Quantum Sign Permutation Polytopes

Convex polytopes are convex hulls of point sets in the $n$-dimensional space \E^n that generalize 2-dimensional convex polygons and 3-dimensional convex polyhedra. We concentrate on the class of $n$-dimensional polytopes in \E^n called sign permutation polytopes. We characterize sign permutation polytopes before relating their construction to constructions over the space of quantum density matrices. Finally, we consider the problem of state identification and show how sign permutation polytopes may be useful in addressing issues of robustness

The escape problem under stochastic volatility: the Heston model

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure

2D pattern evolution constrained by complex network dynamics

Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies of such networks are being revealed and understood, efforts have also been directed at investigating how such connectivity properties define and constrain the dynamics of systems unfolding on such structures. However, lesser attention has been focused on hybrid systems, \textit{i.e.} involving more than one type of network and/or dynamics. Because several real systems present such an organization (\textit{e.g.} the dynamics of a disease coexisting with the dynamics of the immune system), it becomes important to address such hybrid systems. The current paper investigates a specific system involving a diffusive (linear and non-linear) dynamics taking place in a regular network while interacting with a complex network of defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models, whose nodes can be displaced spatially. More specifically, the complex network is expected to control, and if possible to extinguish, the diffusion of some given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination, and virus or bacteria reproduction during an infection). Two types of pattern evolution are considered: Fick and Gray-Scott. The nodes of the defensive network then interact with the diffusing patterns and communicate between themselves in order to control the spreading. The main findings include the identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome

Stability of central finite difference schemes for the Heston PDE

This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large semi-discrete systems with non-normal matrices A. By employing the logarithmic spectral norm we prove practical, rigorous stability bounds. Our theoretical stability results are illustrated by ample numerical experiments

Pricing Exotic Options in a Path Integral Approach

In the framework of Black-Scholes-Merton model of financial derivatives, a path integral approach to option pricing is presented. A general formula to price European path dependent options on multidimensional assets is obtained and implemented by means of various flexible and efficient algorithms. As an example, we detail the cases of Asian, barrier knock out, reverse cliquet and basket call options, evaluating prices and Greeks. The numerical results are compared with those obtained with other procedures used in quantitative finance and found to be in good agreement. In particular, when pricing at-the-money and out-of-the-money options, the path integral approach exhibits competitive performances.Comment: 21 pages, LaTeX, 3 figures, 6 table

The prognostic value of tumor mitotic rate in children and adolescents with cutaneous melanoma:A retrospective cohort study

Background: Mitotic rate is a strong predictor of outcome in adult patients with primary cutaneous melanoma, but for children and adolescent patients this is unknown. Objective: We sought to assess the prognostic value of primary tumor mitotic rate in children and adolescents with primary melanoma. Methods: This was a cohort study of 156 patients who were <20 years of age and who had clinically localized cutaneous melanoma. Patients <12 years of age were classified as children and those 12 to 19 years of age as adolescents. Clinicopathologic and outcome data were collected. Recurrence-free and melanoma-specific survival were calculated. Univariable and multivariable analyses were performed using Cox proportional hazard models. Results: Thirteen of 156 patients (8%) were children. The mitotic rate was ≥1/mm2 in 104 patients (67%) and correlated with increasing Breslow thickness. A positive sentinel node was found in 23 of 61 patients (38%) in whom a sentinel lymph node biopsy specimen was obtained. The median follow-up was 61 months. Five-year melanoma-specific and recurrence-free survival rates were 91% and 84%, respectively. Mitotic rate was a stronger predictor of outcome than tumor thickness and was the only factor independently associated with recurrence-free survival. Limitations: This research was conducted at a single institution and the sample size was small. Conclusion: Mitotic rate is an independent predictor of recurrence-free survival in children and adolescents with clinically localized melanoma

Санитарно-эпидемиологическая экспертиза импортной пищевой продукции и продовольственного сырья как составляющая профилактического направления транспортной медицины

Санітарно епідеміологічна експертиза імпортної харчової продукції й продовольчої сировини (далі експертиза) є одним з пріоритетних напрямів діяльності транспортних підрозділів санепідслужби. Здійснюючи функцію по контролю, виявленню та попередженню впливу небезпечних факторів, пов’язаних з перевезенням вантажів, вона є однією зі складових частин профілактичного напряму транспортної медицини. Експертиза імпортованої продукції харчового призначення нерозривно пов’язана та базується на загальних принципах всієї державної політики у сфері безпеки харчової продукції та продовольчої сировини. Основою для проведення усього комплексу робіт санітарно епідеміологічного направлення є нормативна база, яка була сформована в нашій країні кілька десятиліть назад. Механізм визначення безпеки продукції та ті критерії оцінки, які були закладені в її основі, вимагають перегляду у відповідності з вимогами сьогодення та враховуючи розвиток міжнародних відносин. Зроблені деякі кроки у цьому напрямку. Наприклад, визначення експертизи у законі «Про внесення змін до закону України «Про якість та безпеку харчових продуктів та продовольчої сировини» поряд зі встановленням відповідності продукції нормативним вимогам передбачає оцінку ризику дії шкідливих факторів у процесі обігу харчових продуктів, що відповідає сучас ним вимогам до вирішення задач профілактичного напрямку, запобігання шкідливого впливу факторів, керування санітарно-епідеміологічною ситуацією взагалі та на етапі транспортування харчових грузів зокрема. Такий підхід потрібно враховувати при подальшому необхідному перегляді та формуванні нової нормативної бази.Sanіtarу epidemiological examination of imported foodstuffs and edible raw materials (then «examination») is one of the priority directions of transport sanіtarу epidemiological servise. Examination controls, discovers and prevents an influence of dangerous factors while in transportation of loads. So it’s one of the component of the transport medicine preventive activity. Examination of import foodstuffs and edible raw materials inseparably linked with and based on general principles of the food safety state policy. The foundation of the sanitary service work is the normative base, that was formed in our country about twenty years ago. It is necessary to review the mechanism of the food safety determination and its criteria in accordance with requirements of present day time and with account of the development of the international relations. One of taken steps in this direction is a characteristic of examination in law «About contributing the modification to law of the Ukraine «About quality and safety of foodstuffs and foodraw materials» where along with determination of the products correspondence to the normative requirements is provided forrisk assessment of the harmful factors in process of the turn of the food stuffs. Such approach corresponds with modern requests to decision of the prophylactic problems, prevention bad influence dangerous factors, management sanіtarу epidemiological situation in general and in step of transportation food cargo in particular. And it should be taken into account during the further necessary process of revision and forming the new normative base

LNK suppresses interferon signaling in melanoma.

LNK (SH2B3) is a key negative regulator of JAK-STAT signaling which has been extensively studied in malignant hematopoietic diseases. We found that LNK is significantly elevated in cutaneous melanoma; this elevation is correlated with hyperactive signaling of the RAS-RAF-MEK pathway. Elevated LNK enhances cell growth and survival in adverse conditions. Forced expression of LNK inhibits signaling by interferon-STAT1 and suppresses interferon (IFN) induced cell cycle arrest and cell apoptosis. In contrast, silencing LNK expression by either shRNA or CRISPR-Cas9 potentiates the killing effect of IFN. The IFN-LNK signaling is tightly regulated by a negative feedback mechanism; melanoma cells exposed to IFN upregulate expression of LNK to prevent overactivation of this signaling pathway. Our study reveals an unappreciated function of LNK in melanoma and highlights the critical role of the IFN-STAT1-LNK signaling axis in this potentially devastating disease. LNK may be further explored as a potential therapeutic target for melanoma immunotherapy