5,872 research outputs found
The design of a Pulse Position Modulated /PPM/ optical communication system
Design of pulse position modulation optical communication syste
Product Integral Representations of Wilson Lines and Wilson Loops, and Non-Abelian Stokes Theorem
We make use of product integrals to provide an unambiguous mathematical
representation of Wilson line and Wilson loop operators. Then, drawing upon
various properties of product integrals, we discuss such properties of these
operators as approximating them with partial sums, their convergence, and their
behavior under gauge transformations. We also obtain a surface product integral
representation for the Wilson loop operator. The result can be interpreted as
the non-abelian version of Stokes theorem.Comment: 20 pages, LaTe
Communication theory for the free space optical channel Interim technical report
Quantum detectors, noise mechanisms, and application to optical communication theor
Enhanced Operational Semantics in Systems Biology
We are faced with a great challenge: the cross-fertilization between the fields of formal methods for concurrency, in the computer science domain, and systems biology in the biological realm
A preliminary shield design for a SNAP-8 power system
A preliminary shield design for a nuclear power system utilizing a SNAP-8 reactor for space base application is presented. A representative space base configuration was selected to set the geometry constraints imposed on the design. The base utilizes two independent power packages each with a reactor operating at 600 kwt and each producing about 50 kwe. The crew compartment is located about 200 feet from each reactor and is large enough in extent to intercept a total shadow angle of 60 deg measured about the center line of each reactor
Will That Be First Class, Business Class, or Pet Class - Changing Legal Trends for the Traveling Pet
This Article discusses the recently enacted British and European Union legislation that eases the restrictions on pet travel from the United States and Canada to European countries and its effect on the ailing airline and travel industries
Sum-of-squares lower bounds for planted clique
Finding cliques in random graphs and the closely related "planted" clique
variant, where a clique of size k is planted in a random G(n, 1/2) graph, have
been the focus of substantial study in algorithm design. Despite much effort,
the best known polynomial-time algorithms only solve the problem for k ~
sqrt(n).
In this paper we study the complexity of the planted clique problem under
algorithms from the Sum-of-squares hierarchy. We prove the first average case
lower bound for this model: for almost all graphs in G(n,1/2), r rounds of the
SOS hierarchy cannot find a planted k-clique unless k > n^{1/2r} (up to
logarithmic factors). Thus, for any constant number of rounds planted cliques
of size n^{o(1)} cannot be found by this powerful class of algorithms. This is
shown via an integrability gap for the natural formulation of maximum clique
problem on random graphs for SOS and Lasserre hierarchies, which in turn follow
from degree lower bounds for the Positivestellensatz proof system.
We follow the usual recipe for such proofs. First, we introduce a natural
"dual certificate" (also known as a "vector-solution" or "pseudo-expectation")
for the given system of polynomial equations representing the problem for every
fixed input graph. Then we show that the matrix associated with this dual
certificate is PSD (positive semi-definite) with high probability over the
choice of the input graph.This requires the use of certain tools. One is the
theory of association schemes, and in particular the eigenspaces and
eigenvalues of the Johnson scheme. Another is a combinatorial method we develop
to compute (via traces) norm bounds for certain random matrices whose entries
are highly dependent; we hope this method will be useful elsewhere
Complex-linear invariants of biochemical networks
The nonlinearities found in molecular networks usually prevent mathematical
analysis of network behaviour, which has largely been studied by numerical
simulation. This can lead to difficult problems of parameter determination.
However, molecular networks give rise, through mass-action kinetics, to
polynomial dynamical systems, whose steady states are zeros of a set of
polynomial equations. These equations may be analysed by algebraic methods, in
which parameters are treated as symbolic expressions whose numerical values do
not have to be known in advance. For instance, an "invariant" of a network is a
polynomial expression on selected state variables that vanishes in any steady
state. Invariants have been found that encode key network properties and that
discriminate between different network structures. Although invariants may be
calculated by computational algebraic methods, such as Gr\"obner bases, these
become computationally infeasible for biologically realistic networks. Here, we
exploit Chemical Reaction Network Theory (CRNT) to develop an efficient
procedure for calculating invariants that are linear combinations of
"complexes", or the monomials coming from mass action. We show how this
procedure can be used in proving earlier results of Horn and Jackson and of
Shinar and Feinberg for networks of deficiency at most one. We then apply our
method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity
regulator and the mammalian
6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator,
whose networks have deficiencies up to four. We show that bifunctionality leads
to different forms of concentration control that are robust to changes in
initial conditions or total amounts. Finally, we outline a systematic procedure
for using complex-linear invariants to analyse molecular networks of any
deficiency.Comment: 36 pages, 6 figure
Measurement of thermal conductance of multilayer and other insulation materials Final report
Thermal conductance measurements of multilayer, aluminumized polymeric films for space suit insulation material
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