Short lists with short programs in short time - a short proof

Bauwens, Mahklin, Vereshchagin and Zimand [ECCC TR13-007] and Teutsch [arxiv:1212.6104] have shown that given a string x it is possible to construct in polynomial time a list containing a short description of it. We simplify their technique and present a shorter proof of this result

On Algorithmic Statistics for space-bounded algorithms

Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities in the data. However this idea can not be used in practice because Kolmogorov complexity is not computable. In this paper we develop algorithmic statistics using space-bounded Kolmogorov complexity. We prove an analogue of one of the main result of `classic' algorithmic statistics (about the connection between optimality and randomness deficiences). The main tool of our proof is the Nisan-Wigderson generator.Comment: accepted to CSR 2017 conferenc

Gale–Nikaido–Debreu and Milgrom–Shannon: Communal interactions with endogenous community structures

© 2016 Elsevier Inc.This paper examines Nash jurisdictional stability in a model with a continuum of agents whose characteristics are distributed over a unidimensional interval. Communal benefits and costs of each individual depend on her identity and the composition of the community which she belongs to. Since the framework is too general to yield an existence of Nash equilibrium, we introduce the essentiality of membership in one of the communities for all individuals. We highlight the Border Indifference Property (BIP), when all individuals located on a border between two adjacent jurisdictions are indifferent about joining either of them and show that BIP is a necessary condition for yielding a Nash equilibrium. We invoke the celebrated Gale–Nikaido–Debreu Lemma to guarantee the existence of a partition that satisfies BIP. We then proceed to demonstrate that BIP is not sufficient to yield a Nash equilibrium. The equilibrium existence under BIP is rescued when we use the Milgrom–Shannon monotone comparative statics conditions

Non-local anomaly of the axial-vector current for bound states

We demonstrate that the amplitude $<\rho\gamma|\partial_\nu (\bar q\gamma_\nu \gamma_5 q)|0>$ does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet-finite as guaranteed by the presence of the bound-state wave function. As a result, the amplitude behaves like $\sim 1/p^2$ in the limit of a large momentum $p$ of the current. This is to be compared with the amplitude $$ which remains finite in the limit $p^2\to\infty$. The observed effect leads to the modification of the classical equation of motion of the axial-vector current in terms of the non-local operator and can be formulated as a non-local axial anomaly for bound states.Comment: revtex, 4 pages, numerical value for $\kappa$ in Eq. (19) is corrected, Eqs. (22) and (23) are modified. New references added. Results remain unchange

Regge Behavior of DIS Structure Functions

Building on previous works of the mid 1960's, we construct an integral equation for forward elastic scattering (t=0) at arbitrary virtuality Q^2 and large s=W^2. This equation sums the ladder production of massless intermediate bosons to all orders, and the solution exhibits Regge behavior. The equation is used to study scattering in a simple chi^2 phi scalar theory, where it is solved appoximately and applied to the study of DIS at small x. We find that the model can naturally describe the quark distribution in both the large x region and the small x region dominated by Reggeon exchange.Comment: 13 pages with 5 figure

NLO evolution kernels for skewed transversity distributions

We present a calculation of the two-loop evolution kernels of the twist-two transversally polarized quark and linearly polarized gluon skewed parton distributions in the minimal subtraction scheme and discuss a solution of the evolution equations suitable for numerical implementations.Comment: 14 pages LaTe

Skewed parton distributions and the scale dependence of the transverse size parameter

We discuss the scale dependence of a skewed parton distribution of the pion obtained from a generalized light-cone wave function overlap formula. Using a simple ansatz for the transverse momentum dependence of the light-cone wave function and restricting ourselves to the case of a zero skewedness parameter, the skewed parton distribution can be expressed through an ordinary parton distribution multiplied by an exponential function. Matching the generalized and ordinary DGLAP evolution equations of the skewed and ordinary parton distributions, respectively, we derive a constraint for the scale dependence of the transverse size parameter, which describes the width of the pion wave function in transverse momentum space. This constraint has implications for the Fock state probability and valence distribution. We apply our results to the pion form factor.Comment: 10 pages, 4 figures; version to appear in Phys. Rev. D; Refs. added, new discussion of results for pion form factor in view of new dat

Nitric oxide regulates synaptic transmission between spiny projection neurons

Recurrent axon collaterals are a major means of communication between spiny projection neurons (SPNs) in the striatum and profoundly affect the function of the basal ganglia. However, little is known about the molecular and cellular mechanisms that underlie this communication. We show that intrastriatal nitric oxide (NO) signaling elevates the expression of the vesicular GABA transporter (VGAT) within recurrent collaterals of SPNs. Down-regulation of striatal NO signaling resulted in an attenuation of GABAergic signaling in SPN local collaterals, down-regulation of VGAT expression in local processes of SPNs, and impaired motor behavior. PKG1 and cAMP response element-binding protein are involved in the signal transduction that transcriptionally regulates VGAT by NO. These data suggest that transcriptional control of the vesicular GABA transporter by NO regulates GABA transmission and action selection.United States Army Medical Research Acquisition Activity (Grant W81XWH-09-1-0108

Next-to-next-to leading order corrections to deeply virtual Compton scattering: the non-singlet case

We study perturbative QCD corrections to deeply virtual Compton scattering on an unpolarized nucleon target in the flavor non-singlet sector to next-to-next-to-leading order accuracy, restricting ourselves to the kinematically dominant amplitude. The difference between the standard minimal subtraction and the conformal scheme, in which conformal symmetry is manifest, is studied to next-to-leading order. Beyond this order we employ conformal symmetry for the evaluation of perturbative corrections. Within a certain class of generalized parton distributions we find moderate radiative corrections.Comment: 13 pages, 2 figures, minor corrections, Phys. Lett. B versio