aux patients atteints de troubles cognitifs légers". Le questionnaire a été présenté à plus de trois cents répondants potentiels. Environ cent vingt ont accepté de le remplir, et soixante ont rempli tout le questionnaire. Les résultats ont été analysés pour produire des lignes directrices pour les futures applications techniques des systèmes AAL pour les patients MCI et l'avenir de la recherche. Les statistiques descriptives montrent un soutien à la mise en oeuvre de l'AAL général et des variantes pour les patients MCI. L'analyse comparative des données ordinales pour des groupes spécifiques de répondants est effectuée à l'aide de tests non paramétriques. Le test de Mann-Whitney-Wilcoxon et le test de Kruskal-Wallis sont appliqués. Les résultats des questions de tableau sont analysés avec le chi carré pour les tableaux de fréquence. L'analyse de groupe a démontré une uniformité positive relative dans les réponses à l'appui de l'AAL des patients MCI

Finite groups with almost distinct character degrees

AbstractFinite groups with the nonlinear irreducible characters of distinct degrees, were classified by the authors and Berkovich. These groups are clearly of even order. In groups of odd order, every irreducible character degree occurs at least twice. In this article we classify finite nonperfect groups G, such that χ(1)=θ(1) if and only if θ=χ¯ for any nonlinear χ≠θ∈Irr(G). We also present a description of finite groups in which xG′⊆class(x)∪class(x−1) for every x∈G−G′. These groups generalize the Frobenius groups with an abelian complement, and their description is needed for the proof of the above mentioned result on characters