On Revenue Monotonicity in Combinatorial Auctions

Along with substantial progress made recently in designing near-optimal mechanisms for multi-item auctions, interesting structural questions have also been raised and studied. In particular, is it true that the seller can always extract more revenue from a market where the buyers value the items higher than another market? In this paper we obtain such a revenue monotonicity result in a general setting. Precisely, consider the revenue-maximizing combinatorial auction for $m$ items and $n$ buyers in the Bayesian setting, specified by a valuation function $v$ and a set $F$ of $nm$ independent item-type distributions. Let $REV(v, F)$ denote the maximum revenue achievable under $F$ by any incentive compatible mechanism. Intuitively, one would expect that $REV(v, G)\geq REV(v, F)$ if distribution $G$ stochastically dominates $F$. Surprisingly, Hart and Reny (2012) showed that this is not always true even for the simple case when $v$ is additive. A natural question arises: Are these deviations contained within bounds? To what extent may the monotonicity intuition still be valid? We present an {approximate monotonicity} theorem for the class of fractionally subadditive (XOS) valuation functions $v$, showing that $REV(v, G)\geq c\,REV(v, F)$ if $G$ stochastically dominates $F$ under $v$ where $c>0$ is a universal constant. Previously, approximate monotonicity was known only for the case $n=1$: Babaioff et al. (2014) for the class of additive valuations, and Rubinstein and Weinberg (2015) for all subaddtive valuation functions.Comment: 10 page

Atom Formation Rates Behind Shock Waves in Hydrogen and the Effect of Added Oxygen, July 1965 - July 1966

Formation rate of atomic hydrogen behind shock waves in hydrogen-argon mixture

Auctions with Heterogeneous Items and Budget Limits

We study individual rational, Pareto optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. For multi-dimensional valuations we show that there can be no deterministic mechanism with these properties for divisible items. We use this to show that there can also be no randomized mechanism that achieves this for either divisible or indivisible items. For single-dimensional valuations we show that there can be no deterministic mechanism with these properties for indivisible items, but that there is a randomized mechanism that achieves this for either divisible or indivisible items. The impossibility results hold for public budgets, while the mechanism allows private budgets, which is in both cases the harder variant to show. While all positive results are polynomial-time algorithms, all negative results hold independent of complexity considerations

Diffusion, Viscosity and Crystal Growth in Microgravity

The diffusivity of TriGlycine Sulfate (TGS), Potassium Dihydrogen Phosphate (KDP), Ammonium Dihydrogen Phosphate (ADF) and other compounds of interest to microgravity crystal growth, in supersaturated solutions as a function of solution concentration, 'age' and 'history was studied experimentally. The factors that affect the growth of crystals from water solutions in microgravity have been examined. Three non-linear optical materials have been studied, potassium dihydrogen phosphate (KDP), ammonium dihydrogen phosphate (ADP) and triglycine sulfate (TGC). The diffusion coefficient and viscosity of supersaturated water solutions were measured. Also theoretical model of diffusivity and viscosity in a metastable state, model of crystal growth from solution including non-linear time dependent diffusivity and viscosity effect and computer simulation of the crystal growth process which allows simulation of the microgravity crystal growth were developed

Theory of Metastable State Relaxation in a Gravitational Field for Non-Critical Binary Systems with Non-Conserved Order Parameter

A new mathematical ansatz is developed for solution of the time-dependent Ginzburg-Landau nonlinear partial differential equation describing metastable state relaxation in binary (solute+solvent) non-critical solutions with non-conserved scalar order parameter in presence of a gravitational field. It has been demonstrated analytically that in such systems metastability initiates heterogeneous solute redistribution which results in the formation of a non-equilibrium singly-periodic spatial solute structure in the new solute-rich phase. The critical radius of nucleation and the induction time in these systems are gravity-dependent. It has also been proved that metastable state relaxation in vertical columns of supersaturated non-critical binary solutions leads to formation of the solute concentration gradient. Analytical expression for this concentration gradient is found and analysed. It is concluded that gravity can initiate phase separation (nucleation or spinodal decomposition)

Randomized Revenue Monotone Mechanisms for Online Advertising

Online advertising is the main source of revenue for many Internet firms. A central component of online advertising is the underlying mechanism that selects and prices the winning ads for a given ad slot. In this paper we study designing a mechanism for the Combinatorial Auction with Identical Items (CAII) in which we are interested in selling $k$ identical items to a group of bidders each demanding a certain number of items between $1$ and $k$. CAII generalizes important online advertising scenarios such as image-text and video-pod auctions [GK14]. In image-text auction we want to fill an advertising slot on a publisher's web page with either $k$ text-ads or a single image-ad and in video-pod auction we want to fill an advertising break of $k$ seconds with video-ads of possibly different durations. Our goal is to design truthful mechanisms that satisfy Revenue Monotonicity (RM). RM is a natural constraint which states that the revenue of a mechanism should not decrease if the number of participants increases or if a participant increases her bid. [GK14] showed that no deterministic RM mechanism can attain PoRM of less than $\ln(k)$ for CAII, i.e., no deterministic mechanism can attain more than $\frac{1}{\ln(k)}$ fraction of the maximum social welfare. [GK14] also design a mechanism with PoRM of $O(\ln^2(k))$ for CAII. In this paper, we seek to overcome the impossibility result of [GK14] for deterministic mechanisms by using the power of randomization. We show that by using randomization, one can attain a constant PoRM. In particular, we design a randomized RM mechanism with PoRM of $3$ for CAII

Global and regional left ventricular myocardial deformation measures by magnetic resonance feature tracking in healthy volunteers: comparison with tagging and relevance of gender

This work was funded by a grant from the Engineering and Physical Sciences Research Council (EP/G030693/1) and supported by the Oxford British Heart Foundation Centre of Research Excellence and the National Institute for Health Research Oxford Biomedical Research Centr

Concentration Dependence of Solution Shear Viscosity and Solute Mass Diffusivity in Crystal Growth from Solutions

The physical properties of a supersaturated binary solution such as its density rho, shear viscosity eta, and solute mass diffusivity D are dependent on the solute concentration c: rho = rho(c), eta = eta(c), and D = D(c). The diffusion boundary layer equations related to crystal growth from solution are derived for the case of natural convection with a solution density, a shear viscosity, and a solute diffusivity that are all depen- dent on solute concentration. The solution of these equations has demonstrated the following. (1) At the vicinity of the saturation concentration c(sub s) the solution shear viscosity eta depends on rho as eta(sub s) = eta(rho(sub s))varies as square root of rho(c(sub s)). This theoretically derived result has been verified in experiments with several aqueous solutions of inorganic and organic salts. (2) The maximum solute mass transfer towards the growing crystal surface can be achieved for values of c where the ratio of d ln(D(c)/dc) to d ln(eta(c)/dc) is a maximum

Impurity incorporation in solution crystallization: diagnosis, prevention, and control

Despite their widespread use for purification, our current methods for the development of solution crystallization processes lack a sufficient understanding on how impurities incorporate in growing crystals. This is, in part, due to the large number of mechanisms often encountered for impurity incorporation, and due to limitations in our methods for diagnosis of those mechanisms. These limitations propagate into largely empirical process development strategies, which are still based on trial and error and centered on solvent selection. This manuscript highlights recent developments in the diagnosis, prevention, and control of impurity incorporation during batch and continuous crystallization. The goal is to provide process development scientists with an updated toolkit for understanding how specific impurities are retained in the solid product, and to review recent prevention and control strategies that may be used to improve crystal purity in industrial crystallization processes

Emergence of a measurement basis in atom-photon scattering

The process of quantum measurement has been a long standing source of debate. A measurement is postulated to collapse a wavefunction onto one of the states of a predetermined set - the measurement basis. This basis origin is not specified within quantum mechanics. According to the theory of decohernce, a measurement basis is singled out by the nature of coupling of a quantum system to its environment. Here we show how a measurement basis emerges in the evolution of the electronic spin of a single trapped atomic ion due to spontaneous photon scattering. Using quantum process tomography we visualize the projection of all spin directions, onto this basis, as a photon is scattered. These basis spin states are found to be aligned with the scattered photon propagation direction. In accordance with decohernce theory, they are subjected to a minimal increase in entropy due to the photon scattering, while, orthogonal states become fully mixed and their entropy is maximally increased. Moreover, we show that detection of the scattered photon polarization measures the spin state of the ion, in the emerging basis, with high fidelity. Lastly, we show that while photon scattering entangles all superpositions of pointer states with the scattered photon polarization, the measurement-basis states themselves remain classically correlated with it. Our findings show that photon scattering by atomic spin superpositions fulfils all the requirements from a quantum measurement process