Three-by-three bound entanglement with general unextendible product bases

We discuss the subject of Unextendible Product Bases with the orthogonality condition dropped and we prove that the lowest rank non-separable positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are always locally equivalent to a projection onto the orthogonal complement of a linear subspace spanned by an orthogonal Unextendible Product Basis. The product vectors in the kernels of the states belong to a non-zero measure subset of all general Unextendible Product Bases, nevertheless they can always be locally transformed to the orthogonal form. This fully confirms the surprising numerical results recently reported by Leinaas et al. Parts of the paper rely heavily on the use of Bezout's Theorem from algebraic geometry.Comment: 36 page

Traffic signal settings optimization using fradient descent

We investigate performance of a gradient descent optimization (GR) applied to the traffic signal setting problem and compare it to genetic algorithms. We used neural networks as metamodels evaluating quality of signal settings and discovered that both optimization methods produce similar results, e.g., in both cases the accuracy of neural networks close to local optima depends on an activation function (e.g., TANH activation makes optimization process converge to different minima than ReLU activation)

Generation of Mapping Cones from Small Sets

We answer in the affirmative a recently-posed question that asked if there exists an "untypical" convex mapping cone -- i.e., one that does not arise from the transpose map and the cones of k-positive and k-superpositive maps. We explicitly construct such a cone based on atomic positive maps. Our general technique is to consider the smallest convex mapping cone generated by a single map, and we derive several results on such mapping cones. We use this technique to also present several other examples of untypical mapping cones, including a family of cones generated by spin factors. We also provide a full characterization of mapping cones generated by single elements in the qubit case in terms of their typicality.Comment: 18 page

Product numerical range in a space with tensor product structure

We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.Comment: 17 pages, 4 figures. Original preprint "Local numerical range: a versatile tool in the theory of quantum information" [arXiv:0905.3646v1] was broadened and split into two papers: "Restricted numerical range: a versatile tool in the theory of quantum information", and "Product numerical range in a space with tensor product structure

Positive maps, positive polynomials and entanglement witnesses

We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic forms that are not sums of squares. Although the general problem of describing the set of positive maps remains open, in some particular cases we solve the corresponding polynomial inequalities and obtain explicit conditions for positivity.Comment: 17 pages, 1 figur

Influence of soil contaminated with cadmium on cell death in the digestive epithelium of soil centipede Lithobius forficatus (Myriapoda, Chilopoda)

Cadmium is a heavy metal that is treated as an environmental pollutant (air, water, soil). In order to understand the potential effects of cadmium in soil and soil invertebrates, it is important to describe all alterations which appear at different levels in organisms. The main aim of this study was to investigate, analyze and describe the alterations caused by cadmium short- and long-term intoxication at different levels in the organisms: from tissues to cells and organelles. In addition, the activation of cell deathmechanisms that take part in homeostasismaintenance according to cadmium has been studied. Therefore, as the species for this project, a terrestrial and well-known widespread European species – the centipede Lithobius forficatus (Myriapoda, Chilopoda, Lithobiomorpha) – was chosen. This omnivorous species lives under upper layers of soil, under stones, litter, rocks, and leaves, and it is also commonly found in human habitats. The animals were divided into three groups: C – the control group, animals cultured in a horticultural soil; Cd1 – animals cultured in a horticultural soil supplemented with 80 mg/kg (dry weight) of CdCl2, 12 days – short-term exposure; Cd2 – animals cultured in a horticultural soil supplemented with 80 mg/kg (dry weight) of CdCl2, 45 days – long-term exposure. The midgut was isolated from each specimen and it was prepared for analysis using some histological, histochemical and immunohistochemical methods. Our studies showed that short-term intoxication causes intensification of autophagy and digestion of reserve material, while long-term exposure to this heavy metal causes activation of cell death processes together with inhibition of autophagy connected with the lack of reserve material. Additionally, we can infer that autophagy and cell death are nutrient deprivation-induced processes. Finally, we can conclude that short- and long-term exposure of soil centipede to cadmium affects different mechanisms and processes of cell death

Myosin VI in PC12 cells plays important roles in cell migration and proliferation but not in catecholamine secretion

Myosin VI (MVI) is the only known myosin walking towards minus end of actin filaments and is believed to play distinct role(s) than other myosins. We addressed a role of this unique motor in secretory PC12 cells, derived from rat adrenal medulla pheochromocytoma using cell lines with reduced MVI synthesis (produced by means of siRNA). Decrease of MVI expression caused severe changes in cell size and morphology, and profound defects in actin cytoskeleton organization and Golgi structure. Also, significant inhibition of cell migration as well as cell proliferation was observed. Flow cytometric analysis revealed that MVI-deficient cells were arrested in G0/G1 phase of the cell cycle but did not undergo increased senescence as compared with control cells. Also, neither polyploidy nor aneuploidy were detected. Surprisingly, no significant effect on noradrenaline secretion was observed. These data indicate that in PC12 cells MVI is involved in cell migration and proliferation but is not crucial for stimulation-dependent catecholamine release