Remarks on the Formulation of Quantum Mechanics on Noncommutative Phase Spaces

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry.Comment: 25 pages, JHEP3 style; minor changes; Published in JHE

A Weakly-Robust PTAS for Minimum Clique Partition in Unit Disk Graphs

We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a {\em weakly robust} polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths, it either (i) computes a clique partition or (ii) gives a certificate that the graph is not a UDG; for the case (i) that it computes a clique partition, we show that it is guaranteed to be within (1+\eps) ratio of the optimum if the input is UDG; however if the input is not a UDG it either computes a clique partition as in case (i) with no guarantee on the quality of the clique partition or detects that it is not a UDG. Noting that recognition of UDG's is NP-hard even if we are given edge lengths, our PTAS is a weakly-robust algorithm. Our algorithm can be transformed into an O(\frac{\log^* n}{\eps^{O(1)}}) time distributed PTAS. We consider a weighted version of the clique partition problem on vertex weighted UDGs that generalizes the problem. We note some key distinctions with the unweighted version, where ideas useful in obtaining a PTAS breakdown. Yet, surprisingly, it admits a (2+\eps)-approximation algorithm for the weighted case where the graph is expressed, say, as an adjacency matrix. This improves on the best known 8-approximation for the {\em unweighted} case for UDGs expressed in standard form.Comment: 21 pages, 9 figure

Rare association of turner syndrome with neurofibromatosis type 1 and tuberous sclerosis complex

We report a rare association of Turner syndrome with both Neurofibromatosis type I and Tuberous Sclerosis. The patient had XO karyotype with Turners stigmata and also had features of Neurofibromatosis 1 in the form of significant cafe-au-lait spots and Plexiform neurofibroma along with typical features of Tuberous Sclerosis complex. Pedigree analysis revealed that the elder brother of the proband in the family also suffered from Tuberous Sclerosis without the manifestation of Neurofibromatosis or any other genetic disorders. We hypothesize that these associations could be due to new independent mutations and also increased maternal and paternal age in a pre-disposition of Turner syndrome

A genetic algorithm

Castelli, M., Dondi, R., Manzoni, S., Mauri, G., & Zoppis, I. (2019). Top k 2-clubs in a network: A genetic algorithm. In J. J. Dongarra, J. M. F. Rodrigues, P. J. S. Cardoso, J. Monteiro, R. Lam, V. V. Krzhizhanovskaya, M. H. Lees, ... P. M. A. Sloot (Eds.), Computational Science. ICCS 2019: 19th International Conference, 2019, Proceedings (Vol. 5, pp. 656-663). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11540 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-030-22750-0_63The identification of cohesive communities (dense sub-graphs) is a typical task applied to the analysis of social and biological networks. Different definitions of communities have been adopted for particular occurrences. One of these, the 2-club (dense subgraphs with diameter value at most of length 2) has been revealed of interest for applications and theoretical studies. Unfortunately, the identification of 2-clubs is a computationally intractable problem, and the search of approximate solutions (at a reasonable time) is therefore fundamental in many practical areas. In this article, we present a genetic algorithm based heuristic to compute a collection of Top k 2-clubs, i.e., a set composed by the largest k 2-clubs which cover an input graph. In particular, we discuss some preliminary results for synthetic data obtained by sampling Erdös-Rényi random graphs.authorsversionpublishe

Investigation of the presence of an aliphatic biopolymer in cyanobacteria: Implications for kerogen formation

Algaenan has been suggested to be one of the main precursors of certain kerogens. It is a non-hydrolysable and insoluble biomolecule of high molecular weight. It has been found in a limited number of microalgae species. There is considerable uncertainty about its formation and preservation, as well as its role in kerogen formation and the implications for the global C cycle. We tested whether the cyanobacterium Chlorogloeopsis fritschii can synthesise a biomacromolecule similar to algaenan with potential to contribute to kerogen via selective preservation. Two freshwater green microalgae, Pseudochoricystis ellipsoidea and Scenedesmus obliquus, as well as C. fritschii, were subjected to harsh solvent extraction and hydrolysis steps to obtain an insoluble and non-hydrolysable macromolecule. The residues from all three species were analysed using pyrolysis–gas chromatography–mass spectrometry and solid-state nuclear magnetic resonance spectroscopy. The analysis revealed that C. fritschii indeed contains a resistant biomacromolecule exhibiting the characteristic aliphatic structure of algaenan, similar to the algaenan residues from the two microalgae. Due to the robust nature of Chlorogloeopsis compared with eukaryotes, it can prevail in extreme environmental conditions such as freezing, thawing, desiccation and overheating – conditions prevalent on the primeval earth. The presence of a resistant aliphatic biopolymer in Chlorogloeopsis suggests that cyanobacteria could have contributed to kerogen via selective preservation

On Structural Parameterizations of the Bounded-Degree Vertex Deletion Problem

We study the parameterized complexity of the Bounded-Degree Vertex Deletion problem (BDD), where the aim is to find a maximum induced subgraph whose maximum degree is below a given degree bound. Our focus lies on parameters that measure the structural properties of the input instance. We first show that the problem is W[1]-hard parameterized by a wide range of fairly restrictive structural parameters such as the feedback vertex set number, pathwidth, treedepth, and even the size of a minimum vertex deletion set into graphs of pathwidth and treedepth at most three. We thereby resolve an open question stated in Betzler, Bredereck, Niedermeier and Uhlmann (2012) concerning the complexity of BDD parameterized by the feedback vertex set number. On the positive side, we obtain fixed-parameter algorithms for the problem with respect to the decompositional parameter treecut width and a novel problem-specific parameter called the core fracture number

A generic algorithm for layout of biological networks

BackgroundBiological networks are widely used to represent processes in biological systems and to capture interactions and dependencies between biological entities. Their size and complexity is steadily increasing due to the ongoing growth of knowledge in the life sciences. To aid understanding of biological networks several algorithms for laying out and graphically representing networks and network analysis results have been developed. However, current algorithms are specialized to particular layout styles and therefore different algorithms are required for each kind of network and/or style of layout. This increases implementation effort and means that new algorithms must be developed for new layout styles. Furthermore, additional effort is necessary to compose different layout conventions in the same diagram. Also the user cannot usually customize the placement of nodes to tailor the layout to their particular need or task and there is little support for interactive network exploration.ResultsWe present a novel algorithm to visualize different biological networks and network analysis results in meaningful ways depending on network types and analysis outcome. Our method is based on constrained graph layout and we demonstrate how it can handle the drawing conventions used in biological networks.ConclusionThe presented algorithm offers the ability to produce many of the fundamental popular drawing styles while allowing the exibility of constraints to further tailor these layouts.publishe

Protein Tpr is required for establishing nuclear pore-associated zones of heterochromatin exclusion

Amassments of heterochromatin in somatic cells occur in close contact with the nuclear envelope (NE) but are gapped by channel- and cone-like zones that appear largely free of heterochromatin and associated with the nuclear pore complexes (NPCs). To identify proteins involved in forming such heterochromatin exclusion zones (HEZs), we used a cell culture model in which chromatin condensation induced by poliovirus (PV) infection revealed HEZs resembling those in normal tissue cells. HEZ occurrence depended on the NPC-associated protein Tpr and its large coiled coil-forming domain. RNAi-mediated loss of Tpr allowed condensing chromatin to occur all along the NE's nuclear surface, resulting in HEZs no longer being established and NPCs covered by heterochromatin. These results assign a central function to Tpr as a determinant of perinuclear organization, with a direct role in forming a morphologically distinct nuclear sub-compartment and delimiting heterochromatin distribution