Hamiltonian formalism for nonlocal Lagrangians

A Hamiltonian formalism is set up for nonlocal Lagrangian systems. The method is based on obtaining an equivalent singular first order Lagrangian, which is processed according to the standard Legendre transformation and then, the resulting Hamiltonian formalism is pulled back onto the phase space defined by the corresponding constraints. Finally, the standard results for local Lagrangians of any order are obtained as a particular case.

Exact results for Wilson loops in arbitrary representations

We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of TeX = 4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain integrals in a Gaussian matrix model, which we do using the method of orthogonal polynomials. Our results are particularly simple for Wilson loops in antisymmetric representations; in this case, we observe that the final answers admit an expansion where the coefficients are positive integers, and can be written in terms of sums over skew Young diagrams. As an application of our results, we use them to discuss the exact Bremsstrahlung functions associated to the corresponding heavy probes.

Subjectively adapted high capacity lossless image data hiding based on prediction errors

This article reports on a lossless data hiding scheme for digital images where the data hiding capacity is either determined by minimum acceptable subjective quality or by the demanded capacity. In the proposed method data is hidden within the image prediction errors, where the most well-known prediction algorithms such as the median edge detector (MED), gradient adjacent prediction (GAP) and Jiang prediction are tested for this purpose. In this method, first the histogram of the prediction errors of images are computed and then based on the required capacity or desired image quality, the prediction error values of frequencies larger than this capacity are shifted. The empty space created by such a shift is used for embedding the data. Experimental results show distinct superiority of the image prediction error histogram over the conventional image histogram itself, due to much narrower spectrum of the former over the latter. We have also devised an adaptive method for hiding data, where subjective quality is traded for data hiding capacity. Here the positive and negative error values are chosen such that the sum of their frequencies on the histogram is just above the given capacity or above a certain quality.

Generalization of Vélu’s formulae for isogenies between elliptic curves

Given an elliptic curve E and a finite subgroup G, V ́lu’s formulae concern to a separable isogeny IG : E → E ′ with kernel G. In particular, for a point P ∈ E these formulae express the first elementary symmetric polynomial on the abscissas of the points in the set P + G as the difference between the abscissa of IG (P ) and the first elementary symmetric polynomial on the abscissas of the nontrivial points of the kernel G. On the other hand, they express Weierstraß coefficients of E ′ as polynomials in the coefficients of E and two additional parameters: w0 = t and w1 = w. We generalize this by defining parameters wn for all n ≥ 0 and giving analogous formulae for all the elementary symmetric polynomials and the power sums on the abscissas of the points in P +G. Simultaneously, we obtain an efficient way of performing computations concerning the isogeny when G is a rational group.

Integrability of a linear center perturbed by a fourth degree homogeneous polynomial

In this work we study the integrability of a two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fourth degree. We give sufficient conditions for integrability in polar coordinates. Finally we establish a conjecture about the independence of the two classes of parameters which appear in the system; if this conjecture is true the integrable cases found will be the only possible ones.

Integrability of a linear center perturbed by a fifth degree homogeneous polynomial

In this work we study the integrability of two-dimensional autonomous system in the plane with linear part of center type and non-linear part given by homogeneous polynomials of fifth degree. We give a simple characterisation for the integrable cases in polar coordinates. Finally we formulate a conjecture about the independence of the two classes of parameters which appear on the system; if this conjecture is true the integrable cases found will be the only possible ones.

Humeral development from neonatal period to skeletal maturity—application in age and sex assessment

The goal of the present study is to examine cross-sectional information on the growth of the humerus based on the analysis of four measurements, namely, diaphyseal length, transversal diameter of the proximal (metaphyseal) end of the shaft, epicondylar breadth and vertical diameter of the head. This analysis was performed in 181 individuals (90 ♂ and 91 ♀) ranging from birth to 25 years of age and belonging to three documented Western European skeletal collections (Coimbra, Lisbon and St. Bride). After testing the homogeneity of the sample, the existence of sexual differences (Student"s t- and Mann-Whitney U-test) and the growth of the variables (polynomial regression) were evaluated. The results showed the presence of sexual differences in epicondylar breadth above 20 years of age and vertical diameter of the head from 15 years of age, thus indicating that these two variables may be of use in determining sex from that age onward. The growth pattern of the variables showed a continuous increase and followed first- and second-degree polynomials. However, growth of the transversal diameter of the proximal end of the shaft followed a fourth-degree polynomial. Strong correlation coefficients were identified between humeral size and age for each of the four metric variables. These results indicate that any of the humeral measurements studied herein is likely to serve as a useful means of estimating sub-adult age in forensic samples.

Effects of heparin on the uptake of lipoprotein lipase in rat liver

BACKGROUND: Lipoprotein lipase (LPL) is anchored at the vascular endothelium through interaction with heparan sulfate. It is not known how this enzyme is turned over but it has been suggested that it is slowly released into blood and then taken up and degraded in the liver. Heparin releases the enzyme into the circulating blood. Several lines of evidence indicate that this leads to accelerated flux of LPL to the liver and a temporary depletion of the enzyme in peripheral tissues. RESULTS: Rat livers were found to contain substantial amounts of LPL, most of which was catalytically inactive. After injection of heparin, LPL mass in liver increased for at least an hour. LPL activity also increased, but not in proportion to mass, indicating that the lipase soon lost its activity after being bound/taken up in the liver. To further study the uptake, bovine LPL was labeled with 125I and injected. Already two min after injection about 33 % of the injected lipase was in the liver where it initially located along sinusoids. With time the immunostaining shifted to the hepatocytes, became granular and then faded, indicating internalization and degradation. When heparin was injected before the lipase, the initial immunostaining along sinusoids was weaker, whereas staining over Kupffer cells was enhanced. When the lipase was converted to inactive before injection, the fraction taken up in the liver increased and the lipase located mainly to the Kupffer cells. CONCLUSIONS: This study shows that there are heparin-insensitive binding sites for LPL on both hepatocytes and Kupffer cells. The latter may be the same sites as those that mediate uptake of inactive LPL. The results support the hypothesis that turnover of endothelial LPL occurs in part by transport to and degradation in the liver, and that this transport is accelerated after injection of heparin.

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Percutaneous access versus standard femoral exposure for endovascular abdominal aortic aneurysm repair: a randomized, controlled trial

The treatment of abdominal aortic aneurysm (AAA) has shifted from the exposure of the aorta artery in an open repair technique to a small groin cut in an endovascular repair. Recently, a percutaneous access for endovascular repair has appeared. This new technique aims to minimize the complications of the common femoral artery exposure, the patient discomfort and the length of hospitalizationObjectives: To compare the proportion of discharged patients within the first 48 postoperative hours of two common femoral artery accesses for endovascular repair of AAA: the open exposure technique and the percutaneous technique. Secondary objectives include to evaluate the total procedure time, the femoral access complications, the need for extra analgesia and the patient satisfaction and groin discomfort of the two techniquesDesign: Randomized controlled trial conducted between 2014 and 2017Participants: Patients diagnosed with abdominal aortic aneurysm with elective endovascular repair indication