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Working paper

In this article we prove that quasi-free algebra over noetherian ring is coherent. In particular, we get that the category of left finite-presented modules over this algebra is abelian.

Added: Oct 14, 2013

Working paper

We define the triangulated category of relative singularities of a closed subscheme in a scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations of the related section of a line bundle, and their analogues with locally free sheaves replaced by coherent ones. The appropriate exotic derived category of coherent matrix factorizations is then identified with the triangulated category of relative singularities, while the similar exotic derived category of locally free matrix factorizations is its full subcategory. The latter category is identified with the kernel of the direct image functor corresponding to the closed embedding of the zero locus and acting between the conventional (absolute) triangulated categories of singularities. Similar results are obtained for matrix factorizations of infinite rank; and two different "large" versions of the triangulated category of relative singularities, corresponding to the approaches of Orlov and Krause, are identified in the case of a Cartier divisor. Contravariant (coherent) and covariant (quasi-coherent) versions of the Serre-Grothendieck duality theorems for matrix factorizations are established, and pull-backs and push-forwards of matrix factorizations are discussed at length. A number of general results about derived categories of the second kind for CDG-modules over quasi-coherent CDG-algebras are proven on the way. Hochschild (co)homology of matrix factorization categories are discussed in an appendix written in collaboration with A.I. Efimov.

Added: Dec 22, 2013

Working paper

The convolution ring K^{GL_n(\OOO)⋊ℂ×}(Gr_{GL_n}) was identified with a quantum unipotent cell of the loop group LSL_2 in [Cautis-Williams, arXiv:1801.08111]. We identify the basis formed by the classes of irreducible equivariant perverse coherent sheaves with the dual canonical basis of the quantum unipotent cell.

Added: Jun 9, 2019

Working paper

A Hermitian symplectic manifold is a complex manifold endowed with a symplectic form ω, for which the bilinear form ω(I·, ·) is positive definite. In this work we prove ddc -lemma for 1- and (1,1)-forms for compact Hermitian symplectic manifolds of dimension 3. This shows that Albanese map for such manifolds is well-defined and allows one to prove Kahlerness if the dimension of the Albanese image of a manifold is maximal.

Added: Nov 19, 2015

Working paper

Efficient regulation of internal homeostasis and defending it against perturbations
requires complex behavioral strategies. However, the computational principles mediating brain’s
homeostatic regulation of reward and associative learning remain undefined. Here we use a
definition of primary rewards, as outcomes fulfilling physiological needs, to build a normative
theory showing how learning motivated behavior is modulated by the internal state of the animal.
The theory proves that seeking rewards is equivalent to the fundamental objective of
physiological stability, defining the notion of physiological rationality of behavior. We further
give a formal basis for temporal discounting of reward. It also explains how animals learn to act
predictively to preclude prospective homeostatic challenges, and attributes a normative
computational role to the modulation of midbrain dopaminergic activity by hypothalamic signals.

Added: Jan 29, 2016

Working paper

Keramati M.,

Biorxiv. 005140. Cold Spring Harbor Laboratory, 2014
Efficient regulation of internal homeostasis and defending it against perturbations requires complex behavioral strategies. However, the computational principles mediating brain's homeostatic regulation of reward and associative learning remain undefined. Here we use a definition of primary rewards, as outcomes fulfilling physiological needs, to build a normative theory showing how learning motivated behavior is modulated by the internal state of the animal. The theory proves that seeking rewards is equivalent to the fundamental objective of physiological stability, defining the notion of physiological rationality of behavior. We further give a formal basis for temporal discounting of reward. It also explains how animals learn to act predictively to preclude prospective homeostatic challenges, and attributes a normative computational role to the modulation of midbrain dopaminergic activity by hypothalamic signals.

Added: Dec 29, 2014

Working paper

Collections of parabolic orbits in homogeneous spaces, homogeneous dynamics and hyperkahler geometry

Let M be a hyperk\"ahler manifold with b2(M)≥5. We improve our earlier results on the Morrison-Kawamata cone conjecture by showing that the Beauville-Bogomolov square of the primitive MBM classes (i.e. the classes whose orthogonal hyperplanes bound the K\"ahler cone in the positive cone, or, in other words, the classes of negative extremal rational curves on deformations of M) is bounded in absolute value by a number depending only on the deformation class of M. The proof uses ergodic theory on homogeneous spaces.

Added: Sep 7, 2016

Working paper

What role can collective action by foreign investors play in an environment characterized by incomplete institutions? We study this question by looking on foreign business associations in the Russian Federation. By interviewing 17 foreign business associations and conducting an online survey of their member firms, we find that business associations play an important welfare-enhancing role in providing a series of support and informational services. However, they do not play a significant role in lobbying the collective interests of their member firms, especially in the current political context in Russia where since the start of the Ukraine crisis the business community seems to have suffered a general loss of influence on political decision making

Added: Feb 2, 2016

Working paper

Belmonte A.,

Political Science. PS. Высшая школа экономики, 2017. No. WP BRP 43/PS/2017 .
To what extent does the degree of authoritarian political support depend on collective memories of a past experience with democracy? And how costly is it for a dictator to manipulate such memories with the help of propaganda? In this paper, we develop a political economy model with endogenous reference points, where a dictator strategically recalls traumatic collective memories of past political instability with the help of propaganda, to convince the population that an autocratic status quo is superior to a potential democratic alternative. In our model, both the optimal level of propaganda and collective memories are jointly determined. We show how the marginal benefit of propaganda is positively correlated both with the amount of rent distribution within the elite, and the intensity of a past traumatic experience with democracy. We illustrate our theoretical findings with case-studies of two authoritarian regimes that were preceded by periods of political instability -- the Russian Federation under Vladimir Putin, and Chile under Augusto Pinochet. We then also provide cross-country empirical evidence in support of our argument.

Added: Feb 16, 2017

Working paper

A common feature of the Hungarian, Irish, Spanish and Turkish higher education admission systems is that the students apply for programmes and they are ranked according to their scores. Students who apply for a programme with the same score are in a tie. Ties are broken by lottery in Ireland, by objective factors in Turkey (such as date of birth) and other precisely defined rules in Spain. In Hungary, however, an equal treatment policy is used, students applying for a programme with the same score are all accepted or rejected together. In such a situation there is only one question to decide, whether or not to admit the last group of applicants with the same score who are at the boundary of the quota. Both concepts can be described in terms of stable score-limits. The strict rejection of the last group with whom a quota would be violated corresponds to the concept of H-stable (i.e. higher-stable) score-limits that is currently used in Hungary. We call the other solutions based on the less strict admission policy as L-stable (i.e. lower-stable) score-limits. We show that the natural extensions of the Gale-Shapley algorithms produce stable score-limits, moreover, the applicant-oriented versions result in the lowest score-limits (thus optimal for students) and the college-oriented versions result in the highest score-limits with regard to each concept. When comparing the applicant-optimal H-stable and L-stable score-limits we prove that the former limits are always higher for every college. Furthermore, these two solutions provide upper and lower bounds for any solution arising from a tie-breaking strategy. Finally we show that both the H-stable and the L-stable applicant-proposing scorelimit algorithms are manipulable.

Added: Mar 11, 2013

Working paper

Let $\Psi$ be the projectivization (i.e., the set of one-dimensional vector
subspaces) of a vector space of dimension $\ge 3$ over a field. Let $H$ be a
closed (in the pointwise convergence topology) subgroup of the permutation
group $\mathfrak{S}_{\Psi}$ of the set $\Psi$. Suppose that $H$ contains the
projective group and an arbitrary self-bijection of $\Psi$ transforming a
triple of collinear points to a non-collinear triple. It is well-known from
\cite{KantorMcDonough} that if $\Psi$ is finite then $H$ contains the
alternating subgroup $\mathfrak{A}_{\Psi}$ of $\mathfrak{S}_{\Psi}$.
We show in Theorem \ref{density} below that $H=\mathfrak{S}_{\Psi}$, if
$\Psi$ is infinite.

Added: Nov 21, 2014

Working paper

Corruption, i.e. regular abuse of public office for private gains, draws substantial attention of researchers in many disciplines. Our paper adds to the experimental literature on corruption a novel experiment on corruption-at-the-top among the real Russian police officers of senior middle rank as experimental subjects (apparently the first study of that kind), which is contrasted to that of ordinary citizens (students in economics). Our experimental design explicitly takes account of the peculiarities of the Russian case during police reform, as well as social and institutional constraints facing anticorruption policies. We find that taking bribes, and especially defending against possible checks of corruption, is quite common to Russian police officers, yet even more typical is their readiness to contribute towards the decrease of the likelihood of this anti-corruption check, even if this contribution leads to private losses. Another typical feature is increased volatility of the frequency and scale of bribery among the police officers (as contrasted to ordinary citizens) when measures aimed at fighting corruption are introduced. We discuss robustness of these findings, as well as their implications for anti-corruption policy.

Added: Jun 7, 2015

Working paper

Corruption, i.e. regular abuse of public office for private gains, draws substantial attention of
researchers in many disciplines. Our paper adds to the experimental literature on corruption a novel
experiment on corruption-at-the-top among the real Russian police officers of senior middle rank as
experimental subjects (apparently the first study of that kind), which is contrasted to that of ordinary
citizens (students in economics). Our experimental design explicitly takes account of the peculiarities
of the Russian case during police reform, as well as social and institutional constraints facing anticorruption
policies. We fi nd that taking bribes, and especially defending against possible checks
of corruption, is quite common to Russian police officers, yet even more typical is their readiness
to contribute towards the decrease of the likelihood of this anti-corruption check, even if this
contribution leads to private losses. Another typical feature is increased volatility of the frequency
and scale of bribery among the police offi cers (as contrasted to ordinary citizens) when measures
aimed at fighting corruption are introduced. We discuss robustness of these findings, as well as their
implications for anti-corruption policy.

Added: Dec 25, 2015

Working paper

This paper proposes a method of bid-rigging detection, which allows us to reveal cartels in procurement auctions without any prior knowledge of the market structure. We apply it to data on highway construction procurements in one of the Russian regions and show that five suppliers demonstrated passive bidding behavior, which is consistent with the so called ‘rotating bidding’ scheme of collusion. The suggested methodology can be potentially used by both researchers and anti-trust agencies for cartel disclosure in various markets.

Added: Mar 26, 2013

Working paper

This paper demonstrates that even established and verified facts of agreements among producers are not a sufficient condition for cartel identification and, as a consequence, prosecution of agreement participants. Such requires looking at institutional details and the wider context of these and similar appearances or occurrences of documents and actions when qualifying the actions of market participants and their effects. This paper discusses a recent antitrust case brought against Russian manufacturers of large diameter pipes (LDPs) that examined supposedly abusive practices by these firms that were contrary to the law on the Protection of Competition, which prohibits market division. An analysis of the materials in this case using modern economic theory indicates that the presence of collusion is inconsistent with the active participation of the main consumer of LDPs in that agreement. The chosen format for the cooperation between pipe manufacturing companies and OJSC Gazprom, namely indicative planning, may be explained from the perspective of reducing contract risk in an environment characterized by large-scale private investments.

Added: Feb 12, 2014

Working paper

We introduce a new asset pricing model to account for risk asymmetrically in a very natural way. Assuming asymmetric investor behavior we develop a utility function similar to a quadratic utility but include a colog measure for capturing risk attitude. Asymmetry in investor preferences follows the asymmetric relationships between asset and market returns in equilibrium. Moreover the local version of the model depends on the characteristics of domestic markets, which is reflected in the different relationship between asset and market returns. We test the model in the Russian and South African markets and show that market premium in the Russian market is higher than in the South African market.

Added: Jan 24, 2014

Working paper

Added: Nov 2, 2012

Working paper

Added: Sep 2, 2018

Working paper

Blokh A., Oversteegen L., Ptacek R. et al. arxiv.org. math. Cornell University, 2014

To construct a model for a connectedness locus of polynomials of degree $d\ge
3$ (cf with Thurston's model of the Mandelbrot set), we define \emph{linked}
geolaminations $\mathcal{L}_1$ and $\mathcal{L}_2$. An \emph{accordion} is
defined as the union of a leaf $\ell$ of $\mathcal{L}_1$ and leaves of
$\mathcal{L}_2$ crossing $\ell$. We show that any accordion behaves like a gap
of one lamination and prove that the maximal \emph{perfect} (without isolated
leaves) sublaminations of $\mathcal{L}_1$ and $\mathcal{L}_2$ coincide.
In the cubic case let $\mathcal{D}_3\subset \mathcal{M}_3$ be the set of all
\emph{dendritic} (with only repelling cycles) polynomials. Let $\mathcal{MD}_3$
be the space of all \emph{marked} polynomials $(P, c, w)$, where $P\in
\mathcal{D}_3$ and $c$, $w$ are critical points of $P$ (perhaps, $c=w$). Let
$c^*$ be the \emph{co-critical point} of $c$ (i.e., $P(c^*)=P(c)$ and, if
possible, $c^*\ne c$). By Kiwi, to $P\in \mathcal{D}_3$ one associates its
lamination $\sim_P$ so that each $x\in J(P)$ corresponds to a convex polygon
$G_x$ with vertices in $\mathbb{S}$. We relate to $(P, c, w)\in \mathcal{MD}_3$
its \emph{mixed tag} $\mathrm{Tag}(P, c, w)=G_{c^*}\times G_{P(w)}$ and show
that mixed tags of distinct marked polynomials from $\mathcal{MD}_3$ are
disjoint or coincide. Let $\mathrm{Tag}(\mathcal{MD}_3)^+ =
\bigcup_{\mathcal{D}_3}\mathrm{Tag}(P,c,w)$. The sets $\mathrm{Tag}(P, c, w)$
partition $\mathrm{Tag}(\mathcal{MD}_3)^+$ and generate the corresponding
quotient space $\mathrm{MT}_3$ of $\mathrm{Tag}(\mathcal{MD}_3)^+$. We prove
that $\mathrm{Tag}:\mathcal{MD}_3\to \mathrm{MT}_3$ is continuous so that
$\mathrm{MT}_3$ serves as a model space for $\mathcal{MD}_3$.

Added: Feb 11, 2015

Working paper

As noticed by R. Kulkarni, the conjugacy classes of subgroups of the modular group correspond bijectively to bipartite cuboid graphs. We'll explain how to recover the graph corresponding to a subgroup $G$ of $PSL_2(\mathbb{Z})$ from the combinatorics of the right action of $PSL_2(\mathbb{Z})$ on the right cosets $G\setminus PSL_2(\mathbb{Z})$ This gives a method of constructing nice fundamental domains (which Kulkarni calls "special polygons") for the action of $G$ on the upper half plane. For the classical congruence subgroups $\Gamma(N),\Gamma_0(N),\Gamma_1(N)$ etc. the number of operations the method requires is the index times something that grows not faster than a polynomial in $log(N)$. We also give algorithms to locate a given element of the upper half-plane on the fundamental domain and to write a given element of $G$ as a product of independent generators.

Added: Apr 4, 2014

Working paper

Added: Nov 2, 2012