Parallel algorithms of the Purcell method for direct solution of linear systems

In this paper, we first demonstrate that the classical Purcell's vector method when combined with row pivoting yields a consistently small growth factor in comparison to the well-known Gauss elimination method, the Gauss–Jordan method and the Gauss–Huard method with partial pivoting. We then present six parallel algorithms of the Purcell method that may be used for direct solution of linear systems. The algorithms differ in ways of pivoting and load balancing. We recommend algorithms V and VI for their reliability and algorithms III and IV for good load balance if local pivoting is acceptable. Some numerical results are presented.

Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.

On velocity-based local model networks for nonlinear identification

This paper exposes the strengths and weaknesses of the recently proposed velocity-based local model (LM) network. The global dynamics of the velocity-based blended representation are directly related to the dynamics of the underlying local models, an important property in the design of local controller networks. Furthermore, the sub-models are continuous-time and linear providing continuity with established linear theory and methods. This is not true for the conventional LM framework, where the global dynamics are only weakly related to the affine sub-models. In this paper, a velocity-based multiple model network is identified for a highly nonlinear dynamical system. The results show excellent dynamical modelling performances, highlighting the value of the velocity-based approach for the design and analysis of LM based control. Three important practical issues are also addressed. These relate to the blending of the velocity-based local models, the use of normalised Gaussian basis functions and the requirement of an input derivative.

Structural changes in quasi-one-dimensional many-electron systems: From linear to zigzag and beyond

Many-electron systems confined to a quasi-one-dimensional geometry by a cylindrical distribution of positive charge have been investigated by density functional computations in the unrestricted local spin density approximation. Our investigations have been focused on the low-density regime, in which electrons are localized. The results reveal a wide variety of different charge and spin configurations, including linear and zig-zag chains, single-and double-strand helices, and twisted chains of dimers. The spin-spin coupling turns from weakly antiferromagnetic at relatively high density, to weakly ferromagnetic at the lowest densities considered in our computations. The stability of linear chains of localized charge has been investigated by analyzing the radial dependence of the self-consistent potential and by computing the dispersion relation of low-energy harmonic excitations.

An Autopilot Based on a Local Control Network Design for an Unmanned Surface Vehicle

Over recent years, a number of marine autopilots designed using linear techniques have underperformed owing to their inability to cope with nonlinear vessel dynamics. To this end, a new design framework for the development of nonlinear autopilots is proposed herein. Local control networks (LCNs) can be used in the design of nonlinear control systems. In this paper, a LCN approach is taken in the design of a nonlinear autopilot for controlling the nonlinear yaw dynamics of an unmanned surface vehicle known as Springer. It is considered the approach is the first of its kind to be used in marine control systems design. Simulation results are presented and the performance of the nonlinear autopilot is compared with that of an existing Springer linear quadratic Gaussian (LQG) autopilot using standard system performance criteria. From the results it can be concluded the LCN autopilot out performed that based on LQG techniques in terms of the selected criteria. Also it provided more energy saving control strategies and would thereby increase operational duration times for the vehicle during real-time missions.

Non-linear finite-element analysis of punching capacities of steel-concrete bridge deck slabs

Punching failure is the common failure mode in concrete bridge deck slabs when these structural components are subjected to local patch loads, such as tyre loads. Past research has shown that reinforced concrete slabs in girder–slab type bridges have a load-carrying capacity far greater than the ultimate static loads predicted by traditional design methods, because of the presence of compressive membrane action. However, due to the instability problems from punching failure, it is difficult to predict ultimate capacities accurately in numerical analyses. In order to overcome the instability problems, this paper establishes an efficient non-linear finite-element analysis using the commercial finite-element package Abaqus. In the non-linear finite-element analysis, stabilisation methods were adopted and failure criteria were established to predict the ultimate punching behaviour of deck slabs in composite steel–concrete bridges. The proposed non-linear finite-element analysis predictions showed a good correlation on punching capacities with experimental tests.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

Detection of sensor decalibration using the asymptotic local approach

A novel method for the detection of linear decalibration of sensors is proposed. The presence of a fault is indicated as a change in the mean of a white noise sequence. A simulation example is described which shows the success of the technique.

Approximate credal network updating by linear programming with applications to decision making

Credal nets are probabilistic graphical models which extend Bayesian nets to cope with sets of distributions. An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to accurate inferences. A transformation is also derived to reduce decision making in credal networks based on the maximality criterion to updating. The decision task is proved to have the same complexity of standard inference, being NPPP-complete for general credal nets and NP-complete for polytrees. Similar results are derived for the E-admissibility criterion. Numerical experiments confirm a good performance of the method.

Properties of extragalactic dust inferred from linear polarimetry of Type Ia Supernovae

Aims
The aim of this paper is twofold: 1) to investigate the properties of extragalactic dust and compare them to what is seen in the Galaxy; 2) to address in an independent way the problem of the anomalous extinction curves reported for reddened Type Ia Supernovae (SN) in connection to the environments in which they explode. 

Methods
The properties of the dust are derived from the wavelength dependence of the continuum polarization observed in four reddened Type Ia SN: 1986G, 2006X, 2008fp, and 2014J. The method is based on the observed fact that Type Ia SN have a negligible intrinsic continuum polarization. This and their large luminosity makes them ideal tools to probe the dust properties in extragalactic environments.

Results
All four objects are characterized by exceptionally low total-to-selective absorption ratios (R<inf>V</inf>) and display an anomalous interstellar polarization law, characterized by very blue polarization peaks. In all cases the polarization position angle is well aligned with the local spiral structure. While SN 1986G is compatible with the most extreme cases of interstellar polarization known in the Galaxy, SN 2006X, 2008fp, and 2014J show unprecedented behaviours. The observed deviations do not appear to be connected to selection effects related to the relatively large amounts of reddening characterizing the objects in the sample.

Conclusions
The dust responsible for the polarization of these four SN is most likely of interstellar nature. The polarization properties can be interpreted in terms of a significantly enhanced abundance of small grains. The anomalous behaviour is apparently associated with the properties of the galactic environment in which the SN explode, rather than with the progenitor system from which they originate. For the extreme case of SN 2014J, we cannot exclude the contribution of light scattered by local material; however, the observed polarization properties require an ad hoc geometrical dust distribution.

An approach to determine the local boundary of small disturbance voltage stability region in a cut-set power space:基于微扰的割集电压稳定域局部边界求解方法

A new approach to determine the local boundary of voltage stability region in a cut-set power space (CVSR) is presented. Power flow tracing is first used to determine the generator-load pair most sensitive to each branch in the interface. The generator-load pairs are then used to realize accurate small disturbances by controlling the branch power flow in increasing and decreasing directions to obtain new equilibrium points around the initial equilibrium point. And, continuous power flow is used starting from such new points to get the corresponding critical points around the initial critical point on the CVSR boundary. Then a hyperplane cross the initial critical point can be calculated by solving a set of linear algebraic equations. Finally, the presented method is validated by some systems, including New England 39-bus system, IEEE 118-bus system, and EPRI-1000 bus system. It can be revealed that the method is computationally more efficient and has less approximation error. It provides a useful approach for power system online voltage stability monitoring and assessment. This work is supported by National Natural Science Foundation of China (No. 50707019), Special Fund of the National Basic Research Program of China (No. 2009CB219701), Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 200439), Tianjin Municipal Science and Technology Development Program (No. 09JCZDJC25000), National Major Project of Scientific and Technical Supporting Programs of China During the 11th Five-year Plan Period (No. 2006BAJ03A06). ©2009 State Grid Electric Power Research Institute Press.

Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.

Approximating Credal Network Inferences by Linear Programming

An algorithm for approximate credal network updating is presented. The problem in its general formulation is a multilinear optimization task, which can be linearized by an appropriate rule for fixing all the local models apart from those of a single variable. This simple idea can be iterated and quickly leads to very accurate inferences. The approach can also be specialized to classification with credal networks based on the maximality criterion. A complexity analysis for both the problem and the algorithm is reported together with numerical experiments, which confirm the good performance of the method. While the inner approximation produced by the algorithm gives rise to a classifier which might return a subset of the optimal class set, preliminary empirical results suggest that the accuracy of the optimal class set is seldom affected by the approximate probabilities

Estimation of unemployment rates in small areas of Portugal: a best linear unbiased prediction approach versus a hierarchical Bayes approach

The high level of unemployment is one of the major problems in most European countries nowadays. Hence, the demand for small area labor market statistics has rapidly increased over the past few years. The Labour Force Survey (LFS) conducted by the Portuguese Statistical Office is the main source of official statistics on the labour market at the macro level (e.g. NUTS2 and national level). However, the LFS was not designed to produce reliable statistics at the micro level (e.g. NUTS3, municipalities or further disaggregate level) due to small sample sizes. Consequently, traditional design-based estimators are not appropriate. A solution to this problem is to consider model-based estimators that "borrow information" from related areas or past samples by using auxiliary information. This paper reviews, under the model-based approach, Best Linear Unbiased Predictors and an estimator based on the posterior predictive distribution of a Hierarchical Bayesian model. The goal of this paper is to analyze the possibility to produce accurate unemployment rate statistics at micro level from the Portuguese LFS using these kinds of stimators. This paper discusses the advantages of using each approach and the viability of its implementation.

Análise estática não linear de um edifício em betão armado

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Civil