On the Positivity Problem for Simple Linear Recurrence Sequences

Given a linear recurrence sequence (LRS) over the integers, the Positivity Problem} asks whether all terms of the sequence are positive. We show that, for simple LRS (those whose characteristic polynomial has no repeated roots) of order 9 or less, Positivity is decidable, with complexity in the Counting Hierarchy.Comment: arXiv admin note: substantial text overlap with arXiv:1307.277

Rural credit in developing countries

Subsidized formal credit to the agricultural sector has been advocated as more efficient, equitable, and easier to implement than, say, land reform. But the record on subsidized credit to farmers is dismal. It shows a significant failure either to achieve an increase of agricultural output cost-effectively or to improve rural income distribution and alleviate poverty. Many of the financial institutions have proven to be inept and to lack accountability. Common features of the success stories are tougher stands on default; strict auditing and accounting procedures and financial control; and some form of joint responsibility or liability by small groups of farmers, whereby default by one member cancels future loans to the whole group.Banks&Banking Reform,Environmental Economics&Policies,Economic Theory&Research,Financial Intermediation,Insurance&Risk Mitigation

Institutional aspects of credit cooperatives

The most common form of government intervention in the rural sector has been massive lending at subsidized interest rates. Credit programs generally aim to reach small farmers. However, despite the expansion of credit over the last three decades, few farmers in low income countries seem to have received or benefited from such credit. It has thus been common for small-scale farmers to resort to the formation of organized credit groups or cooperatives. This paper is a normative analysis of cooperatives viewed as institutions to improve the plight of small-scale farmers. The purpose is to analyze which structures are most successful, then to promote credit cooperatives and to design an optimal incentive scheme in place of subsidized credit policies of the past. The paper concludes by stating that a policy of providing assistance to existing and potential credit groups on how to set incentives, implement monitoring schemes and develop centralized resources is more desirable and more cost effective than the old fashioned and largely regressive subsidized credit policies.Banks&Banking Reform,Strategic Debt Management,Economic Theory&Research,Environmental Economics&Policies,Insurance&Risk Mitigation

Agricultural reform in developing countries : reflections for Eastern Europe

The reform of formerly centrally planned economies involves freeing the price system, developing a competitive environment, and privatizing many of the state-owned or controlled assets and services, while simultaneously generating the social, economic and legal infrastructure that undergrids a market economy. This paper takes an important look at what the reforming countries of Eastern Europe can and cannot learn from the developing countries, including discussions on: (a) reforming prices; (b) credit, financial institutions and marketing boards; (c) property rights, land tenure and privatization; (d) research, extension and technology; and (e) efforts to remediate environmental degradation. A central dilemma in the reform of the Eastern European economies is the tension between commitment and flexibility. Western technical assistance and international financial help can be effective only if professionals of the East and West work together, as this is a process of joint learning, not a pure transfer of knowledge.Environmental Economics&Policies,Economic Theory&Research,Banks&Banking Reform,Markets and Market Access,Access to Markets

A finite analog of the AGT relation I: finite W-algebras and quasimaps' spaces

Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain structures on the (equivariant) intersection cohomology of the Uhlenbeck partial compactification of the moduli space of framed G-bundles on P^2. More precisely, it predicts the existence of an action of the corresponding W-algebra on the above cohomology, satisfying certain properties. We propose a "finite analog" of the (above corollary of the) AGT conjecture. Namely, we replace the Uhlenbeck space with the space of based quasi-maps from P^1 to any partial flag variety G/P of G and conjecture that its equivariant intersection cohomology carries an action of the finite W-algebra U(g,e) associated with the principal nilpotent element in the Lie algebra of the Levi subgroup of P; this action is expected to satisfy some list of natural properties. This conjecture generalizes the main result of arXiv:math/0401409 when P is the Borel subgroup. We prove our conjecture for G=GL(N), using the works of Brundan and Kleshchev interpreting the algebra U(g,e) in terms of certain shifted Yangians.Comment: minor change

Proposal to demonstrate the non-locality of Bohmian mechanics with entangled photons

Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.Comment: 6 pages, 4 figure

Surface Operators in N=2 Abelian Gauge Theory

We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally under the SL(2,Z) duality of the theory. However, for nontrivially-embedded surface operators, exact S-duality holds if and only if the "quantum" parameter effectively vanishes, while the overall SL(2,Z) duality holds up to a c-number at most, regardless. Nevertheless, this observation sets the stage for a physical proof of a remarkable mathematical result by Kronheimer and Mrowka--that expresses a "ramified" analog of the Donaldson invariants solely in terms of the ordinary Donaldson invariants--which, will appear, among other things, in forthcoming work. As a prelude to that, the effective interaction on the corresponding u-plane will be computed. In addition, the dependence on second Stiefel-Whitney classes and the appearance of a Spin^c structure in the associated low-energy Seiberg-Witten theory with surface operators, will also be demonstrated. In the process, we will stumble upon an interesting phase factor that is otherwise absent in the "unramified" case.Comment: 46 pages. Minor refinemen