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Parallel Block Hessenberg Reduction using Algorithms-By-Tiles for Multicore Architectures Revisited
Get PDFThe objective of this paper is to extend and redesign the
block matrix reduction applied for the family of two-sided factorizations,
introduced by Dongarra et al. [9], to the context of multicore architec-
tures using algorithms-by-tiles. In particular, the Block Hessenberg Re-
duction is very often used as a pre-processing step in solving dense linear
algebra problems, such as the standard eigenvalue problem. Although
expensive, orthogonal transformations are commonly used for this re-
duction because they guarantee stability, as opposed to Gaussian Elimi-
nation. Two versions of the Block Hessenberg Reduction are presented in
this paper, the rst one with Householder re
ectors and the second one
with Givens rotations. A short investigation on variants of Fast Givens
Rotations is also mentioned. Furthermore, in the last Top500 list from
June 2008, 98% of the fastest parallel systems in the world are based
on multicores. The emerging petascale systems consisting of hundreds
of thousands of cores have exacerbated the problem even more and it
becomes judicious to eciently integrate existing or new numerical lin-
ear algebra algorithms suitable for such hardwares. By exploiting the
concepts of algorithms-by-tiles in the multicore environment (i.e., high
level of parallelism with ne granularity and high performance data rep-
resentation combined with a dynamic data driven execution), the Block
Hessenberg Reduction presented here achieves 72% of the DGEMM peak
on a 12000 12000 matrix with 16 Intel Tigerton 2:4 GHz processors
A Formal Framework for User-centric Control of Multi-Agent Cyber-physical Systems
Get PDFCyber physical systems are examples of a new emerging modelling paradigm that can be defined as multi-dimensional system co-engineering (MScE). In MScE, different aspects of complex systems are considered altogether, producing emergent properties, or loosing some useful ones. This holistic approach requires interdisciplinary methods that result from formal mathematical and AI co-engineering. In this paper, we propose a formal framework consisting of a reference model for multi-agent cyber physical systems, and a formal logic for expressing safety properties. The agents we consider are enabled with continuous physical mobility and evolve in an uncertain physical environment. Moreover, the model is user centric, by defining a complex control that considers the output of a runtime verification process, and possible commands of a human controller. The
formal logic, called safety analysis logic (SafAL), combines probabilities with epistemic operators. In SafAL, one can specify the reachability
properties of one agent, as well as prescriptive commands to the user. We define symmetry reduction semantics and a new concept of bisimulation for agents. A full abstraction theorem is presented, and it is proved that SafAL represents a logical characterization of bisimulation. A foundational study is carried out for model checking SafAL formulae against Markov models. A fundamental result states that the bisimulation preserves the probabilities of the reachable state sets
Joint Longitudinal and Survival-cure Models with Constrained Parameters in Tumour Xenograft Experiments
Get PDFIn tumour xenograft experiments, treatment regimens are ad-
ministered and the tumour volume of each individual is measured repeatedly
over time. Survival data are recorded due to the death of some individuals
during the observation time period. Also, cure data are observed due to a
portion of individuals who are completely cured in the experiments. When
modelling these data, certain constraints have to be imposed on the param-
eters in the models to account for the intrinsic growth of the tumour in the
absence of treatment. Also, the likely inherent association of longitudinal
and survival-cure data has to be taken into account in order to obtain unbi-
ased estimators of parameters. In this paper, we propose such models for the
joint modelling of longitudinal and survival-cure data arising in xenograft experiments. Estimators of parameters in the joint models are obtained us-
ing a Markov chain Monte Carlo approach. Real data analysis of a xenograft
experiment is carried out and simulation studies are also conducted, show-
ing that the proposed joint modelling approach outperforms the separate
modelling methods in the sense of mean squared errors
Applications/Algorithms Roadmapping Activity. First Stage Final Report
Get PDFThis final report of the initially funded stage of the HPC/NA roadmapping activity brings together
elements from the individual workshops to date, the input from various groups and the completed
desk work reflecting related activities.
The report is the result of a 9‐month funded roadmapping activity in which there were three
workshops bringing together HPC application researchers and developers, computer scientists and
numerical analysts, a significant desk‐based study of existing activities and contact with many groups
around the UK.
The resulting findings should not be taken as the final word, as there are still groups who may not
have had the opportunity to contribute or comment, and the picture is by necessity evolving. The
work that has started with this initial project will continue and the roadmap as presented will
continue to grow in evidence base.
During the latter part of this project an international activity, the International Exascale Software
Project (www.exascale.org) was initiated to develop an international collaboration to form a
roadmap for software infrastructure for extreme computing. We have included the findings of that
activity to date in this report as it is clear that the UK roadmap must sit within the context of the
IESP roadmap
One lump or two?
Get PDFWe investigate methods for modelling metabolism within populations of cells. Typically one represents the interaction of a cloned population of cells with their environment as though it were one large cell. The question is as to whether any dynamics are lost by this assumption, and as to whether it might be more appropriate to instead model each cell individually. We show that it is sufficient to model at an intermediate level of granularity, representing the population as two interacting lumps of tissue
Elongated S-cone stimuli reveal the importance of the intermediate temporal filter
Get PDFThe relative involvement of different temporal frequency-selective filters underlying detection of chromatic stimuli were studied. Diverse spectral stimuli were used, namely flashed blue and yellow light spots, wide bars and narrow bars. The stimuli were temporally modulated in luminance having constant wavelength. Although stimulus elongation apparently reduced the sensitivity at short and long wavelengths, the cone-opponent mechanism still remained responsible for the actual stimulus detection at different temporal frequencies. Stimulus elongation increased sensitivity for temporal frequencies around 3-6 Hz, revealing involvement of the intermediate temporal frequency-selective filters to detection, the so-called first transient-1 filter. A probability summation model for the method of adjustment was developed that assumes that detection depends on the properties of the temporal filters underlying the temporal frequency-sensitivity curve. The model supports the notion that at least two temporal frequency-selective filters are necessary to account for the shape of the sensitivity curves obtained for blue stimuli
A new approach for MOR of second order Dynamical Systems
Get PDFWe consider a new idea for model reduction of second order dynamical systems.
It is based on a new theorem which shows under which conditions one can recover the second order form of a dynamical system. This theorem adds some constraints on the projection matrices that will be used to construct the reduced
model
Modelling evolvable component systems
Get PDFWe develop a logical modelling approach to describe evolvable computational systems. In this account, evolvable systems are built hierarchically from components where each component may have an associated supervisory process. The supervisor's purpose is to monitor and possibly change its associated component. Evolutionary change may be determined purely internally from observations made by the supervisor or may be in response to external change. Supervisory processes may be present at any level in the component hierarchy allowing us to use evolutionary behaviour as an integral part of system design.
We model such systems in a revision-based first-order logical framework in which supervisors are modelled as theories which are at a logical meta-level to the theories of their components. This enables evolutionary change of the component to be induced by revision-based changes of the supervisor at the meta-level. In this way, the intervention required in evolutionary change is modelled purely logically.
The hierarchical component-based structure is fairly intricate so we present the basic ideas firstly in a simple setting, the well-known blocks world, before introducing tree-based structures to represent component hierarchies. We also introduce some techniques for establishing the behaviour of evolvable systems specified in this logical framework. The ideas and concepts are driven by example throughout. We conclude with a more substantial example, that of a simple model of an evolvable system of automated bank teller machines
Breaking size-segregation waves and particle recirculation in granular avalanches
Get PDFParticle-size segregation is a common feature of dense gravity driven granular free-surface flows, where sliding and frictional grain-grain interactions dominate. Provided that the diameter ratio of the particles is not too large, the grains segregate by a process called kinetic sieving, which, on average, causes the large particles to rise to the surface and the small grains to sink to the base of the avalanche. When the flowing layer is brought to rest this stratification is often preserved in the deposit and is known by geologists as inverse grading. Idealized experiments with bi-disperse mixtures of differently sized grains have shown that inverse grading can be extremely sharp on rough beds at low inclination angles, and may be modelled as a concentration jump or shock. Several authors have developed hyperbolic conservation laws for segregation that naturally lead to a perfectly inversely-graded state, with a pure phase of coarse particles separated from a pure phase of fines below, by a sharp concentration jump. A generic feature of these models is that monotonically decreasing sections of this concentration shock, steepen and eventually break when the layer is sheared. In this paper, we investigate the structure of the subsequent breaking, which is important for large particle recirculation at the bouldery margins of debris flows and for fingering instabilities of dry granular flows. We develop an exact quasi-steady travelling wave solution for the structure of the breaking/recirculation zone, which consists of two shocks and two expansion fans that are arranged in a \lq lens\rq-like structure. A high-resolution shock capturing numerical scheme is used to investigate the temporal evolution of a linearly decreasing shock towards a steady-state lens, as well as the interaction of two recirculation zones that travel at different speeds and eventually coalesce to form a single zone
The PlayStation 3 for High Performance Scientific Computing
Get PDFThe heart of the Sony PlayStation 3, the
STI CELL processor, was not originally intended
for scientific number crunching, and the
PlayStation 3 itself was not meant primarily to
serve such purposes. Yet, both these items may
impact the High Performance Computing world.
This introductory article takes a closer look at
the cause of this potential disturbance