Search results for "SEP"
showing 10 items of 2642 documents
Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables
2014
28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…
On the usage of joint diagonalization in multivariate statistics
2022
Scatter matrices generalize the covariance matrix and are useful in many multivariate data analysis methods, including well-known principal component analysis (PCA), which is based on the diagonalization of the covariance matrix. The simultaneous diagonalization of two or more scatter matrices goes beyond PCA and is used more and more often. In this paper, we offer an overview of many methods that are based on a joint diagonalization. These methods range from the unsupervised context with invariant coordinate selection and blind source separation, which includes independent component analysis, to the supervised context with discriminant analysis and sliced inverse regression. They also enco…
Dimension reduction for time series in a blind source separation context using r
2021
Funding Information: The work of KN was supported by the CRoNoS COST Action IC1408 and the Austrian Science Fund P31881-N32. The work of ST was supported by the CRoNoS COST Action IC1408. The work of JV was supported by Academy of Finland (grant 321883). We would like to thank the anonymous reviewers for their comments which improved the paper and package considerably. Publisher Copyright: © 2021, American Statistical Association. All rights reserved. Multivariate time series observations are increasingly common in multiple fields of science but the complex dependencies of such data often translate into intractable models with large number of parameters. An alternative is given by first red…
Separation of Uncorrelated Stationary time series using Autocovariance Matrices
2015
Blind source separation (BSS) is a signal processing tool, which is widely used in various fields. Examples include biomedical signal separation, brain imaging and economic time series applications. In BSS, one assumes that the observed $p$ time series are linear combinations of $p$ latent uncorrelated weakly stationary time series. The aim is then to find an estimate for an unmixing matrix, which transforms the observed time series back to uncorrelated latent time series. In SOBI (Second Order Blind Identification) joint diagonalization of the covariance matrix and autocovariance matrices with several lags is used to estimate the unmixing matrix. The rows of an unmixing matrix can be deriv…
Validity of the electroneutrality and goldman constant-field assumptions in describing the diffusion potential for ternary electrolyte systems in sim…
1986
Abstract Three numerical algorithms capable of simulating transport processes through simple, porous membranes in the steady state have been employed in order to study the change in the diffusion potential with the membrane thickness and the ionic concentrations for the ternary systems NaClHClH20 and CaCI2NaC1H 2 O. The first simulation procedure uses Poisson's equation, the two others replace this equation by the electroneutrality and Goldman constant-field approximations respectively. From the results presented here, conditions for the applicability of the electroneutrality and constantfield assumption to ternary electrolyte systems are given.
A finite-difference method for numerical solution of the steady-state nernst—planck equations with non-zero convection and electric current density
1986
Abstract A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the t…
Characterization of the binding of benzodiazepines to human serum albumin
1973
The binding of eleven benzodiazepine derivatives to human serum albumin (HSA) was determined by means of sephadex gel filtration. The albumin binding of the substances was characterized by the percentage of bound drug, the binding constants k +, K 1 and m, the number of binding sites per albumin molecule, and the free binding energy. Under the conditions chosen in these experiments there seems to exist only one binding site of the same type for all investigated benzodiazepines at the HSA molecule. The affinities of the benzodiazepines to this binding site are very different. It is discussed which part of the benzodiazepine molecule represents the main binding group.
Individual stereoisomers of phosphinic dipeptide inhibitor of leucine aminopeptidase
2008
Abstract Individual stereoisomers of the phosphinic pseudodipeptide hPheψ[P(O)(OH)CH2]Phe were obtained by stereoselective liquid chromatographic separation as N- and C-terminally protected derivative on quinidine carbamate modified silica stationary phase. The stereoisomeric purity, exceeding 95% for each fraction, was determined before and after deprotection using two independent methods. The absolute configuration was rationally assigned by application of enantiomerically pure phosphinic acid substrates in the synthetic procedure and correlation with biological activity of the products. Substantial differences in inhibition of leucine aminopeptidase by the individual isomers revealed nov…
Rotenoids, Flavonoids, and Chalcones from the Root Bark of Millettia usaramensis.
2015
Five new compounds, 4-O-geranylisoliquiritigenin (1), 12-dihydrousararotenoid B (2), 12-dihydrousararotenoid C (3), 4'-O-geranyl-7-hydroxyflavanone (4), and 4'-O-geranyl-7-hydroxydihydroflavanol (5), along with 12 known natural products (6-17) were isolated from the CH2Cl2/MeOH (1:1) extract of the root bark of Millettia usaramensis ssp. usaramensis by chromatographic separation. The purified metabolites were identified by NMR spectroscopic and mass spectrometric analyses, whereas their absolute configurations were established on the basis of chiroptical data and in some cases also by X-ray crystallography. The crude extract was moderately active (IC50 = 11.63 μg/mL) against the ER-negative…
Exploration of the Solid-State Sorption Properties of Shape-Persistent Macrocyclic Nanocarbons as Bulk Materials and Small Aggregates.
2020
Porous molecular materials combine benefits such as convenient processability and the possibility for atom-precise structural fine-tuning which makes them remarkable candidates for specialty applications in the areas of gas separation, catalysis, and sensing. In order to realize the full potential of these materials and guide future molecular design, knowledge of the transition from molecular properties into materials behavior is essential. In this work, the class of compounds termed cycloparaphenylenes (CPPs)-shape-persistent macrocycles with built-in cavities and radially oriented π-systems-was selected as a conceptually simple class of intrinsically porous nanocarbons to serve as a platf…