# Publications

Using a simplified multistage bidding model with asymmetrically informed agents, De Meyer and Saley [17] demonstrated an idea of endogenous origin of the Brownian component in the evolution of prices on stock markets: random price fluctuations may be caused by strategic randomization of “insiders.” The model is reduced to a repeated game with incomplete information. This paper presents a survey of numerous researches inspired by the pioneering publication of De Meyer and Saley.

We compare the Egalitarian rule (aka Egalitarian Equivalent) and the Competitive rule (aka Competitive Equilibrium with Equal Incomes) to divide bads (chores). They are both welfarist: the competitive disutility profile(s) are the critical points of their Nash product on the set of efficient feasible profiles. The C rule is Envy Free, Maskin Monotonic, and has better incentives properties than the E rule. But, unlike the E rule, it can be wildly multivalued, admits no selection continuous in the utility and endowment parameters, and is harder to compute. Thus in the division of bads, unlike that of goods, no rule normatively dominates the other.

This research is motivated by the global warming problem, which is likely influenced by human activity. Fast-growing oil palm plantations in the tropical belt of Africa, Southeast Asia and parts of Brazil lead to significant loss of rainforest and contribute to the global warming by the corresponding decrease of carbon dioxide absorption. We propose a novel approach to monitoring of the development of such plantations based on an application of state-of-the-art Fully Convolutional Neural Networks (FCNs) to solve Semantic Segmentation Problem for Landsat imagery.

Among the bryophytes, biological growth rhythms have not yet been identified due to a lack of long‐term precision observations. Here we carry out precision field monitoring of the growth of the peat moss *Sphagnum riparium* using the recent geotropic curvature method. For four years, using the observation intervals of 2‐5 days, we measured 116 469 shoots and received 4 493 estimates of growth rates. We found three rhythmic growth components. The seasonal rhythm of growth has a period of about 180 days, which coincides with the seasonal temperature cycle. The circalunar growth rhythm has a period of about 29.5 days and coincides with the synodic lunar cycle. There is an acceleration near the new moon, and a slowdown in growth near the full moon. The third rhythm has a period of 7‐16 days and is always synchronized with the circalunar growth rhythm. From the models of the sums of sinusoids, we found that the total contribution of all three rhythms to the growth rate is R2 = 0.51‐0.78, and without taking into account the seasonal rhythm, R2 = 0.36‐0.42. Thus, our study gives the first data on the biological rhythms and the contribution of these rhythms to the growth process of bryophytes. We attribute the unexpectedly high contribution of rhythms to the synchronous growth of the Sphagnum mat, which is necessary to reduce the loss of moisture.

The Gibbard–Satterthwaite theorem is a cornerstone of social choice theory, stating that an onto social choice function cannot be both strategy-proof and non-dictatorial if the number of alternatives is at least three. The Duggan–Schwartz theorem proves an analogue in the case of set-valued elections: if the function is onto with respect to singletons, and can be manipulated by neither an optimist nor a pessimist, it must have a weak dictator. However, the assumption that the function is onto with respect to singletons makes the Duggan–Schwartz theorem inapplicable to elections which necessarily select multiple winners. In this paper we make a start on this problem by considering rules which always elect exactly two winners (such as the consulship of ancient Rome). We establish that if such a *consular election rule* cannot be expressed as the union of two disjoint social choice functions, then strategy-proofness implies the existence of a dictator. Although we suspect that a similar result holds for *k*-winner rules for k>2k>2, there appear to be many obstacles to proving it, which we discuss in detail.

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of the majority’s most preferred candidates is the measure of majority power; and the minimal share of voters that allows the minority to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on such minimal shares for voting rules that are popular in the literature and used in real elections. We order the rules according to majority power and veto power. Instant-runoff voting has both the highest majority power and the highest veto power; plurality rule has the lowest. In general, the greater is the majority power of a voting rule, the greater its veto power. The three exceptions are: voting with proportional veto power, Black’s rule and Borda’s rule, which have relatively weak majority power and strong veto power, thus providing minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

The land area covered by freely available very high-resolution (VHR) imagery has grown dramatically over recent years, which has considerable relevance for forest observation and monitoring. For example, it is possible to recognize and extract a number of features related to forest type, forest management, degradation and disturbance using VHR imagery. Moreover, time series of medium-to-high-resolution imagery such as MODIS, Landsat or Sentinel has allowed for monitoring of parameters related to forest cover change. Although automatic classification is used regularly to monitor forests using medium-resolution imagery, VHR imagery and changes in web-based technology have opened up new possibilities for the role of visual interpretation in forest observation. Visual interpretation of VHR is typically employed to provide training and/or validation data for other remote sensing-based techniques or to derive statistics directly on forest cover/forest cover change over large regions. Hence, this paper reviews the state of the art in tools designed for visual interpretation of VHR, including Geo-Wiki, LACO-Wiki and Collect Earth as well as issues related to interpretation of VHR imagery and approaches to quality assurance. We have also listed a number of success stories where visual interpretation plays a crucial role, including a global forest mask harmonized with FAO FRA country statistics; estimation of dryland forest area; quantification of deforestation; national reporting to the UNFCCC; and drivers of forest change.

Global gridded crop models (GGCMs) are essential tools for estimating agricultural crop yields and externalities at large scales, typically at coarse spatial resolutions. Higher resolution estimates are required for robust agricultural assessments at regional and local scales, where the applicability of GGCMs is often limited by low data availability and high computational demand. An approach to bridge this gap is the application of meta-models trained on GGCM output data to covariates of high spatial resolution. In this study, we explore two machine learning approaches – extreme gradient boosting and random forests - to develop meta-models for the prediction of crop model outputs at fine spatial resolutions. Machine learning algorithms are trained on global scale maize simulations of a GGCM and exemplary applied to the extent of Mexico at a finer spatial resolution. Results show very high accuracy with R2>0.96 for predictions of maize yields as well as the hydrologic externalities evapotranspiration and crop available water with also low mean bias in all cases. While limited sets of covariates such as annual climate data alone provide satisfactory results already, a comprehensive set of predictors covering annual, growing season, and monthly climate data is required to obtain high performance in reproducing climate-driven inter-annual crop yield variability. The findings presented herein provide a first proof of concept that machine learning methods are highly suitable for building crop meta-models for spatio-temporal downscaling and indicate potential for further developments towards scalable crop model emulators.

A tournament can be represented as a set of candidates and the results from pairwise comparisons of the candidates. In our setting, candidates may form coalitions. The candidates can choose to fix who wins the pairwise comparisons within their coalition. A coalition is winning if it can guarantee that a candidate from this coalition will win each pairwise comparison. This approach divides all coalitions into two groups and is, hence, a simple game. We show that each minimal winning coalition consists of a certain uncovered candidate and its dominators. We then apply solution concepts developed for simple games and consider the desirability relation and the power indices which preserve this relation. The tournament solution, defined as the maximal elements of the desirability relation, is a good way to select the strongest candidates. The Shapley–Shubik index, the Penrose–Banzhaf index, and the nucleolus are used to measure the power of the candidates. We also extend this approach to the case of weak tournaments.

√√ Abstract Let f(a,b,c,d) = a2+b2 + c2+d2 − (a+c)2+(b+d)2, let

(a,b,c,d) stand for a,b,c,d ∈ Z0 such that ad − bc = 1. Defines

In other words, we consider the sum of the powers of the triangle inequality defects for the lattice parallelograms (in the first quadrant) of area one. We prove that F(s) converges when s > 1 and diverges at s = 1/2. We also prove that

1=1,(a,b,c,d) (a+c)2(b+d)2(a+b+c+d)2 3