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Working paper

Fino A., Grantcharov G.,

math. arxive. Cornell University, 2016
Let M be a complex nilmanifold, that is, a compact quotient of a nilpotent Lie group endowed with an invariant complex structure by a discrete lattice. A holomorphic differential on M is a closed, holomorphic 1-form. We show that a(M) ⩽ k, where a(M) is the algebraic dimension a(M) (i.e. the transcendence degree of the field of meromorphic functions) and k is the dimension of the space of holomorphic differentials. We prove a similar result about meromorphic maps to Kahler manifolds.

Added: Mar 16, 2016

Working paper

In 1970s, a method was developed for integration of nonlinear equations by means of algebraic geometry. Starting from a Lax representation with a spectral parameter, the algebro-geometric method allows to solve the system explicitly in terms of Theta functions of Riemann surfaces. However, the explicit formulas obtained in this way fail to answer such natural topological questions as whether a given singular solution is stable or not. In the present paper, the problem of stability for equilibrium points is considered, and it is shown that this problem can also be approached by means of algebraic geometry.

Added: Nov 19, 2013

Working paper

We classify all connected affine algebraic groups G such that there are only finitely many G-orbits in every algebraic G-variety containing a dense open G-orbit. We also prove that G enjoys this property if and only if every irreducible algebraic G-variety X is modality-regular, i.e., the modality of X (in the sense of V. Arnol’d) equals to that of a family which is open in X.

Added: Jul 24, 2017

Working paper

Kamenova L.,

math. arxive. Cornell University, 2016
A projective manifold is algebraically hyperbolic if the degree of any curve is bounded from above by its genus times a constant, which is independent from the curve. This is a property which follows from Kobayashi hyperbolicity. We prove that hyperk¨ahler manifolds are non algebraically hyperbolic when the Picard rank is at least 3, or if the Picard rank is 2 and the SYZ conjecture on existence of Lagrangian fibrations is true. We also prove that if the automorphism group of a hyperk¨ahler manifold is infinite then it is algebraically non-hyperbolic.

Added: Apr 21, 2016

Working paper

Russkov A.,

, math. arxive. Cornell University, 2020. No. 2006.00561.
The parallel annealing method is one of the promising approaches for large scale simulations as potentially scalable on any parallel architecture. We present an implementation of the algorithm on the hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible redistributing replicas and to do that efficiently. We provide details of the testing on Intel Skylake/Nvidia V100 based hardware running in parallel more than two million replicas of the Ising model sample. The results are quite optimistic because the acceleration grows toward the perfect line with the growing complexity of the simulated system.

Added: Jun 2, 2020

Working paper

Branzei S.,

Computer Science and Game Theory (cs.GT), arXiv:1907.01766. arxiv. Cornell university, 2019
We study the problem of allocating divisible bads (chores) among multiple agents with additive utilities, when money transfers are not allowed. The competitive rule is known to be the best mechanism for goods with additive utilities and was recently extended to chores by Bogomolnaia et al (2017). For both goods and chores, the rule produces Pareto optimal and envy-free allocations. In the case of goods, the outcome of the competitive rule can be easily computed. Competitive allocations solve the Eisenberg-Gale convex program; hence the outcome is unique and can be approximately found by standard gradient methods. An exact algorithm that runs in polynomial time in the number of agents and goods was given by Orlin. In the case of chores, the competitive rule does not solve any convex optimization problem; instead, competitive allocations correspond to local minima, local maxima, and saddle points of the Nash Social Welfare on the Pareto frontier of the set of feasible utilities. The rule becomes multivalued and none of the standard methods can be applied to compute its outcome. In this paper, we show that all the outcomes of the competitive rule for chores can be computed in strongly polynomial time if either the number of agents or the number of chores is fixed. The approach is based on a combination of three ideas: all consumption graphs of Pareto optimal allocations can be listed in polynomial time; for a given consumption graph, a candidate for a competitive allocation can be constructed via explicit formula; and a given allocation can be checked for being competitive using a maximum flow computation as in Devanur et al (2002). Our algorithm immediately gives an approximately-fair allocation of indivisible chores by the rounding technique of Barman and Krishnamurthy (2018).

Added: Sep 24, 2019

Working paper

We consider single machine problems with opposite criteria, namely we consider the maximization of total tardiness, the maximization of the number of tardy jobs and the maximization of total completion time (in contrast to usual minimization problems)and a minimization version of the Knapsack problem.

Added: Mar 4, 2013

Working paper

The scheduling problem of minimizing total tardiness on a single machine is knownto be NP-hard in the ordinary sense. In this paper, we consider the special case of the problem when the processing times $p_j$ and the due dates $d_j$ of the jobs $j, \, j \in N = \{ 1, 2, \ldots, n \}$, are oppositely ordered: $p_1\ge p_2\ge\dots\ge p_n$ and $d_1\le d_2\le\dots\le d_n$. It is shown that already this special case is $NP$-hard in the ordinary sense, too. The set of jobs $N$ is partitioned into $\Bbbk, 1 \le \Bbbk \le n$, subsets$\mathcal{M}_1,\mathcal{M}_2,\dots,\mathcal{M}_\Bbbk$,$\mathcal{M}_\nu \bigcap \mathcal{M}_\mu=\emptyset$ for $\nu\ne \mu,$$N=\mathcal{M}_1\bigcup\mathcal{M}_2\bigcup\dots\bigcup\mathcal{M}_\Bbbk$,such that$\max_{i,j\in\mathcal{M}_\nu}|d_i-d_j|\le\min_{j\in\mathcal{M}_\nu}p_j$for each $\nu=1,2,\dots,\Bbbk$. We propose algorithms which solve the problem: in $O(\Bbbk n\sum p_j)$ time if $1\le \Bbbk< n$ in $O(n^2)$ time if $\Bbbk= n$ and in $O(n^2)$ time if $\max_{i,j\in N}|d_i-d_j|\le 1$. The polynomial algorithms do neitherrequire the conditions $p_1\ge p_2\ge\dots\ge p_n$ mentioned above nor integer processing times to construct an optimal schedule. Finally, we apply the idea of the presented algorithm for the case $\Bbbk = 1$ to the even-odd partition problem

Added: Mar 4, 2013

Working paper

Migration in any context may be approached from myriad perspectives and with varied techniques; in this study, we examine migration in Russia using the life-course perspective. We investigate two core issues: the factors of migration and the position of migration in the Russian life course. In addition, we perform data exploration and assess at what stage of the Zelinsky mobility transition model Russia is. We use exploratory analytical tools and life-course analytical methods such as event history analysis (EHA) and sequence analysis (SA) in this study. The exploratory data analysis (EDA) and EHA reveal interesting, albeit in some cases contradictory, results. We find that Russians are not very mobile, particularly in large cities; movement more often occurs in mid-sized cities and towns. One intriguing observation is the prevalence of what may well be return migration to rural areas among women born in 1990-1995. Furthermore, the military is shown empirically to be a major factor; in all, we find that enlistment, sex, generation, and type of education are significant factors in migration, with soldiers, women, younger generations, and those with higher education exhibiting higher likelihoods of migration. The SA results show that migration is often positioned as a starting event in Russians biographies; more interestingly, it is also positioned to work potentially as a deferment or avoidance tool (e.g., draft avoidance). Our observations and test results lead us to conclude that Russia is at the “advanced society” stage of the Zelinsky mobility transition model.

Added: Nov 15, 2017

Working paper

Added: Sep 25, 2016

Working paper

It is proved that any strictly exceptional collection generating the derived category of coherent sheaves on a smooth projective variety X with \rk K_0(X) = \dim X + 1 constists of locally free sheaves up to a common shift.

Added: Feb 23, 2014

Working paper

The Robbins-Monro algorithm is a recursive, simulation-based stochastic procedure to approximate
the zeros of a function that can be written as an expectation. It is known that under some technical
assumptions, a Gaussian convergence can be established for the procedure. Here, we are interested in the
local limit theorem, that is, quantifying this convergence on the density of the involved objects. The analysis
relies on a parametrix technique for Markov chains converging to diffusions, where the drift is unbounded.

Added: Oct 25, 2018

Working paper

The Competitive Industrial Performance index (developed by experts of the UNIDO) is designed as a measure of national competitiveness. Index is an aggregate of eight observable variables, representing different dimensions of competitive industrial performance. Instead of using a cardinal aggregation function, what CIP’s authors do, it is proposed to apply ordinal ranking methods borrowed from social choice: either direct ranking methods based on the majority relation (e.g. the Copeland rule, the Markovian method) or a multistage procedure of selection and exclusion of the best alternatives, as determined by a majority relation-based social choice solution concept (tournament solution), such as the uncovered set and the minimal externally stable set. The same method of binary comparisons based on the majority rule is used to analyse rank correlations. It is demonstrated that the ranking is robust but some of the new aggregate rankings represent the set of criteria better than the original ranking based on the CIP.

Added: Sep 25, 2014

Working paper

The paper examines the effects of ambiguity in regulation on the equilibrium allocation. Under ambiguous bailout policy, agents’ suffer from a lack of information with regards to the insolvency resolution method, which would be chosen by the regulator if a financial institution fails. In this case, beliefs of bankers regarding whether an insolvent bank is liquidated, may differ from those of depositors. The beliefs may be asymmetric even if bankers and depositors possess absolutely symmetric information about the policy of the regulator. It is shown that such asymmetry in beliefs can generate an allocative inefficiency of the bank based economy.

Added: Jun 27, 2018

Working paper

This article focuses on the presidential rhetoric of Russian and American leaders at the end of their latest campaigns, taking their victory speeches given immediately after winning their respective elections as examples. The comparative cross-cultural research presented in this study includes cognitive, corpus, and rhetorical approaches and is carried out within the framework of critical discourse analysis. The interconnection between language, culture and politics is evident through metaphors used by national leaders. The metaphor THE RUSSIAN NATION IS AT WAR reconstructed in President Putin’s victory speech is quite different from the metaphor THE AMERICAN NATION IS ONE FAMILY found in President Obama’s victory speech. Archetypal metaphors found in both speeches reflect public values that turn out to be highly contrastive and explain some cultural and political differences between the great powers.

Added: Jan 17, 2014

Working paper

The paper presents a comparative legal study of compliance regulation in the areas of AML/CFT and anti-corruption. The main question is whether existing expirience of AML/CFT complaince regulation can/should be considered in the anti-corruption field. The author identifies distinctive features of two different approaches to regulation and the challenges arizing from these, and then analyzes the role of international soft law, national laws and regulations, and compliance programmes of multinational companies.

Added: Nov 2, 2019

Working paper

Durand B., Shen A.,

arxiv.org. math. Cornell University, 2012. No. 2896.
We describe all Ammann tilings of a plane, a half-plane and a quadrant. In our description, every tiling is associated to an infinite sequence of two letters. We provide simple criteria of (a) whether a tiling associated with a sequence tiles the entire plane, a half-plane or a quadrant and (b) whether tiling associated with two sequences are congruent. It is well known that all Ammann tilings are aperiodic; we show how one can use this fact to construct an aperiodic 2-dimensional sub-shift of finite type

Added: Dec 11, 2013

Working paper

The decisions to reduce, leave unchanged, or increase an ordered choice variable (such
as a policy rate) are often characterized by abundant no-change outcomes that may be
generated by di¤erent processes. In addition, the decreases and increases may also be
driven by distinct decision-making paths. Neither standard nor zero-inated models for
ordinal responses are well-suited to address these issues. This paper develops a exible
mixture model with endogenously switching regimes. Three latent regimes, interpreted
in the interest rate setting context as loose, neutral and tight policy stances, create
separate processes for the rate hikes and cuts, and overlap at a status quo outcome,
generating three di¤erent types of zeros. The new model shows good small-sample
performance in Monte Carlo experiments, whereas the traditional models deliver biased
estimates of choice probabilities and marginal e¤ects. In an application to the policy
rate, not only is the new model strongly favored by the statistical tests, but it also
produces economically more meaningful estimates with respect to the existing models,
and shows that only sixty percents of zeros are generated by a neutral policy stance,
suggesting a high degree of intentional interest-rate smoothing.

Added: Sep 29, 2014

Working paper

“Achieving oneself” is not a subject of a systematic scientific research in Russian personality psychology. The goal of the current study is to justify the significance of such research in current socio-cultural and scientific context. “Achieving oneself” is understood in this paper as an integral reflectively mediated fulfillment of the I’s potential in leading vital relations hips of a person. The field of study is “the new personology”, the method is hermeneutics. This study offers a reflective model of the I’s potential towards the Other and presents an application of this model to the analysis of the process of achieving one self in a loving relationship.

Added: Jan 28, 2014

Working paper

We examine the novel concept for repeated noncooperative games with bounded rationality: ``Nash-2'' equilibrium, called also ``threatening-proof profile'' in (Iskakov~M., Iskakov A., 2012). It is weaker than Nash equilibrium and equilibrium in secure strategies: a player takes into account not only current strategies but also the next-stage responses of the partners to her deviation from the current situation that reduces her relevant choice set. We provide a condition for Nash-2 existence, criteria for a strategy profile to be the Nash-2 equilibrium in strictly competitive games, apply this concept to Bertrand and Hotelling game and interpret the results as tacit collusion.

Added: Oct 21, 2014

Working paper

In this paper, we present a modification of dynamic programming algorithms (DPA), which we denote as graphical algorithms (GrA). For the knapsack problem and some single machine scheduling problems, it is shown that the time complexity of the GrA is less that the time complexity of the standard DPA. Moreover, the average running time of the GrA is often essentially smaller. A GrA can also solve largescale instances and instances, where the parameters are not integer. In addition, for some problems, GrA has a polynomial time complexity in contrast to a pseudo-polynomial complexity of DPA.

Added: Mar 4, 2013