We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized da-ta points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approxi-mation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data pointswith respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can bequite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimension-al Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

Schiff bases, named after Hugo Schiff, are aldehyde- or ketone-like compounds in which the carbonyl group is replaced by imine or azomethine group. They are widely used for industrial purposes and also have a broad range of applications as antioxidants. An overview of antioxidant applications of Schiff bases and their complexes is discussed in this review. A brief history of the synthesis and reactivity of Schiff bases and their complexes is presented. Factors of antioxidants are illustrated and discussed. Copyright © 2016 John Wiley & Sons, Ltd.

Synthesis and antioxidant activities of Schiff bases and their complexes: a review

Synthesis, spectral and X-ray structural characterization of [cis-MoO2(L)(solv)] (L=salicylidene salicyloyl hydrazine) and its use as catalytic oxidant

http://www.optimization-online.org/DB_FILE/2012/03/3410.pdf

How to solve a semi-infinite optimization problem

Cobalt(II), copper(II), zinc(II) and palladium(II) Schiff base complexes: Synthesis, characterization and catalytic performance in selective oxidation of sulfides using hydrogen peroxide under solvent-free conditions

Synthesis and characterization of cis-dioxomolybdenum(VI) Schiff base complexes derived from 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone

This paper deals with nonsmooth semi-infinite programming problem which in recent years has become an important field of active research in mathematical programming. A semi-infinite programming problem is characterized by an infinite number of inequality constraints. We formulate Wolfe as well as Mond-Weir type duals for the nonsmooth semi-infinite programming problem and establish weak, strong and strict converse duality theorems relating the problem and the dual problems. To the best of our knowledge such results have not been done till now.

Duality for nonsmooth semi-infinite programming problems

A new series of eight complexes of dioxouranium(VI) with soma Schiff bases derived from 3-methyl-4-p-nitrobenzoyl-1-phenyl-2-pyrazolin-5-one and certain aromatic amines, viz., p-anisidine (MNBPHP-PAH), m-phenetidine (MNBPHP-MPH), O-toluldine (MNBPHP-OTH), ethylenediamine (MNBFHP-ENDH2), o-phenylenediamine (MNBPHP-OPHDH2), m-phenylenediamine (MNBPHP-MPHDH2), p-enylenediamine (MNBPHP-PPHDH2) or benzidine (MNBPHP-BZH2) have been synthesized. These complexes have been characterized by elemental analyses, molar conductances, magnetic measurements, electronic and infrared spectral studies, and are formulated as [(UO2)2(u-OH)2(L)2(H2O)2] (1), (2) and (3) (where LH - MNBHP-PAH, MNBPHP-MPH or MNBPHP-OTH), [(UO2)3(μ-OH)4(u-MNBPHP-END)] (4), [(UO2)2(μ-L)(u-OH)2] (5) and (6) (where LH2 - MNBPHP-OPHDH2 or MNBPHP-MPHDH2) and [(UO2)2(H2O)2-(μ-L)(OH)2] (7) and (8) (here LH2 - MNBPHP-PPHDH2 or MNBPHP-BZH2). Di- and trinuclear structures have been proposed for these complexes where complexes (1)-(3) appear to cont...

The Coordination Chemistry of Dioxouranium(VI): Studies on Some Novel Di- and Trinuclear Dioxouranium(VI) Complexes with Pyrazolone Based Schiff Bases

We consider a registration-based approach for localizing sensor networks from range measurements. This is based on the assumption that one can find overlapping cliques spanning the network. That is, for each sensor, one can identify geometric neighbors for which all inter-sensor ranges are known. Such cliques can be efficiently localized using multidimensional scaling. However, since each clique is localized in some local coordinate system, we are required to register them in a global coordinate system. In other words, our approach is based on transforming the localization problem into a problem of registration. In this context, the main contributions are as follows. First, we describe an efficient method for partitioning the network into overlapping cliques. Second, we study the problem of registering the localized cliques, and formulate a necessary rigidity condition for uniquely recovering the global sensor coordinates. In particular, we present a method for efficiently testing rigidity, and a proposal for augmenting the partitioned network to enforce rigidity. A recently proposed semidefinite relaxation of global registration is used for registering the cliques. We present simulation results on random and structured sensor networks to demonstrate that the proposed method compares favourably with state-of-the-art methods in terms of run time, accuracy, and scalability.

On a Registration-Based Approach to Sensor Network Localization

In this paper, we establish necessary and sufficient optimality conditions for nonsmooth semi-infinite programming problem using the powerful tool of limiting subdifferentials. We also formulate Wolfe and Mond-Weir type duals for nonsmooth semi-infinite programming problem and establish weak, strong and strict converse duality theorems for semi-infinite programming problem and the corresponding dual problems.

Monika Jaiswal

Papers

Synthesis and characterization of cis-dioxomolybdenum(VI) Schiff base complexes derived from 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone

Duality for nonsmooth semi-infinite programming problems

The Coordination Chemistry of Dioxouranium(VI): Studies on Some Novel Di- and Trinuclear Dioxouranium(VI) Complexes with Pyrazolone Based Schiff Bases

On a Registration-Based Approach to Sensor Network Localization

Nonsmooth semi-infinite programming problem using Limiting subdifferentials