21,629 research outputs found
Chance Constrained Mixed Integer Program: Bilinear and Linear Formulations, and Benders Decomposition
In this paper, we study chance constrained mixed integer program with
consideration of recourse decisions and their incurred cost, developed on a
finite discrete scenario set. Through studying a non-traditional bilinear mixed
integer formulation, we derive its linear counterparts and show that they could
be stronger than existing linear formulations. We also develop a variant of
Jensen's inequality that extends the one for stochastic program. To solve this
challenging problem, we present a variant of Benders decomposition method in
bilinear form, which actually provides an easy-to-use algorithm framework for
further improvements, along with a few enhancement strategies based on
structural properties or Jensen's inequality. Computational study shows that
the presented Benders decomposition method, jointly with appropriate
enhancement techniques, outperforms a commercial solver by an order of
magnitude on solving chance constrained program or detecting its infeasibility
Local Primitive Causality and the Common Cause Principle in Quantum Field Theory
If \{A(V)\} is a net of local von Neumann algebras satisfying standard axioms
of algebraic relativistic quantum field theory and V_1 and V_2 are spacelike
separated spacetime regions, then the system (A(V_1),A(V_2),\phi) is said to
satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of
projections A \in A(V_1), B \in A(V_2) correlated in the normal state \phi
there exists a projection C belonging to a von Neumann algebra associated with
a spacetime region V contained in the union of the backward light cones of V_1
and V_2 and disjoint from both V_1 and V_2, a projection having the properties
of a Reichenbachian common cause of the correlation between A and B. It is
shown that if the net has the local primitive causality property then every
local system (A(V_1),A(V_2),\phi) with a locally normal and locally faithful
state \phi and open bounded V_1 and V_2 satisfies the Weak Reichenbach's Common
Cause Principle.Comment: 14 pages, Late
A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information
Copyright q 2012 Hongli Dong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German
Tighter quantum uncertainty relations follow from a general probabilistic bound
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy
UR are often considered to be hallmarks of quantum theory. Here, a simple
derivation of these URs is presented based on a single classical inequality
from estimation theory, a Cram\'er-Rao-like bound. The Heisenberg-Robertson UR
is then obtained by using the Born rule and the Schr\"odinger equation. This
allows a clear separtion of the probabilistic nature of quantum mechanics from
the Hilbert space structure and the dynamical law. It also simplifies the
interpretation of the bound. In addition, the Heisenberg-Robertson UR is
tightened for mixed states by replacing one variance by the so-called quantum
Fisher information. Thermal states of Hamiltonians with evenly-gapped energy
levels are shown to saturate the tighter bound for natural choices of the
operators. This example is further extended to Gaussian states of a harmonic
oscillator. For many-qubit systems, we illustrate the interplay between
entanglement and the structure of the operators that saturate the UR with
spin-squeezed states and Dicke states.Comment: 8 pages, 1 figure. v2: improved presentation, references added,
results on the connection between saturated inequality and entanglement
structure for multi-qubit states adde
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