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In this paper, we address the design of multi-user multiple-input single-output (MU-MISO) precoders for indoor visible light communication (VLC) systems. The goal is to minimize the transmitted optical power per light emitting diode (LED) under imperfect channel state information (CSI) at the transmitter side. Robust precoders for imperfect CSI available in the literature include noisy and outdated channel estimation cases. However, to the best of our knowledge, no work has considered adding robustness against channel quantization. In this paper, we fill this gap by addressing the case of imperfect CSI due to the quantization of VLC channels. We model the quantization errors in the CSI through polyhedric uncertainty regions. For polyhedric uncertainty regions and positive real channels, as is the case of VLC channels, we show that the robust precoder against channel quantization errors that minimizes the transmitted optical power while guaranteeing a target signal to noise plus interference ratio (SNIR) per user is the solution of a second order cone programming (SOCP) problem. Finally, we evaluate its performance under different quantization levels through numerical simulations. [ABSTRACT FROM AUTHOR]

Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly supported, it is smaller than any of its dual quantizations while the dominated original measure is greater than any of its stationary (and therefore any of its quadratic optimal) primal quantization. Moreover, the quantization errors then correspond to martingale couplings between each original probability measure and its quantization. This permits to prove that any martingale coupling between the original probability measures can be approximated by a martingale coupling between their quantizations in Wassertein distance with a rate given by the quantization errors but also in the much finer adapted Wassertein distance. As a consequence, while the stability of (Weak) Martingale Optimal Transport problems with respect to the marginal distributions has only been established in dimension 1 so far, their value function computed numerically for the quantized marginals converges in any dimension to the value for the original probability measures as the numbers of quantization points go to ∞. [ABSTRACT FROM AUTHOR]

In this paper, a new high-performance lossy compression technique based on DCT is proposed. The image is partitioned into blocks of a size of NxN (where N is multiple of 2), each block is categorized whether it is high frequency (uncorrelated block) or low frequency (correlated block) according to its spatial details, this done by calculating the energy of block by taking the absolute sum of differential pulse code modulation (DPCM) differences between pixels to determine the level of correlation by using a specified threshold value. The image blocks will be scanned and converted into 1D vectors using horizontal scan order. Then, 1D-DCT is applied for each vector to produce transform coefficients. The transformed coefficients will be quantized with different quantization values according to the energy of the block. Finally, an enhanced entropy encoder technique is applied to store the quantized coefficients. To test the level of compression, the quantitative measures of the peak signal-to-noise ratio (PSNR) and compression ratio (CR) is used to ensure the effectiveness of the suggested system. The PSNR values of the reconstructed images are taken between the intermediate range from 28dB to 40dB, the best attained compression gain on standard Lena image has been increased to be around (96.60 %). Also, the results were compared to those of the standard JPEG system utilized in the “ACDSee Ultimate 2020” software to evaluate the performance of the proposed system. [ABSTRACT FROM AUTHOR]

This paper investigates the output feedback $ {\mathcal {H}_{\infty }}$ control problem for a class of continuous-time nonlinear systems with both output and input quantization. The nonlinear plant is represented by a Takagi–Sugeno fuzzy model. The measurement output and the control input signals will be quantized by dynamic quantizers. The attention of this paper is focused on the design of the output feedback controller and quantizers such that the fuzzy closed-loop system is asymptotically stable and also achieves a prescribed $ {\mathcal {H}_{\infty }}$ noise attenuation level with respect to the effect of quantization. In the presence of quantization, two novel $ {\mathcal {H}_{\infty }}$ performance analysis criteria are presented for the considered fuzzy systems based on the descriptor representation approach. Then, sufficient conditions for the existence of the feedback $ {\mathcal {H}_{\infty }}$ controller gain and the quantizers’ dynamic parameters are expressed in terms of linear matrix inequalities. An adjusting scheme on quantizers’ parameters is proposed for the fuzzy system. Simulation examples are provided to show the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

Haralick texture features are common texture descriptors in image analysis. To compute the Haralick features, the image gray-levels are reduced, a process called quantization. The resulting features depend heavily on the quantization step, so Haralick features are not reproducible unless the same quantization is performed. The aim of this work was to develop Haralick features that are invariant to the number of quantization gray-levels. By redefining the gray-level co-occurrence matrix (GLCM) as a discretized probability density function, it becomes asymptotically invariant to the quantization. The invariant and original features were compared using logistic regression classification to separate two classes based on the texture features. Classifiers trained on the invariant features showed higher accuracies, and had similar performance when training and test images had very different quantizations. In conclusion, using the invariant Haralick features, an image pattern will give the same texture feature values independent of image quantization. [ABSTRACT FROM AUTHOR]

We investigate the upper and lower bounds on the quantization distortions for independent and identically distributed continuous sources in the finite block-length regime. We derive a lower bound on the quantization distortion, as well as an upper bound on the quantization distortion based on random quantization codebooks. Moreover, we apply the obtained bounds to the continuous Gaussian source. For the Gaussian source, we propose a computationally tractable method to numerically compute the upper and lower bounds, for both bounded and unbounded quantization codebooks. Numerical results show that the gap between the upper and lower bounds is small for the block length of several hundreds, and the upper and lower bounds are tighter than those proposed in the existing works. [ABSTRACT FROM AUTHOR]

Sampling above the Nyquist rate is at the heart of sigma–delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback filter at the encoder, in conjunction with a low-pass filter at the decoder. The goal of this paper is to characterize the optimal trade-off between the per-sample quantization rate and the resulting mean-squared-error distortion under various restrictions on the feedback filter. To this end, we establish a duality relation between the performance of sigma–delta modulation and the performance of differential pulse-code modulation when applied to (discrete-time) band-limited inputs. As the optimal trade-off for the latter scheme is fully understood, the full characterization for sigma–delta modulation, as well as the optimal feedback filters, immediately follows. [ABSTRACT FROM AUTHOR]

Highlights • One-bit quantizer design is investigated for weak-signal detection in GGN and lossy binary communication channel. • It is proved that the optimal threshold can be efficiently calculated. • The optimal threshold is proved zero when the shape coefficient is less than 1 for binary symmetric channel and 2 for binary asymmetric channel. • Numerical simulations are conducted to evaluate the performance of the proposed method. Abstract In this paper, quantizer design for weak-signal detection under arbitrary binary channel in generalized Gaussian noise is studied. Since the performances of the generalized likelihood ratio test (GLRT) and Rao test are asymptotically characterized by the noncentral chi-squared probability density function (PDF), the threshold design problem can be formulated as a noncentrality parameter maximization problem. The theoretical property of the noncentrality parameter with respect to the threshold is investigated, and the optimal threshold is shown to be found in polynomial time with appropriate numerical algorithm and proper initializations. In certain cases, the optimal threshold is proved to be zero. Finally, numerical experiments are conducted to substantiate the theoretical analysis. [ABSTRACT FROM AUTHOR]

Highlights • A novel unified formulation for Hashing learning is put forward that overall performance can be optimized. • We give a general framework for OPH such that it can be incorporated with different Hashing methods. • For the orthogonality-constrained problem of OPH, we put forward an effective learning algorithm. • We carry out extensive experiments for ANN search and CBDR. Results validate the effectiveness of OPH. Abstract Hashing, which seeks for binary codes to represent data, has drawn increasing research interest in recent years. Most existing Hashing methods follow a projection-quantization framework which first projects high-dimensional data into compact low-dimensional space and then quantifies the compact data into binary codes. The projection step plays a key role in Hashing and academia has paid considerable attention to it. Previous works have proven that a good projection should simultaneously 1) preserve important information in original data, and 2) lead to compact representation with low quantization error. However, they adopted a greedy two-step strategy to consider the above two properties separately. In this paper, we empirically show that such a two-step strategy will result in a sub-optimal solution because the optimal solution to 1) limits the feasible set for the solution to 2). We put forward a novel projection learning method for Hashing, dubbed Optimized Projection (OPH). Specifically, we propose to learn the projection in a unified formulation which can find a good trade-off such that the overall performance can be optimized. A general framework is given such that OPH can be incorporated with different Hashing methods for different situations. We also introduce an effective gradient-based optimization algorithm for OPH. We carried out extensive experiments for Hashing-based Approximate Nearest Neighbor search and Content-based Data Retrieval on six benchmark datasets. The results show that OPH significantly outperforms several state-of-the-art related Hashing methods. [ABSTRACT FROM AUTHOR]

In this paper, the target tracking problem is investigated for a class of wireless localization systems with degraded measurements and quantization effects. The measurement degradations induced by unreliable channels are characterized by a random parameter matrix, and the quantization effects are modeled by sector-bounded uncertainties. A recursive filtering algorithm is proposed in order to track the plant states as accurately as possible. An upper bound on the filtering error covariance is first derived and such an upper bound is then minimized by properly designing the filter gain at each sampling instant. The desired filter parameters are obtained by solving two sets of Riccati-like difference equations that are in a recursive form suitable for online application. Finally, a simulation experiment is carried out for the scenario of personnel localization/tracking problems in a mine industrial site and the effectiveness of the proposed filter method is demonstrated. [ABSTRACT FROM AUTHOR]

This work studies the stochastic stability of Markovian jump linear systems in a communication network-based environment. By modeling quantization density as well as the sensor-to-controller and controller-to-actuator delays as Markov chains, the closed-loop networked control systems are expressed as switched linear systems. The necessary and sufficient conditions of stochastic stability are derived. By solving a set of linear matrix inequalities with matrix inversion constraints, this work presents a three-mode-dependent state-feedback controller. Its control performance is illustrated via a numerical example. [ABSTRACT FROM AUTHOR]

Abstract The classical time of arrival in the interacting case is quantized by way of quantizing its expansion about the free time of arrival. The quantization is formulated in coordinate representation which represents ordering rules in terms of two variable polynomial functions. This leads to representations of the quantized time of arrival operators as integral operators whose kernels are determined by the chosen ordering rule. The formulation lends itself to generalization which allows construction of time of arrival operators that cannot be obtained by direct quantization using particular ordering rules. Weyl, symmetric and Born–Jordan quantizations are specifically studied. The dynamics of the eigenfunctions of the different time of arrival operators are investigated. The eigenfunctions exhibit unitary arrival at the intended arrival point at their respective eigenvalues. [ABSTRACT FROM AUTHOR]

Observables have a dual nature in both classical and quantum kinematics: they are at the same time quantities, allowing to separate states by means of their numerical values, and generators of transformations, establishing relations between different states. In this work, we show how this twofold role of observables constitutes a key feature in the conceptual analysis of classical and quantum kinematics, shedding a new light on the distinguishing feature of the quantum at the kinematical level. We first take a look at the algebraic description of both classical and quantum observables in terms of Jordan-Lie algebras and show how the two algebraic structures are the precise mathematical manifestation of the twofold role of observables. Then, we turn to the geometric reformulation of quantum kinematics in terms of Kähler manifolds. A key achievement of this reformulation is to show that the twofold role of observables is the constitutive ingredient defining what an observable is. Moreover, it points to the fact that, from the restricted point of view of the transformational role of observables, classical and quantum kinematics behave in exactly the same way. Finally, we present Landsman’s general framework of Poisson spaces with transition probability, which highlights with unmatched clarity that the crucial difference between the two kinematics lies in the way the two roles of observables are related to each other. [ABSTRACT FROM AUTHOR]

We have investigated the proton radioactivity half-lives of 45 proton emitters within the framework of the Wentzel–Kramers–Brillouin (WKB) method by considering the Bohr–Sommerfeld quantization condition. The orientation angle dependent Woods–Saxon, Coulomb, and spin–orbit potentials and centrifugal potential have been used in calculations. We observed that using the orientation angle dependent formalism decreases the values of calculated half-lives. [ABSTRACT FROM AUTHOR]

It is revealed that there is a link between the quantization approach employed and the dimension of the vector parameter which can be accurately estimated by a quantized estimation system. A critical quantity called inestimable dimension for quantized data (IDQD) is introduced, which does not depend on the quantization regions and the statistical models of the observations but instead depends only on the number of sensors and on the precision of the vector quantizers employed by the system. It is shown that the IDQD describes a quantization-induced fundamental limitation on the estimation capabilities of the system. To be specific, if the dimension of the desired vector parameter is larger than the IDQD of the quantized estimation system, then the Fisher information matrix for estimating the desired vector parameter is singular, and, moreover, there exist infinitely many nonidentifiable vector parameter points in the vector parameter space. Furthermore, it is shown that under some common assumptions on the statistical models of the observations and the quantization system, a smaller IDQD can be obtained, which can specify an even more limiting quantization induced fundamental limitation on the estimation capabilities of the system. [ABSTRACT FROM AUTHOR]

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of quantized H∞ filtering for multi-output discrete-time systems over independent identically distributed (i.i.d.) fading channels and Markov fading channels, respectively. The measurement outputs are quantized by a logarithmic quantizer, and then transmitted to the filter over fading channels. For the i.i.d. fading channels, the stochastic multiplicative noise form is used to model the unreliable communication environment. For the Markov fading channels, a set of Markov channel state processes is introduced to model time-varying fading channels, which characterizes various configurations of the physical communication environment and/or different channel fading amplitudes. The sufficient condition for stochastic stability with a prescribed H∞ performance is obtained by using a Lyapunov method and matrix decoupling technique. The corresponding filter design casts into a convex optimization problem. Finally, simulation results are provided to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

We consider the problem of recovering a high-dimensional structured signal from independent Gaussian linear measurements each of which is quantized to $b$ bits. The focus is on a specific method of signal recovery that extends a procedure originally proposed by Plan and Vershynin for one-bit quantization to a multi-bit setting. At the heart of this paper is a characterization of the optimal trade-off between the number of measurements m$ and the bit depth per measurement b$ given a total budget of B = m \cdot b -error in estimating the signal. It turns out that the choice b = 1$ is optimal for estimating the unit vector (direction) corresponding to the signal for any level of additive Gaussian noise before quantization as well as for a specific model of adversarial noise, whereas in a noiseless setting the choice b = 2$ is optimal for estimating the direction and the norm (scale) of the signal. Moreover, Lloyd–Max quantization is shown to be an optimal quantization scheme with respect to -estimation error. Our analysis is corroborated by the numerical experiments showing nearly perfect agreement with our theoretical predictions. This paper is complemented by an empirical comparison to alternative methods of signal recovery. The results of that comparison point to a regime change depending on the noise level: in a low-noise setting, the approach under study falls short of more sophisticated competitors while being competitive in moderate- and high-noise settings. [ABSTRACT FROM PUBLISHER]

We prove a criterion for a "magnetic" Weyl operator to be trace-class by extending a method developed by Cordes, Kato and Arsu. Using the Calderon-Vaillancourt type Theorem for magnetic Weyl operators and an interpolation argument we also give a criterion for a "magnetic" Weyl operator to be in a Schatten-von Neumann class with 1 < p < ∞. [ABSTRACT FROM AUTHOR]

Abstract: A fundamental problem regarding the Dirac quantization of a free particle on an N − 1 ( N ≥ 2) curved hypersurface embedded in N flat space is the impossibility to give the same form of the curvature‐induced quantum potential, the geometric potential as commonly called, as that given by the Schrödinger equation method where the particle moves in a region confined by a thin‐layer sandwiching the surface. This problem is resolved by means of a previously proposed scheme that hypothesizes a simultaneous quantization of positions, momenta, and Hamiltonian, among which the operator‐ordering‐free section is identified and is then found sufficient to lead to the expected form of geometric potential. [ABSTRACT FROM AUTHOR]

This contribution provides a validation to the earlier proposal of hadron mass quantization in the units of 70 MeV mass quanta. The linear experimental Hadronic Regge Trajectories constructed from the recent 2014 Particle Data Group Listings serve as a prominent tool in solving the Hadronic mass spectrum mystery. Application of the Barut's solution to relativistic Balmer formula helps in deriving quark masses for mesons and baryons. This astonishingly produces the quark masses very close the 70 MeV mass quanta, which turns out to be the mass quantum for buliding hadrons. The slight deviation from this mass quantization is also evidently explained. [ABSTRACT FROM AUTHOR]

We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed. [ABSTRACT FROM AUTHOR]

Nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest. Learning to hash is one of the major solutions to this problem and has been widely studied recently. In this paper, we present a comprehensive survey of the learning to hash algorithms, categorize them according to the manners of preserving the similarities into: pairwise similarity preserving, multiwise similarity preserving, implicit similarity preserving, as well as quantization, and discuss their relations. We separate quantization from pairwise similarity preserving as the objective function is very different though quantization, as we show, can be derived from preserving the pairwise similarities. In addition, we present the evaluation protocols, and the general performance analysis, and point out that the quantization algorithms perform superiorly in terms of search accuracy, search time cost, and space cost. Finally, we introduce a few emerging topics. [ABSTRACT FROM PUBLISHER]

These notes are an expanded version of a mini-course given at the Poisson 2016 conference in Geneva. Starting from classical integrable systems in the sense of Liouville, we explore the notion of non-degenerate singularities and expose recent research in connection with semi-toric systems. The quantum and semiclassical counterparts are also presented, in the viewpoint of the inverse question: from the quantum mechanical spectrum, can one recover the classical system? [ABSTRACT FROM AUTHOR]

The Duflo map is a valuable tool for operator ordering in contexts in which the Kirillov–Kostant–Souriau bracket and its quantization play a role. It has beautiful properties on the subspace of the symmetric algebra over a Lie algebra consisting of elements invariant under the adjoint action. In the present work, we focus on its action beyond this subspace: We calculate the image of the exponential map, to obtain a certain deformation of SU(2), and we discuss and compare modifications of its action on non-invariant elements. Also, an application to the calculation of Chern–Simons theory expectation values is discussed. [ABSTRACT FROM AUTHOR]

We propose a quantization of the Kadomtsev-Petviashvili equation on a cylinder equivalent to an infinite system of nonrelativistic one-dimensional bosons with the masses m = 1, 2,.... The Hamiltonian is Galilei-invariant and includes the split and merge terms $$\Psi _{{m_1}}^\dag \Psi _{{m_2}}^\dag {\Psi _{{m_1} + {m_2}}}$$ and $$\Psi _{{m_1} + {m_2}}^\dag {\Psi _{{m_1}}}{\Psi _{{m_2}}}$$ for all combinations of particles with masses m , m , and m + m for a special choice of coupling constants. We construct the Bethe eigenfunctions for the model and verify the consistency of the coordinate Bethe ansatz and hence the quantum integrability of the model up to the mass M=8 sector. [ABSTRACT FROM AUTHOR]

Kerr-Newman black hole entropy in phase space is systematically investigated by constructing the six-dimensional phase space within gauge transformation. Then considering the corresponding mechanical quantities as operators and making them quantized, entropy spectrum of Kerr-Newman black hole is obtained. Our results demonstrate that Kerr-Newman black hole has an equal-interval entropy spectrum, which coincides with the view of Bekenstein. It also shows that Kerr-Newman black hole entropy is not zero, but exists a ground-state entropy, which still retains some basic information. [ABSTRACT FROM AUTHOR]

The symplectic analysis, initiated by Faddeev and Jackiw, is applied to the first-order (Palatini) form of the Einstein-Hilbert action in 1 + 1 dimensions. The constraints that arise are shown to result in the same gauge transformations that follow from the first-class constraints occurring when the Dirac constraint formalism is applied to this action. Problems associated with gauge fixing are discussed. [ABSTRACT FROM AUTHOR]

Dissipation in Quantum Mechanics took some time to become a robust field of investigation after the birth of the field. The main issue hindering developments in the field is that the Quantization process was always tightly connected to the Hamiltonian formulation of Classical Mechanics. In this paper we present a quantization process that does not depend upon the Hamiltonian formulation of Classical Mechanics (although still departs from Classical Mechanics) and thus overcome the problem of finding, from first principles, a completely general Schrödinger equation encompassing dissipation. This generalized process of quantization is shown to be nothing but an extension of a more restricted version that is shown to produce the Schrödinger equation for Hamiltonian systems from first principles (even for Hamiltonian velocity dependent potential). [ABSTRACT FROM AUTHOR]

This paper is concerned with the finite-horizon quantized H ∞ filter design problem for a class of time-varying systems with quantization effects and event-triggered measurement transmissions. A componentwise event-triggered transmission strategy is put forward to reduce the unnecessary communication burden for the purpose of energy efficiency. The transmitted measurements triggered according to prespecified events are quantized by a logarithmic quantizer. Special attention is paid to the design of the filter such that a prescribed H ∞ performance can be guaranteed over a given finite horizon in the presence of nonlinearities, quantization effects and event-triggered transmissions. Two sets of Riccati difference equations are introduced to ensure the H ∞ estimation performance of the designed filter. The filter design algorithm is recursive and thus suitable for online computation. A simulation example is illustrated to show the effectiveness of the proposed algorithm applied to the fault detection problem. [ABSTRACT FROM AUTHOR]

We describe the implementation of new commercial pulse-bias electronics that have enabled an improvement in the generation of quantum-accurate waveforms both with and without low-frequency compensation biases. We have used these electronics to apply a multilevel pulse bias to the Josephson arbitrary waveform synthesizer and have generated, for the first time, a quantum-accurate bipolar sinusoidal waveform without the use of a low-frequency compensation bias current. This uncompensated 1 kHz waveform was synthesized with an rms amplitude of 325 mV and maintained its quantum accuracy over a 1.5 mA operating current range. The same technique and equipment was also used to synthesize a quantum-accurate 1 MHz sinusoid with a 1.2 mA operating margin. In addition, we have synthesized a compensated 1 kHz sinusoid with an rms amplitude of 1 V and a 2.7 mA operating margin. [ABSTRACT FROM PUBLISHER]

This paper focuses on a distributed optimization problem associated with a time-varying multi-agent network with quantized communication, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on subgradient methods, we propose a distributed algorithm to solve this problem under the additional constraint that agents can only communicate quantized information through the network. We consider two kinds of quantizers and analyze the quantization effects on the convergence of the algorithm. Furthermore, we provide explicit error bounds on the convergence rates that highlight the dependence on the quantization levels. Finally, some simulation results on a l1-regression problem are presented to demonstrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A gauge fixing condition is presented here for non-Abelian gauge theory on the manifold R ⊗ S 1 ⊗ S 1 ⊗ S 1 . It is proved that the new gauge fixing condition is continuous and free from the Gribov ambiguity. While perturbative calculations based on the new gauge condition behave like those based on the axial gauge in ultraviolet region, infrared behaviours of the perturbative series under the new gauge fixing condition are quite nontrivial. The new gauge condition, which reads n ⋅ ∂ n ⋅ A = 0 , may not satisfy the boundary condition A μ ( ∞ ) = 0 as required by conventional perturbative calculations for gauge theories on the manifold S 4 . However, such contradiction is not harmful for the theory considered here. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of fault detection (FD) for discrete-time delayed fuzzy networked control systems with quantization and packet dropouts. Different from existing results for FD, the proposed ones are toward closed-loop design problem, that is, the controller gain, and the fault detection filter (FDF) gains are designed simultaneously. The missing phenomenon is assumed to occur, in the communication links for quantizer-to-FDF and controller-to-physical plant, where the missing probability of packet dropouts is governed by an individual random binary distribution, while the quantization errors are treated as sector-bound uncertainties. The discrete-time fuzzy networked system is first transformed into the form of interconnection of two subsystems by applying an input–output method and a two-term approximation approach, which is employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy fault detection filter (FFDF) such that, for all data missing conditions, and measurement quantization, the residual system is stochastically stable with a guaranteed H ∞ performance. Sufficient conditions are first established via introducing some slack matrices to facilitate the FDF design procedure by eliminating the coupling between the Lyapunov matrices and the system matrices. Numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method. [ABSTRACT FROM AUTHOR]

This review considers methods and algorithms for fast estimation of distance/similarity measures between initial data from vector representations with binary or integer-valued components obtained from initial data that are mainly high-dimensional vectors with different distance measures (angular, Euclidean, and others) and similarity measures (cosine, inner product, and others). Methods without learning that mainly use random projections with the subsequent quantization and also sampling methods are discussed. The obtained vectors can be applied in similarity search, machine learning, and other algorithms. [ABSTRACT FROM AUTHOR]

We investigate transport through graphene nanoribbons in the presence of disorder scattering. We show that size quantization patterns are only present when [ABSTRACT FROM AUTHOR]

The central extension of mapping class groups of punctured surfaces of finite type that arises in Chekhov–Fock quantization is 12 times of the Meyer class plus the Euler classes of the punctures, which agree with the one arising in the Kashaev quantization. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problems of stabilization of networked control systems with quantization and actuator saturation via delta operator approach. The definition of the domain of attraction for delta operator systems is introduced to analyze the stochastic stability of the closed-loop networked control systems. The quantizer is a uniform one with arbitrary quantization regions, and the packet dropout process is modeled as a Bernoulli process. On the basis of the zoom strategy and Lyapunov theory in delta domain, sufficient conditions are given for the closed-loop delta operator systems to be mean square stable, and the feedback controllers are designed to ensure the stability of networked control systems. A single link direct joint driven manipulator model is presented to show the effectiveness of the main results. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We extend the quantization à la Faddeev–Jackiw for non-autonomous singular systems. This leads to a generalization of the Schrödinger equation for those systems. The method is exemplified by the quantization of the damped harmonic oscillator and the relativistic particle in an external electromagnetic field. [ABSTRACT FROM AUTHOR]

For a unital completely positive map $${\Phi}$$ ('quantum channel') governing the time propagation of a quantum system, the Stinespring representation gives an enlarged system evolving unitarily. We argue that the Stinespring representations of each power $${\Phi^m}$$ of the single map together encode the structure of the original quantum channel and provide an interaction-dependent model for the bath. The same bath model gives a 'classical limit' at infinite time $${m\to\infty}$$ in the form of a noncommutative 'manifold' determined by the channel. In this way, a simplified analysis of the system can be performed by making the large- m approximation. These constructions are based on a noncommutative generalization of Berezin quantization. The latter is shown to involve very fundamental aspects of quantum-information theory, which are thereby put in a completely new light. [ABSTRACT FROM AUTHOR]

Low-power excitation and/or low sensitivity transducers, such as electromagnetic acoustic transducers, piezoelectric paints, air-coupled transducers, and small elements of dense arrays, may produce signals below the noise threshold at the receiver. The information from those noisy signals can be recovered after averaging or pulse compression using binary (1-b) quantization only without experiencing significant losses. Hence, no analog-to-digital converter is required, which reduces the data throughput and makes the electronics faster, more compact, and energy efficient. All these are especially attractive for applications that require arrays with many channels and high sampling rates, where the sampling rate can be as high as the system clock. In this paper, the theory of binary quantization is reviewed, mainly from previous work on wireless sensor networks, and the signal-to-noise ratio (SNR) of the input signals under which binary quantization is of practical interest for ultrasound applications is investigated. The main findings are that in most practical cases binary quantization can be used with small errors when the input SNR is on the order of 8 dB or less. Moreover, the maximum SNR after binary quantization and averaging can be estimated as 10\log 10N-2~\mathrm {dB} , where $N$ is the number of averages. [ABSTRACT FROM PUBLISHER]

In this article we prove that many Hamiltonian systems that cannot be separably quantized in the classical approach of Robertson and Eisenhart can be separably quantized if we extend the class of admissible quantizations through a suitable choice of Riemann space adapted to the Poisson geometry of the system. Actually, in this article we prove that for every quadratic in momenta Stäckel system (defined on 2 n dimensional Poisson manifold) for which Stäckel matrix consists of monomials in position coordinates there exist infinitely many quantizations–parametrized by n arbitrary functions–that turn this system into a quantum separable Stäckel system. [ABSTRACT FROM AUTHOR]

By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al. [ABSTRACT FROM AUTHOR]

The spectroscopy of a weakly isolated horizon has been investigated. We obtain an equally spaced entropy spectrum with its quantum equal to the one given by Bekenstein (Phys Rev D 7:2333, 1973). We demonstrate that the quantization of entropy and area is a generic property of horizons which exists in a wide class of spacetimes admitting weakly isolated horizons. Our method based on the tunneling method also indicates that the entropy quantum of black hole horizons is closely related to Hawking temperature. [ABSTRACT FROM AUTHOR]

In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer's perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary. [ABSTRACT FROM AUTHOR]