Mathematical Models for Estimating the Risk of vCJD Transmission

We present two different simple models for vCJD transmission by blood transfusion. Both models indicate that transfusions alone are unlikely to cause more than a few infections, unless the number of primary cases increases. To improve our models, future work should pursue data collection, empirical estimation of the model parameters, and examination of the underlying assumptions of our frameworks. Further improvements could also include examining susceptibility to vCJD infection by age group and iatrogenic infections introduced through surgical instruments. Regarding the latter, it may be worthwhile to conduct experiments to quantify the transmission of prions from an infected surgical instrument after repeated sterilization procedures

Creating a Micro-Enterprise for the Development and Marketing of a Chili Sauce Based on Sambo Seeds: Market Analysis

The present work was carried out to promote a chili sauce made with the seeds of the sambo fruit – a local variety of pumpkin. Presently, the sauce is consumed only in Ecuador and is prepared using just the fleshy part of the fruit, while the seeds are discarded. The authors of this article see a larger potential application of the fruit in the food industry, as the fruit not only adds a pleasant flavor but is also full of nutrition. They have made a new chili sauce with a base of sambo seeds. The research was carried out using an inductive method, where people were selected at random. Variables such as gender, age, level, and consumption preferences, among others, were analyzed. The study was conducted in Riobamba canton on 164 people, aged 20 and over, considering various aspects. The instrument used was a questionnaire. The results showed that 71.95% of those surveyed consumed chili-based sauces, and 54.88% of them consumed it at least once a week. In addition, 63.41% of them consumed or had consumed sambo seeds, thus denoting that consumers were aware of and were consuming this product. The current research allowed us to innovate the product using correct methods and techniques, and adapt the best use of seeds in the food industry. Keywords: chili, sambo, economic analysis, consumption, commercialization. RESUMEN El presente trabajo se realizó con el objetivo de dar a conocer la aceptación y el beneficio económico de la salsa de ají con adición de semillas del fruto de sambo en el mercado, actualmente su consumo se da en todo el país y se aprovecha únicamente la parte carnosa de la fruta, las semillas son desechadas, por cuanto vemos una potencial aplicación en la industria alimentaria de estas, a más de aportar con sabor agradable aportan nutricionalmente, y se las han adicionado en una salsa de ají, al integrar al mercado una nueva salsa elaborada con este producto icónico además se busca utilizar las semillas de la calabaza local conocida como sambo. Esta investigación se realizó mediante un método inductivo, donde las personas fueron seleccionadas al azar, se analizaron variables como: género, edad, nivel y preferencias de consumo, entre otras. La búsqueda de información fue en el cantón Riobamba, a 164 personas, de 20 años en adelante, considerando varios aspectos; el instrumento aplicado fue cuestionario. Los resultados demuestran que el 71.95% de los How to encuestados consumen salsas elaboradas a base de ají, y de estos 54.88% lo consumen como mínimo una vez a la semana, además que el 63,41% consume o ha consumido semillas de sambo, denotando así que los consumidores conocen y consumen estos productos. La actual investigación nos permitió innovar el producto, utilizando correctamente métodos y técnicas adaptando el mejor uso de las semillas en la industria alimentaria. Palabras Clave: Ají, sambo, semillas, análisis económico, consumo, comercialización

Hilbert number for a family of piecewise nonautonomous equations

For family $x'=(a_0+a_1\cos t+a_2 \sin t)|x|+b_0+b_1 \cos t+b_2 \sin t$, we solve three basic problems related with its dynamics. First, we characterize when it has a center (Poincar\'e center focus problem). Second, we show that each equation has a finite number of limit cycles (finiteness problem), and finally we give a uniform upper bound for the number of limit cycles (Hilbert's 16th problem).Comment: 16 pages, no figure

Resonant transmission of light through finite chains of subwavelength holes

In this paper we show that the extraordinary optical transmission phenomenon found before in 2D hole arrays is already present in a linear chain of subwavelength holes, which can be considered as the basic geometrical unit showing this property. In order to study this problem we have developed a new theoretical framework, able to analyze the optical properties of finite collections of subwavelength apertures and/or dimples (of any shape and placed in arbitrary positions) drilled in a metallic film.Comment: Accepted for publication in Phys. Rev. Let

Dominant negative phenotype of Bacillus thuringiensis Cry1Ab, Cry11Aa and Cry4Ba mutants suggest hetero-oligomer formation among different Cry toxins.

Background - Bacillus thuringiensis Cry toxins are used worldwide in the control of different insect pests important in agriculture or in human health. The Cry proteins are pore-forming toxins that affect the midgut cell of target insects. It was shown that non-toxic Cry1Ab helix a-4 mutants had a dominant negative (DN) phenotype inhibiting the toxicity of wildtype Cry1Ab when used in equimolar or sub-stoichiometric ratios (1:1, 0.5:1, mutant:wt) indicating that oligomer formation is a key step in toxicity of Cry toxins. Methodology/Principal Findings - The DN Cry1Ab-D136N/T143D mutant that is able to block toxicity of Cry1Ab toxin, was used to analyze its capacity to block the activity against Manduca sexta larvae of other Cry1 toxins, such as Cry1Aa, Cry1Ac, Cry1Ca, Cry1Da, Cry1Ea and Cry1Fa. Cry1Ab-DN mutant inhibited toxicity of Cry1Aa, Cry1Ac and Cry1Fa. In addition, we isolated mutants in helix a-4 of Cry4Ba and Cry11Aa, and demonstrate that Cry4Ba-E159K and Cry11Aa-V142D are inactive and completely block the toxicity against Aedes aegypti of both wildtype toxins, when used at sub-stoichiometric ratios, confirming a DN phenotype. As controls we analyzed Cry1Ab-R99A or Cry11Aa-E97A mutants that are located in helix a-3 and are affected in toxin oligomerization. These mutants do not show a DN phenotype but were able to block toxicity when used in 10:1 or 100:1 ratios (mutant:wt) probably by competition of binding with toxin receptors. Conclusions/Significance - We show that DN phenotype can be observed among different Cry toxins suggesting that may interact in vivo forming hetero-oligomers. The DN phenotype cannot be observed in mutants affected in oligomerization, suggesting that this step is important to inhibit toxicity of other toxin