1,767 research outputs found
Maximal determinants and saturated D-optimal designs of orders 19 and 37
A saturated D-optimal design is a {+1,-1} square matrix of given order with
maximal determinant. We search for saturated D-optimal designs of orders 19 and
37, and find that known matrices due to Smith, Cohn, Orrick and Solomon are
optimal. For order 19 we find all inequivalent saturated D-optimal designs with
maximal determinant, 2^30 x 7^2 x 17, and confirm that the three known designs
comprise a complete set. For order 37 we prove that the maximal determinant is
2^39 x 3^36, and find a sample of inequivalent saturated D-optimal designs. Our
method is an extension of that used by Orrick to resolve the previously
smallest unknown order of 15; and by Chadjipantelis, Kounias and Moyssiadis to
resolve orders 17 and 21. The method is a two-step computation which first
searches for candidate Gram matrices and then attempts to decompose them. Using
a similar method, we also find the complete spectrum of determinant values for
{+1,-1} matrices of order 13.Comment: 28 pages, 4 figure
Finding D-optimal designs by randomised decomposition and switching
A square {+1,-1}-matrix of order n with maximal determinant is called a saturated D-optimal design. We consider some cases of saturated Doptimal designs where n > 2, n ≢ 0 mod 4, so the Hadamard bound is not attainable, but bounds due to Barba or Ehlic
A feasibility approach for constructing combinatorial designs of circulant type
In this work, we propose an optimization approach for constructing various
classes of circulant combinatorial designs that can be defined in terms of
autocorrelations. The problem is formulated as a so-called feasibility problem
having three sets, to which the Douglas-Rachford projection algorithm is
applied. The approach is illustrated on three different classes of circulant
combinatorial designs: circulant weighing matrices, D-optimal matrices, and
Hadamard matrices with two circulant cores. Furthermore, we explicitly
construct two new circulant weighing matrices, a and a
, whose existence was previously marked as unresolved in the most
recent version of Strassler's table
D-optimal matrices of orders 118, 138, 150, 154 and 174
We construct supplementary difference sets (SDS) with parameters
, , , and
. These SDSs give D-optimal designs (DO-designs) of
two-circulant type of orders 118,138,150,154 and 174. Until now, no DO-designs
of orders 138,154 and 174 were known. While a DO-design (not of two-circulant
type) of order 150 was constructed previously by Holzmann and Kharaghani, no
such design of two-circulant type was known. The smallest undecided order for
DO-designs is now 198. We use a novel property of the compression map to speed
up some computations.Comment: 14 pages. arXiv admin note: substantial text overlap with
arXiv:1409.596
A few new orders for D-optimal matrices
The first examples of D-optimal matrices of orders 222, 234, 258 and 278 are
constructed.Comment: 9 pages, 3 table
The fidelity of dynamic signaling by noisy biomolecular networks
This is the final version of the article. Available from Public Library of Science via the DOI in this record.Cells live in changing, dynamic environments. To understand cellular decision-making, we must therefore understand how fluctuating inputs are processed by noisy biomolecular networks. Here we present a general methodology for analyzing the fidelity with which different statistics of a fluctuating input are represented, or encoded, in the output of a signaling system over time. We identify two orthogonal sources of error that corrupt perfect representation of the signal: dynamical error, which occurs when the network responds on average to other features of the input trajectory as well as to the signal of interest, and mechanistic error, which occurs because biochemical reactions comprising the signaling mechanism are stochastic. Trade-offs between these two errors can determine the system's fidelity. By developing mathematical approaches to derive dynamics conditional on input trajectories we can show, for example, that increased biochemical noise (mechanistic error) can improve fidelity and that both negative and positive feedback degrade fidelity, for standard models of genetic autoregulation. For a group of cells, the fidelity of the collective output exceeds that of an individual cell and negative feedback then typically becomes beneficial. We can also predict the dynamic signal for which a given system has highest fidelity and, conversely, how to modify the network design to maximize fidelity for a given dynamic signal. Our approach is general, has applications to both systems and synthetic biology, and will help underpin studies of cellular behavior in natural, dynamic environments.We acknowledge support from a Medical Research Council and Engineering and Physical Sciences Council funded Fellowship in Biomedical Informatics (CGB) and a Scottish Universities Life Sciences Alliance chair in Systems Biology (PSS). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
Combinatorics and Probability
For the past few decades, Combinatorics and Probability Theory have had a fruitful symbiosis, each benefitting from and influencing developments in the other. Thus to prove the existence of designs, probabilistic methods are used, algorithms to factorize integers need combinatorics and probability theory (in addition to number theory), and the study of random matrices needs combinatorics. In the workshop a great variety of topics exemplifying this interaction were considered, including problems concerning designs, Cayley graphs, additive number theory, multiplicative number theory, noise sensitivity, random graphs, extremal graphs and random matrices
On the decomposition threshold of a given graph
We study the -decomposition threshold for a given graph .
Here an -decomposition of a graph is a collection of edge-disjoint
copies of in which together cover every edge of . (Such an
-decomposition can only exist if is -divisible, i.e. if and each vertex degree of can be expressed as a linear combination of
the vertex degrees of .)
The -decomposition threshold is the smallest value ensuring
that an -divisible graph on vertices with
has an -decomposition. Our main results imply
the following for a given graph , where is the fractional
version of and :
(i) ;
(ii) if , then
;
(iii) we determine if is bipartite.
In particular, (i) implies that . Our proof
involves further developments of the recent `iterative' absorbing approach.Comment: Final version, to appear in the Journal of Combinatorial Theory,
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Construction of a support tool for the design of the activity structures based computer system architectures
This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.This thesis is a reapproachment of diverse design concepts, brought to bear upon the computer system
engineering problem of identification and control of highly constrained multiprocessing (HCM)
computer machines. It contributes to the area of meta/general systems methodology, and brings
a new insight into the design formalisms, and results afforded by bringing together various design
concepts that can be used for the construction of highly constrained computer system architectures.
A unique point of view is taken by assuming the process of identification and control of HCM
computer systems to be the process generated by the Activity Structures Methodology (ASM).
The research in ASM has emerged from the Neuroscience research, aiming at providing the
techniques for combining the diverse knowledge sources that capture the 'deep knowledge' of this
application field in an effective formal and computer representable form. To apply the ASM design
guidelines in the realm of the distributed computer system design, we provide new design definitions
for the identification and control of such machines in terms of realisations. These realisation definitions
characterise the various classes of the identification and control problem. The classes covered
consist of:
1. the identification of the designer activities,
2. the identification and control of the machine's distributed structures of behaviour,
3. the identification and control of the conversational environment activities (i.e. the randomised/
adaptive activities and interactions of both the user and the machine environments),
4. the identification and control of the substrata needed for the realisation of the machine, and
5. the identification of the admissible design data, both user-oriented and machineoriented,
that can force the conversational environment to act in a self-regulating
manner.
All extent results are considered in this context, allowing the development of both necessary
conditions for machine identification in terms of their distributed behaviours as well as the substrata
structures of the unknown machine and sufficient conditions in terms of experiments on the unknown
machine to achieve the self-regulation behaviour.
We provide a detailed description of the design and implementation of the support software tool
which can be used for aiding the process of constructing effective, HCM computer systems, based
on various classes of identification and control. The design data of a highly constrained system, the
NUKE, are used to verify the tool logic as well as the various identification and control procedures.
Possible extensions as well as future work implied by the results are considered.Government of Ira
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