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

A case of an accessory testicular artery

Dissection of an adult male cadaver revealed the presence of an accessory left testicular artery in addition to the normal right and left testicular arteries. In this case the accessory left testicular artery originated from the ventrolateral wall of the descending aorta. The origin was located between the superior mesenteric artery and the left renal vein. The accessory artery continued to course from the aorta laterally toward the superior ventral portion of the left kidney and then passed ventrally to the kidney on its course inferiorly to the pelvic region. Communication was observed between the accessory left testicular artery and the left renal artery. This variation of gonadal vasculature is of interest from the point of view of its embryogenesis, and possible clinical significance

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

Anatomical variations of the superficial and deep palmar arches

The use of radial arteries as an arterial bypass conduit is an invasive procedure which is becoming popular among various medical centres. The greatest risk associated with harvesting the radial artery is ischaemia of the soft tissues of the hand. In this study we dissected 200 hands derived from 100 formalin-fixed cadavers in order to identify arterial patterns that will allow safe removal of the radial artery for use in bypass procedures. A complete superficial palmar arch (SPA) was found in 90% of the cases and divided into 5 types, while the remaining 10% possessed an incomplete palmar arch. Types of SPA are designated by the letter S. In type S-I (40%), the SPA is formed by anastomosis of the superficial volar branch of the radial artery to the ulnar artery. Type S-II (35%) is formed entirely of the ulnar artery. Type S-III (15%) is formed by anastomosis of the ulnar and median arteries. Type S-IV (6%) is formed by anastomosis of the ulnar, radial, and median arteries and Type S-V (4%) is formed by a branch of the deep palmar arch (DPA) communicating with the SPA.DPA was identified in all specimens and classified into three types, all designated by the letter D. Type D-I (60%) is formed by anastomosis of the deep volar branch of the radial artery and the inferior deep branch of the ulnar branch. Type D-II (30%) is formed by anastomosis of the deep volar branch of the radial artery and the superior deep branch of the ulnar artery. Type D-III (10%) is formed by anastomosis of the deep volar branch of the radial artery with both deep branches of the ulnar artery. This data could provide an important source of information for vascular surgeons harvesting radial arteries