scholarly journals Operational Algorithms for Separable Qubit X States

2019 ◽  
Vol 4 (3) ◽  
pp. 64
Author(s):  
Demosthenes Ellinas
Keyword(s):  
State Space ◽  
Quantum Measurement ◽  
Unitary Operator ◽  
Probability Distributions ◽  
Quantum Walk ◽  
Higher Order ◽  
Quantum Measurements ◽  
Uniform Hypergraph ◽  
Extended State ◽  
Quantum Polynomial

This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems.

Extended State Space of the Rational sl(2) Gaudin Model in Terms of Laguerre Polynomials

2013 ◽  
Vol 58 (11) ◽  
pp. 1084-1091
Author(s):  
Yu.V. Bezvershenko ◽  
◽  
P.I. Holod ◽  
Keyword(s):  
State Space ◽  
Laguerre Polynomials ◽  
Gaudin Model ◽  
Extended State

scholarly journals Decoherence and its role in the modern measurement problem

2012 ◽  
Vol 370 (1975) ◽  
pp. 4576-4593 ◽  
Author(s):  
David Wallace
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Measurement ◽  
Measurement Problem ◽  
Scientific Practice ◽  
Measurement Theory ◽  
Quantum Measurements ◽  
Quantum Measurement Problem ◽  
Modern Physics ◽  
Conceptual Problems

Decoherence is widely felt to have something to do with the quantum measurement problem, but getting clear on just what is made difficult by the fact that the ‘measurement problem’, as traditionally presented in foundational and philosophical discussions, has become somewhat disconnected from the conceptual problems posed by real physics. This, in turn, is because quantum mechanics as discussed in textbooks and in foundational discussions has become somewhat removed from scientific practice, especially where the analysis of measurement is concerned. This paper has two goals: firstly (§§1–2), to present an account of how quantum measurements are actually dealt with in modern physics (hint: it does not involve a collapse of the wave function) and to state the measurement problem from the perspective of that account; and secondly (§§3–4), to clarify what role decoherence plays in modern measurement theory and what effect it has on the various strategies that have been proposed to solve the measurement problem.

scholarly journals Classroom note: An inductive derivation of Stirling numbers of the second kind and their applications in statistics

1997 ◽  
Vol 1 (2) ◽  
pp. 151-157 ◽  
Author(s):  
Anwar H. Joarder ◽  
Munir Mahmood
Keyword(s):  
Probability Distributions ◽  
Stirling Numbers ◽  
Higher Order ◽  
Inductive Method ◽  
Higher Order Moments ◽  
Discrete Probability ◽  
Discrete Probability Distributions

An inductive method has been presented for finding Stirling numbers of the second kind. Applications to some discrete probability distributions for finding higher order moments have been discussed.

scholarly journals Perceptual insensitivity to higher-order statistical moments of coherent random dot motion

2018 ◽  
Author(s):  
Michael L. Waskom ◽  
Janeen Asfour ◽  
Roozbeh Kiani
Keyword(s):  
Visual Processing ◽  
Probability Distributions ◽  
Higher Order ◽  
Statistical Moments ◽  
Coherent Motion ◽  
It Use ◽  
Higher Order Moments ◽  
Dynamic Stimuli ◽  
Dot Motion ◽  
The Individual

ABSTRACTWhen the visual system analyses distributed patterns of sensory inputs, what features of those distributions does it use? It has been previously demonstrated that higher-order statistical moments of luminance distributions influence perception of static surfaces and textures. Here, we tested whether the brain also represents higher-order moments of dynamic stimuli. We constructed random dot kinematograms where dots moved according to probability distributions that selectively differed in terms of their mean, variance, skewness, or kurtosis. When viewing these stimuli, human observers were sensitive to the mean direction of coherent motion and to the variance of the individual dot displacement angles, but they were insensitive to skewness and kurtosis. Observer behavior accorded with a model of directional motion energy, suggesting that information about higher-order moments is discarded early in the visual processing hierarchy. These results demonstrate that use of higher-order moments is not a general property of visual perception.

scholarly journals Higher-Order Cumulants Drive Neuronal Activity Patterns, Inducing UP-DOWN States in Neural Populations

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 477 ◽  
Author(s):  
Roman Baravalle ◽  
Fernando Montani
Keyword(s):  
Probability Distributions ◽  
Activity Patterns ◽  
Gaussian Model ◽  
Random Variable ◽  
Neural System ◽  
Higher Order ◽  
Second Order ◽  
Specific Information ◽  
Neuronal Populations ◽  
Binder Cumulant

A major challenge in neuroscience is to understand the role of the higher-order correlations structure of neuronal populations. The dichotomized Gaussian model (DG) generates spike trains by means of thresholding a multivariate Gaussian random variable. The DG inputs are Gaussian distributed, and thus have no interactions beyond the second order in their inputs; however, they can induce higher-order correlations in the outputs. We propose a combination of analytical and numerical techniques to estimate higher-order, above the second, cumulants of the firing probability distributions. Our findings show that a large amount of pairwise interactions in the inputs can induce the system into two possible regimes, one with low activity (“DOWN state”) and another one with high activity (“UP state”), and the appearance of these states is due to a combination between the third- and fourth-order cumulant. This could be part of a mechanism that would help the neural code to upgrade specific information about the stimuli, motivating us to examine the behavior of the critical fluctuations through the Binder cumulant close to the critical point. We show, using the Binder cumulant, that higher-order correlations in the outputs generate a critical neural system that portrays a second-order phase transition.

scholarly journals Improved predictive functional control for ethylene cracking furnace

2019 ◽  
Vol 52 (5-6) ◽  
pp. 526-539
Author(s):  
Han Song ◽  
Cheng-li Su ◽  
Hui-yuan Shi ◽  
Ping Li ◽  
Jiang-tao Cao
Keyword(s):  
Control System ◽  
State Space ◽  
Control Method ◽  
Balance Control ◽  
State Space Model ◽  
Industrial Process ◽  
Outlet Temperature ◽  
Extended State ◽  
Predictive Functional Control ◽  
Functional Control

The objective of this paper is to show the design and application of pass temperature balance control system using an improved predictive functional control method in eight 800 tone/year USC ethylene cracking furnaces. The advanced pass temperature balance controller is developed using the proposed method and implemented in proprietary APC-ISYS software, which is connected to Yokogawa distributed control system via an OPC server. The advantage of it lies in the fact that the dynamics of pass temperature with nonlinearity and time delay are described by Takagi–Sugeno model and transformed into time-varying extended state space model, and thus, the proposed controller can regulate pass temperature based on the extended state space formulation. In addition, the control law with a linear iterative form, easily applied to industrial process, is derived. The robust analysis for the set point, input disturbance and output disturbance to the output verifies the ability of tracking and disturbance rejection of the proposed method. Application results from an industrial furnace are shown to be markedly better in terms of lower variability in the outlet temperature of both the passes compared to the current proportional–integral–derivative control scheme.

scholarly journals Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
M. Vahidi ◽  
V. Jafari ◽  
M. H. Abyaneh ◽  
SH. Vahdani
Keyword(s):  
State Space ◽  
Displacement Field ◽  
Order Approximation ◽  
Computational Cost ◽  
Higher Order ◽  
Linear Displacement ◽  
Large Displacement ◽  
Approximation Techniques ◽  
Engineering Problems

This paper investigates different approximation techniques for planar beam column elements in force-based methods. The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. Using these three approximation fields, the responses and their accuracies in some systems are compared in examples. Finally, focusing on the accuracy and regarding the performed analyses, it seems that the computational cost is reduced and accuracy of responses is elevated in many engineering problems using the higher-order approximation field in state space.

scholarly journals Some Moment Relations for the Hipp approximation

1996 ◽  
Vol 26 (1) ◽  
pp. 117-121 ◽  
Author(s):  
Jan Dhaene ◽  
Bjørn Sundt ◽  
Nelson De Pril
Keyword(s):  
Finite Number ◽  
Present Note ◽  
Order Approximation ◽  
Probability Distributions ◽  
Higher Order ◽  
Exact Distribution ◽  
Higher Order Moments ◽  
The Moment

AbstractIn the present note we consider the Hipp approximation to the convolution of a finite number of probability distributions on the non-negative integers. It is shown that the moment up to and including order r of the rth order approximation are equal to the corresponding moments of the exact distribution. We also give a relation between the exact and approximated (r + 1)th order moments and indicate how similar relations can be obtained for higher order moments.

State-space forms for higher-order discrete-time models

1998 ◽  
Vol 34 (1-2) ◽  
pp. 23-31 ◽  
Author(s):  
A.Raymond Comeau ◽  
Noriyuki Hori
Keyword(s):  
State Space ◽  
Discrete Time ◽  
Higher Order ◽  
Space Forms ◽  
Discrete Time Models
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