131,620 research outputs found
First-order methods of smooth convex optimization with inexact oracle
No full textIn this paper, we analyze different first-order methods of smooth convex optimization employing inexact first-order information. We introduce the notion of an approximate first-order oracle. The list of examples of such an oracle includes smoothing technique, Moreau-Yosida regularization, Modified Lagrangians, and many others. For different methods, we derive complexity estimates and study the dependence of the desired accuracy in the objective function and the accuracy of the oracle. It appears that in inexact case, the superiority of the fast gradient methods over the classical ones is not anymore absolute. Contrary to the simple gradient schemes, fast gradient methods necessarily suffer from accumulation of errors. Thus, the choice of the method depends both on desired accuracy and accuracy of the oracle. We present applications of our results to smooth convex-concave saddle point problems, to the analysis of Modified Lagrangians, to the prox-method, and some others.smooth convex optimization, first-order methods, inexact oracle, gradient methods, fast gradient methods, complexity bounds
New type of hill-top inflation
No full textJournal of Cosmology and Astroparticle Physics
Volume 2016, Issue 1, 20 January 2016, Article number 036
New type of hill-top inflation (Article)
Barvinsky, A.O.abc ,
Kamenshchik, A.Yu.de ,
Nesterov, D.V.a
a Theory Department, Lebedev Physics Institute, Leninsky Prospect 53, Moscow, Russian Federation
b Department of Physics, Tomsk State University, Lenin Ave. 36, Tomsk, Russian Federation
c Department of Physics and Astronomy, Pacific Institue for Theoretical Physics, University of British Columbia, 6224 Agricultural Road, Vancouver, BC, Canada
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Abstract
We suggest a new type of hill-top inflation originating from the initial conditions in the form of the microcanonical density matrix for the cosmological model with a large number of quantum fields conformally coupled to gravity. Initial conditions for inflation are set up by cosmological instantons describing underbarrier oscillations in the vicinity of the inflaton potential maximum. These periodic oscillations of the inflaton field and cosmological scale factor are obtained within the approximation of two coupled oscillators subject to the slow roll regime in the Euclidean time. This regime is characterized by rapid oscillations of the scale factor on the background of a slowly varying inflaton, which guarantees smallness of slow roll parameters and η of the following inflation stage. A hill-like shape of the inflaton potential is shown to be generated by logarithmic loop corrections to the tree-level asymptotically shift-invariant potential in the non-minimal Higgs inflation model and R2-gravity. The solution to the problem of hierarchy between the Planckian scale and the inflation scale is discussed within the concept of conformal higher spin fields, which also suggests the mechanism bringing the model below the gravitational cutoff and, thus, protecting it from large graviton loop corrections
Double smoothing technique for infinite-dimensional optimization problems with applications to optimal control
No full textIn this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. We show that it is possible to reconstruct an approximate primal solution. In order to accelerate our schemes, we apply double-smoothing technique. As a result, our method has complexity O (1/[epsilon] ln 1/[epsilon]) gradient iterations, where [epsilon] is the desired accuracy of the solution of the primal-dual problem. Our approach covers, in particular, the optimal control problems with trajectory governed by a system of ordinary differential equations. The additional requirement could be that the trajectory crosses in certain moments of time some convex sets.convex optimization, optimal control, fast gradient methods, complexity bounds, smoothing technique
Effective action and heat kernel in a toy model of brane-induced gravity
No full textWe apply a recently suggested technique of the Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the (d+1)-dimensional flat bulk supplied with the d-dimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the Dvali-Gabadadze-Porrati (DGP) model. We obtain the inverse mass expansion of the effective action and its ultraviolet divergences which turn out to be nonvanishing for both even and odd spacetime dimensionality d. For the massless case, which corresponds to a limit of the toy DGP model, we obtain the Coleman-Weinberg type effective potential of the system. We also obtain the proper-time expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing second-order tangential derivatives. We show that in addition to the usual integer and half-integer powers of the proper time this expansion exhibits, depending on the dimension d, either logarithmic terms or powers multiple of one quarter. This property is considered in the context of strong ellipticity of the boundary value problem, which can be violated when the Euclidean action of the theory is not positive definite
Origin of inflation in CFT driven cosmology: R 2 -gravity and non-minimally coupled inflaton models
No full textWe present a detailed derivation of the recently suggested new type of hill-top inflation [arXiv:1509.07270] originating from the microcanonical density matrix initial conditions in cosmology driven by conformal field theory (CFT). The cosmological instantons of topology S-1 x S-3, which set up these initial conditions, have the shape of a garland with multiple periodic oscillations of the scale factor of the spatial S-3-section. They describe underbarrier oscillations of the inflaton and scale factor in the vicinity of the inflaton potential maximum, which gives a sufficient amount of inflation required by the known CMB data. We build the approximation of two coupled harmonic oscillators for these garland instantons and show that they can generate inflation consistent with the parameters of the CMB primordial power spectrum in the non-minimal Higgs inflation model and in R-2 gravity. In particular, the instanton solutions provide smallness of inflationary slow-roll parameters is an element of and eta < 0 and their relation is an element of similar to eta(2) characteristic of these two models. We present the mechanism of formation of hill-like inflaton potentials, which is based on logarithmic loop corrections to the asymptotically shift-invariant tree-level potentials of these models in the Einstein frame. We also discuss the role of R-2-gravity as an indispensable finite renormalization tool in the CFT driven cosmology, which guarantees the nondynamical (ghost free) nature of its scale factor and special properties of its cosmological garland-type instantons. Finally, as a solution to the problem of hierarchy between the Planckian scale and the inflation scale we discuss the concept of a hidden sector of conformal higher spin fields
Solventless VOC chemisorption by silver metallocycles
No full textSolventless VOC chemisorption by silver metallocycles
Oumarou C. S.a, Tekarli S.,b Nesterov V.,b Omary M. A.,b Burini A.,a Galassi R.,a
aSchool of Science and Technology, Chemistry Division, University of Camerino, Via S. Agostino 1, 62032 Camerino; e-mail: [email protected]
b Department of Chemistry, University of North Texas, Denton, TX 76203, USA
Prior work has focused on detection/sensing aspects of VOCs,[1] this work proposes a method for their simultaneous filtration and removal through their strong chemisorption to a silver(I) metallocyclic trimer.[2] A solid cyclotrimer can quantitatively remove entire molar integers of VOCs (1-3 equivalents of VOCs per mole of the nitrated trimer) from the vapor phase in a solventless “green” chemical process, which is unprecedented for this class of cyclic d10 complexes.
Figure 1. Illustration of quadrupole-dipole interactions involving the [Ag(μ-Pz-2CF3)]3 or [Ag(3,5-(NO2)2pz)]3 trimers and acetonitrile using M06/CEP-31G(d). MEP surfaces are plotted in two manners, either mapped on electron density surfaces (rainbow plots with the color scale shown; isodensity = 0.0004) or positive (blue) and negative (red) regions in space (range = ± 2.2 a. u.; isodensity = 0.02)
[1] Yaghi et al., PNAS 2008, 105, 11623
[2] R. Galassi, S. Ricci, A. Burini, A. Macchioni, L. Rocchigiani, F. Marmottini, S. Tekarli, V. Nesterov, M. A. Omary, J. Am. Chem. Soc., 2013, submitted
MeSH term explosion and author rank improve expert recommendations
No full textInformation overload is an often-cited phenomenon that reduces the productivity, efficiency and efficacy of scientists. One challenge for scientists is to find appropriate collaborators in their research. The literature describes various solutions to the problem of expertise location, but most current approaches do not appear to be very suitable for expert recommendations in biomedical research. In this study, we present the development and initial evaluation of a vector space model-based algorithm to calculate researcher similarity using four inputs: 1) MeSH terms of publications; 2) MeSH terms and author rank; 3) exploded MeSH terms; and 4) exploded MeSH terms and author rank. We developed and evaluated the algorithm using a data set of 17,525 authors and their 22,542 papers. On average, our algorithms correctly predicted 2.5 of the top 5/10 coauthors of individual scientists. Exploded MeSH and author rank outperformed all other algorithms in accuracy, followed closely by MeSH and author rank. Our results show that the accuracy of MeSH term-based matching can be enhanced with other metadata such as author rank
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Nesterov smoothing for sampling without smoothness
No full textWe study the problem of sampling from a target distribution in
whose potential is not smooth. Compared with the sampling problem with smooth
potentials, this problem is much less well-understood due to the lack of
smoothness. In this paper, we propose a novel sampling algorithm for a class of
non-smooth potentials by first approximating them by smooth potentials using a
technique that is akin to Nesterov smoothing. We then utilize sampling
algorithms on the smooth potentials to generate approximate samples from the
original non-smooth potentials. We select an appropriate smoothing intensity to
ensure that the distance between the smoothed and un-smoothed distributions is
minimal, thereby guaranteeing the algorithm's accuracy. Hence we obtain
non-asymptotic convergence results based on existing analysis of smooth
sampling. We verify our convergence result on a synthetic example and apply our
method to improve the worst-case performance of Bayesian inference on a
real-world example
On angular momentum of gravitational radiation
No full textThe quasigroup approach to the conservation laws [Phys. Rev. D 56 (1997) R7498] is completed by imposing new gauge conditions for asymptotic symmetries. Noether charge associated with an arbitrary element of the Poincar� quasialgebra is free from the supertranslational ambiguity and identically vanishes in a flat spacetime. � 1998 Published by Elsevier Science B.V
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