Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

Innovator resilience potential: A process perspective of individual resilience as influenced by innovation project termination

Innovation projects fail at an astonishing rate. Yet, the negative effects of innovation project failures on the team members of these projects have been largely neglected in research streams that deal with innovation project failures. After such setbacks, it is vital to maintain or even strengthen project members’ innovative capabilities for subsequent innovation projects. For this, the concept of resilience, i.e. project members’ potential to positively adjust (or even grow) after a setback such as an innovation project failure, is fundamental. We develop the second-order construct of innovator resilience potential, which consists of six components – self-efficacy, outcome expectancy, optimism, hope, self-esteem, and risk propensity – that are important for project members’ potential of innovative functioning in innovation projects subsequent to a failure. We illustrate our theoretical findings by means of a qualitative study of a terminated large-scale innovation project, and derive implications for research and management

Confirmation of low genetic diversity and multiple breeding females in a social group of Eurasian badgers from microsatellite and field data

The Eurasian badger ( Meles meles ) is a facultatively social carnivore that shows only rudimentary co-operative behaviour and a poorly defined social hierarchy. Behavioural evidence and limited genetic data have suggested that more than one female may breed in a social group. We combine pregnancy detection by ultrasound and microsatellite locus scores from a well-studied badger population from Wytham Woods, Oxfordshire, UK, to demonstrate that multiple females reproduce within a social group. We found that at least three of seven potential mothers reproduced in a group that contained 11 reproductive age females and nine offspring. Twelve primers showed variability across the species range and only five of these were variable in Wytham. The microsatellites showed a reduced repeat number, a significantly higher number of nonperfect repeats, and moderate heterozygosity levels in Wytham. The high frequency of imperfect repeats and demographic phenomena might be responsible for the reduced levels of variability observed in the badger

Why Are Male Social Relationships Complex in the Doubtful Sound Bottlenose Dolphin Population?

Copyright 2008 Elsevier B.V., All rights reserved.Peer reviewedPublisher PD

The role of Comprehension in Requirements and Implications for Use Case Descriptions

Within requirements engineering it is generally accepted that in writing specifications (or indeed any requirements phase document), one attempts to produce an artefact which will be simple to comprehend for the user. That is, whether the document is intended for customers to validate requirements, or engineers to understand what the design must deliver, comprehension is an important goal for the author. Indeed, advice on producing ‘readable’ or ‘understandable’ documents is often included in courses on requirements engineering. However, few researchers, particularly within the software engineering domain, have attempted either to define or to understand the nature of comprehension and it’s implications for guidance on the production of quality requirements. Therefore, this paper examines thoroughly the nature of textual comprehension, drawing heavily from research in discourse process, and suggests some implications for requirements (and other) software documentation. In essence, we find that the guidance on writing requirements, often prevalent within software engineering, may be based upon assumptions which are an oversimplification of the nature of comprehension. Hence, the paper examines guidelines which have been proposed, in this case for use case descriptions, and the extent to which they agree with discourse process theory; before suggesting refinements to the guidelines which attempt to utilise lessons learned from our richer understanding of the underlying discourse process theory. For example, we suggest subtly different sets of writing guidelines for the different tasks of requirements, specification and design

Visualizing the molecular recognition trajectory of an intrinsically disordered protein using multinuclear relaxation dispersion NMR

Despite playing important roles throughout biology, molecular recognition mechanisms in intrinsically disordered proteins remain poorly understood. We present a combination of (1)H(N), (13)C', and (15)N relaxation dispersion NMR, measured at multiple titration points, to map the interaction between the disordered domain of Sendai virus nucleoprotein (NT) and the C-terminal domain of the phosphoprotein (PX). Interaction with PX funnels the free-state equilibrium of NT by stabilizing one of the previously identified helical substates present in the prerecognition ensemble in a nonspecific and dynamic encounter complex on the surface of PX. This helix then locates into the binding site at a rate coincident with intrinsic breathing motions of the helical groove on the surface of PX. The binding kinetics of complex formation are thus regulated by the intrinsic free-state conformational dynamics of both proteins. This approach, providing high-resolution structural and kinetic information about a complex folding and binding interaction trajectory, can be applied to a number of experimental systems to provide a general framework for understanding conformational disorder in biomolecular function

An SU(N) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling

The Hubbard model, containing only the minimum ingredients of nearest neighbor hopping and on-site interaction for correlated electrons, has succeeded in accounting for diverse phenomena observed in solid-state materials. One of the interesting extensions is to enlarge its spin symmetry to SU(N>2), which is closely related to systems with orbital degeneracy. Here we report a successful formation of the SU(6) symmetric Mott insulator state with an atomic Fermi gas of ytterbium (173Yb) in a three-dimensional optical lattice. Besides the suppression of compressibility and the existence of charge excitation gap which characterize a Mott insulating phase, we reveal an important difference between the cases of SU(6) and SU(2) in the achievable temperature as the consequence of different entropy carried by an isolated spin. This is analogous to Pomeranchuk cooling in solid 3He and will be helpful for investigating exotic quantum phases of SU(N) Hubbard system at extremely low temperatures.Comment: 20 pages, 6 figures, to appear in Nature Physic