Realization Theory Research Articles

Exact dimension estimation of interacting qubit systems assisted by a single quantum probe

Estimating the dimension of an Hilbert space is an important component of quantum system identification. In quantum technologies, the dimension of a quantum system (or its corresponding accessible Hilbert space) is an important resource, as larger dimensions determine e.g. the performance of quantum computation protocols or the sensitivity of quantum sensors. Despite being a critical task in quantum system identification, estimating the Hilbert space dimension is experimentally challenging. While there have been proposals for various dimension witnesses capable of putting a lower bound on the dimension from measuring collective observables that encode correlations, in many practical scenarios, especially for multiqubit systems, the experimental control might not be able to engineer the required initialization, dynamics and observables. Here we propose a more practical strategy, that relies not on directly measuring an unknown multiqubit target system, but on the indirect interaction with a local quantum probe under the experimenter's control. Assuming only that the interaction model is given and the evolution correlates all the qubits with the probe, we combine a graph-theoretical approach and realization theory to demonstrate that the dimension of the Hilbert space can be exactly estimated from the model order of the system. We further analyze the robustness in the presence of background noise of the proposed estimation method based on realization theory, finding that despite stringent constrains on the allowed noise level, exact dimension estimation can still be achieved.

A categorical approach to minimal realization for a fuzzy language

In this study, we provide a general theory of minimal realization for a given fuzzy language in a category theory setting. We introduce categorical characterizations of a run map, reachability map, and observability map for a crisp deterministic fuzzy automaton. Finally, we show that all minimal realizations for a given fuzzy language are isomorphic to the Nerode realization for the same case.

In Memoriam

In Memoriam

Multidimensional realisation theory and polynomial system solving

ABSTRACTMultidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional systems is linked to multivariate polynomials, and is therefore more difficult than the well-known analysis of one-dimensional systems, which is linked to univariate polynomials. In the current paper, we relate the realisation theory for overdetermined autonomous multidimensional systems to the problem of solving a system of polynomial equations. We show that basic notions of linear algebra suffice to analyse and solve the problem. The difference equations are associated with a Macaulay matrix formulation, and it is shown that the null space of the Macaulay matrix is a multidimensional observability matrix. Application of the classical shift trick from realisation theory allows for the computation of the corresponding system matrices in a multidimensional state-space setting. This reduces the task of solving a system of polynomial equations to computing an eigenvalue decomposition. We study the occurrence of multiple solutions, as well as the existence and analysis of solutions at infinity, which allow for an interpretation in terms of multidimensional descriptor systems.

To the Geometrical Theory of Differential Realization of Dynamic Processes in a Hilbert Space*

In the context of the qualitative theory of realization of infinite-dimensional dynamic systems, the authors demonstrate some results related to investigation of the geometrical properties of families of continuous controlled dynamic processes (“input–output” mappings) in the problem of solvability of this differential realization in a class of linear ordinary non-stationary differential equations in a separable Hilbert space.

Dignity realization of patients with stroke in hospital care: A grounded theory.

Dignity is seen as an important but complex concept in the healthcare context. In this context, the discussion of dignity includes concepts of other ethical principles such as autonomy and privacy. Patients consider dignity to cover individuality, patient's feelings, communication, and the behavior of healthcare personnel. However, there is a lack of knowledge concerning the realization of patients' dignity in hospital care and the focus of the study is therefore on the realization of dignity of the vulnerable group of patients with stroke. The aim of the study was to create a theoretical construct to describe the dignity realization of patients with stroke in hospital care. Patients with stroke (n = 16) were interviewed in 2015 using a semi-structured interview containing open questions concerning dignity. The data were analyzed using constant comparison of Grounded Theory. Ethical approval for the research was obtained from the Ethics Committee of the University. The permission for the research was given by the hospital. Informed consent was obtained from participants. The "Theory of Dignity Realization of Patients with Stroke in Hospital Care" consists of a core category including generic elements of the new situation and dignity realization types. The core category was identified as "Dignity in a new situation" and the generic elements as health history, life history, individuality and stroke. Dignity of patients with stroke is realized through specific types of realization: person-related dignity type, control-related dignity type, independence-related dignity type, social-related dignity type, and care-related dignity type. The theory has similar elements with the previous literature but the whole construct is new. The theory reveals possible special characteristics in dignity realization of patients with stroke. For healthcare personnel, the theory provides a frame for a better understanding and recognition of how dignity of patients with stroke is realized.

Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators

Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones.

The theory of parallel climate realizations as a new framework for teleconnection analysis

Teleconnections are striking features of the Earth climate system which appear as statistically correlated climate-related patterns between remote geographical regions of the globe. In a changing climate, however, the strength of teleconnections might change, and an appropriate characterization of these correlations and their change (more appropriate than detrending the time series) is lacking in the literature. Here we present a novel approach, based on the theory of snapshot attractors, corresponding in our context to studying parallel climate realizations. Imagining an ensemble of parallel Earth systems, instead of the single one observed (i.e., the real Earth), the ensemble, after some time, characterizes the appropriate probabilities of all options permitted by the climate dynamics, reflecting the internal variability of the climate. We claim that the relevant quantities for characterizing teleconnections in a changing climate are correlation coefficients taken over the temporally evolving ensemble in any time instant. As a particular example, we consider the teleconnections of the North Atlantic Oscillation (NAO). In a numerical climate model, we demonstrate that this approach provides the only statistically correct characterization, in contrast to commonly used temporal correlations evaluated along single detrended time series. The teleconnections of the NAO are found to survive the climate change, but their strength might be time-dependent.

First-order quarter-and mixed-moment realizability theory and Kershaw closures for a Fokker-Planck equation in two space dimensions

Mixed-moment models, introduced before for one space dimension, are a modification of the method of moments applied to a (linear) kinetic equation, by choosing mixtures of different partial moments. They are well-suited to handle such equations where collisions of particles are modelled with a Laplace-Beltrami operator. We generalize the concept of mixed moments to two dimension. The resulting hyperbolic system of equations has desirable properties, removing some drawbacks of the well-known $\MN[1]$ model. We furthermore provide a realizability theory for a first-order system of mixed moments by linking it to the corresponding quarter-moment theory. Additionally, we derive a type of Kershaw closures for mixed- and quarter-moment models, giving an efficient closure (compared to minimum-entropy models). The derived closures are investigated for different benchmark problems.

Yongming Yanshou’s Sudden Enlightenment and Sudden Practice : The Inheritance and Transformation of Tang Dynasty Theories of Cultivation and Realization

In this paper I shed light on how Yongming Yanshou （904―976） himself inherited and built upon Chan Buddhist theories involving the cultivation of enlightenment from the Tang period.BR In the traditional Buddhist understanding which came from India it was not thought that living beings could attain enlightenment and become buddhas in this present life. In the Chan Buddhism that emerged in the Tang period, however, the position that people are already buddhas in this present moment raised new discussions and ideas about enlightenment and practice. In order to shed light on Yongming Yanshou’s theories of practice and enlightenment, in my opinion it is necessary to analyze the progression of theories of practice and enlightenment from the three essential figures Shenhui, Mazu, and Zongmi and how their thoughts came to Yongming Yanshou.BR Shenhui (684-758) promoted what is called the “southern sudden, northern gradual” theory- “sudden enlightenment” was promoted by the true dharma heir Huineng, while “gradual enlightenment was promoted by the divergent Northern School of Shenxiu- even though after attaining enlightenment suddenly, gradual practice would be needed later to strengthen wisdom. As Shenhui does not discuss gradual practice very much, it is unclear what position it has in his thought.BR Mazu (709-788) maintains that the mind of sentient beings is in itself buddha (ji xin shi fo 卽心是佛), and it only remains that one suddenly awaken to this truth. From the position that the mind is already buddha, all practice in order to become a buddha is rejected and after sudden awakening one only has to as it is (ren yun 任運).BR Zongmi (780-841) criticized Mazu’s sudden awakening as not complete enlightenment and “the sickness of resigning oneself to reality as it is” (ren bing 任病). While on the one hand Zongmi gave a high appraisal to Shenhui, according to him gradual practice would be necessary as afflictions would be left after sudden enlightenment.BR While Yongshou accepted Zongmi’s “sudden enlightenment with gradual practice” with weak aptitude for cultivating the dharma, but the circumstances for those with the most excellent faculties for cultivating the dharma (shang shang gen 上上根) are attaining enlightenment and completing practice suddenly where he viewed Mazu’s effortlessly resigning oneself to reality (任運) as the actions of a buddha. In short, Yanshou’s theory of attainment and practice led people from the traditional Buddhist view where “it is impossible to become a buddha in this life” to the new view where “one can become a buddha in this life.”

Realization Theory for LPV State-Space Representations With Affine Dependence

We present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA). We show that minimality of LPV-SSAs is equivalent to observability and span-reachability rank conditions, and that minimal LPV-SSAs of the same input-output map are isomorphic. We present necessary and sufficient conditions for existence of an LPV-SSA in terms of the rank of a Hankel-matrix and a Ho-Kalman-like realization algorithm.

Predicting the performance of a floating wind energy converter in a realistic sea

In this paper, the performances of a floating wind energy converter (the National Renewable Energy Laboratory 5 MW wind turbine installed on the ITI energy barge) in a realistic, multi-directional random sea are rigorously investigated. The wind loads acting on the floating wind energy converter are also fully considered in the numerical simulation process. Meanwhile, in order to improve the simulation efficiency, a new state space model (the FDI-SS model) is utilized to approximate the convolution integral term when solving the motion equation of the floating wind energy converter. For comparison purpose, the simulation results when the convolution integral term in the motion equation is approximated by a commonly used state space model based on the time domain (TD) realization theory are also included. The simulation results in this paper are systematically analyzed and compared, and the accuracy and efficiency of the new FDI-SS model are verified. Moreover, the simulation results in this article demonstrate the great necessity of using a realistic, multi-directional random sea state when calculating the generated electrical power and the dynamic responses of a floating wind energy converter.

Fractal Dimension Change Point Model for Hydrothermal Alteration Anomalies in Silk Road Economic Belt, the Beishan Area, Gansu, China

Remote sensing plays an important role in mineral exploration of “One Belt One Road” plan. One of its applications is extracting and locating hydrothermal alteration zones that are related to mines. At present, the extracting method for alteration anomalies from principal component image mainly relies on the data's normal distribution, without considering the nonlinear characteristics of geological anomaly. In this study, a Fractal Dimension Change Point Model (FDCPM), calculated by the self-similarity and mutability of alteration anomalies, is employed to quantitatively acquire the critical threshold of alteration anomalies. The realization theory and access mechanism of the model are elaborated by an experiment with ASTER data in Beishan mineralization belt, also the results are compared with traditional method (De-Interfered Anomalous Principal Component Thresholding Technique, DIAPCTT). The results show that the findings produced by FDCPM are agree with well with a mounting body of evidence from different perspectives, with the extracting accuracy over 80%, indicating that FDCPM is an effective extracting method for remote sensing alteration anomalies, and could be used as an useful tool for mineral exploration in similar areas in Silk Road Economic Belt.

The power of prospection: mental contrasting and behavior change

AbstractPeople often immerse themselves in dreams and fantasies about a desired future. Though such future fantasies are pleasant, they do not necessarily lead to the effort required to attain the desired future. Indeed, the more positively people fantasize about their desired futures, the less effort they invest and the less successful they are in realizing these futures. However, when fantasies about a desired future are complemented with a clear sense of reality, people find the direction and energy needed to realize their fantasies. We review Fantasy Realization Theory, which explicates these ideas and led to the discovery of mental contrasting future and reality, a self‐regulation strategy of behavior change. Mental contrasting helps people figure out what they really want and wisely select, commit to, and actively pursue prioritized wishes while constructively dealing with setbacks. It helps them live a rewarding life through work, play, health, and relationships.

Modal identification of arch dams using balanced stochastic subspace identification

Dynamic characteristics extracted from ambient and forced vibration tests are always associated with some level of uncertainties because of unknown nature of applied forces, existence of ambient noises as well as measurement errors. Stochastic Subspace Methods are among the most accurate and consistent methods within the domain of operational modal analysis. In this research, a new technique for Operational Modal Analysis is proposed using Stochastic Realization Theory and Canonical Correlation Analysis, which in comparison with previous methodologies, identification process are directly performed in the prediction space by extracting orthonormal vectors of data space. Considering its optimized nature, the proposed method is expected to have superior accuracy in terms of elimination of unstable poles as well as low time consumption analysis. To indicate the efficiency and accuracy of the proposed algorithm, it is applied to reanalyze the results of the forced vibration tests performed on the Shahid-Rajaee arch dam in northern Iran. These tests were conducted via steady-state sinusoidal stimulation method. More accurate natural frequencies are obtained compared to those of previously reported results, besides the fact that the first three modes of the structure were identified by the new approach, while they were not observed via the previous one. In order to examine the capabilities of the proposed method for processing of ambient vibration records, the dynamic characteristics of the Pacoima dam was identified using the recorded responses during 2001 earthquake in San Fernando, California. The results indicated good accuracy in the obtained frequencies and damping ratios compared to those obtained via data driven subspace method. Time consumption of identification process were reduced significantly (up to 50%) for both case studies indicating a faster convergence rate provided by the proposed method.

Application of Balanced Realizations for Model-Order Reduction of Dynamic Power System Equivalents

This paper reviews and applies the balanced realization (BR) theory to obtain reduced-order models from dynamic system equivalents of electric power networks. BR allows obtaining reduced-order models via a process in which the original asymptotic stable system is internally balanced. The balanced system is truncated according to its dominant dynamics. It can be proven that the truncated, that is, reduced-order, system is also stable. This paper applies the BR method to dynamic system equivalents represented as frequency-dependent network equivalents (FDNEs). Furthermore, it shows that an assumed reduced-order FDNE can be further reduced via the BR process. Four case studies, involving one transmission network and three wind power plants, are presented.

A brief review of E theory

I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of nonlinear realisations and Kac–Moody algebras, I explain how to construct the nonlinear realisation based on the Kac–Moody algebra [Formula: see text] and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space–time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space–time, lead to precisely the equations of motion of 11-dimensional supergravity theory. By taking different group decompositions of [Formula: see text] we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the nonlinear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the [Formula: see text] conjecture given many years ago.

A Study of the Theory of Mind-nature & the Theory of Cultivation and Realization of Northern School

본 논문은 북종선의 심성론과 수증론을 논하고 있다. 먼저 심성론은 신수의 저작인 『관심론』과 신수의 저작으로 인정 되는 『대승무생방편문』을 중심으로 논한다. 신수는 마음의 작용을 염심과 정심의 2종류로 나누고 정심은 진여의 마음이며 염심은 무명의 마음이라고 하여 염정이심론을 설하고 있다. 그는 자기 마음이 체이고 체의 작용에는 정심과 염심이 있다고 본다. 심체가 청정함을 자각하고 지혜로써 염심을 제거하여 해탈을 얻을 수 있다고 논하고 있다. 다음은 수증론을 논한다. 남종의 하택신회는 북종선법을 온전히 점수라고 비판하고 있으나 남종선 못지않게 돈오적인 부분이 있다는 사실을 『대승무생방편문』 등 돈황출토의 전적을 의지하여 밝히는데 중점을 두고 있다. 특히 『대승무생방편문』은 5종의 대승경전을 의지하여 체[선정]와 용[지혜]이 상즉하고 불이함을 논하여 돈오선법을 설하고 있다.

Realizations of abstract regular polytopes from a representation theoretic view

Peter McMullen has developed a theory of realizations of abstract regular polytopes, and has shown that the realizations up to congruence form a pointed convex cone which is the direct product of certain irreducible subcones. We show that each of these subcones is isomorphic to a set of positive semi-definite hermitian matrices of dimension $m$ over either the real numbers, the complex numbers or the quaternions. In particular, we correct an erroneous computation of the dimension of these subcones by McMullen and Monson. We show that the automorphism group of an abstract regular polytope can have an irreducible character $\chi$ with $\chi\neq \overline{\chi}$ and with arbitrarily large essential Wythoff dimension. This gives counterexamples to a result of Herman and Monson, which was derived from the erroneous computation mentioned before. We also discuss a relation between cosine vectors of certain pure realizations and the spherical functions appearing in the theory of Gelfand pairs.

Free loci of matrix pencils and domains of noncommutative rational functions

Consider a monic linear pencil L(x)=I-A_1x_1-\cdots-A_gx_g whose coefficients A_j are d\times d matrices. It is naturally evaluated at g -tuples of matrices X using the Kronecker tensor product, which gives rise to its free locus \mathcal (L)=\{X:\det L(X)=0\} . In this article it is shown that the algebras \mathcal A and \widetilde{\mathcal A} generated by the coefficients of two linear pencils L and \widetilde{L} , respectively, with equal free loci are isomorphic up to radical, i.e., \mathcal A/\mathrm {rad}\mathcal A\cong \widetilde{\mathcal A}/\mathrm {rad}\widetilde{\mathcal A} . Furthermore, \mathcal (L)\subseteq \mathcal(\widetilde{L}) if and only if the natural map sending the coefficients of \widetilde{L} to the coefficients of L induces a homomorphism \widetilde{\mathcal A}/\mathrm {rad}\widetilde{\mathcal A}\to \mathcal A/\mathrm {rad}\mathcal A . Since linear pencils are a key ingredient in studying noncommutative rational functions via realization theory, the above results lead to a characterization of all noncommutative rational functions with a given domain. Finally, a quantum version of Kippenhahn's conjecture on linear pencils is formulated and proved: if hermitian matrices A_1,\dots,A_g generate M_d(\mathbb C) as an algebra, then there exist hermitian matrices X_1,\dots,X_g such that \sum_iA_i\otimes X_i has a simple eigenvalue.