Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.Comment: The final version will appear in ICONIP 2018. A DOI identifier to the final version will be added to the preprint, as soon as it is availabl

Transverse instabilities of multiple vortex chains in superconductor-ferromagnet bilayers

Using scanning tunneling microscopy and Ginzburg-Landau simulations we explore vortex configurations in magnetically coupled NbSe$_2$-Permalloy superconductor-ferromagnet bilayer. The Permalloy film with stripe domain structure induces periodic local magnetic induction in the superconductor creating a series of pinning-antipinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-1D arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the system becomes non-linear due to a change in both the number of vortices and the confining potential. The longitudinal instabilities of the resulting vortex structures lead to vortices `levitating' in the anti-pinning channels.Comment: accepted in PRB-Rapid

The chemistry of stabilised sulphonium ylides

The review is devoted to the chemistry of stabilised sulphonium ylides, i. e. ylides with substituents at the carbanionic carbon atom capable of delocalising its negative charge. The physical properties of compounds of this class are examined and the methods of synthesis of stabilised sulphonium ylides, their rearrangements, and their reactions with electrophiles and nucleophiles are described. The structures and reactivities of the complexes of stabilised sulphonium ylides with transition metals and their organometallic derivatives are considered. The practical applications of the stabilised sulphonium ylides are indicated. © 1981 IOP Publishing Ltd

Non-Redundant Spectral Dimensionality Reduction

Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known as the "repeated Eigen-directions" phenomenon. That is, many of the embedding coordinates they produce typically capture the same direction along the data manifold. This leads to redundant and inefficient representations that do not reveal the true intrinsic dimensionality of the data. In this paper, we propose a general method for avoiding redundancy in spectral algorithms. Our approach relies on replacing the orthogonality constraints underlying those methods by unpredictability constraints. Specifically, we require that each embedding coordinate be unpredictable (in the statistical sense) from all previous ones. We prove that these constraints necessarily prevent redundancy, and provide a simple technique to incorporate them into existing methods. As we illustrate on challenging high-dimensional scenarios, our approach produces significantly more informative and compact representations, which improve visualization and classification tasks

Mathematical Modeling of a Bioluminescent E. Coli Based Biosensor

In this work we present a mathematical model for the bioreporter activity of an E. coli based bioluminescent bioreporter. This bioreporter is based on a genetically modified E. coli which harbors the recA promoter, a member of the bacterial SOS response, fused to the bacterial luminescence (lux) genes. This bioreporter responds to the presence of DNA damaging agents such as heavy metals, H2O2 and Nalidixic Acid (NA) that activate the SOS response. In our mathematical model we implemented basic physiological mechanisms such as: the penetration of the NA into the biosensor; gyrase enzyme inhibition by the NA; gyrase level regulation; creation of chromosomal DNA damage; DNA repair and release of ssDNA into the cytoplasm; SOS induction and chromosomal DNA repair; activation of lux genes by the fused recA promoter carried on a plasmidal DNA; transcription and translation of the luminescence responsible enzymes; luminescence cycle; energy molecules level regulation and the regulation of the O2 consumption. The mathematical model was defined using a set of ordinary differential equations (ODE) and solved numerically. We simulated the system for different concentrations of NA in water for specific biosensors concentration, and under limited O2 conditions. The simulated results were compared to experimental data and satisfactory matching was obtained. This manuscript presents a proof of concept showing that real biosensors can be modeled and simulated. This sets the ground to the next stage of implementing a comprehensive physiological model using experimentally extracted parameters. Following the completion of the next stage, it will be possible to construct a “Computer Aided Design” tool for the simulation of the genetically engineered biosensors. We define a term “bioCAD” for a Biological System Computer Aided Design. The specific bioCAD that is described here is aimed towards whole cell biosensors which are under investigation today for functional sensing. Usage of the bioCAD will improve the biosensors design process and boost their performance. It will also reduce Non Recurring Engineering (NRE) cost and time. Finally, using a parameterized solution will allow fair and quick evaluation of whole cell biosensors for various applications

Transductive Segmentation of Textured Meshes

International audienceThis paper addresses the problem of segmenting a textured mesh into objects or object classes, consistently with user-supplied seeds. We view this task as transductive learning and use the flexibility of kernel-based weights to incorporate a various number of diverse features. Our method combines a Laplacian graph regularizer that enforces spatial coherence in label propagation and an SVM classifier that ensures dissemination of the seeds characteristics. Our interactive framework allows to easily specify classes seeds with sketches drawn on the mesh and potentially refine the segmentation. We obtain qualitatively good segmentations on several architectural scenes and show the applicability of our method to outliers removing

Reaction of benzylidenephenylsulfonylacetophenone with trimethyl phosphite and tris(dimethylamino) phosphine

1. Benzylidenephenylsulfonylacetophenone (I) reacts with trimethyl phosphite (80°, C6H6) to give 2,2,2-trimethoxy-3,5-diphenyl-4-phenylsulfonyl-1,2-oxa-4-phospholene (II). 2. Two processes take place simultaneously at high temperatures (160°): isomerization of phosphorane (II) to give the dimethyl ester of 1,3-diphenyl-2-phenylsulfonyl-3-methoxy-2-propenephosphonic acid (VI), and decomposition of phosphorane (II) to the starting reactants with a cleavage of the P-C bond. 3. When phosphorane (II) is reacted with proton-donor reagents the phosphorane ring is opened at the P-O bond to give the dimethyl ester of 1-phenyl-2-benzoyl-2-phenylsulfonylethanephosphonic acid (III). 4. Benzylidenephenylsulfonylacetophenone (I) reacts with tris(dimethylamino)phosphine to give the 1:1 adduct with a bipolar structure (VII) and containing the P-C bond. Its hydrolysis and reaction with dry HCl gas were studied. © 1973 Consultants Bureau

Reaction of S-benzyl-substituted sulfonium ylids of dimedon with triphenylphosphine and tris(dimethylamino)phosphine

1. S-Benzyl-substituted sulfonium ylids of dimedon are dealkylated by triphenylphosphine and tris(dimethylamino) phosphine to give phosphonium salts that are stabilized by etiolate anion. 2. Migration of the phenyl group to the phosphorus atom is not observed when 2-benzylphenylsulfuranylidenedimedon is reacted with triphenylphosphine or tris(dimethylamino)phosphine. In the case of 2-benzyl-methylsulfuranylidenedimedon the migration of the benzyl group is predominant in the reaction with triphenyl-phosphine, while only the methyl group migrates in the reaction with tris(dimethylamino)phosphine. © 1978 Plenum Publishing Corporation

Reaction of 2-methylphenylsulfuranylidenedimedon with sulfides

Dibenzyl sulfide and methyl benzyl sulfide demethylate and transylidate 2-methylphenylsulfuranylidenedimedon, in which connection the demethylation predominates. © 1980 Plenum Publishing Corporation

Uncertainty quantification in graph-based classification of high dimensional data

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we introduce, develop algorithms for, and investigate the properties of, a variety of Bayesian models for the task of binary classification; via the posterior distribution on the classification labels, these methods automatically give measures of uncertainty. The methods are all based around the graph formulation of semi-supervised learning. We provide a unified framework which brings together a variety of methods which have been introduced in different communities within the mathematical sciences. We study probit classification in the graph-based setting, generalize the level-set method for Bayesian inverse problems to the classification setting, and generalize the Ginzburg-Landau optimization-based classifier to a Bayesian setting; we also show that the probit and level set approaches are natural relaxations of the harmonic function approach introduced in [Zhu et al 2003]. We introduce efficient numerical methods, suited to large data-sets, for both MCMC-based sampling as well as gradient-based MAP estimation. Through numerical experiments we study classification accuracy and uncertainty quantification for our models; these experiments showcase a suite of datasets commonly used to evaluate graph-based semi-supervised learning algorithms.Comment: 33 pages, 14 figure