Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Ab initio theoretical comparative study of magnetic coupling in KNiF3 and K2NiF4s

The origin of magnetic coupling in KNiF3 and K2 NiF4 is studied by means of an ab initio cluster model approach. By a detailed study of the mapping between eigenstates of the exact nonrelativistic and spin model Hamiltonians it is possible to obtain the magnetic coupling constant J and to compare ab initio cluster-model values with those resulting from ab initio periodic Hartree-Fock calculations. This comparison shows that J is strongly determined by two-body interactions; this is a surprising and unexpected result. The importance of the ligands surrounding the basic metal-ligand-metal interacting unit is reexamined by using two different partitions and the constrained space orbital variation method of analysis. This decomposition enables us to show that this effect is basically environmental. Finally, dynamical electronic correlation effects have found to be critical in determining the final value of the magnetic coupling constant.

Local character of magnetic coupling in ionic solids

Magnetic interactions in ionic solids are studied using parameter-free methods designed to provide accurate energy differences associated with quantum states defining the Heisenberg constant J. For a series of ionic solids including KNiF3, K2NiF4, KCuF3, K2CuF4, and high- Tc parent compound La2CuO4, the J experimental value is quantitatively reproduced. This result has fundamental implications because J values have been calculated from a finite cluster model whereas experiments refer to infinite solids. The present study permits us to firmly establish that in these wide-gap insulators, J is determined from strongly local electronic interactions involving two magnetic centers only thus providing an ab initio support to commonly used model Hamiltonians.

Magnetic coupling in the weac ferromagnet CuF2

CuF2 is known to be an antiferromagnetic compound with a weak ferromagnetism due to the anisotropy of its monoclinic unit cell (Dzialoshinsky-Moriya mechanism). We investigate the magnetic ordering of this compound by means of ab initio periodic unrestricted Hartree-Fock calculations and by cluster calculations which employ state-of-the-art configuration interaction expansions and modern density functional theory techniques. The combined use of periodic and cluster models permits us to firmly establish that the antiferromagnetic order arises from the coupling of one-dimensional subunits which themselves exhibit a very small ferromagnetic coupling between Cu neighbor cations. This magnetic order could be anticipated from the close correspondence between CuF2 and rutile crystal structures.

Cardiac motion estimation by joint alignment of tagged MRI sequences

Image registration has been proposed as an automatic method for recovering cardiac displacement fields from Tagged Magnetic Resonance Imaging (tMRI) sequences. Initially performed as a set of pairwise registrations, these techniques have evolved to the use of 3D+t deformation models, requiring metrics of joint image alignment (JA). However, only linear combinations of cost functions defined with respect to the first frame have been used. In this paper, we have applied k-Nearest Neighbors Graphs (kNNG) estimators of the -entropy (H ) to measure the joint similarity between frames, and to combine the information provided by different cardiac views in an unified metric. Experiments performed on six subjects showed a significantly higher accuracy (p < 0.05) with respect to a standard pairwise alignment (PA) approach in terms of mean positional error and variance with respect to manually placed landmarks. The developed method was used to study strains in patients with myocardial infarction, showing a consistency between strain, infarction location, and coronary occlusion. This paper also presentsan interesting clinical application of graph-based metric estimators, showing their value for solving practical problems found in medical imaging.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

Joint physical-MAC layer design of the broadcast channel protocol in adhoc networks

Broadcast transmission mode in ad hoc networks is critical to manage multihop routing or providing medium accesscontrol (MAC)-layer fairness. In this paper, it is shown that ahigher capacity to exchange information among neighbors may beobtained through a physical-MAC cross-layer design of the broadcastprotocol exploiting signal separation principles. Coherentdetection and separation of contending nodes is possible throughtraining sequences which are selected at random from a reducedset. Guidelines for the design of this set are derived for a lowimpact on the network performance and the receiver complexity.

Joint array combining and MLSE for single-user receivers in multipath Gaussian multiuser channels

The well-known structure of an array combiner along with a maximum likelihood sequence estimator (MLSE) receiveris the basis for the derivation of a space-time processor presentinggood properties in terms of co-channel and intersymbol interferencerejection. The use of spatial diversity at the receiver front-endtogether with a scalar MLSE implies a joint design of the spatialcombiner and the impulse response for the sequence detector. Thisis faced using the MMSE criterion under the constraint that thedesired user signal power is not cancelled, yielding an impulse responsefor the sequence detector that is matched to the channel andcombiner response. The procedure maximizes the signal-to-noiseratio at the input of the detector and exhibits excellent performancein realistic multipath channels.

Positive time-frequency distributions based on joint marginal constraints

This correspondence studies the formulation of members ofthe Cohen-Posch class of positive time-frequency energy distributions.Minimization of cross-entropy measures with respect to different priorsand the case of no prior or maximum entropy were considered. It isconcluded that, in general, the information provided by the classicalmarginal constraints is very limited, and thus, the final distributionheavily depends on the prior distribution. To overcome this limitation,joint time and frequency marginals are derived based on a "directioninvariance" criterion on the time-frequency plane that are directly relatedto the fractional Fourier transform.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.

The role of intramolecular barriers on the glass transition of polymers: computer simulations versus mode coupling theory

We present computer simulations of a simple bead-spring model for polymer melts with intramolecular barriers. By systematically tuning the strength of the barriers, we investigate their role on the glass transition. Dynamic observables are analyzed within the framework of the mode coupling theory (MCT). Critical nonergodicity parameters, critical temperatures, and dynamic exponents are obtained from consistent fits of simulation data to MCT asymptotic laws. The so-obtained MCT λ-exponent increases from standard values for fully flexible chains to values close to the upper limit for stiff chains. In analogy with systems exhibiting higher-order MCT transitions, we suggest that the observed large λ-values arise form the interplay between two distinct mechanisms for dynamic arrest: general packing effects and polymer-specific intramolecular barriers. We compare simulation results with numerical solutions of the MCT equations for polymer systems, within the polymer reference interaction site model (PRISM) for static correlations. We verify that the approximations introduced by the PRISM are fulfilled by simulations, with the same quality for all the range of investigated barrier strength. The numerical solutions reproduce the qualitative trends of simulations for the dependence of the nonergodicity parameters and critical temperatures on the barrier strength. In particular, the increase in the barrier strength at fixed density increases the localization length and the critical temperature. However the qualitative agreement between theory and simulation breaks in the limit of stiff chains. We discuss the possible origin of this feature.

A signaling mechanism coupling netrin-1/deleted in colorectal cancer chemoattraction to SNARE-mediated exocytosis in axonal growth cones

Directed cell migration and axonal guidance are essential steps in neural development. Both processes are controlled by specific guidance cues that activate the signaling cascades that ultimately control cytoskeletal dynamics. Another essential step in migration and axonal guidance is the regulation of plasmalemma turnover and exocytosis in leading edges and growth cones. However, the cross talk mechanisms linking guidance receptors and membrane exocytosis are not understood. Netrin-1 is a chemoattractive cue required for the formation of commissural pathways. Here, we show that the Netrin-1 receptor deleted in colorectal cancer (DCC) forms a protein complex with the t-SNARE (target SNARE) protein Syntaxin-1 (Sytx1). This interaction is Netrin-1 dependent both in vitro and in vivo, and requires specific Sytx1 and DCC domains. Blockade of Sytx1 function by using botulinum toxins abolished Netrin-1-dependent chemoattraction of axons in mouse neuronal cultures. Similar loss-of-function experiments in the chicken spinal cord in vivo using dominant-negative Sytx1 constructs or RNAi led to defects in commissural axon pathfinding reminiscent to those described in Netrin-1 and DCC loss-of-function models. We also show that Netrin-1 elicits exocytosis at growth cones in a Sytx1-dependent manner. Moreover, we demonstrate that the Sytx1/DCC complex associates with the v-SNARE (vesicle SNARE) tetanus neurotoxin-insensitive vesicle-associated membrane protein (TI-VAMP) and that knockdown of TI-VAMP in the commissural pathway in the spinal cord results in aberrant axonal guidance phenotypes. Our data provide evidence of a new signaling mechanism that couples chemotropic Netrin-1/DCC axonal guidance and Sytx1/TI-VAMP SNARE proteins regulating membrane turnover and exocytosis.

A signaling mechanism coupling netrin-1/deleted in colorectal cancer chemoattraction to SNARE-mediated exocytosis in axonal growth cones

Directed cell migration and axonal guidance are essential steps in neural development. Both processes are controlled by specific guidance cues that activate the signaling cascades that ultimately control cytoskeletal dynamics. Another essential step in migration and axonal guidance is the regulation of plasmalemma turnover and exocytosis in leading edges and growth cones. However, the cross talk mechanisms linking guidance receptors and membrane exocytosis are not understood. Netrin-1 is a chemoattractive cue required for the formation of commissural pathways. Here, we show that the Netrin-1 receptor deleted in colorectal cancer (DCC) forms a protein complex with the t-SNARE (target SNARE) protein Syntaxin-1 (Sytx1). This interaction is Netrin-1 dependent both in vitro and in vivo, and requires specific Sytx1 and DCC domains. Blockade of Sytx1 function by using botulinum toxins abolished Netrin-1-dependent chemoattraction of axons in mouse neuronal cultures. Similar loss-of-function experiments in the chicken spinal cord in vivo using dominant-negative Sytx1 constructs or RNAi led to defects in commissural axon pathfinding reminiscent to those described in Netrin-1 and DCC loss-of-function models. We also show that Netrin-1 elicits exocytosis at growth cones in a Sytx1-dependent manner. Moreover, we demonstrate that the Sytx1/DCC complex associates with the v-SNARE (vesicle SNARE) tetanus neurotoxin-insensitive vesicle-associated membrane protein (TI-VAMP) and that knockdown of TI-VAMP in the commissural pathway in the spinal cord results in aberrant axonal guidance phenotypes. Our data provide evidence of a new signaling mechanism that couples chemotropic Netrin-1/DCC axonal guidance and Sytx1/TI-VAMP SNARE proteins regulating membrane turnover and exocytosis.