Quasistationarity of continuous-time Markov chains with positive drift

We shall study continuous-time Markov chains on the nonnegative integers which are both irreducible and transient, and which exhibit discernible stationarity before drift to infinity sets in. We will show how this 'quasi' stationary behaviour can be modelled using a limiting conditional distribution: specifically, the limiting state probabilities conditional on not having left 0 for the last time. By way of a dual chain, obtained by killing the original process on last exit from 0, we invoke the theory of quasistationarity for absorbing Markov chains. We prove that the conditioned state probabilities of the original chain are equal to the state probabilities of its dual conditioned on non-absorption, thus allowing us to establish the simultaneous existence and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasistationary distribution in the usual sense, a similar statement is not possible for the original chain.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

New methods for determining quasi-stationary distributions for Markov chains

We shall be concerned with the problem of determining quasi-stationary distributions for Markovian models directly from their transition rates Q. We shall present simple conditions for a mu-invariant measure m for Q to be mu-invariant for the transition function, so that if m is finite, it can be normalized to produce a quasi-stationary distribution. (C) 2000 Elsevier Science Ltd. All rights reserved.

Jordan-Wigner fermionization of the one-dimensional Bariev model of three coupled XY chains

The Jordan-Wigner fermionization for the one-dimensional Bariev model of three coupled XY chains is formulated. The L-matrix in terms of fermion operators and the R-matrix are presented explicitly. Furthermore, the graded reflection equations and their solutions are discussed.

On the theory of mixing-frequency electron spin-echo envelope modulation spectroscopy

It has recently been stated that the parametrization of the time variables in the one-dimensional (I-D) mixing-frequency electron spin-echo envelope modulation (MIF-ESEEM) experiment is incorrect and hence the wrong frequencies for correlated nuclear transitions are predicted. This paper is a direct response to such a claim, its purpose being to show that the parametrization in land 2-D MIF-ESEEM experiments possesses the same form as that used in other 4-pulse incrementation schemes and predicts the same correlation frequencies. We show that the parametrization represents a shearing transformation of the 2-D time-domain and relate the resulting frequency domain spectrum to the HYSCORE spectrum in terms of a skew-projection. It is emphasized that the parametrization of the time-domain variables may be chosen arbitrarily and affects neither the computation of the correct nuclear frequencies nor the resulting resolution. The usefulness or otherwise of the MIF parameters \gamma\ > 1 is addressed, together with the validity of the original claims of the authors with respect to resolution enhancement in cases of purely homogeneous and inhomogeneous broadening. Numerical simulations are provided to illustrate the main points.

Spin states of C-60(3-) and C120On- (n=2, 3, 4) anions using electron spin transient nutation spectroscopy

Electron spin transient nutation (ESTN) experiments show that the spin multiplicity of the ground state of C-60(3-) in frozen solution is a doublet with S = 1/2. In purified samples, there is no evidence for excited states or other species with higher multiplicity. In the anions Of C120On- (n = 2, 3, 4), where the CW EPR experiments have shown that a mixture of species is present, ESTN experiments confirm that a doublet with S = 1/2 is associated with the 3- anion and triplets with S = 1 are associated with the 2- and 4- anions. A weak nutation peak attributable to m(s) = -1/2 1/2 transitions within a quartet state may arise from association of anions with spins of 1/2 and 1 in solute aggregates.

NMR characterization of blends of poly(hydroxybutyrate-co-hydroxyvalerate) with poly(vinyl acetate)

The extent of mixing in blends of poly(hydroxybutyrate-co-hydroxyvalerate) (PHBV) (27% HV) and poly(vinyl acetate) (PVAc) has been measured using a number of different techniques, principally solid-state NMR. Differential scanning calorimetry DSC measurements indicated effective mixing of the polymer chains on a scale of several nanometres. The results of H-1 T-1 and H-1 T-1rho. measurements confirm intimate mixing of the chains. A change on blending in the H-1 T-1rho, and the H-1 NMR line width of the signal from the protons of PVAc was consistent with an increase in the amplitude and frequency of motion of this component. The PVAc chains reside within the inter-lamellar space, as confirmed by spin diffusion measurements after H-1 T-1rho preparation. (C) 2003 Society of Chemical Industry.

Characterization of the rat exploratory behavior in the elevated plus-maze with Markov chains

The elevated plus-maze is an animal model of anxiety used to study the effect of different drugs on the behavior of the animal It consists of a plus-shaped maze with two open and two closed arms elevated 50 cm from the floor The standard measures used to characterize exploratory behavior in the elevated plus-maze are the time spent and the number of entries in the open arms In this work we use Markov chains to characterize the exploratory behavior of the rat in the elevated plus-maze under three different conditions normal and under the effects of anxiogenic and anxiolytic drugs The spatial structure of the elevated plus-maze is divided into squares which are associated with states of a Markov chain By counting the frequencies of transitions between states during 5-min sessions in the elevated plus-maze we constructed stochastic matrices for the three conditions studied The stochastic matrices show specific patterns which correspond to the observed behaviors of the rat under the three different conditions For the control group the stochastic matrix shows a clear preference for places in the closed arms This preference is enhanced for the anxiogenic group For the anxiolytic group the stochastic matrix shows a pattern similar to a random walk Our results suggest that Markov chains can be used together with the standard measures to characterize the rat behavior in the elevated plus-maze (C) 2010 Elsevier B V All rights reserved

Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighboring P-donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position, and interdonor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, while the magnitude of the double occupancy probability can affect the error rate.

Molecular motion in miscible polymer blends .1. Motion in blends of PEO and PVPh studied by solid-state C-13 T-1 rho measurements

Changes in molecular motion in blends of PEO-PVPh have been studied using measurements of C-13 T-1 rho relaxation times. C-13 T-1 rho relaxation has been confirmed as arising from spin-lattice interactions by observation of the variation in T-1 rho with rf field strength and temperature. In the pure homopolymers a minimum in T-1 rho is observed at ca. 50 K above the glass transition temperatures detected by DSC. After blending, the temperature of the minimum in T-1 rho for PEO increased, while that for PVPh decreased, however, the minima, which correspond to the temperatures where the average correlation times for reorientation are close to 3.1 mu s, are separated by 45 K (in a 45% PEO-PVPh blend). These phenomena are explained in terms of the local nature of T-1 rho measurements. The motions of the individual homopolymer chains are only partially coupled in the blend. A short T-1 rho has been observed for protonated aromatic carbons, and assigned to phenyl rings undergoing large-angle oscillatory motion, The effects of blending, and temperature, on the proportion of rings undergoing oscillatory motion are analyzed.

Glycosaminoglycan chains from alpha(5)beta(1) integrin are involved in fibronectin-dependent cell migration

alpha(5)beta(1) integrin from both wild-type CHO cells (CHO-K1) and deficient in proteoglycan biosynthesis (CHO-745) is post-translationally modified by glycosaminoglycan chains. We demonstrated this using [(35)S]sulfate metabolic labeling of the cells, enzymatic degradation, immunoprecipitation reaction with monoclonal antibody, fluorescence microscopy, and flow cytometry. The alpha(5)beta(1) integrin heterodimer is a hybrid proteoglycan containing both chondroitin and heparan sulfate chains. Xyloside inhibition of sulfate incorporation into alpha(5)beta(1) integrin also supports that integrin is a proteoglycan. Also. cells grown with xyloside adhered on fibronectin with no alteration in alpha(5)beta(1) integrin expression. However, haptotactic motility on fibronectin declined in cells grown with xyloside or chlorate as compared with controls. Thus, alpha(5)beta(1) integrin is a proteoglycan and the glycosaminoglycan chains of the integrin influence cell motility on fibronectin. Similar glycosylation of alpha(5)beta(1) integrin was observed in other normal and malignant cells, suggesting that this modification is conserved and important in the function of this integrin. Therefore, these glycosaminoglycan chains of alpha(5)beta(1) integrin are involved in cellular migration on fibronectin.

Spin-orbit mixing and nephelauxetic effects in the electronic spectra of nickel(II)-encapsulating complexes involving nitrogen and sulfur donors

A study of spin-orbit mixing and nephelauxetic effects in the electronic spectra of nickel(II)-encapsulating complexes involving mixed nitrogen and sulfur donors is reported. As the number of sulfur donors is systematically varied through the series [Ni(N6-xSx)](2+) (x = 0-6), the spin-forbidden (3)A(2)g --> E-1(g) and (3)A(2g) --> (1)A(1g) transitions undergo a considerable reduction in energy whereas the spin-allowed transitions are relatively unchanged. The [Ni(diAMN(6)sar)](2+) and [Ni(AMN(5)Ssar)](2+) complexes exhibit an unusual band shape for the (3)A(2g) --> T-3(2g) transition which is shown to arise from spin-orbit mixing of the E spin-orbit levels associated with the E-1(g) and T-3(2g) states. A significant differential nephelauxetic effect also arises from the covalency differences between the t(2g) and e(g) orbitals with the result that no single set of Racah B and C interelectron repulsion parameters adequately fit the observed spectra. Using a differential covalency ligand-field model, the spectral transitions are successfully reproduced with three independent variables corresponding to 10Dq and the covalency parameters f(t) and f(e), associated with the t(2g) and e(g) orbitals, respectively. The small decrease in f(t) from unity is largely attributed to central-field covalency effects whereas the dramatic reduction in f(e) with increasing number of sulfur donors is a direct consequence of the increased metal-ligand covalency associated with the sulfur donors. Covalency differences between the t(2g) and e(g) orbitals also result in larger 10Dq values than those obtained simply from the energy of the (3)A(2g) --> T-3(2g) spin-allowed transition.

Further Study of the Psychometric Qualities of a Brief Screening Tool for Social Phobia (MINI-SPIN) Applied to Clinical and Nonclinical Samples

PURPOSE. The purpose of this study was to further assess the psychometric qualities of the Mini-Social Phobia Inventory (MS) to screen for social anxiety disorder (SAD). DESIGN AND METHODS. The MS and other self- and clinician-rated scales for anxiety and social anxiety were applied in 2,314 university students and in samples of SAD patients (n = 88) and nonpatients (n = 90). FINDINGS. The MS revealed adequate discriminative validity, internal consistency (alpha = 0.49-0.73), convergent validity with the Social Phobia Inventory, Brief Social Phobia Scale, and Self-Statements During Public Speaking Scale and convergent and divergent validity with the Beck Anxiety Inventory. PRACTICE IMPLICATIONS. The MS has shown to be a fast and efficient screening instrument for SAD in different cultures and contexts.

Integrable anisotropic spin-ladder model

We present an integrable spin-ladder model, which possesses a free parameter besides the rung coupling J. Wang's system based on the SU(4) symmetry can be obtained as a special case. The model is exactly solvable by means of the Bethe ansatz method. We determine the dependence on the anisotropy parameter of the phase transition between gapped and gapless spin excitations and present the phase diagram. Finally, we show that the model is a special case of a more general Hamiltonian with three free parameters.