Abstract:
In this paper, a simple and unified method is developed that predicts the relativistic alterations of physical measures when the behavior of a natural system is characterized by means of a specific operator equation. Separation of variables is the simple underlying procedure.

Abstract:
Using the exact path integral solution for the damped harmonic oscillator it is shown that in general there does not exist an exact dissipative Liouville operator describing the dynamics of the oscillator for arbitrary initial bath preparations. Exact non-stationary Liouville operators can be found only for particular preparations. Three physically meaningful examples are examined. An exact new master equation is derived for thermal initial conditions. Second, the Liouville operator governing the time-evolution of equilibrium correlations is obtained. Third, factorizing initial conditions are studied. Additionally, one can show that there are approximate Liouville operators independent of the initial preparation describing the long time dynamics under appropriate conditions. The general form of these approximate master equations is derived and the coefficients are determined for special cases of the bath spectral density including the Ohmic, Drude and weak coupling cases. The connection with earlier work is discussed.

Abstract:
A theory of vibrational energy relaxation based on a semiclassical treatment of the quantum master equation is presented. Using new results on the semiclassical expansion of dipole matrix elements, we show that in the classical limit the master equation reduces to the Zwanzig energy diffusion equation. The leading quantum corrections are determined and discussed for the harmonic and Morse potentials.

Abstract:
In these lectures, we review the D=11 supermembrane and supersymmetric matrix models at an introductory level. We also discuss some more recent developments in connection with non-perturbative string theory.

Abstract:
To date, the clinical significance of combined antinuclear (ANA) and anti-cytoplasmic (ACA) indirect immunofluorescent staining has not been comprehensively studied. ANA + ACA staining was observed in 43 (0.6%) out of 7.121 consecutive sera during ANA screening for immunologic disorders in a referral hospital; both inpatient and outpatient population were included. Homogeneous ANA + cytoplasmic was by far the most common staining pattern among 6 different fluorescent combinations detected. Disease distribution was similar in groups of patients with ANA + ACA and in those with only ANA +. We conclude that information provided by mixed antibody pattern is similar to the one obtained with the sole presence of ANA; also that the presence of the mixed pattern does not characterize any particular subgroup of LES patiens. Aunque se ha investigado extensamente el significado clínico de los anticuerpos antinucleares (ANA) y se han reconocido algunas correlaciones, no está establecido el valor diagnóstico del patrón mixto de ANA y anticitoplasmáticos (ANA + ACA). Nosotros observamos dicho patrón mixto en el suero de 43 pacientes de un total de 7.121 examinados (0.6%). La combinación más común fue con el patrón homogéneo de ANA. Las entidades asociadas al patrón mixto son básicamente las mismas que se asocian con los diferentes ANA; el Lupus Eritematoso Sistémico (LES) es la más frecuente. Concluimos que la información obtenida del hallazgo de un patrón combinado ANA + ACA es la misma que se obtiene con los ANA positivos y que su presencia en pacientes con LES no caracteriza a ningún subgrupo de la enfermedad en particular.

Abstract:
Many problems in fluid modelling require the efficient solution of highly anisotropic elliptic partial differential equations (PDEs) in "flat" domains. For example, in numerical weather- and climate-prediction an elliptic PDE for the pressure correction has to be solved at every time step in a thin spherical shell representing the global atmosphere. This elliptic solve can be one of the computationally most demanding components in semi-implicit semi-Lagrangian time stepping methods which are very popular as they allow for larger model time steps and better overall performance. With increasing model resolution, algorithmically efficient and scalable algorithms are essential to run the code under tight operational time constraints. We discuss the theory and practical application of bespoke geometric multigrid preconditioners for equations of this type. The algorithms deal with the strong anisotropy in the vertical direction by using the tensor-product approach originally analysed by B\"{o}rm and Hiptmair [Numer. Algorithms, 26/3 (2001), pp. 219-234]. We extend the analysis to three dimensions under slightly weakened assumptions, and numerically demonstrate its efficiency for the solution of the elliptic PDE for the global pressure correction in atmospheric forecast models. For this we compare the performance of different multigrid preconditioners on a tensor-product grid with a semi-structured and quasi-uniform horizontal mesh and a one dimensional vertical grid. The code is implemented in the Distributed and Unified Numerics Environment (DUNE), which provides an easy-to-use and scalable environment for algorithms operating on tensor-product grids. Parallel scalability of our solvers on up to 20,480 cores is demonstrated on the HECToR supercomputer.

Abstract:
Memory bound applications such as solvers for large sparse systems of equations remain a challenge for GPUs. Fast solvers should be based on numerically efficient algorithms and implemented such that global memory access is minimised. To solve systems with up to one trillion ($10^{12}$) unknowns the code has to make efficient use of several million individual processor cores on large GPU clusters. We describe the multi-GPU implementation of two algorithmically optimal iterative solvers for anisotropic elliptic PDEs which are encountered in atmospheric modelling. In this application the condition number is large but independent of the grid resolution and both methods are asymptotically optimal, albeit with different absolute performance. We parallelise the solvers and adapt them to the specific features of GPU architectures, paying particular attention to efficient global memory access. We achieve a performance of up to 0.78 PFLOPs when solving an equation with $0.55\cdot 10^{12}$ unknowns on 16384 GPUs; this corresponds to about $3\%$ of the theoretical peak performance of the machine and we use more than $40\%$ of the peak memory bandwidth with a Conjugate Gradient (CG) solver. Although the other solver, a geometric multigrid algorithm, has a slightly worse performance in terms of FLOPs per second, overall it is faster as it needs less iterations to converge; the multigrid algorithm can solve a linear PDE with half a trillion unknowns in about one second.

Abstract:
Decreasing hardware feature sizes and increasing heterogeneity in multicore hardware require software that can adapt to these platforms' properties. We implemented ROMAIN, an OS service providing redundant multithreading on top of the FIASCO.OC microkernel to address the increasing unreliability of hardware. In this paper we review challenges and opportunities for ROMAIN to adapt to such multicore platforms in order to decrease execution overhead, resource requirements, and vulnerability against faults.

Every algorithm which can be executed on a computer can at least in principle be realized in hardware, i.e. by a discrete physical system. The problem is that up to now there is no programming language by which physical systems can constructively be described. Such tool, however, is essential for the compact description and automatic production of complex systems. This paper introduces a programming language, called Akton-Algebra, which provides the foundation for the complete description of discrete physical systems. The approach originates from the finding that every discrete physical system reduces to a spatiotemporal topological network of nodes, if the functional and metric properties are deleted. A next finding is that there exists a homeomorphism between the topological network and a sequence of symbols representing a program by which the original nodal network can be reconstructed. Providing Akton-Algebra with functionality turns it into a flow-controlled general data processing language, which by introducing clock control and addressing can be further transformed into a classical programming language. Providing Akton-Algebra with metrics, i.e. the shape and size of the components, turns it into a novel hardware system construction language.

Guided by key insigths of the four great
philosophers mentioned in the title, here, in review of and expanding on our
earlier work (Burchard, 2005, 2011),
we present an exposition of the role played by language, & in the broader
sense, λογοζ, the Logos, in how the
CNS, the brain, is running the human being. Evolution by neural Darwinism has
been forcing the linguistic nature of mind, enabling it to overcome &
exploit the cognitive gap between an animal and its world by recognizing
environmental structures. Our work was greatly influenced by Heidegger’s
lecture notes on metaphysics (Heidegger, 1935).
We found agreement with recent progress in neuroscience, but also mathematical foundations
of language theory, equating Logos with the mathematical concept of
structure. The mystery of perception across the gap is analyzed as radiation
and molecules impinging on sensory neurons that carry linguistic information
about gross environmental structures, and only remotely about the physical
reality of elementary particles. The most important logical brain function is
Ego or Self, guiding the workings of the brain as a logos machine. Ego or Self
operates from neurons in frontopolar cortex with global receptive fields. The
logos machine can function only by availing itself of global context, its
internally stored noumenal cosmos NK, and the categorical-conceptual
apparatus CCA, updated continually through the neural default mode
network (Raichle, 2005).
In the Transcendental Deduction, Immanuel Kant discovered that Ego or Self is
responsible for conscious control in perception relying on concepts &
categories for a fitting percept to be incorporated intoNK. The entire CNS
runs as a “movie-in-the-brain” (Parvizi & Damasio, 2001),
at peak speed processing simultaneously in a series of cortical centers a stack
of up to twelve frames in gamma rhythm of 25 ms intervals. We equate global
context, or NK, with our human world, Heidegger’s Dasein
being-in-the-world, and are able to demonstrate that the great philosopher in
EM parallels neuro-science concerning the human mind.