On the Generation of Heronian Triangles

We describe several algorithms for the generation of integer Heronian triangles with diameter at most n. Two of them have running time O(n^(2+ε)). We enumerate all integer Heronian triangles for n ≤ 600000 and apply the complete list on some related problems.

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Asymmetric polygons with maximum area

We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given n diameters of a circle and a positive integer k < n, this paper addresses the problem of computing a maximum area asymmetric k-gon having as vertices k < n endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciological applications.

The salvo combat model with area fire

This paper analyzes versions of the salvo model of missile combat where area fire is used by one or both sides in a battle. While these models share some properties with the area fire Lanchester model and the aimed fire salvo model, they also display some interesting differences, especially over the course of several salvos. Whereas the relative size of each force is important with aimed fire, with area fire it is the absolute size that matters. Similarly, while aimed fire exhibits square law behavior, area fire shows approximately linear behavior. When one side uses area and the other uses aimed fire, the model displays a mix of square and linear law behavior.

Theory and data for area summation of contrast with and without uncertainty:evidence for a noisy energy model

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c1.0) or nonlinear (c2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

Using dynamic reconfiguration to reduce the area of a JPEG decoder on FPGA

Partial dynamic reconfiguration of FPGAs can be used to implement complex applications using the concept of virtual hardware. In this work we have used partial dynamic reconfiguration to implement a JPEG decoder with reduced area. The image decoding process was adapted to be implemented on the FPGA fabric using this technique. The architecture was tested in a low cost ZYNQ-7020 FPGA that supports dynamic reconfiguration. The results show that the proposed solution needs only 40% of the resources utilized by a static implementation. The performance of the dynamic solution is about 9X slower than the static solution by trading-off internal resources of the FPGA. A throughput of 7 images per second is achievable with the proposed partial dynamic reconfiguration solution.

Imaging molasse and quaternary sediments in Lake Geneva, Switzerland, with 3-D high-resolution seismic reflection methods: A case study

A high-resolution three-dimensional (3-D) seismic reflection survey was conducted in Lake Geneva, near the city of Lausanne, Switzerland, as part of a project for developing such seismic techniques. Using a single 48-channel streamer, the 3-D site with an area of 1200 m x 600 m was surveyed in 10 days. A variety of complex geologic structures (e.g. thrusts, folds, channel-fill) up to similar to150 m below the water bottom were obtained with a 15 in.(3) water gun. The 3-D data allowed the construction of an accurate velocity model and the distinction of five major seismic facies within the Lower Freshwater Molasse (Aquitanian) and the Quaternary sedimentary units. Additionally, the Plateau Molasse (PM) and Subalpine Molasse (SM) erosional surface, "La Paudeze" thrust fault (PM-SM boundary) and the thickness of Quaternary sediments were accurately delineated in 3-D.

Prévention des adhérences péricardiques avec une membrane biorésorbable [Prevention of pericardial adhesions with a bioresorbable membrane]

A bioresorbable membrane made of sodium hyaluronate and carboxymethycellulose, has been reported to prevent peritoneal adhesion. This study was designed to test its efficiency in the prevention of pericardial adhesions. Two groups of six pigs (mean weight 72 +/- 8 kg) were chosen for the experiment. The heart was exposed through a left thoracotomy and a wide patch of pericardium was excised. In the test group (n = 6), the left ventricular area without pericardium was divided into two areas: area A where six stitches of Prolene were performed, and area B which was left intact. The membrane was applied on the both areas as well as on the adjacent area covered with pericardium (area C). In the control group (n = 6), the same protocol was performed except for the membrane application. The animals were sacrificed one month later. The adhesion status as well as the visibility of the coronary anatomy was assessed according to severity scores ranging from 0 to 3 for the adhesions and from 0 to 2 for the visibility. The difference between groups was considered significant when p < 0.05. The adhesion score of the area A was 1.7 +/- 0.5 in the test group versus 2.5 +/- 0.5 in the control group (p = 0.02) and the visibility score was 1.3 +/- 0.8 and 2 +/- 0 respectively (p = 0.07). In the area B, the adhesion score was 1 +/- 0 in the test group versus 2 +/- 0.6 in the control group (p = 0.03) and the visibility score was 0.7 +/- 0.5 and 2 +/- 0 respectively (p = 0.001). Lastly, in the area C, the adhesion score was 1 +/- 0 in both groups (n.s.) and the visibility score was 0.7 +/- 0.4 in the test group versus 0.5 +/- 0.5 in the control group (n.s.). In this animal model, the role of the bioresorbable membrane in the prevention of pericardial adhesions is limited to the areas without pericardial cover and without foreign material. The presence of foreign material neutralizes its effect.

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.

Time of ruin in a risk model with generalized Erlang (n) interclaim times and a constant dividend barrier

In this paper we analyze the time of ruin in a risk process with the interclaim times being Erlang(n) distributed and a constant dividend barrier. We obtain an integro-differential equation for the Laplace Transform of the time of ruin. Explicit solutions for the moments of the time of ruin are presented when the individual claim amounts have a distribution with rational Laplace transform. Finally, some numerical results and a compare son with the classical risk model, with interclaim times following an exponential distribution, are given.