Nash bargaining in ordinal environments

We analyze the implications of Nash’s (1950) axioms in ordinal bargaining environments; there, the scale invariance axiom needs to be strenghtened to take into account all order-preserving transformations of the agents’ utilities. This axiom, called ordinal invariance, is a very demanding one. For two-agents, it is violated by every strongly individually rational bargaining rule. In general, no ordinally invariant bargaining rule satisfies the other three axioms of Nash. Parallel to Roth (1977), we introduce a weaker independence of irrelevant alternatives axiom that we argue is better suited for ordinally invariant bargaining rules. We show that the three-agent Shapley-Shubik bargaining rule uniquely satisfies ordinal invariance, Pareto optimality, symmetry, and this weaker independence of irrelevant alternatives axiom. We also analyze the implications of other independence axioms

Fully Dynamic Matching in Bipartite Graphs

Maximum cardinality matching in bipartite graphs is an important and well-studied problem. The fully dynamic version, in which edges are inserted and deleted over time has also been the subject of much attention. Existing algorithms for dynamic matching (in general graphs) seem to fall into two groups: there are fast (mostly randomized) algorithms that do not achieve a better than 2-approximation, and there slow algorithms with \O(\sqrt{m}) update time that achieve a better-than-2 approximation. Thus the obvious question is whether we can design an algorithm -- deterministic or randomized -- that achieves a tradeoff between these two: a $o(\sqrt{m})$ approximation and a better-than-2 approximation simultaneously. We answer this question in the affirmative for bipartite graphs. Our main result is a fully dynamic algorithm that maintains a 3/2 + \eps approximation in worst-case update time O(m^{1/4}\eps^{/2.5}). We also give stronger results for graphs whose arboricity is at most \al, achieving a (1+ \eps) approximation in worst-case time O(\al (\al + \log n)) for constant \eps. When the arboricity is constant, this bound is $O(\log n)$ and when the arboricity is polylogarithmic the update time is also polylogarithmic. The most important technical developement is the use of an intermediate graph we call an edge degree constrained subgraph (EDCS). This graph places constraints on the sum of the degrees of the endpoints of each edge: upper bounds for matched edges and lower bounds for unmatched edges. The main technical content of our paper involves showing both how to maintain an EDCS dynamically and that and EDCS always contains a sufficiently large matching. We also make use of graph orientations to help bound the amount of work done during each update.Comment: Longer version of paper that appears in ICALP 201

Magnetic field induced charge and spin instabilities in cuprate superconductors

A d-wave superconductor, subject to strong phase fluctuations, is known to suffer an antiferromagnetic instability closely related to the chiral symmetry breaking in (2+1)-dimensional quantum electrodynamics (QED3). On the basis of this idea we formulate a "QED3 in a box" theory of local instabilities of a d-wave superconductor in the vicinity of a single pinned vortex undergoing quantum fluctuations around its equilibrium position. As a generic outcome we find an incommensurate 2D spin density wave forming in the neighborhood of a vortex with a concomitant "checkerboard" pattern in the local electronic density of states, in agreement with recent neutron scattering and tunneling spectroscopy measurements.Comment: 4 pages REVTeX + 2 PostScript figures included in text. Version to appear in PRL (minor stylistic changes, references updated). For related work and info visit http://www.physics.ubc.ca/~fran

Do measures of memory, language, and attention predict eyewitness memory in children with and without autism?

Background & aims. There are few investigations of the relationship between cognitive abilities (memory, language and attention) and children’s eyewitness performance in typically developing children (TD), and even fewer in children on the autism spectrum. Such investigations are important to identify key cognitive processes underlying eyewitness recall, and assess how predictive such measures are compared to non-verbal IQ, diagnostic group status (autism or TD) and age. Methods. A total of 272 children (162 boys; 110 girls) of age 76 months to 142 months (M = 105 months) took part in this investigation: 71 children with autism and 201 TD children. The children saw a staged event involving a minor mock crime and were asked about what they had witnessed in an immediate Brief Interview. This focused on free recall, included a small number of open-ended questions, and was designed to resemble an initial evidence gathering statement taken by police officers arriving at a crime scene. Children were also given standardised tests of intelligence, memory, language and attention. Results & conclusions. Despite the autism group recalling significantly fewer items of correct information than the TD group at Brief Interview, both groups were equally accurate in their recall: 89% of details recalled by the TD group and 87% of the details recalled by the autism group were correct. To explore the relationship between Brief Interview performance and the cognitive variables, alongside age, diagnostic group status and non-verbal IQ, multiple hierarchical regression analyses were conducted, with Brief Interview performance as the dependant variable. Age and diagnostic group status were significant predictors of correct recall, whereas non-verbal IQ was less important. After age, non-verbal IQ and diagnostic group status had been accounted for, the only cognitive variables that were significant predictors of Brief Interview performance were measures of memory (specifically, memory for faces and memory for stories). There was little evidence of there being differences between the autism and TD groups in the way the cognitive variables predicted the Brief Interview. Implications. The findings provide reassurance that age – the most straightforward information to which all relevant criminal justice professionals have access – provides a helpful indication of eyewitness performance. The accuracy of prediction can be improved by knowing the child’s diagnostic status (i.e., whether the child is on the autism spectrum), and further still by using more specific assessments (namely memory for faces and memory for stories), possibly via the input of a trained professional. Importantly, the findings also confirm that whilst children with autism may recall less information than TD children, the information they do recall is just as accurate

Normal frames for general connections on differentiable fibre bundles

The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The existence of bundle coordinates normal at a given point and/or along injective horizontal path is proved. A necessary and sufficient condition of existence of bundle coordinates normal along injective horizontal mappings is derived.Comment: 24 LaTeX pages. The packages AMS-LaTeX and amsfonts are required. In version 2 some results are generalized and proved under weaker conditions. For other papers on the same topic view the "publication" pages at http://theo.inrne.bas.bg/~bozho

Identification of A-colored Stars and Structure in the Halo of the Milky Way from SDSS Commissioning Data

A sample of 4208 objects with magnitude 15 < g* < 22 and colors of main sequence A stars has been selected from 370 square degrees of Sloan Digital Sky Survey (SDSS) commissioning observations. The data is from two long, narrow stripes, each with an opening angle of greater than 60 deg, at Galactic latitudes 36 < abs(b) < 63 on the celestial equator. An examination of the sample's distribution shows that these stars trace considerable substructure in the halo. Large overdensities of A-colored stars in the North at (l,b,R) = (350, 50, 46 kpc) and in the South at (157, -58, 33 kpc) and extending over tens of degrees are present in the halo of the Milky Way. Using photometry to separate the stars by surface gravity, both structures are shown to contain a sequence of low surface gravity stars consistent with identification as a blue horizontal branch (BHB). Both structures also contain a population of high surface gravity stars two magnitudes fainter than the BHB stars, consistent with their identification as blue stragglers (BSs). From the numbers of detected BHB stars, lower limits to the implied mass of the structures are 6x10^6 M_sun and 2x10^6 M_sun. The fact that two such large clumps have been detected in a survey of only 1% of the sky indicates that such structures are not uncommon in the halo. Simple spheroidal parameters are fit to a complete sample of the remaining unclumped BHB stars and yield (at r < 40 kpc) a fit to a halo distribution with flattening (c/a = 0.65+/-0.2) and a density falloff exponent of alpha = -3.2+/-0.3.Comment: AASTeX v5_0, 26 pages, 1 table, 20 figures, ApJ accepte

Infrared cutoff dependence of the critical flavor number in three-dimensional QED

We solve, analytically and numerically, a gap equation in parity invariant QED_3 in the presence of an infrared cutoff \mu and derive an expression for the critical fermion number N_c as a function of \mu. We argue that this dependence of N_c on the infrared scale might solve the discrepancy between continuum Schwinger-Dyson equations studies and lattice simulations of QED_3.Comment: 5 pages, 1 figure (revtex4), final versio