Efficiency of Truthful and Symmetric Mechanisms in One-sided Matching

We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with {\em dichotomous preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are particularly interested in the well-known {\em Random Serial Dictatorship} mechanism. For dichotomous preferences, we first show that truthful, symmetric and optimal mechanisms exist if intractable mechanisms are allowed. We then provide a connection to online bipartite matching. Using this connection, it is possible to design truthful, symmetric and tractable mechanisms that extract 0.69 of the maximum social welfare, which works under assumption that agents are not adversarial. Without this assumption, we show that Random Serial Dictatorship always returns an assignment in which the expected social welfare is at least a third of the maximum social welfare. For normalized von Neumann-Morgenstern preferences, we show that Random Serial Dictatorship always returns an assignment in which the expected social welfare is at least \frac{1}{e}\frac{\nu(\opt)^2}{n}, where \nu(\opt) is the maximum social welfare and $n$ is the number of both agents and items. On the hardness side, we show that no truthful mechanism can achieve a social welfare better than \frac{\nu(\opt)^2}{n}.Comment: 13 pages, 1 figur

Bargaining over a finite set of alternatives

We analyze bilateral bargaining over a finite set of alternatives. We look for “good” ordinal solutions to such problems and show that Unanimity Compromise and Rational Compromise are the only bargaining rules that satisfy a basic set of properties. We then extend our analysis to admit problems with countably infinite alternatives. We show that, on this class, no bargaining rule choosing finite subsets of alternatives can be neutral. When rephrased in the utility framework of Nash (1950), this implies that there is no ordinal bargaining rule that is finite-valued

Helly-Type Theorems in Property Testing

Helly's theorem is a fundamental result in discrete geometry, describing the ways in which convex sets intersect with each other. If $S$ is a set of $n$ points in $R^d$, we say that $S$ is $(k,G)$-clusterable if it can be partitioned into $k$ clusters (subsets) such that each cluster can be contained in a translated copy of a geometric object $G$. In this paper, as an application of Helly's theorem, by taking a constant size sample from $S$, we present a testing algorithm for $(k,G)$-clustering, i.e., to distinguish between two cases: when $S$ is $(k,G)$-clusterable, and when it is $\epsilon$-far from being $(k,G)$-clusterable. A set $S$ is $\epsilon$-far $(0<\epsilon\leq1)$ from being $(k,G)$-clusterable if at least $\epsilon n$ points need to be removed from $S$ to make it $(k,G)$-clusterable. We solve this problem for $k=1$ and when $G$ is a symmetric convex object. For $k>1$, we solve a weaker version of this problem. Finally, as an application of our testing result, in clustering with outliers, we show that one can find the approximate clusters by querying a constant size sample, with high probability

Experimental and Numerical Investigation on 2-D Wing-Gronnd Interference

The wing collision is a practical aerodynamic problem. All aerodynamics characteristic of the wing are changing in the collision phenomena. In the present project, the collision of 2-D airfoil section with ground will be investigated experimentally and numerically. The study includes a series of wind tunnel experiments to investigate the 2-D wing influence under collision. Numerical simulation by CFD has been carried out using FLUENT software in order to identify the changes of aerodynamics characteristics during the wing collision. The 2-D wing section selected for the study is NACA 4412 airfoil. The investigation has been carried out at different Reynolds Number ranging from (0.1 x 106 to 0.4 x 106), different angles of attack (-4° to 20°) and different height above the ground. Based on take off and landing fly stages the boundary conditions for the experimental and numerical analysis are determined. An experimental set up was designed and constructed to simulate the collision phenomena in a subsonic wind tunnel. The results of the airfoil characteristic are presented in non-dimensional form as lift, drag and pitching moment coefficient

Combinatorial Alexander Duality -- a Short and Elementary Proof

Let X be a simplicial complex with the ground set V. Define its Alexander dual as a simplicial complex X* = {A \subset V: V \setminus A \notin X}. The combinatorial Alexander duality states that the i-th reduced homology group of X is isomorphic to the (|V|-i-3)-th reduced cohomology group of X* (over a given commutative ring R). We give a self-contained proof.Comment: 7 pages, 2 figure; v3: the sign function was simplifie

Experimental and Numerical Investigation on 2-D Wing-Ground Interference

The wing collision is a practical aerodynamic problem. All aerodynamics characteristic of the wing are changing in the collision phenomena. In the present project, the collision of 2-D airfoil section with ground will be investigated experimentally and numerically. The study includes a series of wind tunnel experiments to investigate the 2-D wing influence under collision. Numerical simulation by CFD has been carried out using FLUENT software in order to identify the changes of aerodynamics characteristics during the wing collision. The 2-D wing section selected for the study is NACA 4412 airfoil. The investigation has been carried out at different Reynolds Number ranging from (0.1 x 106 to 0.4 x 106), different angles of attack (-40 to 200) and different height above the ground. Based on take off and landing fly stages the boundary conditions for the experimental and numerical analysis are determined. An experimental set up was designed and constructed to simulate the collision phenomena in a subsonic wind tunnel. The results of the airfoil characteristic ar

Iron environment non-equivalence in both octahedral and tetrahedral sites in NiFe2O4 nanoparticles: study using Mössbauer spectroscopy with a high velocity resolution

Mössbauer spectrum of NiFe2O4 nanoparticles was measured at room temperature in 4096 channels. This spectrum was fitted using various models, consisting of different numbers of magnetic sextets from two to twelve. Non-equivalence of the 57Fe microenvironments due to various probabilities of different Ni2+ numbers surrounding the octahedral and tetrahedral sites was evaluated and at least 5 different microenvironments were shown for both sites. The fit of the Mössbauer spectrum of NiFe 2O4 nanoparticles using ten sextets showed some similarities in the histograms of relative areas of sextets and calculated probabilities of different Ni2+ numbers in local microenvironments. © 2012 American Institute of Physics

EEFECT OF NANO FILLER ADHESIVE IN SINGLE LAP JOINT BONDED STRUCTURES

This work focuses on developing new adhesive formulations based on epoxy/nanostructures carbon forms. Different types of Nano fillers were dispersed in an epoxy matrix for developing toughened epoxy paste aeronautic adhesives. The reinforced adhesives were used for bonding glass fiber/epoxy composite adherents. Data were also compared to the result obtained both for the unfilled adhesive and/or adherents. Single lap joint sample were prepared to measure mechanical strength and adhesion properties of the joint configurations to analyze the types of failure mode using Acoustic emission testing