Join-Reachability Problems in Directed Graphs

For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all graphs of G. Our goal is to compute an efficient representation of J(G). In particular, we consider two versions of this problem. In the explicit version we wish to construct the smallest join-reachability graph for G. In the implicit version we wish to build an efficient data structure (in terms of space and query time) such that we can report fast the set of vertices that reach a query vertex in all graphs of G. This problem is related to the well-studied reachability problem and is motivated by emerging applications of graph-structured databases and graph algorithms. We consider the construction of join-reachability structures for two graphs and develop techniques that can be applied to both the explicit and the implicit problem. First we present optimal and near-optimal structures for paths and trees. Then, based on these results, we provide efficient structures for planar graphs and general directed graphs

Monte Carlo algorithm based on internal bridging moves for the atomistic simulation of thiophene oligomers and polymers

We introduce a powerful Monte Carlo (MC) algorithm for the atomistic simulation of bulk models of oligo- and poly-thiophenes by redesigning MC moves originally developed for considerably simpler polymer structures and architectures, such as linear and branched polyethylene, to account for the ring structure of the thiophene monomer. Elementary MC moves implemented include bias reptation of an end thiophene ring, flip of an internal thiophene ring, rotation of an end thiophene ring, concerted rotation of three thiophene rings, rigid translation of an entire molecule, rotation of an entire molecule and volume fluctuation. In the implementation of all moves we assume that thiophene ring atoms remain rigid and strictly co-planar; on the other hand, inter-ring torsion and bond bending angles remain fully flexible subject to suitable potential energy functions. Test simulations with the new algorithm of an important thiophene oligomer, {\alpha}-sexithiophene ({\alpha}-6T), at a high enough temperature (above its isotropic-to-nematic phase transition) using a new united atom model specifically developed for the purpose of this work provide predictions for the volumetric, conformational and structural properties that are remarkably close to those obtained from detailed atomistic Molecular Dynamics (MD) simulations using an all-atom model. The new algorithm is particularly promising for exploring the rich (and largely unexplored) phase behavior and nanoscale ordering of very long (also more complex) thiophene-based polymers which cannot be addressed by conventional MD methods due to the extremely long relaxation times characterizing chain dynamics in these systems

Evaluation of Compton scattering sequence reconstruction algorithms for a portable position sensitive radioactivity detector based on pixelated Cd(Zn)Te crystals

We present extensive simulation studies on the performance of algorithms for the Compton sequence reconstruction used for the development of a portable spectroscopic instrument (COCAE), with the capability to localize and identify radioactive sources, by exploiting the Compton scattering imaging. Various Compton Sequence reconstruction algorithms have been compared using a large number of simulated events. These algorithms are based on Compton kinematics, as well as on statistical test criteria that exploit the redundant information of events having two or more photon interactions in the active detector's volume. The efficiency of the best performing technique is estimated for a wide range of incident gamma-ray photons emitted from point-like gamma sources.Comment: 16 pages, 17 figure

Μαθηματική Προτυποποίηση του νευρομοντέλου Hodgkin - Huxley

68 σ.Το περιεχόμενο αυτής της διπλωματικής εργασίας είναι η μαθηματική κατασκευή και παρουσίαση του μοντέλου Hodgkin – Huxley που αφορά στη διάδοση του δυναμικού δράσης στο γιγαντιαίο άξονα του καλαμαριού, καθώς και η αριθμητική επίλυση του. Τα δυναμικά δράσης αποτελούν το μηχανισμό μετάδοσης της πληροφορίας από κύτταρο σε κύτταρο. Έτσι περιγράφοντας μαθηματικά το μοντέλο Hodgkin – Huxley γίνεται κατανοητός ο τρόπος με τον οποίο λειτουργεί ο οργανισμός μας όταν μεταδίδεται κάποια πληροφορία στα νευρικά κύτταρα. Στην εισαγωγή δίνεται το απαραίτητο βιολογικό υπόβαθρο και οι αναγκαίες έννοιες που χρειάζονται για την διαδικασία παραγωγής του μοντέλου. Στο δεύτερο κεφάλαιο «Θεμέλια του μοντέλου Hodgkin - Huxley» παρουσιάζονται αναγκαίες εξισώσεις πάνω στις οποίες στηρίζεται η παραγωγή του μοντέλου Hodgkin - Huxley. Στο τρίτο κεφάλαιο «Κατασκευή του μοντέλου Hodgkin - Huxley» γίνεται η κατασκευή του μοντέλου Hodgkin – Huxley από καθαρά μαθηματική σκοπιά, καταλήγοντας σε ένα σύστημα τεσσάρων μη γραμμικών διαφορικών εξισώσεων που περιγράφουν την απόκριση των συναρτήσεων των πυλών και της συνάρτησης του δυναμικού της μεμβράνης συναρτήσει του χρόνου όταν πυροδοτείται ένα δυναμικό δράσης. Στο τέταρτο και τελευταίο κεφάλαιο «Αριθμητικές μέθοδοι για την επίλυση του μοντέλου Hodgkin - Huxley» επιλύεται αριθμητικά το μοντέλο Hodgkin – Huxley με γνωστές αριθμητικές μεθόδους και με τη βοήθεια της γλώσσας προγραμματισμού Matlab γίνονται οι γραφικές παραστάσεις των συναρτήσεων του μοντέλου συναρτήσει του χρόνου.Content of this thesis is the mathematical structure and presentation of the Hodgkin - Huxley model on the propagation of action potentials in the giant squid axon and the numerical solution of it. Action potentials are the transmission mechanism of information from cell to cell. So describing the Hodgkin - Huxley model we understand the way our body works when transmitting any information on nerve cells. In the introduction the necessary biological background and concepts needed are given for the production process of this model. In the second chapter, "Foundations of the Hodgkin – Huxley model» necessary equations are presented underpinning the production of the model. The third chapter "Construction of the Hodgkin – Huxley model» presents the construction of Hodgkin - Huxley model from a purely mathematical point of view, resulting in a system of four nonlinear differential equations describing the response of the gate functions and the function of membrane potential versus time when an action potential is triggered. In the fourth and final chapter "Numerical methods for solving the Hodgkin – Huxley model» the Hodgkin – Huxley model is numerically solved with known numerical methods and function graphs are plotted using Matlab programming languageΖάγκος Δ. Λουκά

The ℓs\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665

Differences in transcription between free-living and CO_2-activated third-stage larvae of Haemonchus contortus

Background: The disease caused by Haemonchus contortus, a blood-feeding nematode of small ruminants, is of major economic importance worldwide. The infective third-stage larva (L3) of this gastric nematode is enclosed in a cuticle (sheath) and, once ingested with herbage by the host, undergoes an exsheathment process that marks the transition from the free-living (L3) to the parasitic (xL3) stage. This study explored changes in gene transcription associated with this transition and predicted, based on comparative analysis, functional roles for key transcripts in the metabolic pathways linked to larval development. Results: Totals of 101,305 (L3) and 105,553 (xL3) expressed sequence tags (ESTs) were determined using 454 sequencing technology, and then assembled and annotated; the most abundant transcripts encoded transthyretin-like, calcium-binding EF-hand, NAD(P)-binding and nucleotide-binding proteins as well as homologues of Ancylostoma-secreted proteins (ASPs). Using an in silico-subtractive analysis, 560 and 685 sequences were shown to be uniquely represented in the L3 and xL3 stages, respectively; the transcripts encoded ribosomal proteins, collagens and elongation factors (in L3), and mainly peptidases and other enzymes of amino acid catabolism (in xL3). Caenorhabditis elegans orthologues of transcripts that were uniquely transcribed in each L3 and xL3 were predicted to interact with a total of 535 other genes, all of which were involved in embryonic development. Conclusion: The present study indicated that some key transcriptional alterations taking place during the transition from the L3 to the xL3 stage of H. contortus involve genes predicted to be linked to the development of neuronal tissue (L3 and xL3), formation of the cuticle (L3) and digestion of host haemoglobin (xL3). Future efforts using next-generation sequencing and bioinformatic technologies should provide the efficiency and depth of coverage required for the determination of the complete transcriptomes of different developmental stages and/or tissues of H. contortus as well as the genome of this important parasitic nematode. Such advances should lead to a significantly improved understanding of the molecular biology of H. contortus and, from an applied perspective, to novel methods of intervention

Gravito-magnetic instabilities in anisotropically expanding fluids

Gravitational instabilities in a magnetized Friedman - Robertson - Walker (FRW) Universe, in which the magnetic field was assumed to be too weak to destroy the isotropy of the model, are known and have been studied in the past. Accordingly, it became evident that the external magnetic field disfavors the perturbations' growth, suppressing the corresponding rate by an amount proportional to its strength. However, the spatial isotropy of the FRW Universe is not compatible with the presence of large-scale magnetic fields. Therefore, in this article we use the general-relativistic (GR) version of the (linearized) perturbed magnetohydrodynamic equations with and without resistivity, to discuss a generalized Jeans criterion and the potential formation of density condensations within a class of homogeneous and anisotropically expanding, self-gravitating, magnetized fluids in curved space-time. We find that, for a wide variety of anisotropic cosmological models, gravito-magnetic instabilities can lead to sub-horizonal, magnetized condensations. In the non-resistive case, the power spectrum of the unstable cosmological perturbations suggests that most of the power is concentrated on large scales (small k), very close to the horizon. On the other hand, in a resistive medium, the critical wave-numbers so obtained, exhibit a delicate dependence on resistivity, resulting in the reduction of the corresponding Jeans lengths to smaller scales (well bellow the horizon) than the non-resistive ones, while increasing the range of cosmological models which admit such an instability.Comment: 10 pages RevTex, 4 figures, accepted for publication in the International Journal of Modern Physics

Radiation hardness qualification of PbWO4 scintillation crystals for the CMS Electromagnetic Calorimeter

This is the Pre-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2010 IOPEnsuring the radiation hardness of PbWO4 crystals was one of the main priorities during the construction of the electromagnetic calorimeter of the CMS experiment at CERN. The production on an industrial scale of radiation hard crystals and their certification over a period of several years represented a difficult challenge both for CMS and for the crystal suppliers. The present article reviews the related scientific and technological problems encountered