The Inverse Shapley Value Problem

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome of the vote. Shapley-Shubik indices were introduced by Lloyd Shapley and Martin Shubik in 1954 \cite{SS54} and are widely studied in social choice theory as a measure of the "influence" of voters. The \emph{Inverse Shapley Value Problem} is the problem of designing a weighted voting scheme which (approximately) achieves a desired input vector of values for the Shapley-Shubik indices. Despite much interest in this problem no provably correct and efficient algorithm was known prior to our work. We give the first efficient algorithm with provable performance guarantees for the Inverse Shapley Value Problem. For any constant \eps > 0 our algorithm runs in fixed poly$(n)$ time (the degree of the polynomial is independent of \eps) and has the following performance guarantee: given as input a vector of desired Shapley values, if any "reasonable" weighted voting scheme (roughly, one in which the threshold is not too skewed) approximately matches the desired vector of values to within some small error, then our algorithm explicitly outputs a weighted voting scheme that achieves this vector of Shapley values to within error \eps. If there is a "reasonable" voting scheme in which all voting weights are integers at most \poly(n) that approximately achieves the desired Shapley values, then our algorithm runs in time \poly(n) and outputs a weighted voting scheme that achieves the target vector of Shapley values to within error $\eps=n^{-1/8}.

A sparse optimization approach to infinite infimal convolution regularization

In this paper we introduce the class of infinite infimal convolution functionals and apply these functionals to the regularization of ill-posed inverse problems. The proposed regularization involves an infimal convolution of a continuously parametrized family of convex, positively one-homogeneous functionals defined on a common Banach space X. We show that, under mild assumptions, this functional admits an equivalent convex lifting in the space of measures with values in X. This reformulation allows us to prove well-posedness of a Tikhonov regularized inverse problem and opens the door to a sparse analysis of the solutions. In the case of finite-dimensional measurements we prove a representer theorem, showing that there exists a solution of the inverse problem that is sparse, in the sense that it can be represented as a linear combination of the extremal points of the ball of the lifted infinite infimal convolution functional. Then, we design a generalized conditional gradient method for computing solutions of the inverse problem without relying on an a priori discretization of the parameter space and of the Banach space X. The iterates are constructed as linear combinations of the extremal points of the lifted infinite infimal convolution functional. We prove a sublinear rate of convergence for our algorithm and apply it to denoising of signals and images using, as regularizer, infinite infimal convolutions of fractional-Laplacian-type operators with adaptive orders of smoothness and anisotropies

Synthesizing Program Input Grammars

We present an algorithm for synthesizing a context-free grammar encoding the language of valid program inputs from a set of input examples and blackbox access to the program. Our algorithm addresses shortcomings of existing grammar inference algorithms, which both severely overgeneralize and are prohibitively slow. Our implementation, GLADE, leverages the grammar synthesized by our algorithm to fuzz test programs with structured inputs. We show that GLADE substantially increases the incremental coverage on valid inputs compared to two baseline fuzzers

Ptychographic X-ray tomography reveals additive zoning in nanocomposite single crystals

Single crystals containing nanoparticles represent a unique class of nanocomposites whose properties are defined by both their compositions and the structural organization of the dispersed phase in the crystalline host. Yet, there is still a poor understanding of the relationship between the synthesis conditions and the structures of these materials. Here ptychographic X-ray computed tomography is used to visualize the three-dimensional structures of two nanocomposite crystals – single crystals of calcite occluding diblock copolymer worms and vesicles. This provides unique information about the distribution of the copolymer nano-objects within entire, micron-sized crystals with nanometer spatial resolution and reveals how occlusion is governed by factors including the supersaturation and calcium concentration. Both nanocomposite crystals are seen to exhibit zoning effects that are governed by the solution composition and interactions of the additives with specific steps on the crystal surface. Additionally, the size and shape of the occluded vesicles varies according to their location within the crystal, and therefore the solution composition at the time of occlusion. This work contributes to our understanding of the factors that govern nanoparticle occlusion within crystalline materials, where this will ultimately inform the design of next generation nanocomposite materials with specific structure/property relationships

CD27 is required for protective lytic EBV antigen-specific CD8+ T-cell expansion

Primary immunodeficiencies in the costimulatory molecule CD27 and its ligand, CD70, predispose for pathologies of uncontrolled Epstein-Barr virus (EBV) infection in nearly all affected patients. We demonstrate that both depletion of CD27+ cells and antibody blocking of CD27 interaction with CD70 cause uncontrolled EBV infection in mice with reconstituted human immune system components. While overall CD8+ T-cell expansion and composition are unaltered after antibody blocking of CD27, only some EBV-specific CD8+ T-cell responses, exemplified by early lytic EBV antigen BMLF1-specific CD8+ T cells, are inhibited in their proliferation and killing of EBV-transformed B cells. This suggests that CD27 is not required for all CD8+ T-cell expansions and cytotoxicity but is required for a subset of CD8+ T-cell responses that protect us from EBV pathology

Transverse-target-spin asymmetry in exclusive ω\omega-meson electroproduction

Hard exclusive electroproduction of $\omega$ mesons is studied with the HERMES spectrometer at the DESY laboratory by scattering 27.6 GeV positron and electron beams off a transversely polarized hydrogen target. The amplitudes of five azimuthal modulations of the single-spin asymmetry of the cross section with respect to the transverse proton polarization are measured. They are determined in the entire kinematic region as well as for two bins in photon virtuality and momentum transfer to the nucleon. Also, a separation of asymmetry amplitudes into longitudinal and transverse components is done. These results are compared to a phenomenological model that includes the pion pole contribution. Within this model, the data favor a positive $\pi\omega$ transition form factor.Comment: DESY Report 15-14

CD8(+) T cells retain protective functions despite sustained inhibitory receptor expression during Epstein-Barr virus infection in vivo

Epstein Barr virus (EBV) is one of the most ubiquitous human pathogens in the world, persistently infecting more than 90% of the adult human population. It drives some of the strongest human CD8+ T cell responses, which can be observed during symptomatic primary infection known as infectious mononucleosis (IM). Despite high viral loads and prolonged CD8+ T cell stimulation during IM, EBV enters latency and is under lifelong immune control in most individuals that experience this disease. We investigated whether changes in T cell function, as frequently characterized by PD-1 up-regulation, occur during IM due to the prolonged exposure to high antigen levels. We readily detected the expansion of PD-1 positive CD8+ T cells together with high frequencies of Tim-3, 2B4, and KLRG1 expression during IM and in mice with reconstituted human immune system components (huNSG mice) that had been infected with a high dose of EBV. These PD-1 positive CD8+ T cells, however, retained proliferation, cytokine production, and cytotoxic abilities. Multiple subsets of CD8+ T cells expanded during EBV infection, including PD-1+ Tim-3+ KLRG1+ cells that express CXCR5 and TCF-1 germinal center homing and memory markers, and may also contain BATF3. Moreover, blocking the PD-1 axis compromised EBV specific immune control and resulted in virus-associated lymphomagenesis. Finally, PD-1+ , Tim-3+ , and KLRG1+ CD8+ T cell expansion coincided with declining viral loads during low dose EBV infection. These findings suggest that EBV infection primes PD-1 positive CD8+ T cell populations that rely on this receptor axis for the efficient immune control of this ubiquitous human tumor virus

Hard Two-Photon Contribution to Elastic Lepton-Proton Scattering: Determined by the OLYMPUS Experiment

The OLYMPUS collaboration reports on a precision measurement of the positron-proton to electron-proton elastic cross section ratio, $R_{2\gamma}$, a direct measure of the contribution of hard two-photon exchange to the elastic cross section. In the OLYMPUS measurement, 2.01~GeV electron and positron beams were directed through a hydrogen gas target internal to the DORIS storage ring at DESY. A toroidal magnetic spectrometer instrumented with drift chambers and time-of-flight scintillators detected elastically scattered leptons in coincidence with recoiling protons over a scattering angle range of $\approx 20\degree$ to $80\degree$. The relative luminosity between the two beam species was monitored using tracking telescopes of interleaved GEM and MWPC detectors at $12\degree$, as well as symmetric M{\o}ller/Bhabha calorimeters at $1.29\degree$. A total integrated luminosity of 4.5~fb$^{-1}$ was collected. In the extraction of $R_{2\gamma}$, radiative effects were taken into account using a Monte Carlo generator to simulate the convolutions of internal bremsstrahlung with experiment-specific conditions such as detector acceptance and reconstruction efficiency. The resulting values of $R_{2\gamma}$, presented here for a wide range of virtual photon polarization $0.456<\epsilon<0.978$, are smaller than some hadronic two-photon exchange calculations predict, but are in reasonable agreement with a subtracted dispersion model and a phenomenological fit to the form factor data.Comment: 5 pages, 3 figures, 2 table