A Subsampling Line-Search Method with Second-Order Results

In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic algorithms that sample problem data, which can jeopardize the guarantees obtained through classical globalization techniques in optimization such as a trust region or a line search. Using subsampled function values is particularly challenging for the latter strategy, which relies upon multiple evaluations. On top of that all, there has been an increasing interest for nonconvex formulations of data-related problems, such as training deep learning models. For such instances, one aims at developing methods that converge to second-order stationary points quickly, i.e., escape saddle points efficiently. This is particularly delicate to ensure when one only accesses subsampled approximations of the objective and its derivatives. In this paper, we describe a stochastic algorithm based on negative curvature and Newton-type directions that are computed for a subsampling model of the objective. A line-search technique is used to enforce suitable decrease for this model, and for a sufficiently large sample, a similar amount of reduction holds for the true objective. By using probabilistic reasoning, we can then obtain worst-case complexity guarantees for our framework, leading us to discuss appropriate notions of stationarity in a subsampling context. Our analysis encompasses the deterministic regime, and allows us to identify sampling requirements for second-order line-search paradigms. As we illustrate through real data experiments, these worst-case estimates need not be satisfied for our method to be competitive with first-order strategies in practice

Einstein Geometrization Philosophy and Differential Identities in PAP-Geometry

The importance of Einstein's geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar identity in the absolute parallelism geometry is given. A more general differential identity in the parameterized absolute parallelism geometry is derived. Comparison and interrelationships between the above mentioned identities and their role in constructing field theories are discussed.Comment: LaTeX file, 17 pages, comments and criticism are welcom

Surface and cross-sectional characterization of titanium-nitride coated nickel–titanium endodontic files

Background/purpose Although the effect of experimental surface modifications on various properties (e.g., fatigue, wear) on coated files have been tested in the past, there is no report for the coating quality of commercially available TiN coated files. The aim of this study was to characterize the surface and cross section of TiN coated endodontic files. Materials and methods TiN coated nickel–titanium endodontic files (EasyShape) were surface and cross-sectionally analyzed via scanning electron microscopy backscattered electron imaging and energy-dispersive X-ray spectroscopy analysis in spot, area, and line scan modes. Results Surface imaging revealed parallel oblong regions with higher mean atomic contrast, a finding attributed to increased Ni content. Cross-sectional analysis showed that the coating’s average total thickness was 0.31 μm and consisted of a thin layered film. Energy-dispersive X-ray spectroscopy analysis revealed the presence of Ti, Ni, N, and O in the coating, whereas only Ni and Ti were identified in the bulk of the file. Ti and O showed their peak compositions at the bulk/coating and coating/surface interfaces, respectively, whereas N displayed a rather constant content within the coated region. The N and O contents started increasing inner to the coating/bulk interface, denoting possible diffusion of both elements to the subcoating region. Conclusion Surface and bulk characterization showed no uncoated areas of the files tested. Apart from Ti, Ni, and N, oxygen was also identified within the coating region

The Results of a Case Study to Evaluate the Application of LIS Implemented by CITL Portsaid Branch in Support of Education andIndustry

The territory of the Suez Canal haswitnessed continuous development activitiesthroughoutthe year 2015, in the heart of those developments resets all activities of logistics. In the light of those developments, the authors of this paper presented in previous work a design of a database and built a logistics information system to support various logistics activities. This paper presents the results of evaluating the application of the implemented LIS system in several places. Some of those places are related to the governmental sector and the other belongs to the private sector. Evaluation methodology based on collecting feedbacks from actual system users. The areas of evaluation are reliability, availability, and serviceability, running cost, time and security. The developed system was tested against manual systems that still exist in abundance and sophisticated LIS such as SAP and Oracle ERP

Titanium Nitride and Nitrogen Ion Implanted Coated Dental Materials

Titanium nitride and/or nitrogen ion implanted coated dental materials have been investigated since the mid-1980s and considered in various applications in dentistry such as implants, abutments, orthodontic wires, endodontic files, periodontal/oral hygiene instruments, and casting alloys for fixed restorations. Multiple methodologies have been employed to create the coatings, but detailed structural analysis of the coatings is generally lacking in the dental literature. Depending on application, the purpose of the coating is to provide increased surface hardness, abrasion/wear resistance, esthetics, and corrosion resistance, lower friction, as well as greater beneficial interaction with adjacent biological and material substrates. While many studies have reported on the achievement of these properties, a consensus is not always clear. Additionally, few studies have been conducted to assess the efficacy of the coatings in a clinical setting. Overall, titanium nitride and/or nitrogen ion implanted coated dental materials potentially offer advantages over uncoated counterparts, but more investigation is needed to document the structure of the coatings and their clinical effectiveness

Thermal Control of the Magnon-Photon Coupling in a Notch Filter coupled to a Yttrium-Iron-Garnet/Platinum System

We report thermal control of mode hybridization between the ferromagnetic resonance (FMR) and a planar resonator (notch filter) working at 4.74 GHz. The chosen magnetic material is a ferrimagnetic insulator (Yttrium Iron Garnet: YIG) covered by 6 nm of platinum (Pt). A current induced heating method has been used in order to enhance the temperature of the YIG/Pt system. The device permits us to control the transmission spectra and the magnon-photon coupling strength at room temperature. These experimental findings reveal potentially applicable tunable microwave filtering function.Comment: 5 pages, 4 figure

The Large Contraction Principle and Existence of Periodic Solutions for Infinite Delay Volterra Difference Equations

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation. (See paper for equation.) We employ a Krasnosel’skii type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified

Observation of the spin Peltier effect

We report the observation of the spin Peltier effect (SPE) in the ferrimagnetic insulator Yttrium Iron Garnet (YIG), i.e. a heat current generated by a spin current flowing through a Platinum (Pt)|YIG interface. The effect can be explained by the spin torque that transforms the spin current in the Pt into a magnon current in the YIG. Via magnon-phonon interactions the magnetic fluctuations modulate the phonon temperature that is detected by a thermopile close to the interface. By finite-element modelling we verify the reciprocity between the spin Peltier and spin Seebeck effect. The observed strong coupling between thermal magnons and phonons in YIG is attractive for nanoscale cooling techniques.Comment: 5 pages, 3 figures, 4 pages supplementary information, 4 supplementary figure

The legal framework for private sector development in a transitional economy : the case of Poland

The economies of Central and Eastern Europe are in the midst of a historic transition from central planning and state ownership to development of a market-driven private sector. This transition requires comprehensive changes in"rules of the game"- including the legal framework for economic activity. A market economy presupposes a set of property rights and a system of laws or customs that allow the exchange of those rights. The legal framework in a market economy has at least three basic functions: defining the universe of property rights; setting the rules for entry into and exit from productive activities; and setting the rules of market exchange. These legal tasks are accomplished by areas of law such as: company, foreign investment, bankruptcy, contract and competition law. Poland has a rich legal tradition dating from pre-socialist times, which was suppressed but not eliminated during its forty years of socialism. This tradition is being revised as the country moves toward a private market economy. The current legal framework in Poland closely follows other continental jurisdictions and has a clear and reasonable internal logic. Many of the laws are old, but most are flexible enough to permit a wide range of modern, market-oriented activity. Property law, however, remains a"jungle". The wide discretion and general lack of precedent create tremendous legal uncertainty that is sure to hamper private sector development.Environmental Economics&Policies,Banks&Banking Reform,Municipal Housing and Land,Legal Products,Land and Real Estate Development