The Complexity of Fairness through Equilibrium

Competitive equilibrium with equal incomes (CEEI) is a well known fair allocation mechanism; however, for indivisible resources a CEEI may not exist. It was shown in [Budish '11] that in the case of indivisible resources there is always an allocation, called A-CEEI, that is approximately fair, approximately truthful, and approximately efficient, for some favorable approximation parameters. This approximation is used in practice to assign students to classes. In this paper we show that finding the A-CEEI allocation guaranteed to exist by Budish's theorem is PPAD-complete. We further show that finding an approximate equilibrium with better approximation guarantees is even harder: NP-complete.Comment: Appeared in EC 201

Simulation of electrically large structures in EMC studies:application to automotive EMC

The aim of this thesis is the study of the simulation of electrically large structures and the application of the results to automotive Electromagnetic Compatibility (EMC). The theoretical and experimental work carried out has led to the development of computational tools and to the further understanding of the mechanisms involved in the representation of solid surfaces by means of wire-grid simplifications. The work was done in the context of a European project GUIDELINES FOR ELECTROMAGNETIC COMPATIBILITY MODELLING FOR AUTOMOTIVE REQUIREMENTS (GEMCAR). The first two chapters of the thesis contain a description of the GEMCAR project, a brief overview of some of the existing numerical methods for electromagnetic simulations (particularly, the ones used in GEMCAR), and the explanation of efficient, general simulation strategies that can be applied to different methods. The concept of adaptive sampling and its application are also introduced there. The main original contributions of this thesis are presented in Chapters 3 through 6. They consist of theoretical and experimental work as follows. We present, in Chapter 3, a modified version of the Numerical Electromagnetics Code (NEC). This version, which we have called Parallel NEC, has been adapted to run on parallel supercomputers, taking advantage of the combined processing power and memory of several processors working as a team. Parallel NEC has been implemented in two different supercomputing architectures to test the portability of the code. The original NEC routines in charge of the calculation and filling of the interaction matrix have been modified to work in a parallel environment. The matrix is now distributed among the available processors and the elements of the matrix are locally and individually calculated by their "owners". Thus the number of integrals carried out to build the complete matrix equation gets shared, diminishing the necessary runtime for this time-consuming operation. The system of equations is also solved using a parallel version of the Gauss-Doolitle algorithm. However, the most important feature of Parallel NEC is the possibility to use the distributed memory of the processors. This allows the calculation of problems of a size never achieved before using this numerical method without the need of using disk-space as swap memory. The code has been tested with models containing over 20.000 segments, exhibiting execution times comparable to those obtained with a single-processor PC calculating models of one tenth of that size in terms of the number of segments. Parallel NEC is also able to adapt itself automatically to its environment. It will detect the number of available processors and will take advantage of all available memory and calculating resources. The validation of Parallel NEC has been carried out in two steps. First, it was validated using simulation results obtained with other numerical methods. Then, it was validated by using experimental data from the GEMCAR project. The experimental setup as well as the validation are presented in Chapter 4. With the purpose of validating the numerical models developed in GEMCAR, we participated in a number of experimental campaigns carried out at Spiez, Switzerland in 2000 and 2001 using the VERIFY (Vertical EMP Radiating Indoor Facility), an EMP simulator belonging to the Swiss Defense Procurement Agency. Measurements of electric and magnetic fields inside a real vehicle (a Volvo S80) featuring different levels of complexity were carried out. These measurements were performed at 8 different points inside the car and at two points on the surface of the body-shell. The above-mentioned levels of complexity consisted of (1) a "simple test case", comprising the vehicle body-shell (without all doors or glazing), (2) a "medium complexity case" which, this time, included the doors, and (3) a "complex case", consisting of the complete car with all mechanical, electrical and electronic equipment installed. The data used in Chaper 4 refer to the "simple test case", although the "medium test case" measurements are also available . Other partners of the GEMCAR project carried out experimental testing on the three models using other sources of illumination (see Chapters 1 and 4). It is interesting to mention for completeness that, as part of the GEMCAR project, a cable harness was installed following the approximate path of the original cabling of the car, but composed of single wires with 50 R terminations. Current measurements were made at 4 observation points located at the ends of the branches of the harness. These current measurements are not given here as the subject of this thesis was limited to field measurements and simulations only1. The developed code was applied to analyze the penetration of electromagnetic fields inside the vehicle's body shell (i.e., the simple case). The computed results agree well with those obtained with the other methods and with the experimental data obtained from measurements. The application of the code to such a large problem permitted the observation of some issues raised by the application of the so-called Equal Area Rule (EAR) for the calculation of the segments' lengths and radii. In Chapter 5, we discuss the wire-grid representation of metallic surfaces in numerical electromagnetic modeling. We present the origins and the evolution of surface wire-grid modeling and, considering two types of geometries, namely (I) a simple cube, and (2) a complex structure represented by the metallic car shell used in Chapter 4, we show that the Equal Area Rule is accurate as long as the wire-grid consists of a simple square mesh. For more complex body-fitted meshes, such as rectangular and triangular grids, the Equal Area Rule appears to be less accurate in reproducing the electromagnetic field scattered by metallic bodies. In Chapter 6 we present a theoretical development that leads, for the case of a square grid representation of a surface, to the same formula proposed by the Equal Area Rule. This development is, to the best of our knowledge, the first physical and mathematical interpretation of the EAR as of today. Our development shows, however, a different value for the radius of the segments if the representation of the surface uses other polygons, such as in the case of a rectangular or a triangular mesh. To compare the two methods (the traditional versus the new EAR), we carried out a simple numerical test and found that the Equal Area Rule does not always predict the optimum wire radius for the mesh-representation of a surface. ------------------------------   1The interested reader is referred to: A. Rubinstein, F. Rachidi, D. Pavanello, and B. Reusser. Electromagnetic field interaction with vehicle cable harness: An experimental analysis. In International Conference on Electromagnetic Compatibility, EMC Europe. Sorrento, volume 1, Sep 2002. Proceedings

Practical algorithms and experimentally validated incentives for equilibrium-based fair division (A-CEEI)

Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is an equilibrium-based solution concept for fair division of discrete items to agents with combinatorial demands. In theory, it is known that in asymptotically large markets: 1. For incentives, the A-CEEI mechanism is Envy-Free-but-for-Tie-Breaking (EF-TB), which implies that it is Strategyproof-in-the-Large (SP-L). 2. From a computational perspective, computing the equilibrium solution is unfortunately a computationally intractable problem (in the worst-case, assuming $\textsf{PPAD}\ne \textsf{FP}$). We develop a new heuristic algorithm that outperforms the previous state-of-the-art by multiple orders of magnitude. This new, faster algorithm lets us perform experiments on real-world inputs for the first time. We discover that with real-world preferences, even in a realistic implementation that satisfies the EF-TB and SP-L properties, agents may have surprisingly simple and plausible deviations from truthful reporting of preferences. To this end, we propose a novel strengthening of EF-TB, which dramatically reduces the potential for strategic deviations from truthful reporting in our experiments. A (variant of) our algorithm is now in production: on real course allocation problems it is much faster, has zero clearing error, and has stronger incentive properties than the prior state-of-the-art implementation.Comment: To appear in EC 202

Visual Vibrometry: Estimating Material Properties from Small Motions in Video

The estimation of material properties is important for scene understanding, with many applications in vision, robotics, and structural engineering. This paper connects fundamentals of vibration mechanics with computer vision techniques in order to infer material properties from small, often imperceptible motion in video. Objects tend to vibrate in a set of preferred modes. The shapes and frequencies of these modes depend on the structure and material properties of an object. Focusing on the case where geometry is known or fixed, we show how information about an object’s modes of vibration can be extracted from video and used to make inferences about that object’s material properties. We demonstrate our approach by estimating material properties for a variety of rods and fabrics by passively observing their motion in high-speed and regular framerate video.National Science Foundation (U.S.) (Robust Intelligence 1212849 Reconstructive Recognition)Shell Oil CompanyQatar Computing Research InstituteNational Science Foundation (U.S.). Graduate Research Fellowshi

Exact time-dependent correlation functions for the symmetric exclusion process with open boundary

As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density $\rho^\ast$ and which initially is in an non-equilibrium state with bulk density $\rho_0$. We calculate the exact time-dependent two-point density correlation function $C_{k,l}(t)\equiv -$ and the mean and variance of the integrated average net flux of particles $N(t)-N(0)$ that have entered (or left) the system up to time $t$. We find that the boundary region of the semi-infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient. The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions. Some implications for the relaxational dynamics of entangled polymers and for single-file diffusion in colloidal systems are discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference 17 adde

Crack-Like Processes Governing the Onset of Frictional Slip

We perform real-time measurements of the net contact area between two blocks of like material at the onset of frictional slip. We show that the process of interface detachment, which immediately precedes the inception of frictional sliding, is governed by three different types of detachment fronts. These crack-like detachment fronts differ by both their propagation velocities and by the amount of net contact surface reduction caused by their passage. The most rapid fronts propagate at intersonic velocities but generate a negligible reduction in contact area across the interface. Sub-Rayleigh fronts are crack-like modes which propagate at velocities up to the Rayleigh wave speed, VR, and give rise to an approximate 10% reduction in net contact area. The most efficient contact area reduction (~20%) is precipitated by the passage of slow detachment fronts. These fronts propagate at anomalously slow velocities, which are over an order of magnitude lower than VR yet orders of magnitude higher than other characteristic velocity scales such as either slip or loading velocities. Slow fronts are generated, in conjunction with intersonic fronts, by the sudden arrest of sub-Rayleigh fronts. No overall sliding of the interface occurs until either of the slower two fronts traverses the entire interface, and motion at the leading edge of the interface is initiated. Slip at the trailing edge of the interface accompanies the motion of both the slow and sub-Rayleigh fronts. We might expect these modes to be important in both fault nucleation and earthquake dynamics.Comment: 19 page, 5 figures, to appear in International Journal of Fractur

In vivo targeting of adoptively transferred T-cells with antibody- and cytokine-conjugated liposomes

In adoptive cell therapy (ACT), autologous tumor-specific T-cells isolated from cancer patients are activated and expanded ex vivo, then infused back into the individual to eliminate metastatic tumors. A major limitation of this promising approach is the rapid loss of ACT T-cell effector function in vivo due to the highly immunosuppressive environment in tumors. Protection of T-cells from immunosuppressive signals can be achieved by systemic administration of supporting adjuvant drugs such as interleukins, chemotherapy, and other immunomodulators, but these adjuvant treatments are often accompanied by serious toxicities and may still fail to optimally stimulate lymphocytes in all tumor and lymphoid compartments. Here we propose a novel strategy to repeatedly stimulate or track ACT T-cells, using cytokines or ACT-cell-specific antibodies as ligands to target PEGylated liposomes to transferred T-cells in vivo. Using F(ab′)[subscript 2] fragments against a unique cell surface antigen on ACT cells (Thy1.1) or an engineered interleukin-2 (IL-2) molecule on an Fc framework as targeting ligands, we demonstrate that > 95% of ACT cells can be conjugated with liposomes following a single injection in vivo. Further, we show that IL-2-conjugated liposomes both target ACT cells and are capable of inducing repeated waves of ACT T-cell proliferation in tumor-bearing mice. These results demonstrate the feasibility of repeated functional targeting of T-cells in vivo, which will enable delivery of imaging contrast agents, immunomodulators, or chemotherapy agents in adoptive cell therapy regimens.National Institutes of Health (U.S.) (CA140476)National Institutes of Health (U.S.) (CA172164)United States. Dept. of Defense (Contract W81XWH-10-1-0290)National Cancer Institute (U.S.) (Koch Institute Support (core) Grant P30-CA14051

A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics

This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment