High-speed polynomial basis multipliers over GF(2(m)) for special pentanomial.

Efficient hardware implementations of arithmetic operations in the Galois field are highly desirable for several applications, such as coding theory, computer algebra and cryptography. Among these operations, multiplication is of special interest because it is considered the most important building block. Therefore, high-speed algorithms and hardware architectures for computing multiplication are highly required. In this paper, bit-parallel polynomial basis multipliers over the binary field GF(2(m)) generated using type II irreducible pentanomials are considered. The multiplier here presented has the lowest time complexity known to date for similar multipliers based on this type of irreducible pentanomials.

El problema de Lagrange en cartografía

Esta Tesis trata sobre las proyecciones de Lagrange, que son proyecciones conformes del elipsoide de revolución sobre el plano, que transforman los meridianos y paralelos en arcos circulares, y que analizamos y revisamos, con especial cuidado en las fuentes originales (Lambert, Lagrange, Bonnet, Chebyshev, etc.) Como herramienta auxiliar, introducimos en cartografía la función caracter ística de una proyección conforme: m = jf0(z)j{u100000}1, z = + iq, fundamentados en que las curvaturas de las imágenes de los meridianos y paralelos son, según J. L. Lagrange (1779): 1 = {u100000}m y 2 = mq, respectivamente (el subíndice indica derivada parcial). Parametrizamos el elipsoide mediante la longitud geodésica o geográ ca y la latitud isométrica q. Una proyección conforme es de Lagrange si y solo si m q = 0. En este trabajo resolvemos el sistema de ecuaciones: logm = 0, m q = 0. De este modo obtenemos a priori la función característica de las proyecciones de Lagrange y también realizamos una primera clasi cación: rectilíneas, formada por tres familias: Cilíndricas conformes, Cónicas y acimutales conformes y Pseudopolares, esta última es nueva en cartografía; y circulares, formada también por tres familias: De Lagrange-Lambert, Unipolares y Apolares, estas dos últimas nuevas en cartografía. En las rectilíneas todos los meridianos o todos los paralelos se transforman en rectas. En las circulares solo algunos meridianos o paralelos son rectilíneos...

Spatial and Functional Organization of Pig Trade in Different European Production Systems: Implications for Disease Prevention and Control

Understanding the complexity of live pig trade organization is a key factor to predict and control major infectious diseases, such as classical swine fever (CSF) or African swine fever (ASF). Whereas the organization of pig trade has been described in several European countries with indoor commercial production systems, little information is available on this organization in other systems, such as outdoor or small-scale systems. The objective of this study was to describe and compare the spatial and functional organization of live pig trade in different European countries and different production systems. Data on premise characteristics and pig movements between premises were collected during 2011 from Bulgaria, France, Italy, and Spain, which swine industry is representative of most of the production systems in Europe (i.e., commercial vs. small-scale and outdoor vs. indoor). Trade communities were identified in each country using the Walktrap algorithm. Several descriptive and network metrics were generated at country and community levels. Pig trade organization showed heterogeneous spatial and functional organization. Trade communities mostly composed of indoor commercial premises were identified in western France, northern Italy, northern Spain, and north-western Bulgaria. They covered large distances, overlapped in space, demonstrated both scale-free and small-world properties, with a role of trade operators and multipliers as key premises. Trade communities involving outdoor commercial premises were identified in western Spain, south-western and central France. They were more spatially clustered, demonstrated scale-free properties, with multipliers as key premises. Small-scale communities involved the majority of premises in Bulgaria and in central and Southern Italy. They were spatially clustered and had scale-free properties, with key premises usually being commercial production premises. These results indicate that a disease might spread very differently according to the production system and that key premises could be targeted to more cost-effectively control diseases. This study provides useful epidemiological information and parameters that could be used to design risk-based surveillance strategies or to more accurately model the risk of introduction or spread of devastating swine diseases, such as ASF, CSF, or foot-and-mouth disease.