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Modular representations of profinite groups
Get PDFOur aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra of a profinite group, where the underlying field is a finite field of characteristic p.
We define the concept of relative projectivity for such a module. We prove a characterization of finitely generated relatively projective modules analogous to the finite case with additions of interest to the profinite theory. We introduce vertices and sources for indecomposable finitely generated modules over the completed group algebra and show that the expected conjugacy properties hold - for sources this requires additional assumptions. Finally we prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p grou
Information geometry and entropy in a stochastic epidemic rate process
Get PDFA commonly recurring approximation to real rate processes is of the form:
dN/dt = -m N
where m is some positive rate constant and N(t) measures the current value of some
property relevant to the process---radioactive decay is our typical student example.
The simplest stochastic version addresses the situation where N(t) is the size of
the current population and the rate constant depends on the distribution of properties
in the population---so different sections decay at different rates. Then the interest
lies in the evolution of the distribution of properties and of the related statistical
features like entropy, mean and variance, for given initial distribution. We show that there
is a simple closed solution for an example of an epidemic in which the latency
and infectivity are distributed properties controlled by a bivariate gamma distribution
Capturing the essence of a metabolic network: A flux balance analysis approach
Get PDFAs genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux Balance Analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented.
Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of a FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole.
Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined
K-theory and the connection index
Get PDFLet G denote a split simply connected almost simple p-adic
group. We study the unramified C*-algebra of G and prove
that the rank of the K-theory group K_0 is the connection
index f(G)
Visible parts of fractal percolation
Get PDFWe study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts
Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts
No full textStratification patterns are formed when a bidisperse mixture of large rough grains and smaller more mobile particles is poured between parallel plates to form a heap. At low flow rates discrete avalanches flow down the free surface and are brought to rest by the propagation of shock waves. Experiments performed in this paper show that the larger particles are segregated to the top of the avalanche, where the velocity is greatest, and are transported to the flow front. Here the particles are overrun but may rise to the free surface again by size segregation to create a recirculating coarse-grained front. Once the front is established composite images show that there is a steady regime in which any additional large grains that reach the front are deposited. This flow is therefore analogous to finger formation in geophysical mass
flows, where the larger less mobile particles are shouldered aside to spontaneously form static lateral levees rather than being removed by basal deposition in two
dimensions. At the heart of all these phenomena is a dynamic feedback between the bulk flow and the evolving particle-size distribution within the avalanche. A fully
coupled theory for such segregation–mobility feedback effects is beyond the scope of this paper. However, it is shown how to derive a simplified uncoupled travelling wave
solution for the avalanche motion and reconstruct the bulk two-dimensional flow field using assumed velocity profiles through the avalanche depth. This allows a simple hyperbolic segregation theory to be used to construct exact solutions for the particle concentration and for the recirculation within the bulk flow. Depending on the material composition and the strength of the segregation and deposition, there are three types of solution. The coarse-particle front grows in length if more large particles arrive than can be deposited. If there are fewer large grains and if the segregation is strong enough, a breaking size-segregation wave forms at a unique position behind the front. It consists of two expansion fans, two shocks and a central ‘eye’ of constant concentration that are arranged in a ‘lens-like’ structure. Coarse grains just behind the front are recirculated, while those reaching the head are overrun and deposited. Upstream of the wave, the size distribution resembles a small-particle ‘sandwich’ with
a raft of rapidly flowing large particles on top and a coarse deposited layer at the bottom, consistent with the experimental observations made here. If the segregation
is weak, the central eye degenerates, and all the large particles are deposited without recirculation
Towards Co-Engineering Communicating Autonomous Cyber-physical Systems
Get PDFIn this paper, we sketch a framework for interdisciplinary modeling of space systems, by proposing
a holistic view. We consider different system dimensions and their interaction. Specifically,we study the interactions between computation, physics, communication, uncertainty and autonomy.
The most comprehensive computational paradigm that supports a holistic perspective on autonomous space systems is given by cyber-physical systems. For these, the state of art consists of collaborating multi-engineering efforts that prompt for an adequate formal foundation. To achieve this, we propose a leveraging of the traditional content of formal modeling by a co-engineering process
Algorithmic Based Fault Tolerance Applied to High Performance Computing
Get PDFWe present a new approach to fault tolerance for High Performance Computing system.
Our approach is based on a careful adaptation of the Algorithmic Based Fault Tolerance technique
(Huang and Abraham, 1984) to the need of parallel distributed computation. We obtain a strongly
scalable mechanism for fault tolerance. We can also detect and correct errors (bit-flip) on the fly of
a computation. To assess the viability of our approach, we have developed a fault tolerant matrixmatrix
multiplication subroutine and we propose some models to predict its running time. Our
parallel fault-tolerant matrix-matrix multiplication scores 1.4 TFLOPS on 484 processors (cluster
jacquard.nersc.gov) and returns a correct result while one process failure has happened. This
represents 65% of the machine peak efficiency and less than 12% overhead with respect to the fastest
failure-free implementation. We predict (and have observed) that, as we increase the processor count,
the overhead of the fault tolerance drops significantly
Parallel Band Two-Sided Matrix Bidiagonalization for Multicore Architectures
Get PDFThe objective of this paper is to extend, in the context of
multicore architectures, the concepts of algorithms-by-tiles [Buttari et
al., 2007] for Cholesky, LU, QR factorizations to the family of two-
sided factorizations. In particular, the bidiagonal reduction of a general,
dense matrix is very often used as a pre-processing step for calculating
the singular value decomposition. Furthermore, in the last Top500 list
from June 2008, 98% of the fastest parallel systems in the world were
based on multicores. The manycore trend has increasingly exacerbated
the problem, and it becomes critical to eciently integrate existing or
new numerical linear algebra algorithms suitable for such hardware. By
exploiting the concept of algorithms-by-tiles in the multicore environment
(i.e., high level of parallelism with ne granularity and high performance
data representation combined with a dynamic data driven execution),
the band bidiagonal reduction presented here achieves 94 G
op/s on a
12000 12000 matrix with 16 Intel Tigerton 2:4 GHz processors