Paraxial Maxwell beams: transformation by general linear optical systems

Extending the work of earlier papers on the relativistic-front description of paraxial optics and the formulation of Fourier optics for vector waves consistent with the Maxwell equations, we generalize the Jones calculus of axial plane waves to describe the action of the most general linear optical system on paraxial Maxwell fields. Several examples are worked out, and in each case it is shown that the formalism leads to physically correct results. The importance of retaining the small components of the field vectors along the axis of the system for a consistent description is emphasized.

Topological analysis of general linear networks

A new method of network analysis, a generalization in several different senses of existing methods and applicable to all networks for which a branch-admittance (or impedance) matrix can be formed, is presented. The treatment of network determinants is very general and essentially four terminal rather than three terminal, and leads to simple expressions based on trees of a simple graph associated with the network and matrix, and involving products of low-order, usually(2 times 2)determinants of tree-branch admittances, in addition to tree-branch products as in existing methods. By comparison with existing methods, the total number of trees and of tree pairs is usually considerably reduced, and this fact, together with an easy method of tree-pair sign determination which is also presented, makes the new method simpler in general. The method can be very easily adapted, by the use of infinite parameters, to accommodate ideal transformers, operational amplifiers, and other forms of network constraint; in fact, is thought to be applicable to all linear networks.

Application of the general linear model to assess the effect of missing data on bone marrow mononuclear cell therapy with infusion timing and follow-up MRI

With most clinical trials, missing data presents a statistical problem in evaluating a treatment's efficacy. There are many methods commonly used to assess missing data; however, these methods leave room for bias to enter the study. This thesis was a secondary analysis on data taken from TIME, a phase 2 randomized clinical trial conducted to evaluate the safety and effect of the administration timing of bone marrow mononuclear cells (BMMNC) for subjects with acute myocardial infarction (AMI).^ We evaluated the effect of missing data by comparing the variance inflation factor (VIF) of the effect of therapy between all subjects and only subjects with complete data. Through the general linear model, an unbiased solution was made for the VIF of the treatment's efficacy using the weighted least squares method to incorporate missing data. Two groups were identified from the TIME data: 1) all subjects and 2) subjects with complete data (baseline and follow-up measurements). After the general solution was found for the VIF, it was migrated Excel 2010 to evaluate data from TIME. The resulting numerical value from the two groups was compared to assess the effect of missing data.^ The VIF values from the TIME study were considerably less in the group with missing data. By design, we varied the correlation factor in order to evaluate the VIFs of both groups. As the correlation factor increased, the VIF values increased at a faster rate in the group with only complete data. Furthermore, while varying the correlation factor, the number of subjects with missing data was also varied to see how missing data affects the VIF. When subjects with only baseline data was increased, we saw a significant rate increase in VIF values in the group with only complete data while the group with missing data saw a steady and consistent increase in the VIF. The same was seen when we varied the group with follow-up only data. This essentially showed that the VIFs steadily increased when missing data is not ignored. When missing data is ignored as with our comparison group, the VIF values sharply increase as correlation increases.^

A general linear model for MEG beamformer imaging

A new general linear model (GLM) beamformer method is described for processing magnetoencephalography (MEG) data. A standard nonlinear beamformer is used to determine the time course of neuronal activation for each point in a predefined source space. A Hilbert transform gives the envelope of oscillatory activity at each location in any chosen frequency band (not necessary in the case of sustained (DC) fields), enabling the general linear model to be applied and a volumetric T statistic image to be determined. The new method is illustrated by a two-source simulation (sustained field and 20 Hz) and is shown to provide accurate localization. The method is also shown to locate accurately the increasing and decreasing gamma activities to the temporal and frontal lobes, respectively, in the case of a scintillating scotoma. The new method brings the advantages of the general linear model to the analysis of MEG data and should prove useful for the localization of changing patterns of activity across all frequency ranges including DC (sustained fields). © 2004 Elsevier Inc. All rights reserved.

Generators of supersymmetric polynomials in positive characteristic

In Kantor and Trishin (1997) [3], Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie superalgebra gl(m vertical bar n) and a related algebra A, of what they called pseudosymmetric polynomials over an algebraically closed field K of characteristic zero. The algebra A(s) was investigated earlier by Stembridge (1985) who in [9] called the elements of A(s) supersymmetric polynomials and determined generators of A(s). The case of positive characteristic p of the ground field K has been recently investigated by La Scala and Zubkov (in press) in [6]. We extend their work and give a complete description of generators of polynomial invariants of the adjoint action of the general linear supergroup GL(m vertical bar n) and generators of A(s).

A generalized Linear Programming based approach to optimal divisible load scheduling

In this paper we propose a general Linear Programming (LP) based formulation and solution methodology for obtaining optimal solution to the load distribution problem in divisible load scheduling. We exploit the power of the versatile LP formulation to propose algorithms that yield exact solutions to several very general load distribution problems for which either no solutions or only heuristic solutions were available. We consider both star (single-level tree) networks and linear daisy chain networks, having processors equipped with front-ends, that form the generic models for several important network topologies. We consider arbitrary processing node availability or release times and general models for communication delays and computation time that account for constant overheads such as start up times in communication and computation. The optimality of the LP based algorithms is proved rigorously.

Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (112), mean square error (MSE) were calculated using language of technical computing package Matlab(R), 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike's Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R(2), lower MSE and A/C Finally, the parameters A, B and k were adjusted in Matlab(R) 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

The importance of gestation process dynamics

Principal Topic In this paper we seek to highlight the important intermediate role that the gestation process plays in entrepreneurship by examining its key antecedents and its consequences for new venture emergence. In doing so we take a behavioural perspective and argue that it is not only what a nascent venture is, but what it does (Katz & Gartner, 1988; Shane & Delmar, 2004; Reynolds, 2007) and when it does it during start-up (Reynolds & Miller, 1992; Lichtenstein, Carter, Dooley & Gartner, 2007) that is important. To extend an analogy from biological development, what we suggest is that the way a new venture is nurtured is just as fundamental as its nature. Much prior research has focused on the nature of new ventures and attempted to attribute variations in outcomes directly to the impact resource endowments and investments have. While there is little doubt that venture resource attributes such as human capital, and specifically prior entrepreneurial experience (Alsos & Kolvereid, 1998), access to social (Davidsson & Honig, 2003) and financial capital have an influence. Resource attributes themselves are distal from successful start-up endeavours and remain inanimate if not for the actions of the nascent venture. The key contribution we make is to shift focus from whether or not actions are taken, but when these actions happen and how that is situated in the overall gestation process. Thus, we suggest that it is gestation process dynamics, or when gestation actions occur, that is more proximal to venture outcomes and we focus on this. Recently scholars have highlighted the complexity that exists in the start-up or gestation process, be it temporal or contextual (Liao, Welsch & Tan, 2005; Lichtenstein et al. 2007). There is great variation in how long a start-up process might take (Reynolds & Miller, 1992), some processes require less action than others (Carter, Gartner & Reynolds, 1996), and the overall intensity of the start-up effort is also deemed important (Reynolds, 2007). And, despite some evidence that particular activities are more influential than others (Delmar & Shane, 2003), the order in which events may happen is, until now, largely indeterminate as regard its influence on success (Liao & Welsch, 2008). We suggest that it is this complexity of the intervening gestation process that attenuates the effect of resource endowment and has resulted in mixed findings in previous research. Thus, in order to reduce complexity we shall take a holistic view of the gestation process and argue that it is its’ dynamic properties that determine nascent venture attempt outcomes. Importantly, we acknowledge that particular gestation processes of themselves would not guarantee successful start-up, but it is more correctly the fit between the process dynamics and the ventures attributes (Davidsson, 2005) that is influential. So we aim to examine process dynamics by comparing sub-groups of venture types by resource attributes. Thus, as an initial step toward unpacking the complexity of the gestation process, this paper aims to establish the importance of its role as an intermediary between attributes of the nascent venture and the emergence of that venture. Here, we make a contribution by empirically examining gestation process dynamics and their fit with venture attributes. We do this by firstly, examining that nature of the influence that venture attributes such as human and social capital have on the dynamics of the gestation process, and secondly by investigating the effect that gestation process dynamics have on venture creation outcomes. Methodology and Propositions In order to explore the importance that gestation processes dynamics have in nascent entrepreneurship we conduct an empirical study of ventures start-ups. Data is drawn from a screened random sample of 625 Australian nascent business ventures prior to them achieving consistent outcomes in the market. This data was collected during 2007/8 and 2008/9 as part of the Comprehensive Australian Study of Entrepreneurial Emergence (CAUSEE) project (Davidsson et al., 2008). CAUSEE is a longitudinal panel study conducted over four years, sourcing information from annually administered telephone surveys. Importantly for our study, this methodology allows for the capture and tracking of active nascent venture creation as it happens, thus reducing hindsight and selection biases. In addition, improved tests of causality may be made given that outcome measures are temporally removed from preceding events. The data analysed in this paper represents the first two of these four years, and for the first time has access to follow-up outcome measures for these venture attempts: where 260 were successful, 126 were abandoned, and 191 are still in progress. With regards to venture attributes as gestation process antecedents, we examine specific human capital measured as successful prior experience in entrepreneurship, and direct social capital of the venture as ‘team start-ups’. In assessing gestation process dynamics we follow Lichtenstein et al. (2007) to suggest that the rate, concentration and timing of gestation activities may be used to summarise the complexity dynamics of that process. In addition, we extend this set of measures to include the interaction of discovery and exploitation by way of changes made to the venture idea. Those ventures with successful prior experience or those who conduct symbiotic parallel start-up attempts may be able to, or be forced to, leave their gestation action until later and still derive a successful outcome. In addition access to direct social capital may provide the support upon which the venture may draw in order to persevere in the face of adversity, turning a seemingly futile start-up attempt into a success. On the other hand prior experience may engender the foresight to terminate a venture attempt early should it be seen to be going nowhere. The temporal nature of these conjectures highlight the importance that process dynamics play and will be examined in this research Statistical models are developed to examine gestation process dynamics. We use multivariate general linear modelling to analyse how human and social capital factors influence gestation process dynamics. In turn, we use event history models and stratified Cox regression to assess the influence that gestation process dynamics have on venture outcomes. Results and Implications What entrepreneurs do is of interest to both scholars and practitioners’ alike. Thus the results of this research are important since they focus on nascent behaviour and its outcomes. While venture attributes themselves may be influential this is of little actionable assistance to practitioners. For example it is unhelpful to say to the prospective first time entrepreneur “you’ll be more successful if you have lots of prior experience in firm start-ups”. This research attempts to close this relevance gap by addressing what gestation behaviours might be appropriate, when actions best be focused, and most importantly in what circumstances. Further, we make a contribution to the entrepreneurship literature, examining the role that gestation process dynamics play in outcomes, by specifically attributing these to the nature of the venture itself. This extension is to the best of our knowledge new to the research field.