Learning Convex Partitions and Computing Game-theoretic Equilibria from Best Response Queries

Suppose that an $m$-simplex is partitioned into $n$ convex regions having disjoint interiors and distinct labels, and we may learn the label of any point by querying it. The learning objective is to know, for any point in the simplex, a label that occurs within some distance $\epsilon$ from that point. We present two algorithms for this task: Constant-Dimension Generalised Binary Search (CD-GBS), which for constant $m$ uses $poly(n, \log \left( \frac{1}{\epsilon} \right))$ queries, and Constant-Region Generalised Binary Search (CR-GBS), which uses CD-GBS as a subroutine and for constant $n$ uses $poly(m, \log \left( \frac{1}{\epsilon} \right))$ queries. We show via Kakutani's fixed-point theorem that these algorithms provide bounds on the best-response query complexity of computing approximate well-supported equilibria of bimatrix games in which one of the players has a constant number of pure strategies. We also partially extend our results to games with multiple players, establishing further query complexity bounds for computing approximate well-supported equilibria in this setting.Comment: 38 pages, 7 figures, second version strengthens lower bound in Theorem 6, adds footnotes with additional comments and fixes typo

Three Wide-Separation L dwarf Companions from the Two Micron All Sky Survey: Gl 337C, Gl 618.1B, and HD 89744B

We present two confirmed wide separation L-dwarf common proper motion companions to nearby stars and one candidate identified from the Two Micron All Sky Survey. Spectral types from optical spectroscopy are L0 V, L2.5 V, and L8 V. Near-infrared low resolution spectra of the companions are provided as well as a grid of known objects spanning M6 V -- T dwarfs to support spectral type assignment for these and future L-dwarfs in the z'JHK bands. Using published measurements, we estimate ages of the companions from physical properties of the primaries. These crude ages allow us to estimate companion masses using theoretical low-mass star and brown dwarf evolutionary models. The new L-dwarfs in this paper bring the number of known wide-binary (Separation >= 100 AU) L-dwarf companions of nearby stars to nine. One of the L-dwarfs is a wide separation companion to the F7 IV-V + extrasolar planet system HD89744Ab.Comment: 20 pages including 6 tables and 4 figures, AJ, in pres

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers’ point of view

Internally Electrodynamic Particle Model: Its Experimental Basis and Its Predictions

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material particles, b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation and c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schr\"odinger equation, mass, Einstein mass-energy relation, Newton's law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A specific solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.Comment: Presentation at the 27th Int Colloq on Group Theo Meth in Phys, 200

The Structure, Anharmonic Vibrational Frequencies, and Intensities of NNHNN+

A semi-global potential energy surface (PES) and quartic force field (QFF) based on fitting high-level electronic structure energies are presented to describe the structures and spectroscopic properties of NNHNN+. The equilibrium structure of NNHNN+ is linear with the proton equidistant between the two nitrogen groups and thus of D(sub h) symmetry. Vibrational second-order perturbation theory (VPT2) calculations based on the QFF fails to describe the proton rattle motion, i.e., the antisymmetric proton stretch, due to the very flat nature of PES around the global minimum, but performs properly for other modes with sharper potential wells. Vibrational self-consistent field/virtual state configuration interaction (VSCF/VCI) calculations using a version of MULTIMODE without angular momentum terms successfully describe this motion and predict the fundamental to be at 759 cm(exp -1). This is in good agreement with the value of 746 cm(exp -1) from a fixed-node diffusion Monte Carlo calculation and the experimental Ar-tagged result of 743 cm(exp -1). Other VSCF/VCI energies are in good agreement with other experimentally reported ones. Both double-harmonic intensity and rigorous MULTIMODE intensity calculations show the proton transfer fundamental has a very strong intensity

A Recombination-Based Tabu Search Algorithm for the Winner Determination Problem

Abstract. We propose a dedicated tabu search algorithm (TSX_WDP) for the winner determination problem (WDP) in combinatorial auctions. TSX_WDP integrates two complementary neighborhoods designed re-spectively for intensification and diversification. To escape deep local optima, TSX_WDP employs a backbone-based recombination opera-tor to generate new starting points for tabu search and to displace the search into unexplored promising regions. The recombination operator operates on elite solutions previously found which are recorded in an global archive. The performance of our algorithm is assessed on a set of 500 well-known WDP benchmark instances. Comparisons with five state of the art algorithms demonstrate the effectiveness of our approach

Towards an Understanding of the Effect of Adding a Foam Core on the Blast Performance of Glass Fibre Reinforced Epoxy Laminate Panels

This paper presents insights into the blast response of sandwich panels with lightweight foam cores and asymmetric (different thicknesses) glass fibre epoxy face sheets. Viscously damped elastic vibrations were observed in the laminates (no core), while the transient response of the sandwich panels was more complex, especially after the peak displacement was observed. The post-peak residual oscillations in the sandwich panels were larger and did not decay as significantly with time when compared to the equivalent mass laminate panel test. Delamination was the predominant mode of failure on the thinner facesheet side of the sandwich panel, whereas cracking and matrix failure were more prominent on the thicker side (which was exposed to the blast). The type of constituent materials used and testing conditions, including the clamping method, influenced the resulting failure modes observed. A probable sequence of damage in the sandwich panels was proposed, based on the transient displacement measurements, a post-test failure analysis, and consideration of the stress wave propagation through the multilayered, multimaterial structure. This work demonstrates the need for detailed understanding of the transient behaviour of multilayered structures with significant elastic energy capacity and a wide range of possible damage mechanisms. The work should prove valuable to structural engineers and designers considering the deployment of foam-core sandwich panels or fibre reinforced polymer laminates in applications when air-blast loading may pose a credible threat

Identification and characterization of the orf virus type I topoisomerase

AbstractVaccinia virus (VV) and Shope fibroma virus (SFV), representatives of the orthopox and leporipox genera, respectively,encode type I DNA topoisomerases. Here we report that the 957-nt F4R open reading frame of orf virus (OV), a representative of the parapox genus, is predicted to encode a 318-aa protein with extensive homology to these enzymes. The deduced amino acid sequence of F4R has 54.7 and 50.6% identity with the VV and SFV enzymes, respectively. One hundred forty amino acids are predicted to be conserved in all three proteins. The F4R protein was expressed in Escherichia coli under the control of an inducible T7 promoter, partially purified, and shown to be a bona fide type I topoisomerase. Like the VV enzyme, the OV enzyme relaxed negatively supercoiled DNA in the absence of divalent cations or ATP and formed a transient covalent intermediate with cleaved DNA that could be visualized by SDS-PAGE. Both the noncovalent and covalent protein/DNA complexes could be detected in an electrophoretic mobility shift assay. The initial PCR used to prepare expression constructs yielded a mutant allele of the OV topoisomerase with a G-A transition at nt 677 that was predicted to replace a highly conserved Tyr residue with a Cys. This allele directed the expression of an enzyme which retained noncovalent DNA binding activity but was severely impaired in DNA cleavage and relaxation. Incubation of pUC19 DNA with the wild-type OV or VV enzyme yielded an indistinguishable set of DNA cleavage fragments, although the relative abundance of the fragments differed for the two enzymes. Using a duplex oligonucleotide substrate containing the consensus site for the VV enzyme, we demonstrated that the OV enzyme also cleaved efficiently immediately downstream of the sequence CCCTT↓