The algebra of adjacency patterns: Rees matrix semigroups with reversion

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the same as the lattice of universal Horn classes of reflexive directed graphs. A number of examples follow, including a limit variety of regular unary semigroups and finite unary semigroups with NP-hard variety membership problems.Comment: 30 pages, 9 figure

A classification of bisymmetric polynomial functions over integral domains of characteristic zero

We describe the class of n-variable polynomial functions that satisfy Acz\'el's bisymmetry property over an arbitrary integral domain of characteristic zero with identity

Optimal discrimination of mixed quantum states involving inconclusive results

We propose a generalized discrimination scheme for mixed quantum states. In the present scenario we allow for certain fixed fraction of inconclusive results and we maximize the success rate of the quantum-state discrimination. This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the Helstrom one. We formulate the extremal equations for the optimal positive operator valued measure describing the discrimination device and establish a criterion for its optimality. We also devise a numerical method for efficient solving of these extremal equations.Comment: 5 pages, 1 figur

Minimax mean estimator for the trine

We explore the question of state estimation for a qubit restricted to the $x$-$z$ plane of the Bloch sphere, with the trine measurement. In our earlier work [H. K. Ng and B.-G. Englert, eprint arXiv:1202.5136[quant-ph] (2012)], similarities between quantum tomography and the tomography of a classical die motivated us to apply a simple modification of the classical estimator for use in the quantum problem. This worked very well. In this article, we adapt a different aspect of the classical estimator to the quantum problem. In particular, we investigate the mean estimator, where the mean is taken with a weight function identical to that in the classical estimator but now with quantum constraints imposed. Among such mean estimators, we choose an optimal one with the smallest worst-case error-the minimax mean estimator-and compare its performance with that of other estimators. Despite the natural generalization of the classical approach, this minimax mean estimator does not work as well as one might expect from the analogous performance in the classical problem. While it outperforms the often-used maximum-likelihood estimator in having a smaller worst-case error, the advantage is not significant enough to justify the more complicated procedure required to construct it. The much simpler adapted estimator introduced in our earlier work is still more effective. Our previous work emphasized the similarities between classical and quantum state estimation; in contrast, this paper highlights how intuition gained from classical problems can sometimes fail in the quantum arena.Comment: 18 pages, 3 figure

Post-processing the results of the topology optimization with the level-set technique

The work was supported by the Technology Agency of the Czech Republic under grant No TN01000024/08 (National Competence Center-Cybernetics and Artificial Intelligence) – sub- project “Automation and production system optimization” within institutional support RVO:61388998 and by the Grant Agency of the Czech Technical University in Prague, under grant No. SGS21/151/OHK2/3T/12

The Development of Blood and Lymph Vessels of Human Parathyroid Glands in Embryonal, Fetal and Postnatal Period

The aim of the article is to investigate the development of blood and lymph systems in human parathyroid glands in prenatal and postnatal periods. The first capillaries are observed in these glands already in the lunar month 2. At the middle of pregnancy blood supply is increased, being extremely abundant in lunar months 9 and 10, as well as during the first year of life. As parts of the lymph system, intercellular lymph spaces are noticed in the parathyroid glands already in the lunar month 2, and also later, when lymph vessels are situated along the gland or in its connective capsule and within the gland parenchyma respectively. All these findings could be connected with the early function of these glands, as well as with the possibility that parathyroid hormone (PTH) is not transferred by blood only but by lymph as well

Lung Lavage Neutrophils, Neutrophil Elastase and Albumin in the Prognosis of Pulmonary Sarcoidosis

The authors measured the bronchoalveolar lavage fluid (BALF) neutrophils, neutrophil elastase and albumin in 60 patients with pulmonary sarcoidosis, 18 patients with other interstitial lung diseases and 14 healthy controls in order to evaluate its significance in the prognosis of sarcoidosis. The concentrations were measured by enzymoimmunoassay and radial immunodiffusion (LC plates). Obtained values were correlated with some clinical indices, radiological stage and lung function values. The patients were followed up for 22.3 6.8 months. At the end of observation period the outcome of sarcoidosis has been evaluated upon the findings of chest radiograms and lung function tests. The length of duration of the disease correlated with the lung lavage neutrophil counts (r = 0.2535; p < 0.05). Significantly higher values of BALF elastase were obtained in III radiologic stage than II and I. Patients with high BALF albumin had more often dispnoa (p < 0.05) and chronic forms of the disease (p < 0.05). The values were high in patients in II and III radiologic stage. Unfavorable outcome of chest radiograms was announced by high BALF albumins (p < 0.05). The measurement of BALF neutrophils, neutrophil elastase and albumin are helpful in clinical management and estimation of the prognosis in patients with pulmonary sarcoidosis