Photometric and spectroscopic variability of 53 Per

A new investigation of the variability of the SPB-type star 53 Per is presented. The analysis of the BRITE photometry allowed us to determine eight independent frequencies and the combination one. Five of these frequencies and the combination one were not known before. In addition, we gathered more than 1800 new moderate and high-resolution spectra of 53 Per spread over approximately six months. Their frequency analysis revealed four independent frequencies and the combination one, all consistent with the BRITE results.Comment: 2 pages, accepted for publication in the Proceedings of the PAS (Proc. of the 2nd BRITE Science conference, Innsbruck

Reconfiguration of Dominating Sets

We explore a reconfiguration version of the dominating set problem, where a dominating set in a graph $G$ is a set $S$ of vertices such that each vertex is either in $S$ or has a neighbour in $S$. In a reconfiguration problem, the goal is to determine whether there exists a sequence of feasible solutions connecting given feasible solutions $s$ and $t$ such that each pair of consecutive solutions is adjacent according to a specified adjacency relation. Two dominating sets are adjacent if one can be formed from the other by the addition or deletion of a single vertex. For various values of $k$, we consider properties of $D_k(G)$, the graph consisting of a vertex for each dominating set of size at most $k$ and edges specified by the adjacency relation. Addressing an open question posed by Haas and Seyffarth, we demonstrate that $D_{\Gamma(G)+1}(G)$ is not necessarily connected, for $\Gamma(G)$ the maximum cardinality of a minimal dominating set in $G$. The result holds even when graphs are constrained to be planar, of bounded tree-width, or $b$-partite for $b \ge 3$. Moreover, we construct an infinite family of graphs such that $D_{\gamma(G)+1}(G)$ has exponential diameter, for $\gamma(G)$ the minimum size of a dominating set. On the positive side, we show that $D_{n-m}(G)$ is connected and of linear diameter for any graph $G$ on $n$ vertices having at least $m+1$ independent edges.Comment: 12 pages, 4 figure

Dust reference frame in quantum cosmology

We give a formulation of quantum cosmology with a pressureless dust and arbitrary additional matter fields. The system has the property that its Hamiltonian constraint is linear in the dust momentum. This feature provides a natural time gauge, leading to a physical hamiltonian that is not a square root. Quantization leads to Schr{\"o}dinger equation for which unitary evolution is directly linked to geodesic completeness. Our approach simplifies the analysis of both Wheeler-deWitt and loop quantum cosmology (LQC) models, and significantly broadens the applicability of the latter. This is demonstrated for arbitrary scalar field potential and cosmological constant in LQC.Comment: 8 pages, iopart style + BibTe

The initial zones of the atrioventricular node: really neglected anatomical features of potential clinical significance?

The constant evolution of medical knowledge and accompanying development of diagnostic and treatment possibilities for arrhythmias and conduction disturbances has reawakened interest in the structure and function of the conduction system of the human heart, especially in the region of the atrioventricular (AV) junction and within the junction itself. Of the large number of studies dealing with the AV junction few focus on the initial zones of the AV node. These were described for the first time by Tawara in 1906. Similarly, Anderson et al. distinguished two origins of the AV node, the left one running towards the basis of the mitral valve and the right one leading towards the tricuspid valve. The differences in length and scale could be the result of the adoption of different reference points. The study was carried out on the material of 50 human hearts, of both sexes and ranging in age from 22 to 93, which were fixed in 10% formalin and 98% ethanol solution. The tissue obtained was fixed in the 10% formalin solution and, after being sunk in the paraffin, was cut into layers of about 10 μm thick. According to the age of the hearts, every 10th or 6th section was stained by the Masson-Goldner method. The preparations were examined under a LEICA 2000 and BIOLAR 2 microscope at magnifications of 2× to 400×. Each of the 50 examined hearts contained the atrioventricular node and its initial parts. We observed that the initial zone of the AV node is created by an assembly of cells typical for a conduction system that can create three groups that are initially independent of each other and are always arranged around the AV nodal artery. In all the hearts examined we found at least two initial parts of the node: the superior and inferior. These two groups were present in 45 hearts (90%). In the last 5 cases (10%) there was also a middle group. No cases were found either with a single initial group or without any initial groups. In the sections examined the superior group appeared to be first in 27 hearts (54%), while in 23 cases (46%) the inferior group was first. The length of each group was measured from its first appearance to its first direct contact with the second part. The length of the superior part varied from 0.15 to 2.91 mm (mean 0.90 ± 0.6 mm), the inferior from 0.11 to 2.41 mm (mean 0.88 ± 0.6 mm) and the middle from 0.67 to 2.21 mm (mean 1.04 ± 0.7 mm). As mentioned above, in all 50 hearts there was a direct connection between the atrial muscle and the upper origin of AV node. Furthermore, in all sections (100%) the same part of the interatrial septal muscle was connected to the compact part of the node. Additionally, in 3 cases (6%) we were able to observe direct connections between the muscle fibres running from the fasciculus limbicus inferior to the initial zone of the AV node: in 2 cases (4%) with the superior group and in 1 case (2%) with the inferior group. In 8% of the material the atrial muscle of the supra-orificial zone made direct contact with the superior initial group and the compact zone of the node and in 10% there was contact between the suborificial muscle and the inferior group and the compact part of the node. This configuration was not observed in relation to the middle and inferior groups

Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

List coloring in the absence of a linear forest.

The k-Coloring problem is to decide whether a graph can be colored with at most k colors such that no two adjacent vertices receive the same color. The Listk-Coloring problem requires in addition that every vertex u must receive a color from some given set L(u)⊆{1,…,k}. Let Pn denote the path on n vertices, and G+H and rH the disjoint union of two graphs G and H and r copies of H, respectively. For any two fixed integers k and r, we show that Listk-Coloring can be solved in polynomial time for graphs with no induced rP1+P5, hereby extending the result of Hoàng, Kamiński, Lozin, Sawada and Shu for graphs with no induced P5. Our result is tight; we prove that for any graph H that is a supergraph of P1+P5 with at least 5 edges, already List 5-Coloring is NP-complete for graphs with no induced H

Wealth condensation and "corruption" in a toy model

We discuss the wealth condensation mechanism in a simple toy economy in which individual agent’s wealths are distributed according to a Pareto power law and the overall wealth is fixed. The observed behaviour is the manifestation of a transition which occurs in Zero Range Processes (ZRPs) or "balls in boxes" models. An amusing feature of the transition in this context is that the condensation can be induced by increasing the exponent in the power law, which one might have naively assumed penalised greater wealths more

Endoscopic Obliteration for Bleeding Peptic Ulcer

A group of 133 patients treated for bleeding peptic ulcer in our Department, is reviewed. Within several hours of admission, all patients underwent upper gastrointestinal tract gastroscopy and obliteration of the bleeding ulcer. Bleeding gastric ulcers were found in 41 patients, and duodenal ulcers in 92 patients. Patients were classified according to the Forrest scale: IA – 11 patients, IB – 49 patients, IIA – 35 patients, lIB – 40 patients. In 126 (94.7%) patients the bleeding was stopped, and 7 required urgent surgery: 3 patients with gastric ulcer underwent gastrectomy, and 4 with duodenal ulcer – truncal vagotomy with pyloroplasty and had the bleeding site underpinned. Fifty-five patients underwent elective surgery: gastrectomy and vagotomy (18 patients with gastric ulcer), highly selective vagotomy (25 patients with duodenal ulcer) and truncal vagotomy and pyloroplasty (12 patients with duodenal ulcer). None of the patients was observed to have recurrent bleeding