On the convergence of generalized hill climbing algorithms

AbstractGeneralized hill climbing (GHC) algorithms provide a general local search strategy to address intractable discrete optimization problems. GHC algorithms include as special cases stochastic local search algorithms such as simulated annealing and the noising method, among others. In this paper, a proof of convergence of GHC algorithms is presented, that relaxes the sufficient conditions for the most general convergence proof for stochastic local search algorithms in the literature. Note that classical convergence proofs for stochastic local search algorithms require either that an exponential distribution be used to model the acceptance of candidate solutions along a search trajectory, or that the Markov chain model of the algorithm must be reversible. The proof in this paper removes these limitations, by introducing a new path concept between global and local optima. Convergence is based on the asymptotic behavior of path probabilities between local and global optima. Examples are given to illustrate the convergence conditions. Implications of this result are also discussed

Dictionary of Hydromechanics

This Dictionary is intended for a broad readership including practising naval architects who wish to acquire and apply knowledge of hydrodynamics and also physicists and theoretical hydrodynami-cists who wish to apply their particular knowledge to the solution of ship problems

Non-Perturbative String Equations for Type 0A

Well-defined non-perturbative formulations of the physics of string theories, sometimes with D-branes present, were identified over a decade ago, from a careful study of double scaled matrix models. Following recent work which recasts some of those old results in the context of type 0 string theory, a study is made of a much larger family of models, which are proposed as type 0A models of the entire superconformal minimal series coupled to gravity. This gives many further examples of important physical phenomena, including non-perturbative descriptions of transitions between D-branes and fluxes, tachyon condensation, and holography. In particular, features of a large family of non-perturbatively stable string equations are studied, and results are extracted which pertain to type 0A string theory, with D-branes and fluxes, in this large class of backgrounds. For the entire construction to work, large parts of the spectrum of the supergravitationally dressed superconformal minimal models and that of the gravitationally dressed bosonic conformal minimal models must coincide, and it is shown how this happens. The example of the super-dressed tricritical Ising model is studied in some detail.Comment: 29 pages LaTe

Tachyon Condensation, Open-Closed Duality, Resolvents, and Minimal Bosonic and Type 0 Strings

Type 0A string theory in the (2,4k) superconformal minimal model backgrounds and the bosonic string in the (2,2k-1) conformal minimal models, while perturbatively identical in some regimes, may be distinguished non-perturbatively using double scaled matrix models. The resolvent of an associated Schrodinger operator plays three very important interconnected roles, which we explore perturbatively and non-perturbatively. On one hand, it acts as a source for placing D-branes and fluxes into the background, while on the other, it acts as a probe of the background, its first integral yielding the effective force on a scaled eigenvalue. We study this probe at disc, torus and annulus order in perturbation theory, in order to characterize the effects of D-branes and fluxes on the matrix eigenvalues. On a third hand, the integrated resolvent forms a representation of a twisted boson in an associated conformal field theory. The entire content of the closed string theory can be expressed in terms of Virasoro constraints on the partition function, which is realized as wavefunction in a coherent state of the boson. Remarkably, the D-brane or flux background is simply prepared by acting with a vertex operator of the twisted boson. This generates a number of sharp examples of open-closed duality, both old and new. We discuss whether the twisted boson conformal field theory can usefully be thought of as another holographic dual of the non-critical string theory.Comment: 37 pages, some figures, LaTe

Pattern selection in a lattice of pulse-coupled oscillators

We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how are they modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.Comment: 7 pages, 8 figures. To be published in Physical Review

Training-induced circuit-specific excitatory synaptogenesis in mice is required for effort control

Synaptogenesis is essential for circuit development; however, it is unknown whether it is critical for the establishment and performance of goal-directed voluntary behaviors. Here, we show that operant conditioning via lever-press for food reward training in mice induces excitatory synapse formation onto a subset of anterior cingulate cortex neurons projecting to the dorsomedial striatum (ACC). Training-induced synaptogenesis is controlled by the Gabapentin/Thrombospondin receptor α2δ−1, which is an essential neuronal protein for proper intracortical excitatory synaptogenesis. Using germline and conditional knockout mice, we found that deletion of α2δ−1 in the adult ACC circuit diminishes training-induced excitatory synaptogenesis. Surprisingly, this manipulation does not impact learning but results in a significant increase in effort exertion without affecting sensitivity to reward value or changing contingencies. Bidirectional optogenetic manipulation of ACC neurons rescues or phenocopies the behaviors of the α2δ−1 cKO mice, highlighting the importance of synaptogenesis within this cortico-striatal circuit in regulating effort exertion.This work was supported by grants from the National Institutes of Health (NS096352 and AG059409 to CE, MH112883 and DA040701 to H.H.Y., MH117429 to I.H.K.). F.P.U.S. was supported by postdoctoral fellowships from the Regeneration Next Initiative and the Ramon y Cajal Young Investigator Award (RYC2021-033202-I). Illustrations were created with BioRender.com. We thank Donna Porter for helping with mouse colony maintenance; Drs. William Wetsel, Staci D. Bilbo, Dolores Irala, Dhanesh Sivadasan Bindu, Alessandro De Simone, and Sehwon Koh for their critical feedback on the manuscript. C.E. is an HHMI Investigator

High-precision calculations of van der Waals coefficients for heteronuclear alkali-metal dimers

Van der Waals coefficients for the heteronuclear alkali-metal dimers of Li, Na, K, Rb, Cs, and Fr are calculated using relativistic ab initio methods augmented by high-precision experimental data. We argue that the uncertainties in the coefficients are unlikely to exceed about 1%.Comment: 11 pages, 2 figs, graphicx.st

The association of dietary choline and betaine with the risk of type 2 diabetes: The atherosclerosis risk in communities (aric) study

OBJECTIVE To examine the association between dietary intake of choline and betaine and the risk of type 2 diabetes. RESEARCH DESIGN AND METHODS Among 13,440 Atherosclerosis Risk in Communities (ARIC) study participants, the prospective longitudinal association between dietary choline and betaine intake and the risk of type 2 diabetes was assessed using interval-censored Cox pro-portional hazards and logistic regression models adjusted for baseline potential confounding variables. RESULTS Among 13,440 participants (55% women, mean age 54 [SD 7.4] years), 1,396 developed incident type 2 diabetes during median follow-up of 9 years from 1987 to 1998. There was no statistically significant association between every 1-SD increase in dietary choline and risk of type 2 diabetes (hazard ratio [HR] 1.01 [95% CI 0.87, 1.16]) nor between dietary betaine intake and the risk of type 2 diabetes (HR 1.01 [0.94, 1.10]). Those in the highest quartile of dietary choline intake did not have a statistically significant higher risk of type 2 diabetes than those in the lowest choline quartile (HR 1.09 [0.84, 1.42]); similarly, dietary betaine intake was not associated with the risk of type 2 diabetes comparing the highest quartile to the lowest (HR 1.06 [0.87, 1.29]). Among women, there was a higher risk of type 2 diabetes, comparing the highest to lowest dietary choline quartile (HR 1.54 [1.06, 2.25]), while in men, the association was null (HR 0.82 [0.57, 1.17]). Nevertheless, there was a nonsignificant interaction between high choline intake and sex on the risk of type 2 diabetes (P 5 0.07). The results from logistic regression were similar. CONCLUSIONS Overall and among male participants, dietary choline or betaine intakes were not associated with the risk of type 2 diabetes. Among female participants, there was a trend for a modestly higher risk of type 2 diabetes among those with the highest as compared with the lowest quartile of dietary choline intake. Our study should inform clinical trials on dietary choline and betaine supplementation in relationship with the risk of type 2 diabetes

Grievances

[First Paragraph] The Virginia Board of Education has adopted a procedure for resolving disputes concerning the application of local board policies, rules, and regulations as they impact the work or disciplinary actions of teachers. It is vital that the principal be aware of the process and the timeline involved in the grievance procedure since the solution should be secured at the lowest administrative level in the process. It is beyond the scope of this article to provide every detail of the grievance process. For a complete detailing of procedure, please refer to Chapter 15, Article 3, Sections 22.1-306 through 22.1-314 of the Code of Virginia

Employability and higher education: contextualising female students' workplace experiences to enhance understanding of employability development

Current political and economic discourses position employability as a responsibility of higher education, which deploys mechanisms such as supervised work experience (SWE) to embed employability skills development into the undergraduate curriculum. However, workplaces are socially constructed complex arenas of embodied knowledge that are gendered. Understanding the usefulness of SWE therefore requires consideration of the contextualised experiences of it, within these complex environments. This study considers higher education's use of SWE as a mechanism of employability skills development through exploration of female students' experiences of accounting SWE, and its subsequent shaping of their views of employment. Findings suggest that women experience numerous, indirect gender-based inequalities within their accounting SWE about which higher education is silent, perpetuating the framing of employability as a set of individual skills and abilities. This may limit the potential of SWE to provide equality of employability development. The study concludes by briefly considering how insights provided by this research could better inform higher education's engagement with SWE within the employability discourse, and contribute to equality of employability development opportunity