A potential approach to solutions for set games

Concerning the solution theory for set games, the paper introduces a new solution by allocating, to any player, the items (taken from an universe) that are attainable for the player, but can not be blocked (by any coalition not containing the player). The resulting value turns out to be an utmost important concept for set games to characterize the family of set game solutions that possess a so-called potential representation (similar to the potential approaches applied in both physics and cooperative game theory). An axiomatization of the new value, called Driessen--Sun value, is given by three properties, namely one type of an efficiency property, the substitution property and one type of a monotonocity property

The Capacity of Linear Computation Broadcast

The two-user computation broadcast problem is introduced as the setting where user 1 wants message W1 and has side information W0 1 , user 2 wants message W2 and has side information W0 2, and (W1;W0 1 ;W2;W0 2) may have arbitrary dependencies. The goal is to minimize the entropy H(S) of the broadcast information S that simultaneously satisfies both users' demands. It is shown that H(S) H(W1jW0 1) + H(W2jW0 2) min I(W1;W2;W0 2jW0 1 ); I(W2;W1;W0 1jW0 2 ) . Furthermore, for the linear computation broadcast problem, where W1;W0 1;W2;W0 2 are comprised of arbitrary linear combinations of a basis set of independent symbols, the bound is shown to be tight

Multiround private information retrieval: Capacity and storage overhead

Private information retrieval (PIR) is the problem of retrieving one message out of $K$ messages from $N$ non-communicating replicated databases, where each database stores all $K$ messages, in such a way that each database learns no information about which message is being retrieved. The capacity of PIR is the maximum number of bits of desired information per bit of downloaded information among all PIR schemes. The capacity has recently been characterized for PIR as well as several of its variants. In every case it is assumed that all the queries are generated by the user simultaneously. Here we consider multiround PIR, where the queries in each round are allowed to depend on the answers received in previous rounds. We show that the capacity of multiround PIR is the same as the capacity of single-round PIR. The result is generalized to also include $T$ -privacy constraints. Combined with previous results, this shows that there is no capacity advantage from multiround over single-round schemes, non-linear over linear schemes or from $\epsilon$ -error over zero-error schemes. However, we show through an example that there is an advantage in terms of storage overhead. We provide an example of a multiround, non-linear, $\epsilon$ -error PIR scheme that requires a strictly smaller storage overhead than the best possible with single-round, linear, zero-error PIR schemes

Onset of unsteady horizontal convection in rectangle tank at Pr=1Pr=1

The horizontal convection within a rectangle tank is numerically simulated. The flow is found to be unsteady at high Rayleigh numbers. There is a Hopf bifurcation of $Ra$ from steady solutions to periodic solutions, and the critical Rayleigh number $Ra_c$ is obtained as $Ra_c=5.5377\times 10^8$ for the middle plume forcing at $Pr=1$, which is much larger than the formerly obtained value. Besides, the unstable perturbations are always generated from the central jet, which implies that the onset of instability is due to velocity shear (shear instability) other than thermally dynamics (thermal instability). Finally, Paparella and Young's [J. Fluid Mech. 466 (2002) 205] first hypotheses about the destabilization of the flow is numerically proved, i.e. the middle plume forcing can lead to a destabilization of the flow.Comment: 4pages, 6 figures, extension of Chin. Phys. Lett. 2008, 25(6), in pres

Kinetics of dissociative chemisorption of methane and ethane on Pt(110)-(1X2)

The initial probability of dissociative chemisorption Pr of methane and ethane on the highly corrugated, reconstructed Pt(110)‐(1×2) surface has been measured in a microreactor by counting the number of carbon atoms on the surface following the reaction of methane and ethane on the surface which was held at various constant temperatures between 450 and 900 K during the reaction. Methane dissociatively chemisorbs on the Pt(110)‐(1×2) surface with an apparent activation energy of 14.4 kcal/mol and an apparent preexponential factor of 0.6. Ethane chemisorbs dissociatively with an apparent activation energy of 2.8 kcal/mol and an apparent preexponential factor of 4.7×10^(−3). Kinetic isotope effects were observed for both reactions. The fact that P_r is a strong function of surface temperature implies that the dissociation reactions proceed via a trapping‐mediated mechanism. A model based on a trapping‐mediated mechanism is used to explain the observed kinetic behavior. Kinetic parameters for C–H bond dissociation of the thermally accommodated methane and ethane are extracted from the model

Matrix approach to consistency of the additive efficient normalization of semivalues

In fact the Shapley value is the unique efficient semivalue. This motivated Ruiz et al. to do additive efficient normalization for semivalues. In this paper, by matrix approach we derive the relationship between the additive efficient normalization of semivalues and the Shapley value. Based on the relationship, we axiomatize the additive efficient normalization of semivalues as the unique solution verifying covariance, symmetry, and reduced game property with respect to the $p-$reduced game

Electroencephalogram evidence for the activation of human mirror neuron system during the observation of intransitive shadow and line drawing actions

This article is available open access from the NCBI website at the link below. Copyright 2013 © Neural Regeneration Research. This is an open-access article distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Previous studies have demonstrated that hand shadows may activate the motor cortex associated with the mirror neuron system in human brain. However, there is no evidence of activity of the human mirror neuron system during the observation of intransitive movements by shadows and line drawings of hands. This study examined the suppression of electroencephalography mu waves (8–13 Hz) induced by observation of stimuli in 18 healthy students. Three stimuli were used: real hand actions, hand shadow actions and actions made by line drawings of hands. The results showed significant desynchronization of the mu rhythm (“mu suppression”) across the sensorimotor cortex (recorded at C3, Cz and C4), the frontal cortex (recorded at F3, Fz and F4) and the central and right posterior parietal cortex (recorded at Pz and P4) under all three conditions. Our experimental findings suggest that the observation of “impoverished hand actions”, such as intransitive movements of shadows and line drawings of hands, is able to activate widespread cortical areas related to the putative human mirror neuron system.The National Natural Science Foundation of China and the Research Fund for the Doctoral Program of Higher Education of China