An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

An algorithm to detect linearly separable clusters of binary patterns

The clusters of binary patterns can be considered as Boolean functions of the (binary) features. Such a relationship between the linearly separable (LS) Boolean functions and LS clusters of binary patterns is examined. An algorithm is presented to answer the questions of the type: “Is the cluster formed by the subsets of the (binary) data set having certain features AND/NOT having certain other features, LS from the remaining set?” The algorithm uses the sequences of Numbered Binary Form (NBF) notation and some elementary (NPN) transformations of the binary data.

Merkel cell carcinoma : Epidemiological study with special reference to polyomavirus and vascular factors in pathogenesis

Merkel cell carcinoma (MCC) is a rare cutaneous malignancy that occurs predominantly on sun exposed skin areas. A new polyomavirus (MCPyV) was identified in MCC tumor tissues in 2008 suggesting that a viral infection might be an etiological factor. A typical MCC is a rapidly growing painless purple nodule. In its early stage it can be misjudged by its appearance as a cyst or abscess. Recurrences are common and approximately half of the patients will develop lymph node metastases and third of the patents will have distant metastases. It affects mostly elderly persons at an average age of 70 at the time of diagnosis. MCC was first described in 1972 and the first MCC patient in Finland was identified in 1983. MCC has been poorly recognized, but increased awareness and better diagnostic accuracy has increased the incidence since the early years. In this study, all cases with a notation of MCC during 1979 2008 were obtained from the Finnish Cancer Registry. Based on this data, the incidence is 0.11 for men and 0.12 for women. It is similar than that of other Nordic countries, but lower than in the USA. For clinical series, the files of patients diagnosed with MCC during 1983 2004 were reviewed, and the tissue samples were re-evaluated, if available (n=181). Third of the patients were men, and the most common site of the primary tumor was the head and neck (53%). The majority of the patients (86%) presented with a clinically node-negative (Stage I or II) disease, but the disease recurred in 38% of them. The treatment schemes were heterogeneous. No additional benefit from a wide margin (≥2 cm) was found compared to a margin of 0.1-1.9 cm, but intralesional excision was more often associated with local recurrence. None of the patients with Stage I-II disease who had received postoperative radiotherapy had local recurrence during the follow-up period. The 5-year relative survival ratio for Stage I disease was 68%, for Stage II 67%, for Stage III 16%, and for Stage IV 0%. The relative excess risk of death was significantly lower among women than among men. Some of these tissue samples were further analyzed for vascular invasion (n=126) by immunohistochemistry using vascular endothelial markers CD-31 and D2-40. Vascular invasion was seen in 93% of the samples and it was observed already in very small, <5mm tumors. The tissue samples were also analyzed for the presence of MCPyV by using a polymerase chain reaction (PCR) and quantitative PCR. MCPyV DNA was present in 80% of 114 samples studied. The patients with virus-positive tumors had better overall survival than patients with virus-negative tumors. Immunohistochemical analyses were performed for the expression of VEGFR-2 (n=21) and endostatin (n=19), but they had no prognostic value. Our results support the concept of treating MCC with margin-negative excision and radiotherapy to the tumor bed to reduce local recurrence. The finding of a high frequency of lymphovascular invasion reduces its value as a prognostic factor, but emphasizes the role of sentinel node biopsy even in very small primary MCC.

Simultaneous display of image and spectrum in the same plane: a generalized analysis

A generalized analysis, using the Vander Lugt operational notation, of the building block optical system comprising a single holographic optical element (HOE) for achieving simultaneous display of the spectrum and the image of an object in a single plane, has been carried out. The salient features of this analysis are: (1) it allows comprehensive characterization of the HOE, (2) it provides insights into the many possible configurations for the system, and (3) it explains the existing results in a consistent manner.

The absolute orientation of a molecule in space: Extension of the 'CIP' system

A scheme for denoting the absolute spatial orientation of molecules and molecular fragments is presented; this is based on three angular deviations - one for each spatial dimension - with respect to a reference orientation, which is itself defined with the help of certain features of the Cahn-Ingold-Prelog stereochemical notation. The new scheme helps in reconstructing the three-dimensional characteristics of molecules from purely verbal descriptors, and may thus find application in various information storage and retrieval processes (e.,-. encrypting holograms, etc.).

An interior penalty method for a sixth-order elliptic equation

We derive and study a C(0) interior penalty method for a sixth-order elliptic equation on polygonal domains. The method uses the cubic Lagrange finite-element space, which is simple to implement and is readily available in commercial software. After introducing some notation and preliminary results, we provide a detailed derivation of the method. We then prove the well-posedness of the method as well as derive quasi-optimal error estimates in the energy norm. The proof is based on replacing Galerkin orthogonality with a posteriori analysis techniques. Using this approach, we are able to obtain a Cea-like lemma with minimal regularity assumptions on the solution. Numerical experiments are presented that support the theoretical findings.

Intensity profile of light scattered from a rough surface

We present in this paper, approximate analytical expressions for the intensity of light scattered by a rough surface, whose elevation. xi(x,y) in the z-direction is a zero mean stationary Gaussian random variable. With (x,y) and (x',y') being two points on the surface, we have h. = 0 with a correlation, = sigma(2)g(r), where r = (x - x')(2) + ( y - y')(2)](1/2) is the distance between these two points. We consider g(r) = exp-r/l)(beta)] with 1 <= beta <= 2, showing that g(0) = 1 and g(r) -> 0 for r >> l. The intensity expression is sought to be expressed as f(v(xy)) = {1 + (c/2y)v(x)(2) + v(y)(2)]}(-y), where v(x) and v(y) are the wave vectors of scattering, as defined by the Beckmann notation. In the paper, we present expressions for c and y, in terms of sigma, l, and beta. The closed form expressions are verified to be true, for the cases beta = 1 and beta = 2, for which exact expressions are known. For other cases, i.e., beta not equal 1, 2 we present approximate expressions for the scattered intensity, in the range, v(xy) = (v(x)(2) + v(y)(2))(1/2) <= 6.0 and show that the relation for f(v(xy)), given above, expresses the scattered intensity quite accurately, thus providing a simple computational methods in situations of practical importance.

Checking Liveness Properties of Presburger Counter Systems Using Reachability Analysis

Counter systems are a well-known and powerful modeling notation for specifying infinite-state systems. In this paper we target the problem of checking liveness properties in counter systems. We propose two semi decision techniques towards this, both of which return a formula that encodes the set of reachable states of the system that satisfy a given liveness property. A novel aspect of our techniques is that they use reachability analysis techniques, which are well studied in the literature, as black boxes, and are hence able to compute precise answers on a much wider class of systems than previous approaches for the same problem. Secondly, they compute their results by iterative expansion or contraction, and hence permit an approximate solution to be obtained at any point. We state the formal properties of our techniques, and also provide experimental results using standard benchmarks to show the usefulness of our approaches. Finally, we sketch an extension of our liveness checking approach to check general CTL properties.

Using formal reasoning on a model of tasks for FreeRTOS

FreeRTOS is an open-source real-time microkernel that has a wide community of users. We present the formal specification of the behaviour of the task part of FreeRTOS that deals with the creation, management, and scheduling of tasks using priority-based preemption. Our model is written in the Z notation, and we verify its consistency using the Z/Eves theorem prover. This includes a precise statement of the preconditions for all API commands. This task model forms the basis for three dimensions of further work: (a) the modelling of the rest of the behaviour of queues, time, mutex, and interrupts in FreeRTOS; (b) refinement of the models to code to produce a verified implementation; and (c) extension of the behaviour of FreeRTOS to multi-core architectures. We propose all three dimensions as benchmark challenge problems for Hoare's Verified Software Initiative.

Contrafactum y adaptación de la canción de Malmaridada en la Península Ibérica : del Cancionero del rey Don Denis al Cancionero para cantar la noche de Navidad de Francisco de Ocaña

Integran este número de la revista ponencias presentadas en Studia Hispanica Medievalia VIII : Actas de las X Jornadas Internacionales de Literatura Española Medieval, 2011, y de Homenaje al Quinto Centenario del Cancionero General de Hernando del Castillo.

Berm cranes at Miraflores Locks

Leonard Carpenter Panama Canal Collection. Photographs: Dredging, Soldiers, and Ships. [Box 1] from the Special Collections & Area Studies Department, George A. Smathers Libraries, University of Florida. Photo notation: These are most economical in handling concrete but not so elastic as the cable way method (ca. 1914)

Treewidth: theory and applications to computer science

This report is an introduction to the concept of treewidth, a property of graphs that has important implications in algorithms. Some basic concepts of graph theory are presented in the first chapter for those readers that are not familiar with the notation. In Chapter 2, the definition of treewidth and some different ways of characterizing it are explained. The last two chapters focus on the algorithmic implications of treewidth, which are very relevant in Computer Science. An algorithm to compute the treewidth of a graph is presented and its result can be later applied to many other problems in graph theory, like those introduced in the last chapter.

A guide to the interpretation of sea trout scales

The overall purpose of this guide is to provide a manual for the collection and interpretation of sea trout scales. A brief introduction considers the advantages and disadvantages of using scales to determine age and growth. To ensure that scales are interpreted in a consistent manner, all major terms are defined and a standard system for age notation is proposed. The methodology for the collection, mounting and interpretation of scales is described in detail, and this is followed by a section on the back-calculation of lengths at different ages. Each topic is discussed critically. The final part of this guide is an atlas illustrating scales from a wide range of sea trout and including not only excellent "type-scales" but also difficult and impossible scales.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.