4,661 research outputs found
The design of a Pulse Position Modulated /PPM/ optical communication system
Design of pulse position modulation optical communication syste
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
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
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
Towards Work-Efficient Parallel Parameterized Algorithms
Parallel parameterized complexity theory studies how fixed-parameter
tractable (fpt) problems can be solved in parallel. Previous theoretical work
focused on parallel algorithms that are very fast in principle, but did not
take into account that when we only have a small number of processors (between
2 and, say, 1024), it is more important that the parallel algorithms are
work-efficient. In the present paper we investigate how work-efficient fpt
algorithms can be designed. We review standard methods from fpt theory, like
kernelization, search trees, and interleaving, and prove trade-offs for them
between work efficiency and runtime improvements. This results in a toolbox for
developing work-efficient parallel fpt algorithms.Comment: Prior full version of the paper that will appear in Proceedings of
the 13th International Conference and Workshops on Algorithms and Computation
(WALCOM 2019), February 27 - March 02, 2019, Guwahati, India. The final
authenticated version is available online at
https://doi.org/10.1007/978-3-030-10564-8_2
Dictionary matching in a stream
We consider the problem of dictionary matching in a stream. Given a set of
strings, known as a dictionary, and a stream of characters arriving one at a
time, the task is to report each time some string in our dictionary occurs in
the stream. We present a randomised algorithm which takes O(log log(k + m))
time per arriving character and uses O(k log m) words of space, where k is the
number of strings in the dictionary and m is the length of the longest string
in the dictionary
Deterministic and Probabilistic Binary Search in Graphs
We consider the following natural generalization of Binary Search: in a given
undirected, positively weighted graph, one vertex is a target. The algorithm's
task is to identify the target by adaptively querying vertices. In response to
querying a node , the algorithm learns either that is the target, or is
given an edge out of that lies on a shortest path from to the target.
We study this problem in a general noisy model in which each query
independently receives a correct answer with probability (a
known constant), and an (adversarial) incorrect one with probability .
Our main positive result is that when (i.e., all answers are
correct), queries are always sufficient. For general , we give an
(almost information-theoretically optimal) algorithm that uses, in expectation,
no more than queries, and identifies the target correctly with probability at
leas . Here, denotes the
entropy. The first bound is achieved by the algorithm that iteratively queries
a 1-median of the nodes not ruled out yet; the second bound by careful repeated
invocations of a multiplicative weights algorithm.
Even for , we show several hardness results for the problem of
determining whether a target can be found using queries. Our upper bound of
implies a quasipolynomial-time algorithm for undirected connected
graphs; we show that this is best-possible under the Strong Exponential Time
Hypothesis (SETH). Furthermore, for directed graphs, or for undirected graphs
with non-uniform node querying costs, the problem is PSPACE-complete. For a
semi-adaptive version, in which one may query nodes each in rounds, we
show membership in in the polynomial hierarchy, and hardness
for
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