63,238 research outputs found
Quantum and Classical Strong Direct Product Theorems and Optimal Time-Space Tradeoffs
A strong direct product theorem says that if we want to compute k independent
instances of a function, using less than k times the resources needed for one
instance, then our overall success probability will be exponentially small in
k. We establish such theorems for the classical as well as quantum query
complexity of the OR function. This implies slightly weaker direct product
results for all total functions. We prove a similar result for quantum
communication protocols computing k instances of the Disjointness function.
Our direct product theorems imply a time-space tradeoff T^2*S=Omega(N^3) for
sorting N items on a quantum computer, which is optimal up to polylog factors.
They also give several tight time-space and communication-space tradeoffs for
the problems of Boolean matrix-vector multiplication and matrix multiplication.Comment: 22 pages LaTeX. 2nd version: some parts rewritten, results are
essentially the same. A shorter version will appear in IEEE FOCS 0
A comparative study of the AHP and TOPSIS methods for implementing load shedding scheme in a pulp mill system
The advancement of technology had encouraged mankind to design and create useful
equipment and devices. These equipment enable users to fully utilize them in various
applications. Pulp mill is one of the heavy industries that consumes large amount of
electricity in its production. Due to this, any malfunction of the equipment might
cause mass losses to the company. In particular, the breakdown of the generator
would cause other generators to be overloaded. In the meantime, the subsequence
loads will be shed until the generators are sufficient to provide the power to other
loads. Once the fault had been fixed, the load shedding scheme can be deactivated.
Thus, load shedding scheme is the best way in handling such condition. Selected load
will be shed under this scheme in order to protect the generators from being
damaged. Multi Criteria Decision Making (MCDM) can be applied in determination
of the load shedding scheme in the electric power system. In this thesis two methods
which are Analytic Hierarchy Process (AHP) and Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS) were introduced and applied. From this thesis,
a series of analyses are conducted and the results are determined. Among these two
methods which are AHP and TOPSIS, the results shown that TOPSIS is the best
Multi criteria Decision Making (MCDM) for load shedding scheme in the pulp mill
system. TOPSIS is the most effective solution because of the highest percentage
effectiveness of load shedding between these two methods. The results of the AHP
and TOPSIS analysis to the pulp mill system are very promising
Adaptive Complex Contagions and Threshold Dynamical Systems
A broad range of nonlinear processes over networks are governed by threshold
dynamics. So far, existing mathematical theory characterizing the behavior of
such systems has largely been concerned with the case where the thresholds are
static. In this paper we extend current theory of finite dynamical systems to
cover dynamic thresholds. Three classes of parallel and sequential dynamic
threshold systems are introduced and analyzed. Our main result, which is a
complete characterization of their attractor structures, show that sequential
systems may only have fixed points as limit sets whereas parallel systems may
only have period orbits of size at most two as limit sets. The attractor states
are characterized for general graphs and enumerated in the special case of
paths and cycle graphs; a computational algorithm is outlined for determining
the number of fixed points over a tree. We expect our results to be relevant
for modeling a broad class of biological, behavioral and socio-technical
systems where adaptive behavior is central.Comment: Submitted for publicatio
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