Comparison of Randomized Multifocal Mapping and Temporal Phase Mapping of Visual Cortex for Clinical Use

fMRI is becoming an important clinical tool for planning and guidance of surgery to treat brain tumors, arteriovenous malformations, and epileptic foci. For visual cortex mapping, the most popular paradigm by far is temporal phase mapping, although random multifocal stimulation paradigms have drawn increased attention due to their ability to identify complex response fields and their random properties. In this study we directly compared temporal phase and multifocal vision mapping paradigms with respect to clinically relevant factors including: time efficiency, mapping completeness, and the effects of noise. Randomized, multifocal mapping accurately decomposed the response of single voxels to multiple stimulus locations and made correct retinotopic assignments as noise levels increased despite decreasing sensitivity. Also, multifocal mapping became less efficient as the number of stimulus segments (locations) increased from 13 to 25 to 49 and when duty cycle was increased from 25% to 50%. Phase mapping, on the other hand, activated more extrastriate visual areas, was more time efficient in achieving statistically significant responses, and had better sensitivity as noise increased, though with an increase in systematic retinotopic mis-assignments. Overall, temporal phase mapping is likely to be a better choice for routine clinical applications though random multifocal mapping may offer some unique advantages for selected applications

Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

Interpreting a conformally flat pure radiation space-time

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can be represented as null (half) hyperplanes rolled around a two-dimensional null cone. In the impulsive limit, the solution reduces to a pp-wave whose direction of propagation depends on retarded time. In the general case, there is a coordinate singularity which corresponds to an envelope of the wave surfaces. The global structure is discussed and a possible vacuum extension through the envelope is proposed.Comment: 9 pages, Plain TeX, 2 figures. To appear in Class. Quantum Grav. Reference adde

On the Symmetries of the Edgar-Ludwig Metric

The conformal Killing equations for the most general (non-plane wave) conformally flat pure radiation field are solved to find the conformal Killing vectors. As expected fifteen independent conformal Killing vectors exist, but in general the metric admits no Killing or homothetic vectors. However for certain special cases a one-dimensional group of homotheties or motions may exist and in one very special case, overlooked by previous investigators, a two-dimensional homethety group exists. No higher dimensional groups of motions or homotheties are admitted by these metrics.Comment: Plain TeX, 7 pages, No figure

Understanding, Finding, and Conceptualizing Core Competence Depth: A Framework, Guide, and Generalization for Corporate Managers and Research Professionals: Working Paper Series--11-03

In recent years, managerial interest in corporate core competencies as competitive tools has risen greatly. Corporate managers and professionals often have several questions regarding them. First, what are corporate core competencies? Second, how can they determine which core competencies, or which aspects of them, their firm holds deeply? More generally, what does it mean for a firm to hold a competence deeply? Utilizing concrete examples, this paper answers the first question by presenting a framework describing the elements of core competencies, their internal dynamic, and their breadth. It answers the second question by providing a usable methodology for discovering the depth a firm's core competencies. As it does so, it answers the third question by presenting a generalized conceptualization of core competence depth. The authors propose that this framework, methodology, and generalization will prove useful to corporate managers and research professionals interested in strengthening their core competencies and applying them more effectively

A new special class of Petrov type D vacuum space-times in dimension five

Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions, we invariantly classify all Petrov type $D$ vacuum solutions for which the Riemann tensor is isotropic in a plane orthogonal to a pair of Weyl alligned null directionsComment: 4 pages, 1 table, no figures. Contribution to the proceedings of the Spanish Relativity Meeting 2010 held in Granada (Spain

Developing Core Competence Related Theory: Working Paper Series--08-06

This article reviews methodological tradeoffs inherent in developing theory related to core competencies. Integrating the position and resource-based views of strategy, it presents an argument that such theoretical development will occur through researching corporate value provision situations encompassing a nomological network of core competencies, the corporate processes they enable, and the customer value delivered by these processes. Next, it briefly discusses phenomena included within this network. Then, the article reviews the applicability of three classes of methodologies to this nomological approach: 1) Field research, including interviews and observation; 2) Survey research; and 3) Unobtrusive research, including document analysis and analysis of existing statistics. Finally, it identifies issues that arise from using these methodologies to develop competence related theory