Cohomological Arithmetic Statistics for Principally Polarized Abelian Varieties over Finite Fields

There is a natural probability measure on the set of isomorphism classes of principally polarized Abelian varieties of dimension $g$ over $\mathbb{F}_q$, weighted by the number of automorphisms. The distributions of the number of $\mathbb{F}_q$-rational points are related to the cohomology of fiber powers of the universal family of principally polarized Abelian varieties. To that end we compute the cohomology $H^i(\mathcal{X}^{\times n}_g,\mathbb{Q}_\ell)$ for $g=1$ using results of Eichler-Shimura and for $g=2$ using results of Lee-Weintraub and Petersen, and we compute the compactly supported Euler characteristics $e_\mathrm{c}(\mathcal{X}^{\times n}_g,\mathbb{Q}_\ell)$ for $g=3$ using results of Hain and conjectures of Bergstr\"om-Faber-van der Geer. In each of these cases we identify the range in which the point counts $\#\mathcal{X}^{\times n}_g(\mathbb{F}_q)$ are polynomial in $q$. Using results of Borel and Grushevsky-Hulek-Tommasi on cohomological stability, we adapt arguments of Achter-Erman-Kedlaya-Wood-Zureick-Brown to pose a conjecture about the asymptotics of the point counts $\#\mathcal{X}^{\times n}_g(\mathbb{F}_q)$ in the limit $g\rightarrow\infty$.Comment: 29 pages, comments welcome

Global thermodynamic behaviour of supercritical fluids: example of methane and ethane

Do to the fluctuations associated with the critical region of fluids. The behavior of thermodynamic properties these can not be predicted by mean field theories. To do so, a global equation of state based on the crossover model has been used. This equation of state is formulated on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity of fluids.The model can be applied in a wide range of temperatures and densities around the critical point for ethane and methane. It is found that the developed model represents most of the reliable experimental data accurately

Do not Waste Money on Advertising Spend: Bid Recommendation via Concavity Changes

In computational advertising, a challenging problem is how to recommend the bid for advertisers to achieve the best return on investment (ROI) given budget constraint. This paper presents a bid recommendation scenario that discovers the concavity changes in click prediction curves. The recommended bid is derived based on the turning point from significant increase (i.e. concave downward) to slow increase (convex upward). Parametric learning based method is applied by solving the corresponding constraint optimization problem. Empirical studies on real-world advertising scenarios clearly demonstrate the performance gains for business metrics (including revenue increase, click increase and advertiser ROI increase).Comment: 10 page

Demystifying Advertising Campaign Bid Recommendation: A Constraint target CPA Goal Optimization

In cost-per-click (CPC) or cost-per-impression (CPM) advertising campaigns, advertisers always run the risk of spending the budget without getting enough conversions. Moreover, the bidding on advertising inventory has few connections with propensity one that can reach to target cost-per-acquisition (tCPA) goals. To address this problem, this paper presents a bid optimization scenario to achieve the desired tCPA goals for advertisers. In particular, we build the optimization engine to make a decision by solving the rigorously formalized constrained optimization problem, which leverages the bid landscape model learned from rich historical auction data using non-parametric learning. The proposed model can naturally recommend the bid that meets the advertisers' expectations by making inference over advertisers' historical auction behaviors, which essentially deals with the data challenges commonly faced by bid landscape modeling: incomplete logs in auctions, and uncertainty due to the variation and fluctuations in advertising bidding behaviors. The bid optimization model outperforms the baseline methods on real-world campaigns, and has been applied into a wide range of scenarios for performance improvement and revenue liftup

THE FACTORS DETERMINING PROFITABILITY OF GRAIN PRODUCTION IN A REGION

The research was conducted in order to determine influence of structural factors on profitability of grain production in the Altai Region, which is one of the main producers of grain in Russia. The influence of specialization and placement on the economic efficiency of grain production in the Altai Region was determined, factors for the formation of financial results and the financial condition of grain-type organizations were revealed. Comparison of agricultural organizations for which grain farming was the main production sector indicates that in case of increase in the cultivation area, the economic efficiency of resource use will be increased, despite higher costs per hectare of grain crops. The variation of organizations in the profitability of production is explained by the imperfection of the management system of the main branches in separate agricultural organizations, including non-optimal production volumes and placement in natural and economic zones. In the largest highly tailored organizations the economic efficiency of the resources used increased in the short-term perspective rose, but risks of its decline are created in the long-term period