Beyond fractional derivatives: local approximation of other convolution integrals

Dynamic systems involving convolution integrals with decaying kernels, of which fractionally damped systems form a special case, are non-local in time and hence infinite dimensional. Straightforward numerical solution of such systems up to time t needs O(t(2)) computations owing to the repeated evaluation of integrals over intervals that grow like t. Finite-dimensional and local approximations are thus desirable. We present here an approximation method which first rewrites the evolution equation as a coupled in finite-dimensional system with no convolution, and then uses Galerkin approximation with finite elements to obtain linear, finite-dimensional, constant coefficient approximations for the convolution. This paper is a broad generalization, based on a new insight, of our prior work with fractional order derivatives (Singh & Chatterjee 2006 Nonlinear Dyn. 45, 183-206). In particular, the decaying kernels we can address are now generalized to the Laplace transforms of known functions; of these, the power law kernel of fractional order differentiation is a special case. The approximation can be refined easily. The local nature of the approximation allows numerical solution up to time t with O(t) computations. Examples with several different kernels show excellent performance. A key feature of our approach is that the dynamic system in which the convolution integral appears is itself approximated using another system, as distinct from numerically approximating just the solution for the given initial values; this allows non-standard uses of the approximation, e. g. in stability analyses.

Inter-helical Interactions in Membrane Proteins: Analysis Based on the Local Backbone Geometry and the Side Chain Interactions

The availability of a significant number of the Structures of helical membrane proteins has prompted us to investigate the mode of helix-helix packing. In the present study, we have considered a dataset of alpha-helical membrane proteins representing Structures solved from all the known superfamilies. We have described the geometry of all the helical residues in terms of local coordinate axis at the backbone level. Significant inter-helical interactions have been considered as contacts by weighing the number of atom-atom contacts, including all the side-chain atoms. Such a definition of local axis and the contact criterion has allowed us to investigate the inter-helical interaction in a systematic and quantitative manner. We show that a single parameter (designated as alpha), which is derived from the parameters representing the Mutual orientation of local axes, is able to accurately Capture the details of helix-helix interaction. The analysis has been carried Out by dividing the dataset into parallel, anti-parallel, and perpendicular orientation of helices. The study indicates that a specific range of alpha value is preferred for interactions among the anti-parallel helices. Such a preference is also seen among interacting residues of parallel helices, however to a lesser extent. No such preference is seen in the case of perpendicular helices, the contacts that arise mainly due to the interaction Of Surface helices with the end of the trans-membrane helices. The Study Supports the prevailing view that the anti-parallel helices are well packed. However, the interactions between helices of parallel orientation are non-trivial. The packing in alpha-helical membrane proteins, which is systematically and rigorously investigated in this study, may prove to be useful in modeling of helical membrane proteins.

Bounding Run-Times of Local Adiabatic Algorithms

A common trick for designing faster quantum adiabatic algorithms is to apply the adiabaticity condition locally at every instant. However it is often difficult to determine the instantaneous gap between the lowest two eigenvalues, which is an essential ingredient in the adiabaticity condition. In this paper we present a simple linear algebraic technique for obtaining a lower bound on the instantaneous gap even in such a situation. As an illustration, we investigate the adiabatic un-ordered search of van Dam et al. [17] and Roland and Cerf [15] when the non-zero entries of the diagonal final Hamiltonian are perturbed by a polynomial (in log N, where N is the length of the unordered list) amount. We use our technique to derive a bound on the running time of a local adiabatic schedule in terms of the minimum gap between the lowest two eigenvalues.

Workers are doing it for themselves? Local labor solidarity in precarious times

Historically, organized labor has played a fundamental role in guaranteeing basic rights and privileges for screen media workers and defending union and guild members (however unevenly) from egregious abuses of power. Yet, despite the recent turn to labor in media and cultural studies, organized labor today has received only scant attention, even less so in locations outside Hollywood. This presentation thus intervenes in two significant ways: first, it acknowledges the ongoing global ‘undoing’ of organized labor as a consequence of footloose production and conglomeration within the screen industries, and second, it examines a case example of worker solidarity and political praxis taking shape outside formal labor institutions in response to those structural shifts. Accordingly, it links an empirical study of individual agency to broader debates associated with the spatial dynamics of screen media production, including local capacity, regional competition, and precariousness. Drawing from ethnographic interviews with local film and television workers in Glasgow, Scotland, I consider the political alliance among three nascent labor organizations in the city: one for below-the-line crew, one for facility operators, and (oddly enough) one for producers. Collectively, the groups share a desire to transform Glasgow into a global production hub, following the infrastructure developments in nearby cities like Belfast, Prague, and Budapest. They furthermore frame their objectives in political terms: establishing global scale is considered a necessary maneuver to improve local working conditions like workplace safety, income disparity, skills training, and job access. Ultimately, I argue these groups are a product of an inadequate union structure and outdated policy vision for the screen sector , once-supportive institutions currently out of sync with the global realities of media production. Furthermore, the groups’ advocacy efforts reveal the extent to which workers themselves (in additional to capital) can seek “spatial fixes” to suture their prospects to specific political and economic goals. Of course, such activities manifest under conditions outside of the workers’ control but nevertheless point to an important tension within capitalist social relations, namely that the agency to reshape the spatial relationships in their own lives recasts the geography of labor in terms that aren’t inherent or exclusive to the interests of global capital.

Investigation of the local Fe magnetic moments at the grain boundaries of the Ca2FeReO6 double perovskite

The local Fe ferromagnetic (FM) moment at the grain boundaries of a ceramic sample of Ca2FeReO6 double perovskite was investigated by means of x-ray magnetic circular dichroism spectroscopy at the Fe L-2,L-3 edges and compared to the overall bulk magnetization. We found that, at the grain boundaries, the Fe FM moments at H=5 T are much smaller than expected and that the MxH curve is harder than in the bulk magnetization. These results suggest a larger degree of Fe/Re antisite disorder at the grain boundaries of this sample, shedding light into the intriguing nonmetallic resistivity behavior despite the reported presence of free carriers. (c) 2007 American Institute of Physics.

Direct bone marrow HSC transplantation enhances local engraftment at the expense of systemic engraftment in NSG mice

Direct bone marrow (BM) injection has been proposed as a strategy to bypass homing inefficiencies associated with intravenous (IV) hematopoietic stem cell (HSC) transplantation. Despite physical delivery into the BM cavity, many donor cells are rapidly redistributed by vascular perfusion, perhaps compromising efficacy. Anchoring donor cells to 3-dimensional (3D) multicellular spheroids, formed from mesenchymal stem/stromal cells (MSC) might improve direct BM transplantation. To test this hypothesis, relevant combinations of human umbilical cord blood-derived CD34(+) cells and BM-derived MSC were transplanted into NOD/SCID gamma (NSG) mice using either IV or intrafemoral (IF) routes. IF transplantation resulted in higher human CD45(+) and CD34(+) cell engraftment within injected femurs relative to distal femurs regardless of cell combination, but did not improve overall CD45(+) engraftment at 8 weeks. Analysis within individual mice revealed that despite engraftment reaching near saturation within the injected femur, engraftment at distal hematopoietic sites including peripheral blood, spleen and non-injected femur, could be poor. Our data suggest that the retention of human HSC within the BM following direct BM injection enhances local chimerism at the expense of systemic chimerism in this xenogeneic model.

Local numerical modelling of magnetoconvection and turbulence - implications for mean-field theories

During the last decades mean-field models, in which large-scale magnetic fields and differential rotation arise due to the interaction of rotation and small-scale turbulence, have been enormously successful in reproducing many of the observed features of the Sun. In the meantime, new observational techniques, most prominently helioseismology, have yielded invaluable information about the interior of the Sun. This new information, however, imposes strict conditions on mean-field models. Moreover, most of the present mean-field models depend on knowledge of the small-scale turbulent effects that give rise to the large-scale phenomena. In many mean-field models these effects are prescribed in ad hoc fashion due to the lack of this knowledge. With large enough computers it would be possible to solve the MHD equations numerically under stellar conditions. However, the problem is too large by several orders of magnitude for the present day and any foreseeable computers. In our view, a combination of mean-field modelling and local 3D calculations is a more fruitful approach. The large-scale structures are well described by global mean-field models, provided that the small-scale turbulent effects are adequately parameterized. The latter can be achieved by performing local calculations which allow a much higher spatial resolution than what can be achieved in direct global calculations. In the present dissertation three aspects of mean-field theories and models of stars are studied. Firstly, the basic assumptions of different mean-field theories are tested with calculations of isotropic turbulence and hydrodynamic, as well as magnetohydrodynamic, convection. Secondly, even if the mean-field theory is unable to give the required transport coefficients from first principles, it is in some cases possible to compute these coefficients from 3D numerical models in a parameter range that can be considered to describe the main physical effects in an adequately realistic manner. In the present study, the Reynolds stresses and turbulent heat transport, responsible for the generation of differential rotation, were determined along the mixing length relations describing convection in stellar structure models. Furthermore, the alpha-effect and magnetic pumping due to turbulent convection in the rapid rotation regime were studied. The third area of the present study is to apply the local results in mean-field models, which task we start to undertake by applying the results concerning the alpha-effect and turbulent pumping in mean-field models describing the solar dynamo.