Computer-aided verification in mechanism design

In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in complicated strategizing. While incentive properties are simple to state, their proofs are specific to the mechanism and can be quite complex. This raises two concerns. From a practical perspective, checking a complex proof can be a tedious process, often requiring experts knowledgeable in mechanism design. Furthermore, from a modeling perspective, if unsophisticated agents are unconvinced of incentive properties, they may strategize in unpredictable ways. To address both concerns, we explore techniques from computer-aided verification to construct formal proofs of incentive properties. Because formal proofs can be automatically checked, agents do not need to manually check the properties, or even understand the proof. To demonstrate, we present the verification of a sophisticated mechanism: the generic reduction from Bayesian incentive compatible mechanism design to algorithm design given by Hartline, Kleinberg, and Malekian. This mechanism presents new challenges for formal verification, including essential use of randomness from both the execution of the mechanism and from the prior type distributions. As an immediate consequence, our work also formalizes Bayesian incentive compatibility for the entire family of mechanisms derived via this reduction. Finally, as an intermediate step in our formalization, we provide the first formal verification of incentive compatibility for the celebrated Vickrey-Clarke-Groves mechanism

A Direct Reduction from k-Player to 2-Player Approximate Nash Equilibrium

We present a direct reduction from k-player games to 2-player games that preserves approximate Nash equilibrium. Previously, the computational equivalence of computing approximate Nash equilibrium in k-player and 2-player games was established via an indirect reduction. This included a sequence of works defining the complexity class PPAD, identifying complete problems for this class, showing that computing approximate Nash equilibrium for k-player games is in PPAD, and reducing a PPAD-complete problem to computing approximate Nash equilibrium for 2-player games. Our direct reduction makes no use of the concept of PPAD, thus eliminating some of the difficulties involved in following the known indirect reduction.Comment: 21 page

Trivial Excitation Energy Transfer to Carotenoids Is an Unlikely Mechanism for Non-photochemical Quenching in LHCII

Higher plants defend themselves from bursts of intense light via the mechanism of Non-Photochemical Quenching (NPQ). It involves the Photosystem II (PSII) antenna protein (LHCII) adopting a conformation that favors excitation quenching. In recent years several structural models have suggested that quenching proceeds via energy transfer to the optically forbidden and short-lived S(1) states of a carotenoid. It was proposed that this pathway was controlled by subtle changes in the relative orientation of a small number of pigments. However, quantum chemical calculations of S(1) properties are not trivial and therefore its energy, oscillator strength and lifetime are treated as rather loose parameters. Moreover, the models were based either on a single LHCII crystal structure or Molecular Dynamics (MD) trajectories about a single minimum. Here we try and address these limitations by parameterizing the vibronic structure and relaxation dynamics of lutein in terms of observable quantities, namely its linear absorption (LA), transient absorption (TA) and two-photon excitation (TPE) spectra. We also analyze a number of minima taken from an exhaustive meta-dynamical search of the LHCII free energy surface. We show that trivial, Coulomb-mediated energy transfer to S(1) is an unlikely quenching mechanism, with pigment movements insufficiently pronounced to switch the system between quenched and unquenched states. Modulation of S(1) energy level as a quenching switch is similarly unlikely. Moreover, the quenching predicted by previous models is possibly an artifact of quantum chemical over-estimation of S(1) oscillator strength and the real mechanism likely involves short-range interaction and/or non-trivial inter-molecular states

Structural Basis for Allosteric Regulation in the Major Antenna Trimer of Photosystem II

The allosteric regulation of protein function proves important in many life-sustaining processes. In plant photosynthesis, LHCII, the major antenna complex of Photosystem II, employs a delicate switch between light harvesting and photoprotective modes. The switch is triggered by an enlarged pH gradient (ΔpH) across the thylakoid membranes. Using molecular simulations and quantum calculations, we show that ΔpH can tune the light-harvesting potential of the antenna via allosteric regulation of the excitonic coupling in chlorophyll-carotenoid pairs. To this end, we propose how the LHCII excited state lifetime is coupled to the environmental conditions. In line with experimental findings, our theoretical model provides crucial evidence toward the elucidation of the photoprotective switch of higher plants at an all-atom resolution

Efficiency in Multi-objective Games

In a multi-objective game, each agent individually evaluates each overall action-profile on multiple objectives. I generalize the price of anarchy to multi-objective games and provide a polynomial-time algorithm to assess it. This work asserts that policies on tobacco promote a higher economic efficiency

Circular Networks from Distorted Metrics

Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into this elementary framework. Alternatively, various network representations have been developed. Circular networks are a natural generalization of leaf-labeled trees interpreted as split systems, that is, collections of bipartitions over leaf labels corresponding to current species. Although such networks do not explicitly model specific evolutionary events of interest, their straightforward visualization and fast reconstruction have made them a popular exploratory tool to detect network-like evolution in genetic datasets. Standard reconstruction methods for circular networks, such as Neighbor-Net, rely on an associated metric on the species set. Such a metric is first estimated from DNA sequences, which leads to a key difficulty: distantly related sequences produce statistically unreliable estimates. This is problematic for Neighbor-Net as it is based on the popular tree reconstruction method Neighbor-Joining, whose sensitivity to distance estimation errors is well established theoretically. In the tree case, more robust reconstruction methods have been developed using the notion of a distorted metric, which captures the dependence of the error in the distance through a radius of accuracy. Here we design the first circular network reconstruction method based on distorted metrics. Our method is computationally efficient. Moreover, the analysis of its radius of accuracy highlights the important role played by the maximum incompatibility, a measure of the extent to which the network differs from a tree.Comment: Submitte

The impact of temperature changes on summer time ozone and its precursors in the Eastern Mediterranean

Changes in temperature due to variability in meteorology and climate change are expected to significantly impact atmospheric composition. The Mediterranean is a climate sensitive region and includes megacities like Istanbul and large urban agglomerations such as Athens. The effect of temperature changes on gaseous air pollutant levels and the atmospheric processes that are controlling them in the Eastern Mediterranean are here investigated. The WRF/CMAQ mesoscale modeling system is used, coupled with the MEGAN model for the processing of biogenic volatile organic compound emissions. A set of temperature perturbations (spanning from 1 to 5 K) is applied on a base case simulation corresponding to July 2004. The results indicate that the Eastern Mediterranean basin acts as a reservoir of pollutants and their precursor emissions from large urban agglomerations. During summer, chemistry is a major sink at these urban areas near the surface, and a minor contributor at downwind areas. On average, the atmospheric processes are more effective within the first 1000 m above ground. Temperature increases lead to increases in biogenic emissions by 9±3% K<sup>−1</sup>. Ozone mixing ratios increase almost linearly with the increases in ambient temperatures by 1±0.1 ppb O<sub>3</sub> K<sup>−1</sup> for all studied urban and receptor stations except for Istanbul, where a 0.4±0.1 ppb O<sub>3</sub> K<sup>−1</sup> increase is calculated, which is about half of the domain-averaged increase of 0.9±0.1 ppb O<sub>3</sub> K<sup>−1</sup>. The computed changes in atmospheric processes are also linearly related with temperature changes

The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games

We analyse the computational complexity of finding Nash equilibria in simple stochastic multiplayer games. We show that restricting the search space to equilibria whose payoffs fall into a certain interval may lead to undecidability. In particular, we prove that the following problem is undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium of G where player 0 wins with probability 1. Moreover, this problem remains undecidable if it is restricted to strategies with (unbounded) finite memory. However, if mixed strategies are allowed, decidability remains an open problem. One way to obtain a provably decidable variant of the problem is restricting the strategies to be positional or stationary. For the complexity of these two problems, we obtain a common lower bound of NP and upper bounds of NP and PSPACE respectively.Comment: 23 pages; revised versio

Образ міста у творчості О. Іваненко (на матеріалі казки “Чарівна квітка”)

Авторка статті досліджує образ міста у творчості відомої письменниці ХХ ст. Оксани Іваненко. Автор робить спробу виокремити особливості творів, що характерні для її манери письма. Приділяється увага тематиці творів письменниці, портретній характеристиці її героїв. Дослідниця робить спробу схарактеризувати образ міста на матеріалі казок “Чарівна квітка”. “Місто боягузів” у казці “Чарівна квітка” О. Іваненко є точкою відліку в казковому часі, не має логіки у взаємозв’язку з дійсністю. Результатом дослідження є висновок про те, що письменниця досліджує процес становлення і розвитку дитини, вивчає особливості психології персонажів. Ключові слова: казка, логіка, образ, місто, тематика, реальність, персонажі.Автор статьи исследует образ города в творчестве известной писательницы ХХ века Оксаны Иваненко. Автор статьи делает попытку выделить особенности произведений, характерные ее письму. Уделяется внимание тематике произведений писательницы, портретной характеристике ее героев. Исследователь делает попытку охарактеризовать образ города на материале сказки “Волшебный цветок”. “Город боягузов” в сказке “Волшебный цветок” Оксаны Иваненко является точкой отсчета в сказочном времени, не имеет логики со взаимосвязью с действительностью. Результатом исследования является вывод о том, что писательница исследует процесс становления и развития юного читателя, изучает особенности психологии персонажей. Ключевые слова: сказка, логика, образ, город, тематика, реальность, персонажи.The author of the article investigates the figure of the city in the O. Ivanenko’s works, the famous writer of the XX th century. The author tries to define the peculiarities of her works. There are paid attentions to the portrait characteristics of the main characters in “Magic flower”, to the themes of her works. The investigator tries to characterise the figure of the city in the “Magic flower”. The “city of timorous people” in the “Magic flower” by O. Ivanenko is the beginning in the time of the tale, it does not have logic. This investigation proves that the writer investigates the process of the child’s growing and growing, studies the psychological peculiarities of the main characters. Keywords: tale, logic, figure, city, themes, reality, main characters