Generalization of the convex-hull-and-line traveling salesman problem

Two instances of the traveling salesman problem, on the same node set (1,2 n} but with different cost matrices C and C, are equivalent iff there exist {a, hi: -1, n} such that for any 1 _i, j _n, j, C(i, j) C(i,j) q-a -t-bj [7]. One ofthe well-solved special cases of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution scheme for this class of TSP given in [9] to a more general class which is closed with respect to the above equivalence relation. The cost matrix in our general class is a certain composition of Kalmanson matrices. This gives a new, non-trivial solvable case of TSP

Some Necessary Conditions and a General Sufficiency Condition for the Validity of A Gilmore-Gomory Type Patching Scheme for the Traveling

One of the most celebrated polynomially solvable cases of the TSP is the Gilmore-Gomory TSP. The patching scheme for the problem developed by Gilmore and Gomory has several interesting features. Its generalization, called the GG-scheme, has been studied by several researchers and polynomially testable sufficiency conditions for its validity have been given, leading to polynomial schemes for large subclasses of the TSP. A good characterization of the subclass of the TSP for which the GG-scheme produces an optimal solution, is an outstanding open problem of both theoretical and practical significance. We give some necessary conditions and a new, polynomially testable sufficiency condition for the validity of the GG-scheme that properly includes all previously known such conditions. Key words: Traveling salesman problem, Gilmore-Gomory TSP, Patching Scheme, Polynomially solvable case

Trioid: A generalization of matroid and the associated polytope

We consider a generalization of the well known greedy algorithm, called m-step greedy algorithm, where m elements are examined in each iteration. When m = 1 or 2, the algorithm reduces to the standard greedy algorithm. For m = 3 we provide a complete characterization of the independence system, called trioid, where the m-step greedy algorithm guarantees an optimal solution for all weight functions. We also characterize the trioid polytope and propose a generalization of submodular functions

Improvement of hydrogen solubility and entrainment in hydrocracker feedstocks. Final technical report

The project consisted of two tasks: (1) development of a thermodynamic model for hydrogen solubility in hydrocarbons and extension of this model to predict solubility of hydrogen in hydrocracker feedstocks at conditions similar to those of hydrocracking operations, and (2) design and construction of a gas solubility apparatus to measure solubility of hydrogen in hydrocarbons and in hydrocracker feedstocks. The theoretical work proposed was fully accomplished by developing a sophisticated model for hydrogen solubility in hydrocarbons and in hydrocracker feedstocks at advanced temperatures and pressures. The proposed experimental work ran into a number of obstacles, especially to get the original and newly designed on-line sampling technique to function properly. A number of calibrations and tests for reproducibility were necessary to assure the accuracy of measured data. Although a very well designed gas solubility apparatus was built, not much time was left to generate significant hydrogen solubility data. The plans are to use the apparatus in future to measure hydrogen solubility data in liquid fuels to facilitate more efficient design of fuel conversion systems

The minimum spanning tree problem with conflict constraints and its variations

AbstractWe consider the minimum spanning tree problem with conflict constraints (MSTC). The problem is known to be strongly NP-hard and computing even a feasible solution is NP-hard. When the underlying graph is a cactus, we show that the feasibility problem is polynomially bounded whereas the optimization version is still NP-hard. When the conflict graph is a collection of disjoint cliques, (equivalently, when the conflict relation is transitive) we observe that MSTC can be solved in polynomial time. We also identify other special cases of MSTC that can be solved in polynomial time. Exploiting these polynomially solvable special cases we derive strong lower bounds. Also, various heuristic algorithms and feasibility tests are discussed along with preliminary experimental results. As a byproduct of this investigation, we show that if an ϵ-optimal solution to the maximum clique problem can be obtained in polynomial time, then a (3ϵ−1)-optimal solution to the maximum edge clique partitioning (Max-ECP) problem can be obtained in polynomial time. As a consequence, we have a polynomial time approximation algorithm for the Max-ECP with performance ratio O(n(loglogn)2log3n), improving the best previously known bound of O(n)

2-Commodity Integer Network Synthesis Problem

We consider the following 2-commodity, integer network synthesis problem: Given two n×n, non-negative, symmetric, integer-valued matrices R = (rij) and S = (sij) of minimum flow requirements of 2 different commodities, construct an undirected network G = [N, E, c] on node set N = {1, 2, . . . , n} with integer edge capacities {c(e) : e ∈ E}, such that: (i) for any two pairs (i, j) and (k, l), i ≠ j, k ≠ l, of nodes in N, we can simultaneously send rij units of flow of commodity 1 from i to j and skl units of flow of commodity 2 from k to l in G; and (ii) z = Σ {c(e) : e ∈ E} is minimum. We present strongly polynomial, combinatorial algorithms for certain special cases of the problem; and for the general problem, we present a strongly polynomial, combinatorial algorithm that produces a feasible solution with objective function value no more than (the optimal objective function value +3)

HIGH TEMPERATURE HIGH PRESSURE THERMODYNAMIC MEASUREMENTS FOR COAL MODEL COMPOUNDS

The flow VLE apparatus designed and built for a previous project was upgraded and recalibrated for data measurements for this project. The modifications include better and more accurate sampling technique, addition of a digital recorder to monitor temperature and pressure inside the VLE cell, and a new technique for remote sensing of the liquid level in the cell. VLE data measurements for three binary systems, tetralin-quinoline, benzene--ethylbenzene and ethylbenzene--quinoline, have been completed. The temperature ranges of data measurements were 325 C to 370 C for the first system, 180 C to 300 C for the second system, and 225 C to 380 C for the third system. The smoothed data were found to be fairly well behaved when subjected to thermodynamic consistency tests. SETARAM C-80 calorimeter was used for incremental enthalpy and heat capacity measurements for benzene--ethylbenzene binary liquid mixtures. Data were measured from 30 C to 285 C for liquid mixtures covering the entire composition range. An apparatus has been designed for simultaneous measurement of excess volume and incremental enthalpy of liquid mixtures at temperatures from 30 C to 300 C. The apparatus has been tested and is ready for data measurements. A flow apparatus for measurement of heat of mixing of liquid mixtures at high temperatures has also been designed, and is currently being tested and calibrated

High Temperature High Pressure Thermodynamic Measurements for Coal Model Compounds

The overall objective of this project is to develop a better thermodynamic model for predicting properties of high-boiling coal derived liquids, especially the phase equilibria of different fractions at elevated temperatures and pressures. The development of such a model requires data on vapor-liquid equilibria (VLE), enthalpy, and heat capacity which would be experimentally determined for binary systems of coal model compounds and compiled into a database. The data will be used to refine existing models such as UNIQUAC and UNIFAC. The flow VLE apparatus designed and built for a previous project was upgraded and recalibrated for data measurements for thk project. The modifications include better and more accurate sampling technique and addition of a digital recorder to monitor temperature, pressure and liquid level inside the VLE cell. VLE data measurements for system benzene-ethylbenzene have been completed. The vapor and liquid samples were analysed using the Perkin-Elmer Autosystem gas chromatography

Proteomics: in pursuit of effective traumatic brain injury therapeutics

Effective traumatic brain injury (TBI) therapeutics remain stubbornly elusive. Efforts in the field have been challenged by the heterogeneity of clinical TBI, with greater complexity among underlying molecular phenotypes than initially conceived. Future research must confront the multitude of factors comprising this heterogeneity, representing a big data challenge befitting the coming informatics age. Proteomics is poised to serve a central role in prescriptive therapeutic development, as it offers an efficient endpoint within which to assess post-TBI biochemistry. We examine rationale for multifactor TBI proteomic studies and the particular importance of temporal profiling in defining biochemical sequences and guiding therapeutic development. Lastly, we offer perspective on repurposing biofluid proteomics to develop theragnostic assays with which to prescribe, monitor and assess pharmaceutics for improved translation and outcome for TBI patients