On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Polarization and readout of coupled single spins in diamond

We study the coupling of a single nitrogen-vacancy center in diamond to a nearby single nitrogen defect at room temperature. The magnetic dipolar coupling leads to a splitting in the electron spin resonance frequency of the nitrogen-vacancy center, allowing readout of the state of a single nitrogen electron spin. At magnetic fields where the spin splitting of the two centers is the same we observe a strong polarization of the nitrogen electron spin. The amount of polarization can be controlled by the optical excitation power. We combine the polarization and the readout in time-resolved pump-probe measurements to determine the spin relaxation time of a single nitrogen electron spin. Finally, we discuss indications for hyperfine-induced polarization of the nitrogen nuclear spin

Co-evolutionnary network approach to cultural dynamics controlled by intolerance

Starting from Axelrod's model of cultural dissemination, we introduce a rewiring probability, enabling agents to cut the links with their unfriendly neighbors if their cultural similarity is below a tolerance parameter. For low values of tolerance, rewiring promotes the convergence to a frozen monocultural state. However, intermediate tolerance values prevent rewiring once the network is fragmented, resulting in a multicultural society even for values of initial cultural diversity in which the original Axelrod model reaches globalization

On the regularization ambiguities in loop quantum gravity

One of the main achievements of LQG is the consistent quantization of the Wheeler-DeWitt equation which is free of UV problems. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities there is the one associated to the SU(2) unitary rep. used in the diffeomorphism covariant pointsplitting regularization of nonlinear funct. of the connection. This ambiguity is labelled by a halfinteger m and, here, it is referred to as the m-ambiguity. The aim of this paper is to investigate the important implications of this ambiguity./ We first study 2+1 gravity quantized in canonical LQG. Only when the regularization of the quantum constraints is performed in terms of the fundamental rep. of the gauge group one obtains the usual TQFT. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear cut choice in the quantization of the constraints in 2+1 LQG./ We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher unit. rep. quantizations of the Hamiltonian constraint. Although the analysis is not complete in D=3+1--due to the difficulties associated to the definition of the physical inner product--it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find physical solutions associated to spin-two local excitations.Comment: 21 page

Aperiodic invariant continua for surface homeomorphisms

We prove that if a homeomorphism of a closed orientable surface S has no wandering points and leaves invariant a compact, connected set K which contains no periodic points, then either K=S and S is a torus, or $K$ is the intersection of a decreasing sequence of annuli. A version for non-orientable surfaces is given.Comment: 8 pages, to appear in Mathematische Zeitschrif

An absolute quantum energy inequality for the Dirac field in curved spacetime

Quantum Weak Energy Inequalities (QWEIs) are results which limit the extent to which the smeared renormalised energy density of a quantum field can be negative. On globally hyperbolic spacetimes the massive quantum Dirac field is known to obey a QWEI in terms of a reference state chosen arbitrarily from the class of Hadamard states; however, there exist spacetimes of interest on which state-dependent bounds cannot be evaluated. In this paper we prove the first QWEI for the massive quantum Dirac field on four dimensional globally hyperbolic spacetime in which the bound depends only on the local geometry; such a QWEI is known as an absolute QWEI

Factor Analysis of the Preschool Behavioral and Emotional Rating Scale for Children in Head Start Programs

Strength-based assessment of behaviors in preschool children provides evidence of emotional and behavioral skills in children, rather than focusing primarily on weaknesses identified by deficit-based assessments. The Preschool Behavioral and Emotional Rating Scales (PreBERS) is a normative assessment of emotional and behavioral strengths in preschool children. The PreBERS has well-established reliability and validity for typically developing children as well as children with identified special education needs, but this has not yet been established for children in Head Start programs, who tend to be at high risk for development of emotional and behavioral concerns. This study explores the factorial validity of the PreBERS scores for a large sample of children participating in Head Start programs around the United States. Results not only confirm the fit of the four-factor model of the PreBERS for this population, but also demonstrate the application of a bifactor model to the structure of the PreBERS which, in turn, allows for the computation of model-based reliability estimates for the four subscales (Emotional Regulation, School Readiness, Social Confidence, Family Involvement) and overall strength index score. The implications suggest that the PreBERS items are reliable scores that can be used to identify behavioral strengths in preschool children in Head Start, and support planning of interventions to selectively address component skills to promote child social and academic success

Autocatalytic plume pinch-off

A localized source of buoyancy flux in a non-reactive fluid medium creates a plume. The flux can be provided by either heat, a compositional difference between the fluid comprising the plume and its surroundings, or a combination of both. For autocatalytic plumes produced by the iodate-arsenous acid reaction, however, buoyancy is produced along the entire reacting interface between the plume and its surroundings. Buoyancy production at the moving interface drives fluid motion, which in turn generates flow that advects the reaction front. As a consequence of this interplay between fluid flow and chemical reaction, autocatalytic plumes exhibit a rich dynamics during their ascent through the reactant medium. One of the more interesting dynamical features is the production of an accelerating vortical plume head that in certain cases pinches-off and detaches from the upwelling conduit. After pinch-off, a new plume head forms in the conduit below, and this can lead to multiple generations of plume heads for a single plume initiation. We investigated the pinch-off process using both experimentation and simulation. Experiments were performed using various concentrations of glycerol, in which it was found that repeated pinch-off occurs exclusively in a specific concentration range. Autocatalytic plume simulations revealed that pinch-off is triggered by the appearance of accelerating flow in the plume conduit.Comment: 10 figures. Accepted for publication in Phys Rev E. See also http://www.physics.utoronto.ca/nonlinear/papers_chemwave.htm

Scheduling over Scenarios on Two Machines

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co