Solving recurrence relations supported by Wolfram Mathematica

El presente trabajo introduce algunos algoritmos para resolver relaciones de recurrencia lineales, homogéneas y no homogéneas, con coeficientes constantes y no constantes, utilizando software como recurso principal en los procesos de resolución. La aplicación comercial Wolfram Mathematica ha brindado el sustento técnico necesario para la implementación de los métodos empleados. Se presentan además, distintos ejemplos de relaciones de recurrencia, mostrando la efectividad y limitaciones de los algoritmos creados por el autor y programados en el ambiente que provee Mathematica.This paper introduces some algorithms for solving linear relationships, homogeneous and non-homogeneous recurrence with constant and non-constant coefficients, using software as the main resource in solving processes. The Mathematica commercial application has provided the technical support necessary for the implementation of the methods used. It also presents other examples of recurrence relations, showing the effectiveness and limitations of the algorithms created by the author and programmed in Mathematica environment that provides

Cell-specific and region-specific transcriptomics in the multiple sclerosis model: Focus on astrocytes.

Changes in gene expression that occur across the central nervous system (CNS) during neurological diseases do not address the heterogeneity of cell types from one CNS region to another and are complicated by alterations in cellular composition during disease. Multiple sclerosis (MS) is multifocal by definition. Here, a cell-specific and region-specific transcriptomics approach was used to determine gene expression changes in astrocytes in the most widely used MS model, experimental autoimmune encephalomyelitis (EAE). Astrocyte-specific RNAs from various neuroanatomic regions were attained using RiboTag technology. Sequencing and bioinformatics analyses showed that EAE-induced gene expression changes differed between neuroanatomic regions when comparing astrocytes from spinal cord, cerebellum, cerebral cortex, and hippocampus. The top gene pathways that were changed in astrocytes from spinal cord during chronic EAE involved decreases in expression of cholesterol synthesis genes while immune pathway gene expression in astrocytes was increased. Optic nerve from EAE and optic chiasm from MS also showed decreased cholesterol synthesis gene expression. The potential role of cholesterol synthesized by astrocytes during EAE and MS is discussed. Together, this provides proof-of-concept that a cell-specific and region-specific gene expression approach can provide potential treatment targets in distinct neuroanatomic regions during multifocal neurological diseases

Volume CVI, Number 19, April 14, 1989

Institute of High Performance Computing, IHPC;University of Perugia, Italy;University of Calgary, Canada;University of Minnesota, MN, USA;Queen's University BelfastInternational Conference on Computational Science and Its Applications - ICCSA 2005 -- 9 May 2005 through 12 May 2005 -- 65625Discrete mathematics is one of the very basic mathematics courses in computer engineering (CE) and/or computer science (CS) departments. This course covers almost all of the basic concepts for many other courses in the curriculum and requires active learning of students. For this purpose, especially "propositions" concept, which cannot be understood well in prior years, should be covered with every detail. Previous studies show that learning by entertaining activities and competition has positive effect on student motivation. In this study, an Internet-based Discrete Mathematics Package (DMP) for "propositions" that can work in mobile devices and encourages competitive learning between students has been developed within related literature. © Springer-Verlag Berlin Heidelberg 2005

On Teaching Discrete Mathematics to Freshman Computer Science Students

Discrete Mathematics is an inevitable part of any undergraduate computer science degree programme. However, today's computer science student typically finds this to be at best a necessary evil with which they struggle to engage. Twenty years ago, we started to address this issue seriously in our university, and we have instituted a number of innovations throughout the years which have had a positive effect on engagement and, thus, attainment. In this paper, we describe and motivate the innovations which we introduced, and provide a detailed analysis of how and why engagement and attainment levels varied over two decades as a direct result of these innovation

A Genome-Wide Association Study of Diabetic Kidney Disease in Subjects With Type 2 Diabetes

dentification of sequence variants robustly associated with predisposition to diabetic kidney disease (DKD) has the potential to provide insights into the pathophysiological mechanisms responsible. We conducted a genome-wide association study (GWAS) of DKD in type 2 diabetes (T2D) using eight complementary dichotomous and quantitative DKD phenotypes: the principal dichotomous analysis involved 5,717 T2D subjects, 3,345 with DKD. Promising association signals were evaluated in up to 26,827 subjects with T2D (12,710 with DKD). A combined T1D+T2D GWAS was performed using complementary data available for subjects with T1D, which, with replication samples, involved up to 40,340 subjects with diabetes (18,582 with DKD). Analysis of specific DKD phenotypes identified a novel signal near GABRR1 (rs9942471, P = 4.5 x 10(-8)) associated with microalbuminuria in European T2D case subjects. However, no replication of this signal was observed in Asian subjects with T2D or in the equivalent T1D analysis. There was only limited support, in this substantially enlarged analysis, for association at previously reported DKD signals, except for those at UMOD and PRKAG2, both associated with estimated glomerular filtration rate. We conclude that, despite challenges in addressing phenotypic heterogeneity, access to increased sample sizes will continue to provide more robust inference regarding risk variant discovery for DKD.Peer reviewe