Sensitivity of the NMR density matrix to pulse sequence parameters : a simplified analytic approach

We present a formalism for the analysis of sensitivity of nuclear magnetic resonance pulse sequences to variations of pulse sequence parameters, such as radiofrequency pulses, gradient pulses or evolution delays. The formalism enables the calculation of compact, analytic expressions for the derivatives of the density matrix and the observed signal with respect to the parameters varied. The analysis is based on two constructs computed in the course of modified density-matrix simulations: the error interrogation operators and error commutators. The approach presented is consequently named the Error Commutator Formalism (ECF). It is used to evaluate the sensitivity of the density matrix to parameter variation based on the simulations carried out for the ideal parameters, obviating the need for finite-difference calculations of signal errors. The ECF analysis therefore carries a computational cost comparable to a single density-matrix or product-operator simulation. Its application is illustrated using a number of examples from basic NMR spectroscopy. We show that the strength of the ECF is its ability to provide analytic insights into the propagation of errors through pulse sequences and the behaviour of signal errors under phase cycling. Furthermore, the approach is algorithmic and easily amenable to implementation in the form of a programming code. It is envisaged that it could be incorporated into standard NMR product-operator simulation packages.

Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

A two-stage item recommendation method using probabilistic ranking with reconstructed tensor model

In a tag-based recommender system, the multi-dimensional correlation should be modeled effectively for finding quality recommendations. Recently, few researchers have used tensor models in recommendation to represent and analyze latent relationships inherent in multi-dimensions data. A common approach is to build the tensor model, decompose it and, then, directly use the reconstructed tensor to generate the recommendation based on the maximum values of tensor elements. In order to improve the accuracy and scalability, we propose an implementation of the -mode block-striped (matrix) product for scalable tensor reconstruction and probabilistically ranking the candidate items generated from the reconstructed tensor. With testing on real-world datasets, we demonstrate that the proposed method outperforms the benchmarking methods in terms of recommendation accuracy and scalability.

A tag-based personalized item recommendation system using tensor modeling and topic model approaches

This research falls in the area of enhancing the quality of tag-based item recommendation systems. It aims to achieve this by employing a multi-dimensional user profile approach and by analyzing the semantic aspects of tags. Tag-based recommender systems have two characteristics that need to be carefully studied in order to build a reliable system. Firstly, the multi-dimensional correlation, called as tag assignment , should be appropriately modelled in order to create the user profiles [1]. Secondly, the semantics behind the tags should be considered properly as the flexibility with their design can cause semantic problems such as synonymy and polysemy [2]. This research proposes to address these two challenges for building a tag-based item recommendation system by employing tensor modeling as the multi-dimensional user profile approach, and the topic model as the semantic analysis approach. The first objective is to optimize the tensor model reconstruction and to improve the model performance in generating quality rec-ommendation. A novel Tensor-based Recommendation using Probabilistic Ranking (TRPR) method [3] has been developed. Results show this method to be scalable for large datasets and outperforming the benchmarking methods in terms of accuracy. The memory efficient loop implements the n-mode block-striped (matrix) product for tensor reconstruction as an approximation of the initial tensor. The probabilistic ranking calculates the probabil-ity of users to select candidate items using their tag preference list based on the entries generated from the reconstructed tensor. The second objective is to analyse the tag semantics and utilize the outcome in building the tensor model. This research proposes to investigate the problem using topic model approach to keep the tags nature as the “social vocabulary” [4]. For the tag assignment data, topics can be generated from the occurrences of tags given for an item. However there is only limited amount of tags availa-ble to represent items as collection of topics, since an item might have only been tagged by using several tags. Consequently, the generated topics might not able to represent the items appropriately. Furthermore, given that each tag can belong to any topics with various probability scores, the occurrence of tags cannot simply be mapped by the topics to build the tensor model. A standard weighting technique will not appropriately calculate the value of tagging activity since it will define the context of an item using a tag instead of a topic.

Optimization and comparison of single- and dual-pump fiber-optical parametric amplifiers with dispersion fluctuations

Solutions for fiber-optical parametric amplifiers (FOPAs) with dispersion fluctuations are derived using matrix operators. On the basis of the propagation matrix product and the hybrid genetic algorithm, we have optimized and compared single- and dual-pump FOPAs with zero-dispersion-wavelength variations. The simulations prove that the design of FOPAs involves multimodal function optimization problems. The numerical results show that dual-pump FOPAs are highly sensitive to dispersion fluctuations whereas dispersion variations have less impact on the gain of single-pump FOPAs. To increase signal gain and reduce ripple, dual-pump FOPAs, instead of single-pump FOPAs, have to be carefully optimized with a suitable multisegment fiber structure rather than a one-segment fiber structure. The different combinations of multisegment fibers can provide highly different gain properties. The increase in gain is at the cost of the ripple.

MA167exam00pdf

Exam questions and solutions in PDF

MA167exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Performance results of running parallel applications on the InteGrade

The InteGrade middleware intends to exploit the idle time of computing resources in computer laboratories. In this work we investigate the performance of running parallel applications with communication among processors on the InteGrade grid. As costly communication on a grid can be prohibitive, we explore the so-called systolic or wavefront paradigm to design the parallel algorithms in which no global communication is used. To evaluate the InteGrade middleware we considered three parallel algorithms that solve the matrix chain product problem, the 0-1 Knapsack Problem, and the local sequence alignment problem, respectively. We show that these three applications running under the InteGrade middleware and MPI take slightly more time than the same applications running on a cluster with only LAM-MPI support. The results can be considered promising and the time difference between the two is not substantial. The overhead of the InteGrade middleware is acceptable, in view of the benefits obtained to facilitate the use of grid computing by the user. These benefits include job submission, checkpointing, security, job migration, etc. Copyright (C) 2009 John Wiley & Sons, Ltd.

Quantum biology. Simulazioni di trasferimento di energia in una struttura dimerica

La quantum biology (QB) è un campo di ricerca emergente che cerca di affronta- re fenomeni quantistici non triviali all’interno dei contesti biologici dotandosi di dati sperimentali di esplorazioni teoriche e tecniche numeriche. I sistemi biologici sono per definizione sistemi aperti, caldi,umidi e rumorosi, e queste condizioni sono per loro imprenscindibili; si pensa sia un sistema soggetto ad una veloce decoerenza che sopprime ogni dinamica quantistica controllata. La QB, tramite i principi di noise assisted transport e di antenna fononica sostiene che la presenza di un adeguato livello di rumore ambientale aumenti l’efficienza di un network di trasporto,inoltre se all’interno dello spettro ambientale vi sono specifici modi vibrazionali persistenti si hanno effetti di risonanza che rigenerano la coerenza quantistica. L’interazione ambiente-sistema è di tipo non Markoviano,non perturbativo e di forte non equi- librio, ed il rumore non è trattato come tradizionale rumore bianco. La tecnica numerica che per prima ha predetto la rigenerazione della coerenza all’interno di questi network proteici è stato il TEBD, Time Evolving Block Decimation, uno schema numerico che permette di simulare sistemi 1-D a molti corpi, caratterizzati da interazioni di primi vicini e leggermente entangled. Tramite gli algoritmi numerici di Orthopol l’hamiltoniana spin-bosone viene proiettata su una catena discreta 1-D, tenendo conto degli effetti di interazione ambiente-sistema contenuti nello spettro(il quale determina la dinamica del sistema).Infine si esegue l’evoluzione dello stato.