A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schrödinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.

Random distributed feedback fibre laser

The concept of random lasers making use of multiple scattering in amplifying disordered media to generate coherent light has attracted a great deal of attention in recent years. Here, we demonstrate a fibre laser with a mirrorless open cavity that operates via Rayleigh scattering, amplified through the Raman effect. The fibre waveguide geometry provides transverse confinement and effectively one-dimensional random distributed feedback, leading to the generation of a stationary near-Gaussian beam with a narrow spectrum, and with efficiency and performance comparable to regular lasers. Rayleigh scattering due to inhomogeneities within the glass structure of the fibre is extremely weak, making the operation and properties of the proposed random distributed feedback lasers profoundly different from those of both traditional random lasers and conventional fibre lasers.

Base modified peptidic nucleic acids: synthesis and crystallographic analysis of intermediates

Peptidic Nucleic Acids (PNAs) are achiral, uncharged nucleic add mimetics, with a novel backbone composed of N-(2-aminoethyl)glycine units attached to the DNA bases through carboxymethylene linkers. With the aim of extending and improving upon the molecular recognition properties of PNAs, the aim of this work was to synthesjse PNA building block intermediates containing a series of substituted purine bases for subsequent use in automated PNA synthesis. Four purine bases: 2,6~diaminopurine (D), isoGuanine (isoG), xanthine (X) and hypoxanthine (H) were identified for incorporation into PNAs targeted to DNA, with the promise of increased hybrid stability over extended pH ranges together with improvements over the use of adenine (A) in duplex formation, and cytosine (C) in triplex formation. A reliable, high-yielding synthesis of the PNA backbone component N -('2- butyloxycarbonyl-aminoethyl)glycinate ethyl ester was establishecl. The precursor N~(2-butyloxycarbonyl)amino acetonitrile was crystallised and analysed by X-ray crystallography for the first time. An excellent refinement (R = 0.0276) was attained for this structure, allowing comparisons with known analogues. Although chemical synthesis of pure, fully-characterised PNA monomers was not achieved, chemical synthesis of PNA building blocks composed of diaminopurine, xanthine and hypoxanthine was completely successful. In parallel, a second objective of this work was to characterise and evaluate novel crystalline intermediates, which formed a new series of substituted purine bases, generated by attaching alkyl substituents at the N9 or N7 sites of purine bases. Crystallographic analysis was undertaken to probe the regiochemistry of isomers, and to reveal interesting structural features of the new series of similarly-substituted purine bases. The attainment of the versatile synthetic intermediate 2,6-dichloro~9- (carboxymethyl)purine ethyl ester, and its homologous regioisomers 6-chloro~9- (carboxymethyl)purine ethyl ester and 6-chloro-7-(carboxymethyl)purine ethyl ester, necessitated the use of X-ray crystallographic analysis for unambiguous structural assignment. Successful refinement of the disordered 2,6-diamino-9-(carboxymethyl) purine ethyl ester allowed comparison with the reported structure of the adenine analogue, ethyl adenin-9-yl acetate. Replacement of the chloro moieties with amino, azido and methoxy groups expanded the internal angles at their point of attachment to the purine ring. Crystallographic analysis played a pivotal role towards confirming the identity of the peralkylated hypoxanthine derivative diethyl 6-oxo-6,7-dihydro-3H-purlne~3,7~djacetate, where two ethyl side chains were found to attach at N3 and N7,

Textural and microstructural studies of zinc sulfide and associated phases in certain base metal deposits

A textural and microstructural study of a variety of zinc sulfide-containing ores has been undertaken, and the possible depositional and deformational controls of textural and microstructural development considered. Samples for the study were taken from both deformed and undeformed zinc ores of the Central U.S. Appalachians, and deformed zinc ores of the English Pennines. A variety of mineralogical techniques were employed, including transmitted and reflected light microscopy of etched and unetched material, transmission electron microscopy and electron microprobe analysis. For the Pennine zinc sulfides, spectroscopic, x-ray diffraction and fluid inclusion studies were also undertaken. Optical and electron optical examination of the Appalachian material confirmed the suitability of zinc sulfide for detailed study with such techniques. Growth and deformation-related microstructures could be distinguished from specimen-preparation induced artifacts. A deformationally-mduced lamelliform optical anisotropy is seen to be developed in areas hosting a dense planar microstructure of {111} twin- and slip-planes. The Pennine zinc sulfide texturally records a changing depositional environment. Thus, for example, delicately growth- zoned crystals are truncated and cross-cut by solution disconformities. Fluid inclusion studies indicate a highly saline (20-25 wt. % equiv. NaCl), low temperature (100-150°C.) fluid. Texturally, two varieties of zinc sulfide can be recognised; a widely developed, iron- banded variety, and a paragenetically early variety, banded due to horizons rich in crystal defects and microscopic inclusions. The zinc sulfide takes the form of a disordered 3C-polytype, with much of the disorder being deformational in origin. Twin- and slip-plane fabrics are developed . A deformation-related optical anisotropy is seen to overprint growth-related anisotropy, along with cuprian alteration of certain {111} deformation planes.

Current practice and opinion in special schools for the maladjusted in England and Wales

This study seeks to describe current practice and opinion in schools for the maladjusted in England and Wales and to exarnlne how far this coincides with earlier descriptions. A review of the literature provides an account of this earlier work, and data accrued from questionnaires completed by 114 schools describe current practice and opinion. The study represents the most extensive empirical enquiry into the work of these schools since 1955 and provides a wide data basis for future research and assessment of progress and change. The data suggest that there is much communality of practice and opinion within the schools, with most schools emphasising their therapeutic rather than their educational purpose. The work is characterised by the wide use and perceived efficacy of warm, caring adult to child relationships, improvement of pupil self-image through success, and individual counselling and discussion, which permeate a structure of routine, discipline and educational concern. Specialised treatments are not used widely and involve only a minority of pupils. Practice tends to be in reference to conduct disordered pupils who are now perceived as the largest single disorder group within the schools, whereas previously neurotic disorders formed the largest single group. The majority of pupils are perceived as underachieving on entry and requiring remedial help: consequently the educational programme has a remedial bias. For staff, qualities of personality are considered to be more valuable than professional skills. The schools differ in the emphasis they allocate to one or more of four identified areas of treatment described as concern for pupils' needs; degree of pupil participation; theoretical orientation: and the use of external controls. There is a diminished reference to psychoanalytical theory and an increased reference to behaviourist theory relative to previous practice. Similarly, the use and perceived importance and effectiveness of pupil participation and unconditional affection has diminished.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Design of a flat-top fiber Bragg filter via quasi-random modulation of the refractive index

The statistics of the reflection spectrum of a short-correlated disordered fiber Bragg grating are studied. The averaged spectrum appears to be flat inside the bandgap and has significantly suppressed sidelobes compared to the uniform grating of the same bandwidth. This is due to the Anderson localization of the modes of a disordered grating. This observation prompts a new algorithm for designing passband reflection gratings. Using the stochastic invariant imbedding approach it is possible to obtain the probability distribution function for the random reflection coefficient inside the bandgap and obtain both the variance of the averaged reflectivity as well as the distribution of the time delay of the grating.

Random input problem for the nonlinear Schrödinger equation

We consider the random input problem for a nonlinear system modeled by the integrable one-dimensional self-focusing nonlinear Schrödinger equation (NLSE). We concentrate on the properties obtained from the direct scattering problem associated with the NLSE. We discuss some general issues regarding soliton creation from random input. We also study the averaged spectral density of random quasilinear waves generated in the NLSE channel for two models of the disordered input field profile. The first model is symmetric complex Gaussian white noise and the second one is a real dichotomous (telegraph) process. For the former model, the closed-form expression for the averaged spectral density is obtained, while for the dichotomous real input we present the small noise perturbative expansion for the same quantity. In the case of the dichotomous input, we also obtain the distribution of minimal pulse width required for a soliton generation. The obtained results can be applied to a multitude of problems including random nonlinear Fraunhoffer diffraction, transmission properties of randomly apodized long period Fiber Bragg gratings, and the propagation of incoherent pulses in optical fibers.

Disconnected brains:what is the role of fMRI in connectivity research?

In this paper we consider how functional Magnetic Resonance Imaging (fMRI) has been used to study cortical connectivity in autism and autistic spectrum disorders (ASD). We discuss those studies that have contributed to the evidence supporting a model of disordered cortical connectivity in autism and (ASD), with a focusing emphasis on the application to research into the underconnectivity model. We note that the analytical techniques employed are limited and do not allow interpretation in terms of effective, or directional connectivity, nor do they provide information about the temporal or spectral characteristics of the functional networks being studied. We highlight how currently the features of neural generators that are being assessed by functional connectivity in fMRI are unclear. In addition, we note the importance in clinical studies of considering the consequences of task choice for the nature of the imaging data that can be collected and also of individual differences in participant state and trait characteristics for the accurate interpretation of imaging data. We discuss how alternative techniques such as EEG/MEG may address the limitations of fMRI in assessing brain connectivity, and additionally consider the potential of multimodal approaches. We conclude that fMRI has made significant contributions towards our understanding of the brain in terms of neural systems but that the conclusions drawn from its application in the sphere of autism research need to be approached with caution. It is important in research of this kind that we are aware of the need to examine the methodological and analytical techniques closely when applying findings in clinical populations, not only when they are used to support the development of theoretical models but also to inform diagnostic or treatment decisions.

BMI not WHR modulates BOLD fMRI responses in a sub-cortical reward network when participants judge the attractiveness of human female bodies

In perceptual terms, the human body is a complex 3d shape which has to be interpreted by the observer to judge its attractiveness. Both body mass and shape have been suggested as strong predictors of female attractiveness. Normally body mass and shape co-vary, and it is difficult to differentiate their separate effects. A recent study suggested that altering body mass does not modulate activity in the reward mechanisms of the brain, but shape does. However, using computer generated female body-shaped greyscale images, based on a Principal Component Analysis of female bodies, we were able to construct images which covary with real female body mass (indexed with BMI) and not with body shape (indexed with WHR), and vice versa. Twelve observers (6 male and 6 female) rated these images for attractiveness during an fMRI study. The attractiveness ratings were correlated with changes in BMI and not WHR. Our primary fMRI results demonstrated that in addition to activation in higher visual areas (such as the extrastriate body area), changing BMI also modulated activity in the caudate nucleus, and other parts of the brain reward system. This shows that BMI, not WHR, modulates reward mechanisms in the brain and we infer that this may have important implications for judgements of ideal body size in eating disordered individuals.

Typical performance of generalised vector channels

We introduce a general matrix formulation for multiuser channels and analyse the special cases of Multiple-Input Multiple-Output channels, channels with interference and relay arrays under LDPC coding using methods developed for the statistical mechanics of disordered systems. We use the replica method to provide results for the typical overlaps of the original and recovered messages and discuss their implications. The results obtained are consistent with belief propagation and density evolution results but also complement them giving additional insights into the information dynamics of these channels with unexpected effects in some cases.

Networking - a statistical physics perspective

Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications. © 2013 IOP Publishing Ltd.

From the physics of interacting polymers to optimizing routes on the London Underground

Optimizing paths on networks is crucial for many applications, ranging from subway traffic to Internet communication. Because global path optimization that takes account of all path choices simultaneously is computationally hard, most existing routing algorithms optimize paths individually, thus providing suboptimal solutions. We use the physics of interacting polymers and disordered systems to analyze macroscopic properties of generic path optimization problems and derive a simple, principled, generic, and distributed routing algorithm capable of considering all individual path choices simultaneously. We demonstrate the efficacy of the algorithm by applying it to: (i) random graphs resembling Internet overlay networks, (ii) travel on the London Underground network based on Oyster card data, and (iii ) the global airport network. Analytically derived macroscopic properties give rise to insightful new routing phenomena, including phase transitions and scaling laws, that facilitate better understanding of the appropriate operational regimes and their limitations, which are difficult to obtain otherwise.