Dynamic Programming for Graphs on Surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2^{O(k log k)} n steps. Our approach combines tools from topological graph theory and analytic combinatorics. In particular, we introduce a new type of branch decomposition called "surface cut decomposition", generalizing sphere cut decompositions of planar graphs introduced by Seymour and Thomas, which has nice combinatorial properties. Namely, the number of partial solutions that can be arranged on a surface cut decomposition can be upper-bounded by the number of non-crossing partitions on surfaces with boundary. It follows that partial solutions can be represented by a single-exponential (in the branchwidth k) number of configurations. This proves that, when applied on surface cut decompositions, dynamic programming runs in 2^{O(k)} n steps. That way, we considerably extend the class of problems that can be solved in running times with a single-exponential dependence on branchwidth and unify/improve most previous results in this direction.Comment: 28 pages, 3 figure

Dynamic programming for graphs on surfaces

We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on n vertices and branchwidth at most k. Our technique applies to general families of problems where standard dynamic programming runs in 2O(k·log k). Our approach combines tools from topological graph theory and analytic combinatorics.Postprint (updated version

Golf Club Valse

https://digitalcommons.library.umaine.edu/mmb-ps/3502/thumbnail.jp

Coordinate representation of particle dynamics in AdS and in generic static spacetimes

We discuss the quantum dynamics of a particle in static curved spacetimes in a coordinate representation. The scheme is based on the analysis of the squared energy operator E^2, which is quadratic in momenta and contains a scalar curvature term. Our main emphasis is on AdS spaces, where this term is fixed by the isometry group. As a byproduct the isometry generators are constructed and the energy spectrum is reproduced. In the massless case the conformal symmetry is realized as well. We show the equivalence between this quantization and the covariant quantization, based on the Klein-Gordon type equation in AdS. We further demonstrate that the two quantization methods in an arbitrary (N+1)-dimensional static spacetime are equivalent to each other if the scalar curvature terms both in the operator E^2 and in the Klein-Gordon type equation have the same coefficient equal to (N-1)/(4N).Comment: 14 pages, no figures, typos correcte

An Experimental Investigation of NACA Submerged Inlets at High Subsonic Speeds I: Inlets Forward of the Wing Leading Edge

This report covers the first part of an experimental investigation of NACA submerged inlets at four locations on the fuselage of a fighter airplane model for Mach numbers from 0.30 to 0.875. Data are presented showing the characteristics of the model without inlets and with inlets 16.7 percent of the root chord forward of the wing-root leading edge and equipped with small boundary-layer deflectors. The data show that variations in the mass of air entering the inlet had a large effect on the ram-recovery ratio. Representative values of ram-recovery ratio were 0.50 with zero flow, 0.90 with 0.6 mass-flow coefficient, and 0.95 with 1.00 mass-flow coefficient. Variations in Mach number and angle of attack, in general, caused less than a 0.03 variation in the ram-recovery ratio

Efficient Exact Algorithms on Planar Graphs: Exploiting Sphere Cut Decompositions

A divide-and-conquer strategy based on variations of the Lipton-Tarjan planar separator theorem has been one of the most common approaches for solving planar graph problems for more than 20 years. We present a new framework for designing fast subexponential exact and parameterized algorithms on planar graphs. Our approach is based on geometric properties of planar branch decompositions obtained by Seymour & Thomas, combined with refined techniques of dynamic programming on planar graphs based on properties of non-crossing partitions. Compared to divide-and-conquer algorithms, the main advantages of our method are a) it is a generic method which allows to attack broad classes of problems; b) the obtained algorithms provide a better worst case analysis. To exemplify our approach we show how to obtain an O(26.903√n) time algorithm solving weighted HAMILTONIAN CYCLE. We observe how our technique can be used to solve PLANAR GRAPH TSP in time O(29.8594√n). Our approach can be used to design parameterized algorithms as well. For example we introduce the first 2O(√ k)nO(1) time algorithm for parameterized Planar k-cycle by showing that for a given k we can decide if a planar graph on n vertices has a cycle of length at least k in time O(213.6√kn + n3)

Comparative study of gp130 cytokine effects on corticotroph AtT-20 cells - Redundancy or specificity of neuroimmunoendocrine modulators?

Objective: This comparative in vitro study examined the effects of all known gp130 cytokines on murine corticotroph AtT-20 cell function. Methods: Cytokines were tested at equimolar concentrations from 0.078 to 10 nM. Tyrosine phosphorylation of the signal transducer and activator of transcription ( STAT) 3 and STAT1, the STAT-dependent suppressor of cytokine signaling (SOCS)-3 promoter activity, SOCS-3 gene expression, STAT-dependent POMC promoter activity and adrenocorticotropic hormone ( ACTH) secretion were determined. Results: Leukemia inhibitory factor (LIF), human oncostatin M (OSM) and cardiotrophin (CT)-1 (LIFR/gp130 ligands), as well as ciliary neurotrophic factor ( CNTF) and novel neurotrophin1/B-cell stimulating factor-3 (CNTFRalpha/LIFR/gp130 ligands) are potent stimuli of corticotroph cells in vitro. In comparison, interleukin (IL)-6 (IL-6R/gp130 ligand) and IL-11 (IL-11R/gp130 ligand) exhibited only modest direct effects on corticotrophs, while murine OSM (OSMR/gp130 ligand) showed no effect. Conclusion: (i) CNTFR complex ligands are potent stimuli of corticotroph function, comparable to LIFR complex ligands; (ii) IL-6 and IL-11 are relatively weak direct stimuli of corticotroph function; (iii) differential effects of human and murine OSM suggest that LIFR/gp130 (OSMR type I) but not OSMR/gp130 (OSMR type II) are involved in corticotroph signaling. (iv) CT-1 has the hitherto unknown ability to stimulate corticotroph function, and (v) despite redundant immuno-neuroendocrine effects of different gp130 cytokines, corticotroph cells are preferably activated through the LIFR and CNTFR complexes. Copyright (C) 2004 S. Karger AG, Basel

Laparoscopic Intragastric Removal of Giant Trichobezoar

This report describes a laparoscopic approach for the removal of a large gastric bezoar

An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure

The paper presents an O^*(1.2312^n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bounds of O^*(1.251^n) by Iwama and Nakashima and O^*(1.260^n) by Eppstein. Our algorithm is a simple branch-and-search algorithm. The only branch rule is designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.Comment: 24 pages and 4 figure

Field Infestation of Phaseolus vulgaris by Acanthoscelides obtectus (Coleoptera: Bruchidae), Parasitoid Abundance, and Consequences for Storage Pest Control

Over a period of 3 yr we collected 19 samples (1 kg each) of recently harvested beans (Phaseolus vulgaris L.) from eight small-scale farms in Restrepo, Valle de Cauca, Colombia. Initial infestation by Acanthoscelides obtectus (Say) was low, but frequent. At harvest, 90% of the bean samples were infested by the weevil. The average level of infestation was 16 weevils per 1,000 beans, with a maximum of 55 weevils. Infested beans usually carried multiple larvae with a maximum of 13 larvae per bean. Emergence data indicate that oviposition by A. obtectus in the field is confined to a very short period before harvest. This relatively narrow time window can be exploited for proper timing of control measures. Only one species of parasitoid, Horismenus ashmeadii (Dalla Torre) (Hymenoptera: Eulophidae), was recorded, emerging from 21% of the samples. Samples with parasitoids had an average of five parasitoids per 1,000 beans, with a maximum of 12 parasitoids. This represented a parasitization level of 18%. During the 16 wk of storage, two weevil generations emerged, which caused visible damage in 0.5 and 34% of the beans (average of 14%). Although H. ashmeadii was successful in attacking the first generation of A. obtectus in the field, it failed to attack or develop under storage conditions. This indivates H. ashmeadii cannot serve as a postharvest control agen