Efficient Algorithms for Computing All Low s-t Edge Connectivities and Related Problems

Given an undirected unweighted graph G = (V, E) and an integer k ≥ 1, we consider the problem of computing the edge connectivities of all those (s, t) vertex pairs, whose edge connectivity is at most k. We present an algorithm with expected running time Õ(m + nk3) for this problem, where |V| = n and |E| = m. Our output is a weighted tree T whose nodes are the sets V1, V2,..., V l of a partition of V, with the property that the edge connectivity in G between any two vertices s ε Vi and t ε Vj, for i ≠ j, is equal to the weight of the lightest edge on the path between Vi and Vj in T. Also, two vertices s and t belong to the same Vi for any i if and only if they have an edge connectivity greater than k. Currently, the best algorithm for this problem needs to compute all-pairs min-cuts in an O(nk) edge graph; this takes Õ(m + n5/2kmin{k1/2, n1/6}) time. Our algorithm is much faster for small values of k; in fact, it is faster whenever k is o(n5/6). Our algorithm yields the useful corollary that in Õ(m + nc3) time, where c is the size of the global min-cut, we can compute the edge connectivities of all those pairs of vertices whose edge connectivity is at most αc for some constant α. We also present an Õ(m + n) Monte Carlo algorithm for the approximate version of this problem. This algorithm is applicable to weighted graphs as well. Our algorithm, with some modifications, also solves another problem called the minimum T-cut problem. Given T ⊆ V of even cardinality, we present an Õ(m + nk3) algorithm to compute a minimum cut that splits T into two odd cardinality components, where k is the size of this cut.

Scattering theory and linear optimal control: Regulator and servo problems

In this paper, several known computational solutions are readily obtained in a very natural way for the linear regulator, fixed end-point and servo-mechanism problems using a certain frame-work from scattering theory. The relationships between the solutions to the linear regulator problem with different terminal costs and the interplay between the forward and backward equations have enabled a concise derivation of the partitioned equations, the forward-backward equations, and Chandrasekhar equations for the problem. These methods have been extended to the fixed end-point, servo, and tracking problems.

Analysis of designed beta-hairpin peptides: molecular conformation and packing in crystals

The crystal structures of several designed peptide hairpins have been determined in order to establish features of molecular conformations and modes of aggregation in the crystals. Hairpin formation has been induced using a centrally positioned (D)Pro-Xxx segment (Xxx = (L)Pro, Aib, Ac(6)c, Ala; Aib = alpha-aminoisobutyric acid; Ac(6)c = 1-aminocyclohexane-1-carboxylic acid). Structures of the peptides Boc-Leu-Phe-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (1), Boc-Leu-Tyr-Val-(D)Pro-(L)Pro-Leu-Phe-Val-OMe (2, polymorphic forms labeled as 2a and 2b), Boc-Leu-Val-Val-(D)Pro-(L)Pro-Leu-Val-Val-OMe (3), Boc-Leu-Phe-Val-(D)Pro-Aib-Leu-Phe-Val-OMe (4, polymorphic forms labeled as 4a and 4b), Boc-Leu-Phe-Val-(D)Pro-Ac(6)c-Leu-Phe-Val-OMe (5) and Boc-Leu-Phe-Val-(D)Pro-Ala-Leu-Phe-Val-OMe (6) are described. All the octapeptides adopt type II' beta-turn nucleated hairpins, stabilized by three or four cross-strand intramolecular hydrogen bonds. The angle of twist between the two antiparallel strands lies in the range of -9.8 degrees to -26.7 degrees. A detailed analysis of packing motifs in peptide hairpin crystals is presented, revealing three broad modes of association: parallel packing, antiparallel packing and orthogonal packing. An attempt to correlate aggregation modes in solution with observed packing motifs in crystals has been made by indexing of crystal faces in the case of three of the peptide hairpins. The observed modes of hairpin aggregation may be of relevance in modeling multiple modes of association, which may provide insights into the structure of insoluble polypeptide aggregates.

A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.

3D simulation of the micro indentation process and relative problems research

In this paper the finite element method was used to simulate micro-scale indentation process. The several standard indenters were simulated with 3D finite element model. The emphasis of this paper was the differences between 2D axisymmetric cone model and

The economic impact of diseases and parasitic problems in freshwater fish production

Diseases and parasitic problems could constitute significant economic losses in fish production if not controlled, thus the need to continue monitoring its prevalence. Based on field studies on feral and intensively raised fish at the Kainji Lake Research Institute Nigeria, some diseases and parasitic problems have been identified. These include; helminthiasis; fungal disease; protozoa which include Myxosoma sp., Myxobolus spp., Henneguya sp., Trichodina sp., Ichthopthrius sp. bacterial mainly Aeromonas sp., Pseudomonas sp., mechanical injuries; death due to unknown causes and economic assessment of myxosporidian infection. Suggestion for disease control in fish production are recommended

Deviation from standard inflationary cosmology and the problems in ekpyrosis

There are two competing models of our universe right now. One is Big Bang with inflation cosmology. The other is the cyclic model with ekpyrotic phase in each cycle. This paper is divided into two main parts according to these two models. In the first part, we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $\langle a_{lm}a_{l'm'}^*\rangle$ of the spherical-harmonic coefficients. We then provide a model and study the two-point correlation of a massless scalar (the inflaton) when the stress tensor contains the energy density from an infinitely long straight cosmic string in addition to a cosmological constant. Finally, we discuss if inflation can reconcile with the Liouville's theorem as far as the fine-tuning problem is concerned. In the second part, we find several problems in the cyclic/ekpyrotic cosmology. First of all, quantum to classical transition would not happen during an ekpyrotic phase even for superhorizon modes, and therefore the fluctuations cannot be interpreted as classical. This implies the prediction of scale-free power spectrum in ekpyrotic/cyclic universe model requires more inspection. Secondly, we find that the usual mechanism to solve fine-tuning problems is not compatible with eternal universe which contains infinitely many cycles in both direction of time. Therefore, all fine-tuning problems including the flatness problem still asks for an explanation in any generic cyclic models.