Matching Dynamics with Constraints

We study uncoordinated matching markets with additional local constraints that capture, e.g., restricted information, visibility, or externalities in markets. Each agent is a node in a fixed matching network and strives to be matched to another agent. Each agent has a complete preference list over all other agents it can be matched with. However, depending on the constraints and the current state of the game, not all possible partners are available for matching at all times. For correlated preferences, we propose and study a general class of hedonic coalition formation games that we call coalition formation games with constraints. This class includes and extends many recently studied variants of stable matching, such as locally stable matching, socially stable matching, or friendship matching. Perhaps surprisingly, we show that all these variants are encompassed in a class of "consistent" instances that always allow a polynomial improvement sequence to a stable state. In addition, we show that for consistent instances there always exists a polynomial sequence to every reachable state. Our characterization is tight in the sense that we provide exponential lower bounds when each of the requirements for consistency is violated. We also analyze matching with uncorrelated preferences, where we obtain a larger variety of results. While socially stable matching always allows a polynomial sequence to a stable state, for other classes different additional assumptions are sufficient to guarantee the same results. For the problem of reaching a given stable state, we show NP-hardness in almost all considered classes of matching games.Comment: Conference Version in WINE 201

Antimicrobial Active Clothes Display No Adverse Effects on the Ecological Balance of the Healthy Human Skin Microflora

The progressive public use of antimicrobial clothes has raised issues concerning skin health. A placebo-controlled side-to-side study was run with antimicrobial clothes versus fabrics of similar structure but minus the antimicrobial activity, to evaluate possible adverse effects on the healthy skin microflora. Sixty volunteers were enrolled. Each participant received a set of form-fitting T-shirts constructed in 2 halves: an antibacterial half, displaying activities of 3–5 log-step reductions due to silver-finishes or silver-loaded fibres and a nonantibacterial control side. The microflora of the scapular skin was analyzed weekly for opportunistic and pathogenic microorganisms over six weeks. The antibacterial halves did not disturb the microflora in number or composition, whereas a silver-containing deodorant displayed a short-term disturbance. Furthermore, parameters of skin morphology and function (TEWL, pH, moisture) did not show any significant shifts. In summary, antimicrobial clothes did not show adverse effects on the ecological balance of the healthy skin microflora

Inelastic Decay of Electrons in the Shockley-type Metal-Organic Interface States

We present a theoretical study of lifetimes of interface states (IS) on metal-organic interfaces PTCDA/Ag(111), NTCDA/Ag(111), PFP/Ag(111), and PTCDA/Ag(100), describing and explaining the recent experimental data. By means of unfolding the band structure of one of the interfaces under study onto the Ag(111) Brillouin zone we demonstrate, that the Brillouin zone folding upon organic monolayer deposition plays a minor role in the phase space for electron decay, and hence weakly affects the resulting lifetimes. The presence of the unoccupied molecular states below the IS gives a small contribution to the IS decay rate mostly determined by the change of the phase space of bulk states upon the energy shift of the IS. The calculated lifetimes follow the experimentally observed trends. In particular, we explain the trend of the unusual increase of the IS lifetimes with rising temperature.Comment: 8 pages, 5 figure

Routing Games over Time with FIFO policy

We study atomic routing games where every agent travels both along its decided edges and through time. The agents arriving on an edge are first lined up in a \emph{first-in-first-out} queue and may wait: an edge is associated with a capacity, which defines how many agents-per-time-step can pop from the queue's head and enter the edge, to transit for a fixed delay. We show that the best-response optimization problem is not approximable, and that deciding the existence of a Nash equilibrium is complete for the second level of the polynomial hierarchy. Then, we drop the rationality assumption, introduce a behavioral concept based on GPS navigation, and study its worst-case efficiency ratio to coordination.Comment: Submission to WINE-2017 Deadline was August 2nd AoE, 201

Theory of Magnetodynamics Induced by Spin Torque in Perpendicularly Magnetized Thin Films

A nonlinear model of spin wave excitation using a point contact in a thin ferromagnetic film is introduced. Large-amplitude magnetic solitary waves are computed, which help explain recent spin-torque experiments. Numerical simulations of the fully nonlinear model predict excitation frequencies in excess of 0.2 THz for contact diameters smaller than 6 nm. Simulations also predict a saturation and red shift of the frequency at currents large enough to invert the magnetization under the point contact. The theory is approximated by a cubic complex Ginzburg-Landau type equation. The mode's nonlinear frequency shift is found by use of perturbation techniques, whose results agree with those of direct numerical simulations.Comment: 5 pages, 4 figures, submitted to PR

Computing Stable Coalitions: Approximation Algorithms for Reward Sharing

Consider a setting where selfish agents are to be assigned to coalitions or projects from a fixed set P. Each project k is characterized by a valuation function; v_k(S) is the value generated by a set S of agents working on project k. We study the following classic problem in this setting: "how should the agents divide the value that they collectively create?". One traditional approach in cooperative game theory is to study core stability with the implicit assumption that there are infinite copies of one project, and agents can partition themselves into any number of coalitions. In contrast, we consider a model with a finite number of non-identical projects; this makes computing both high-welfare solutions and core payments highly non-trivial. The main contribution of this paper is a black-box mechanism that reduces the problem of computing a near-optimal core stable solution to the purely algorithmic problem of welfare maximization; we apply this to compute an approximately core stable solution that extracts one-fourth of the optimal social welfare for the class of subadditive valuations. We also show much stronger results for several popular sub-classes: anonymous, fractionally subadditive, and submodular valuations, as well as provide new approximation algorithms for welfare maximization with anonymous functions. Finally, we establish a connection between our setting and the well-studied simultaneous auctions with item bidding; we adapt our results to compute approximate pure Nash equilibria for these auctions.Comment: Under Revie

Size reduction of complex networks preserving modularity

The ubiquity of modular structure in real-world complex networks is being the focus of attention in many trials to understand the interplay between network topology and functionality. The best approaches to the identification of modular structure are based on the optimization of a quality function known as modularity. However this optimization is a hard task provided that the computational complexity of the problem is in the NP-hard class. Here we propose an exact method for reducing the size of weighted (directed and undirected) complex networks while maintaining invariant its modularity. This size reduction allows the heuristic algorithms that optimize modularity for a better exploration of the modularity landscape. We compare the modularity obtained in several real complex-networks by using the Extremal Optimization algorithm, before and after the size reduction, showing the improvement obtained. We speculate that the proposed analytical size reduction could be extended to an exact coarse graining of the network in the scope of real-space renormalization.Comment: 14 pages, 2 figure

A note on anti-coordination and social interactions

This note confirms a conjecture of [Bramoull\'{e}, Anti-coordination and social interactions, Games and Economic Behavior, 58, 2007: 30-49]. The problem, which we name the maximum independent cut problem, is a restricted version of the MAX-CUT problem, requiring one side of the cut to be an independent set. We show that the maximum independent cut problem does not admit any polynomial time algorithm with approximation ratio better than $n^{1-\epsilon}$, where $n$ is the number of nodes, and $\epsilon$ arbitrarily small, unless P=NP. For the rather special case where each node has a degree of at most four, the problem is still MAXSNP-hard.Comment: 7 page