Constructing optimal entanglement witnesses. II

We provide a class of optimal nondecomposable entanglement witnesses for 4N x 4N composite quantum systems or, equivalently, a new construction of nondecomposable positive maps in the algebra of 4N x 4N complex matrices. This construction provides natural generalization of the Robertson map. It is shown that their structural physical approximations give rise to entanglement breaking channels.Comment: 6 page

A Progress Report on Numerical Solutions of Least Squares Adjustment in GNU Project Gama

GNU project Gama for adjustment of geodetic networks is presented. Numerical solution of Least Squares Adjustment in the project is based on Singular Value Decomposition (SVD) and General Orthogonalization Algorithm (GSO). Both algorithms enable solution of singular systems resulting from adjustment of free geodetic networks.

Evidence that the caudal portion of the neural tube develops by cavitation of a neural cord in the caudal eminence of human embryos

The formation of the secondary neural tube was traced in serial sections of human embryos of developmental stages 13 to 17 (32-41 days after fertilisation). It was found that the secondary neural tube formation begins with cavitation of the neural cord. The minute cavities are seen in embryos at stages 13 and 15. At stages 16 and 17 the numerous cavities coalesce to form a single central canal

Differentiation of the nuclear groups in the posterior horn of the human embryonic spinal cord

The formation of nuclear groups in the posterior horns of the human embryonic spinal cord was traced in serial sections of embryos of developmental stages 13 to 23 (32 to 56 postovulatory days). The following observations, new for the human, are presented: 1. The differentiation of the neural tube into 3 zones (germinal, mantle and marginal) is detected in the middle of the 5th week. 2. The primordia of the posterior horns are marked at stage 14 (33 days). 3. In the middle of the 7th week the nucleus proprius and substantia gelatinosa are discerned. 4. Differentiation of the nuclei within the posterior horns proceeds in the ventrodorsal and rostrocaudal gradients. (Folia Morphol 2011; 70, 4: 245–251

Constructing new optimal entanglement witnesses

We provide a new class of indecomposable entanglement witnesses. In 4 x 4 case it reproduces the well know Breuer-Hall witness. We prove that these new witnesses are optimal and atomic, i.e. they are able to detect the "weakest" quantum entanglement encoded into states with positive partial transposition (PPT). Equivalently, we provide a new construction of indecomposable atomic maps in the algebra of 2k x 2k complex matrices. It is shown that their structural physical approximations give rise to entanglement breaking channels. This result supports recent conjecture by Korbicz et. al.Comment: 9 page

White communicating rami in human embryos at the end of the fifth week

White communicating rami were traced in 8 human embryos of developmental stages 14 and 15 (aged 33 and 36 postovulatory days, respectively). In embryos at stage 14 the white communicating rami were found in the spinal nerves T1 to T9. In embryos at stage 15 the white communicating rami were present at the spinal cord levels T1 to L3. (Folia Morphol 2010; 69, 2: 75-77

The thickness of the ventral midline of the spinal cord in human embryos during the fifth week

The thickness of the ventral midline of the spinal cord was determined in 9 human embryos aged five weeks (developmental stages 13-15). This part of the spinal cord consists of floor plate, mantle and marginal layers. The floor plate ependymal cells form pseudostratified columnar epithelium. The thickness of the investigated structure varied from 20 to 50 micrometers at different levels of the spinal cord

Optimal entanglement witnesses from generalized reduction and Robertson maps

We provide a generalization of the reduction and Robertson positive maps in matrix algebras. They give rise to a new class of optimal entanglement witnesses. Their structural physical approximation is analyzed. As a byproduct we provide a new examples of PPT (Positive Partial Transpose) entangled states.Comment: 14 page

Body mass composition and dietary habits in adolescents with polycystic ovary syndrome

Objectives: The aim of the present study is to assess differences in body composition between female participants in the study group who suffer from PCOS versus a healthy control group. Material and methods: The study included 85, 14–22-year-old, female participants. Participants belonged to one of two groups. Thirty seven participants with a diagnosis of PCOS were in the clinical group, and 48 participants were in the healthy control group with no prior diagnosis of PCOS. Results: A statistically significant difference between groups was found in their answer regarding diet. A correlation was found between the body fat index and the use of dieting among participants; participants with a lower body fat index (in kilograms) were less likely to be on a diet. Conclusions: The young female participants with PCOS were shown to have similar body composition to age-matched healthy controls. However, the clinical group with PCOS reported more frequent use of dieting, with less use of exercise