128,427 research outputs found
Enabling controlling complex networks with local topological information
Complex networks characterize the nature of internal/external interactions in real-world systems
including social, economic, biological, ecological, and technological networks. Two issues keep as
obstacles to fulflling control of large-scale networks: structural controllability which describes the
ability to guide a dynamical system from any initial state to any desired fnal state in fnite time, with a
suitable choice of inputs; and optimal control, which is a typical control approach to minimize the cost
for driving the network to a predefned state with a given number of control inputs. For large complex
networks without global information of network topology, both problems remain essentially open.
Here we combine graph theory and control theory for tackling the two problems in one go, using only
local network topology information. For the structural controllability problem, a distributed local-game
matching method is proposed, where every node plays a simple Bayesian game with local information
and local interactions with adjacent nodes, ensuring a suboptimal solution at a linear complexity.
Starring from any structural controllability solution, a minimizing longest control path method can
efciently reach a good solution for the optimal control in large networks. Our results provide solutions
for distributed complex network control and demonstrate a way to link the structural controllability and
optimal control together.The work was partially supported by National Science Foundation of China (61603209), and Beijing Natural Science Foundation (4164086), and the Study of Brain-Inspired Computing System of Tsinghua University program (20151080467), and Ministry of Education, Singapore, under contracts RG28/14, MOE2014-T2-1-028 and MOE2016-T2-1-119. Part of this work is an outcome of the Future Resilient Systems project at the Singapore-ETH Centre (SEC), which is funded by the National Research Foundation of Singapore (NRF) under its Campus for Research Excellence and Technological Enterprise (CREATE) programme. (61603209 - National Science Foundation of China; 4164086 - Beijing Natural Science Foundation; 20151080467 - Study of Brain-Inspired Computing System of Tsinghua University program; RG28/14 - Ministry of Education, Singapore; MOE2014-T2-1-028 - Ministry of Education, Singapore; MOE2016-T2-1-119 - Ministry of Education, Singapore; National Research Foundation of Singapore (NRF) under Campus for Research Excellence and Technological Enterprise (CREATE) programme)Published versio
String Theory: Progress and Problems
String theory builds on the great legacy of Yukawa and Tomonaga: New degrees
of freedom and control of the UV are two important themes. This talk will give
an overview of some of the progress and some of the unsolved problems that
characterize string theory today. It is divided into two parts: (1) Connecting
String Theory to the Real World; (2) Gauge Theory/String Theory Duality. Two
other major subjects, which I will omit, are Black Holes in String Theory and
The Impact of String Theory on Mathematics.Comment: 14 pages; Presented at the Yukawa--Tomonaga Centennial Symposium v2:
references adde
Why walking the dog takes time: Frechet distance has no strongly subquadratic algorithms unless SETH fails
The Frechet distance is a well-studied and very popular measure of similarity
of two curves. Many variants and extensions have been studied since Alt and
Godau introduced this measure to computational geometry in 1991. Their original
algorithm to compute the Frechet distance of two polygonal curves with n
vertices has a runtime of O(n^2 log n). More than 20 years later, the state of
the art algorithms for most variants still take time more than O(n^2 / log n),
but no matching lower bounds are known, not even under reasonable complexity
theoretic assumptions.
To obtain a conditional lower bound, in this paper we assume the Strong
Exponential Time Hypothesis or, more precisely, that there is no
O*((2-delta)^N) algorithm for CNF-SAT for any delta > 0. Under this assumption
we show that the Frechet distance cannot be computed in strongly subquadratic
time, i.e., in time O(n^{2-delta}) for any delta > 0. This means that finding
faster algorithms for the Frechet distance is as hard as finding faster CNF-SAT
algorithms, and the existence of a strongly subquadratic algorithm can be
considered unlikely.
Our result holds for both the continuous and the discrete Frechet distance.
We extend the main result in various directions. Based on the same assumption
we (1) show non-existence of a strongly subquadratic 1.001-approximation, (2)
present tight lower bounds in case the numbers of vertices of the two curves
are imbalanced, and (3) examine realistic input assumptions (c-packed curves)
A striking correspondence between the dynamics generated by the vector fields and by the scalar parabolic equations
The purpose of this paper is to enhance a correspondence between the dynamics
of the differential equations on and those
of the parabolic equations on a bounded
domain . We give details on the similarities of these dynamics in the
cases , and and in the corresponding cases ,
and dim() respectively. In addition to
the beauty of such a correspondence, this could serve as a guideline for future
research on the dynamics of parabolic equations
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