Mechanism design for aggregating energy consumption and quality of service in speed scaling scheduling

We consider a strategic game, where players submit jobs to a machine that executes all jobs in a way that minimizes energy while respecting the given deadlines. The energy consumption is then charged to the players in some way. Each player wants to minimize the sum of that charge and of their job's deadline multiplied by a priority weight. Two charging schemes are studied, the proportional cost share which does not always admit pure Nash equilibria, and the marginal cost share, which does always admit pure Nash equilibria, at the price of overcharging by a constant factor

Span programs and quantum algorithms for st-connectivity and claw detection

We introduce a span program that decides st-connectivity, and generalize the span program to develop quantum algorithms for several graph problems. First, we give an algorithm for st-connectivity that uses O(n d^{1/2}) quantum queries to the n x n adjacency matrix to decide if vertices s and t are connected, under the promise that they either are connected by a path of length at most d, or are disconnected. We also show that if T is a path, a star with two subdivided legs, or a subdivision of a claw, its presence as a subgraph in the input graph G can be detected with O(n) quantum queries to the adjacency matrix. Under the promise that G either contains T as a subgraph or does not contain T as a minor, we give O(n)-query quantum algorithms for detecting T either a triangle or a subdivision of a star. All these algorithms can be implemented time efficiently and, except for the triangle-detection algorithm, in logarithmic space. One of the main techniques is to modify the st-connectivity span program to drop along the way "breadcrumbs," which must be retrieved before the path from s is allowed to enter t.Comment: 18 pages, 4 figure

Reciprocity in Social Networks with Capacity Constraints

Directed links -- representing asymmetric social ties or interactions (e.g., "follower-followee") -- arise naturally in many social networks and other complex networks, giving rise to directed graphs (or digraphs) as basic topological models for these networks. Reciprocity, defined for a digraph as the percentage of edges with a reciprocal edge, is a key metric that has been used in the literature to compare different directed networks and provide "hints" about their structural properties: for example, are reciprocal edges generated randomly by chance or are there other processes driving their generation? In this paper we study the problem of maximizing achievable reciprocity for an ensemble of digraphs with the same prescribed in- and out-degree sequences. We show that the maximum reciprocity hinges crucially on the in- and out-degree sequences, which may be intuitively interpreted as constraints on some "social capacities" of nodes and impose fundamental limits on achievable reciprocity. We show that it is NP-complete to decide the achievability of a simple upper bound on maximum reciprocity, and provide conditions for achieving it. We demonstrate that many real networks exhibit reciprocities surprisingly close to the upper bound, which implies that users in these social networks are in a sense more "social" than suggested by the empirical reciprocity alone in that they are more willing to reciprocate, subject to their "social capacity" constraints. We find some surprising linear relationships between empirical reciprocity and the bound. We also show that a particular type of small network motifs that we call 3-paths are the major source of loss in reciprocity for real networks

Femtosecond x-ray absorption spectroscopy of spin and orbital angular momentum in photoexcited Ni films during ultrafast demagnetization

We follow for the first time the evolution of the spin and orbital angular momentum of a thin Ni film during ultrafast demagnetization, by means of x-ray magnetic circular dichroism. Both components decrease with a 130 +/- 40 fs time constant upon excitation with a femtosecond laser pulse. Additional x-ray absorption measurements reveal an increase in the spin-orbit interaction by 6 +/- 2 % during this process. This is the experimental demonstration quantifying the importance of spin-orbit mediated processes during the demagnetization

Combination of a magnetic Feshbach resonance and an optical bound-to-bound transition

We use laser light near resonant with an optical bound-to-bound transition to shift the magnetic field at which a Feshbach resonance occurs. We operate in a regime of large detuning and large laser intensity. This reduces the light-induced atom-loss rate by one order of magnitude compared to our previous experiments [D.M. Bauer et al. Nature Phys. 5, 339 (2009)]. The experiments are performed in an optical lattice and include high-resolution spectroscopy of excited molecular states, reported here. In addition, we give a detailed account of a theoretical model that describes our experimental data

Localization of cold atoms in state-dependent optical lattices via a Rabi pulse

We propose a novel realization of Anderson localization in non-equilibrium states of ultracold atoms trapped in state-dependent optical lattices. The disorder potential leading to localization is generated with a Rabi pulse transfering a fraction of the atoms into a different internal state for which tunneling between lattice sites is suppressed. Atoms with zero tunneling create a quantum superposition of different random potentials, localizing the mobile atoms. We investigate the dynamics of the mobile atoms after the Rabi pulse for non-interacting and weakly interacting bosons, and we show that the evolved wavefunction attains a quasi-stationary profile with exponentially decaying tails, characteristic of Anderson localization. The localization length is seen to increase with increasing disorder and interaction strength, oppositely to what is expected for equilibrium localization.Comment: 4 pages, 4 figure

Bohmian Mechanics and Quantum Information

Many recent results suggest that quantum theory is about information, and that quantum theory is best understood as arising from principles concerning information and information processing. At the same time, by far the simplest version of quantum mechanics, Bohmian mechanics, is concerned, not with information but with the behavior of an objective microscopic reality given by particles and their positions. What I would like to do here is to examine whether, and to what extent, the importance of information, observation, and the like in quantum theory can be understood from a Bohmian perspective. I would like to explore the hypothesis that the idea that information plays a special role in physics naturally emerges in a Bohmian universe.Comment: 25 pages, 2 figure

Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision

The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, \ell. We prove an upper bound of O (n\sqrt{\ell}) for all values of \ell. This is an improvement over previous algorithms for all values of \ell. On the other hand, we show that for any \eps < 1 and any \ell <= \eps n^2, there is an \Omega(n\sqrt{\ell}) lower bound for this problem, showing that our algorithm is essentially tight. We first reduce Boolean matrix multiplication to several instances of graph collision. We then provide an algorithm that takes advantage of the fact that the underlying graph in all of our instances is very dense to find all graph collisions efficiently