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We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian. [ABSTRACT FROM AUTHOR]

We consider the Dirac quantization in the first-class formalism to investigate the hypersphere soliton model (HSM) defined on the S 3 hypersphere. To do this, we construct the first-class Hamiltonian possessing the Weyl ordering correction. In the HSM, we evaluate the baryon physical quantities such as the baryon masses, magnetic moments, axial coupling constant and charge radii, most predicted values of which are in good agreement with the corresponding experimental data. Moreover, shuffling the baryon and transition magnetic moments, we find the model independent sum rules. In the HSM we also evaluate the baryon intrinsic frequencies such as ω N = 0.87 × 10 23 s − 1 and ω Δ = 1.74 × 10 23 s − 1 of the nucleon and delta baryon, respectively, to yield the identity ω Δ = 2 ω N . Next, making use of the Nambu-Goto string action and its extended rotating bosonic string theory, we formulate the stringy photon model to obtain the energy of the string configuration, which consists of the rotational and vibrational energies of the open string. Exploiting this total string energy, we evaluate the photon intrinsic frequency ω γ = 9.00 × 10 23 s − 1 , which is comparable to the corresponding baryon intrinsic frequencies. We also predict the photon size 〈 r 2 〉 1 / 2 (photon) = 0.17 fm , which is approximately 21% of the proton magnetic charge radius. [ABSTRACT FROM AUTHOR]

To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R (t) ) representing another observable. In the language of physics, the information carried by R (t) ≠ R † (t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ (t) . From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ (t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the "kinematical input" operator R (t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a (t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R (t) mimicking the birth of the Universe ("Big Bang") at t = 0 . [ABSTRACT FROM AUTHOR]

The angular momentum of any quantum system should be unambiguously quantized. We show that such a quantization fails for a pure Dirac monopole due to a previously overlooked field angular momentum from the monopole-electric charge system coming from the magnetic field of the Dirac string and the electric field of the charge. Applying the point-splitting method to the monopole-charge system yields a total angular momentum which obeys the standard angular momentum algebra, but which is gauge variant. In contrast it is possible to properly quantize the angular momentum of a topological 't Hooft–Polyakov monopole plus charge. This implies that pure Dirac monopoles are not viable – only 't Hooft–Polyakov monopoles are theoretically consistent with angular momentum quantization and gauge invariance. [ABSTRACT FROM AUTHOR]

We show that the strongly coupled field theory holographically dual to the Gubser-Rocha anti-de-Sitter Einstein-Maxwell-Dilaton theory describes not a single non-trivial AdS2 IR fixed point, but a one-parameter family. It is dual to a local quantum critical phase instead of a quantum critical point. This result follows from a detailed analysis of the possible quantizations of the gravitational theory that is consistent with the thermodynamics of the analytical Gubser-Rocha black hole solution. The analytic Gubser-Rocha black hole is only a 2-parameter subset of all possible solutions, and we construct other members numerically. These new numerical solutions correspond to turning on an additional scalar charge. Moreover, each solution has multiple holographic interpretations depending on the quantization chosen. In one particular quantization involving a multitrace deformation the scalar charge is a marginal operator. In other quantizations where the marginal multitrace operator is turned off, the analytic Gubser-Rocha black hole does not describe a finite temperature conformal fluid. [ABSTRACT FROM AUTHOR]

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]

On the basis of revising the quantum concept and reinterpreting Bohr's hydrogen atom structure model in classical physics, this paper deduces the elliptical orbital energy level formula of electrons in hydrogen like atoms in detail. When the electron transition time is taken as unit time (1 s), the energy level formula is completely consistent with Bohr Sommerfeld's atomic structure Theory. [ABSTRACT FROM AUTHOR]

In this study, two effective approaches are combined which are implemented at the element design level and system design level to simultaneously improve the frequency bandwidth and aperture efficiency of a dual-polarized single-layer reflecting metasurface. At the element design level, a broadband behavior is realized by using the polarization conversion technique (PCT) which is a novel technique to enhance the bandwidth of the element. To this end, an anisotropic metasurface with the I-shaped metal patch is proposed for rotating the polarization of the wave emitted from a point source by 90 ∘ and making a continuous phase shift in a full range of 360 ∘ within 8-18 GHz. Therefore, a completely equiphase aperture is achieved leading to enhancing the metasurface performance such as directivity and aperture efficiency and reducing the sidelobe level compared to reflecting metasurface developed by 1-bit phase quantization technique. At the system design level, the three-frequency phase synthesis (TFPS) method, which is based on determining the best constant reference phase for the aperture, is used and the corresponding constant reference phases are optimized to minimize the phase error in the whole band. The combination of TFPS and PCT enhances the effectiveness of the TFPS method considerably. An 841 element reflecting metasurface with aperture dimensions of 290 cm × 290 cm is designed, simulated, and fabricated in Ku-band to verify the concept. The measurement results show that the 1-dB gain bandwidth before and after combining PCT and TFPS techniques are 17.47% (14.1–16.8 GHz) and 30.3% (14–19 GHz), respectively. In addition, the maximum aperture efficiency of the proposed metasurface is 63.62% which occurs at 14.5 GHz. [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]

The hybrid beamforming can significantly improve the spectral and energy efficiencies of the millimeter‐wave (mmWave) massive multiple input multiple output (MIMO) systems without obvious performance loss. However, the fundamental limitation of existing hybrid beamforming is that they include high‐resolution analog‐to‐digital converters (ADCs) which consume high power. To overcome this fundamental limitation, in this paper, spectrum and energy efficient mmWave massive MIMO transmission scheme is proposed that jointly optimizes the hybrid combiner and the number of ADC bits. Particularly, the hybrid combiner is presented as a combination of three parts: the analog combiner matrix, the quantization matrix, and the digital baseband matrix which is based on the Kalman filter. Unlike most existing works that rely on sumrate optimization to design the hybrid combiner, in this work, the mean square error (MSE) is chosen as the main performance metric to describe the reliability of the system. Simulations results confirm that the proposed Kalman based hybrid combiner exhibits the best performance in terms of spectral and energy efficiencies compared to minimum mean square error (MMSE) and zero forcing (ZF) receivers. [ABSTRACT FROM AUTHOR]

Efficient quantizer design is vital in high‐speed optical receivers. In this paper, the authors propose a three‐level (1.5‐bit) reliability‐based quantizer for low‐complexity soft decoding of low‐density parity‐check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate‐compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability‐based quantizer, and it is shown that the resulting quantizer‐aware LDPC codes significantly outperform other existing codes of similar rates. [ABSTRACT FROM AUTHOR]

The system under study is the Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations t = f (t ~) ) decay probability is defined and thus "observers" which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point a = 0 (where a the radial scale factor) is calculated to be of the order ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation. [ABSTRACT FROM AUTHOR]

Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin symmetries and interactions. Several yes-go and no-go results on higher-spin diffeomorphisms are collected from the mathematical literature in order to propose a generalisation of the algebra of differential operators on which higher-spin diffeomorphisms are well-defined. This work is dedicated to the memory of Christiane Schomblond, who taught several generations of Belgian physicists the formative rigor and delicate beauty of theoretical physics. [ABSTRACT FROM AUTHOR]

We reviewed the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analysed the information contained in the solutions of the Wheeler--DeWitt equation and showed their interpretation in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we reviewed three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold, the best framework is the third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian 3-geometries, which turns out to be isomorphic to a (part of a) 1 + 5 Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given, and the creation of the universes is analysed, including their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe--antiuniverse pairs. [ABSTRACT FROM AUTHOR]

More than 100 years ago, Robert Millikan demonstrated the quantization of the electron using charged, falling droplets, but the statistical analysis on many falling droplets did not allow a direct visualization of the quantization of charge. Instead of letting the droplets fall, we have used optical levitation to create a single droplet version of Millikan's experiment where the effects of a single electron removal can be observed by the naked eye and measured with a ruler. As we added charges to the levitated droplet, we observed that its equilibrium position jumped vertically in quantized steps. The discrete nature of the droplet's jumps is a direct consequence of the single-electron changes in the charge on the droplet, and therefore clearly demonstrates the quantization of charge. The steps were optically magnified onto a wall and filmed. We anticipate that the video of these single electron additions can become a straightforward demonstration of the quantization of charge for a general audience. [ABSTRACT FROM AUTHOR]

The interplay between ferromagnetism and topological properties of electronic band structures leads to a precise quantization of Hall resistance without any external magnetic field. This so-called quantum anomalous Hall effect (QAHE) is born out of topological correlations, and is oblivious of low-sample quality. It was envisioned to lead towards dissipation-less and topologically protected electronics. However, no clear framework of how to design such an electronic device out of it exists. Here we construct an ultra-low power, non-volatile, cryogenic memory architecture leveraging the QAHE phenomenon. Our design promises orders of magnitude lower cell area compared with the state-of-the-art cryogenic memory technologies. We harness the fundamentally quantized Hall resistance levels in moiré graphene heterostructures to store non-volatile binary bits (1, 0). We perform the memory write operation through controlled hysteretic switching between the quantized Hall states, using nano-ampere level currents with opposite polarities. The non-destructive read operation is performed by sensing the polarity of the transverse Hall voltage using a separate pair of terminals. We custom design the memory architecture with a novel sensing mechanism to avoid accidental data corruption, ensure highest memory density and minimize array leakage power. Our design provides a pathway towards realizing topologically protected memory devices. [ABSTRACT FROM AUTHOR]

With the advent of massive MIMO and mmWave, Antenna selection is the new frontier in hybrid beamforming employed in 5G base stations. Tele-operators are reworking on the components while upgrading to 5G where the antenna is a last-mile device. The burden on the physical layer not only demands smart and adaptive antennas but also an intelligent antenna selection mechanism to reduce power consumption and improve system capacity while degrading the hardware cost and complexity. This work focuses on reducing the power consumption and finding the optimal number of RF chains for a given millimeter wave massive MIMO system. At first, we investigate the power scaling method for both perfect Channel State Information (CSI) and imperfect CSI where the power is reduced by 1/Nr and 1/√Nr respectively. We further propose to reduce the power consumption by emphasizing on the subdued resolution of Analog-to-Digital Converters (ADCs) with quantization awareness. The proposed algorithm selects the optimal number of antenna elements based on the resolution of ADCs without compromising on the quality of reception. The performance of the proposed algorithm shows significant improvement when compared with conventional and random antenna selection methods. [ABSTRACT FROM AUTHOR]

The propagation characteristics of solitary wave in a degenerate plasma in the presence of Landau-quantised magnetic field and heavy negative ion are studied. The nature of solitary wave in such plasma under the influence of magnetic quantisation and the concentration of both electrons and negative ions, as well as in the presence of degenerate temperature, are studied with the help of a time-independent analytical scheme of the solution of Zakharov–Kuznetsov equation. The electron density, as well as the magnetic quantisation parameter, has an outstanding effect on the features of solitary wave proliferation in such plasma. Interestingly, for any fixed electron density, the magnetic quantisation parameter has an equal control on the maximum height and dispersive properties of the solitary wave. Toward higher temperatures and higher magnetic fields, the width of the solitary wave decreases. For a lower magnetic field, the maximum amplitude of the solitary wave decreases rapidly at higher values of degenerate temperature and negative ion concentration; however, at a lower value of degenerate temperature, the maximum amplitude increases with increasing negative ion concentration. [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]

We show the procedure for the secondary quantization of the electromagnetic field in an inhomogeneous medium, based on the formalism of the scattering matrix. We demonstrate the electromagnetic field profiles, which are obtained as a result of applying the scattering matrix formalism and prove their orthogonality. Finally, we derive the Hamiltonian of the system. The obtained procedure allows us to use more complete representation of quantum theory in a layered medium to describe various effects in layered structures. [ABSTRACT FROM AUTHOR]

We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from super-symmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless, and divergence-free energy-momentum tensor, which gives rise to a holomorphic quadratic differential. Using it we obtain a Pohozaev type identity and finally we can establish the energy identities along a weakly convergent sequence of fields with uniformly bounded energies. [ABSTRACT FROM AUTHOR]

In this paper, we describe ac and dc quantum Hall effect measurements at temperatures above 1.5 K, which is beyond the commonly used value for high precision measurements of the quantum Hall resistance (QHR). It is shown that GaAs devices with high electron density of about $5\times 10^{11}$ cm2 can be used as reliable dc resistance quantum standards with quantization of $R_{\mathrm {H}}$ (2) value with accuracy within a few parts in 109 even at temperatures up to 4.2 K. The devices have exhibited well-developed quantum Hall plateaus in the ac regime too, again at temperatures up to 4.2 K. The measurement system consists of a self-made cryogenic probe with TO-8 type socket together with coaxial wiring and a digitally assisted bridge suitable for ac quantum Hall effect measurements. The experiments were performed with devices placed in new double-shielded TO-8 holders. Our investigations and the evaluation of the measurement system are dedicated for the future realization of the quantum impedance standard based on ac QHR. [ABSTRACT FROM AUTHOR]

This study investigates the quantised-input FIR (finite impulse response) system identification under quantised and event-triggered output observations. For the binary-valued quantisation, they introduce a so-called either-or communication scheme to save communication resources. Based on the received data and the triggered indicator, an identification algorithm is proposed to estimate the unknown parameter by use of the empirical measure and weighted least squares. The convergence performance is established and the communication rate is derived. For the multi-threshold quantisation, it can be seen as a vector-valued observation in which each component represents a binary-valued output, and the corresponding identification problem is discussed. A numerical example is included to illustrate the main results obtained. [ABSTRACT FROM AUTHOR]

Abstract We explain how stochastic TQFT supersymmetry can be made compatible with space supersymmetry. Taking the case of N = 2 supersymmetric quantum mechanics, (the proof would be the same for the Wess–Zumino model), we determine the kernels that ensure the convergence of the stochastic process toward the standard path integral, under the condition that they are covariant under supersymmetry. They depend on a massive parameter M that can be chosen at will and modifies the course of the stochastic evolution, but the infinite stochastic time limit of the correlation functions is in fact independent on the choice of M. [ABSTRACT FROM AUTHOR]

In this paper, we propose two non-uniform quantization (NUQ) codebook-based hybrid precoding schemes for two main hybrid precoding implementations, i.e., the full-connected structure and the sub-connected structure, to reduce the feedback overhead in millimeter wave single user multiple-input multiple-output systems. Specifically, we firstly group the angles of the arrive/departures (AOAs/AODs) of the scattering paths into several spatial lobes by exploiting the sparseness property of the millimeter wave in the angular domain, which divides the total angular domain into effective spatial lobes’ coverage angles and ineffective coverage angles. Then, we map the quantization bits non-uniformly to different coverage angles and construct NUQ codebooks, where high numbers of quantization bits are employed for the effective coverage angles to quantize AoAs/AoDs and zero quantization bit is employed for ineffective coverage angles. Finally, two low-complexity hybrid analog/digital precoding schemes are proposed, which utilize the NUQ codebooks. Simulation results demonstrate that the proposed two NUQ codebook-based hybrid precoding schemes achieve near-optimal spectral efficiencies and show the superiority in reducing the feedback overhead compared with the uniform quantization codebook-based works. [ABSTRACT FROM AUTHOR]

To address the problem of filter parameter perturbation in nonlinear networked systems, a nonfragile quantized dissipative filter is designed by considering the coexistence of random one-step time delay, multipacket losses, and quantization error. We acquired the sufficient conditions for the existence of filter by choosing appropriate Lyapunov function as well as utilizing linear matrix inequality. Furthermore, we obtained the parameter expressions of the designed filter. The designed filter could meet the performance requirements of stability and dissipativity for the filter error system under the condition of allowed time delays, packet loss probability, and quantization density. The effectiveness of the designed filter is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

Receiver diversity combining methods play a key role in combating the detrimental effects of fading in wireless communication and other applications. A novel diversity combining method is proposed, where a universal, i.e., channel independent, orthogonal dimension-reducing space-time transformation is applied prior to quantization of the signals. The scheme may be considered as the counterpart of Alamouti modulation, and more generally of orthogonal space–time block codes. [ABSTRACT FROM AUTHOR]

Interference alignment (IA) is a promising technique to effectively manage the interference. The realization of IA requires a proliferation of feedback bits. In a general centralized feedback model, the feedback rate of the precoder and the decoder affects the performance of the IA directly. In this paper, to improve the feedback efficiency of the precoder and the decoder, a strategy that can adaptively allocate the feedback bits of the precoder and the decoder is proposed. We consider the effect of link loss on the throughput loss caused by the quantization error of the precoder and decoder. An upper bound of leaked interference as a function of the link loss and the feedback bits of the precoders and the decoders is derived. The feasibility conditions for dynamically allocating the feedback bits of the precoder and the decoder are analyzed. It is proven that the properties of general asymmetric interference network can satisfy the feasibility conditions for dynamic feedback scheme. According to the simulation results, our proposed scheme achieves higher throughput compared with the conventional schemes in the asymmetric interference network. [ABSTRACT FROM AUTHOR]

The High Efficiency Video Coding (HEVC/H.265) standard achieves great improvement in compression efficiency over the widely used H.264/AVC standard at a cost of much higher complexity. When encoding videos using HEVC, the selection of the quantization parameter (QP) can significantly affect the coding efficiency. Typical algorithms for adaptive quantization employ fixed bitrate budgeting or fixed QP offsets for different frames and different blocks, without considering detailed input video characteristics, some of which might be captured using computer vision methods. The problem of determining adaptive settings of HEVC coding parameters has not been satisfactorily solved. In this paper, we proposed a Hadamard (“HAD”) energy-based optimized HEVC video encoder, in which HAD energy is used to measure the amount of residual information to be encoded in a block so as to determine the QP value for each block for a better coding efficiency. HAD energy is also used to expedite the time-consuming mode decision process and for a precise scene change detection to avoid flicker artifacts. Experiment using the widely used open source HEVC encoder $\times$ 265-v1.8 showed that the proposed algorithm was able to achieve an average of 14% saving in Bjøntegaard-delta-rate and an average of 20% saving in encoding time as compared the “medium” preset of $\times$ 265, while the proposed algorithm also produced an improvement of 3.3% in coding efficiency for the HEVC reference software HM-16.6. [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]

This paper analyzes how the distortion created by hardware impairments in a multiple-antenna base station affects the uplink spectral efficiency (SE), with a focus on massive multiple input multiple output (MIMO). This distortion is correlated across the antennas but has been often approximated as uncorrelated to facilitate (tractable) SE analysis. To determine when this approximation is accurate, basic properties of distortion correlation are first uncovered. Then, we separately analyze the distortion correlation caused by third-order non-linearities and by quantization. Finally, we study the SE numerically and show that the distortion correlation can be safely neglected in massive MIMO when there are sufficiently many users. Under independent identically distributed Rayleigh fading and equal signal-to-noise ratios (SNRs), this occurs for more than five transmitting users. Other channel models and SNR variations have only minor impact on the accuracy. We also demonstrate the importance of taking the distortion characteristics into account in the receive combining. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal design of a two-stage Wyner-Ziv scalar quantizer with forwardly or reversely degraded side information (SI) for finite-alphabet sources and SI. We assume that the binning is performed optimally and address the design of the quantizer partitions. The optimization problem is formulated as the minimization of a weighted sum of distortions and rates. The proposed solution is globally optimal when the cells in each partition are contiguous. The solution algorithm is based on solving the single-source or the all-pairs minimum-weight path (MWP) problem in certain weighted directed acyclic graphs. When the conventional dynamic programming technique is used to solve the underlying MWP problems, the time complexity achieved is $O(N^{3})$ , where $N$ is the size of the source alphabet. A so-called partial Monge property is additionally introduced, and a faster solution algorithm exploiting this property is proposed. Experimental results assess the practical performance of the proposed scheme. [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]

Low-resolution digital-to-analog converter (DAC) has shown great potential in facilitating cost- and power-efficient implementation of massive multiple-input multiple-output (MIMO) systems. We investigate the performance of a massive MIMO downlink network with low-resolution DACs using regularized zero-forcing (RZF) precoding. It serves multiple receivers equipped with finite-resolution analog-to-digital converters (ADCs). By taking the quantization errors at both the transmitter and receivers into account under spatially correlated channels, the regularization parameter for RZF is optimized with a closed-form solution by applying the asymptotic random matrix theory. The optimal regularization parameter increases linearly with respect to the user loading ratio while independent of the ADC quantization resolution and the channel correlation. Furthermore, asymptotic sum rate performance is characterized and a closed-form expression for the optimal user loading ratio is obtained at a low signal-to-noise ratio. The optimal ratio increases with the DAC resolution while it decreases with the ADC resolution. Numerical simulations verify our observations. [ABSTRACT FROM AUTHOR]

Abstract This paper deals with positive solutions of the fully parabolic system { u t = Δ u − χ ∇ ⋅ (u ∇ v) in Ω × (0 , ∞) , τ 1 v t = Δ v − v + w in Ω × (0 , ∞) , τ 2 w t = Δ w − w + u in Ω × (0 , ∞) under mixed boundary conditions (no-flux and Dirichlet conditions) in a smooth bounded convex domain Ω ⊂ R 4 with positive parameters τ 1 , τ 2 , χ > 0 and nonnegative smooth initial data (u 0 , v 0 , w 0). Global existence and boundedness of solutions were shown if ‖ u 0 ‖ L 1 (Ω) < (8 π) 2 / χ in Fujie–Senba (2017). In the present paper, it is shown that there exist blowup solutions satisfying ‖ u 0 ‖ L 1 (Ω) > (8 π) 2 / χ. This result suggests that the system can be regard as a generalization of the Keller–Segel system, which has 8 π / χ -dichotomy. The key ingredients are a Lyapunov functional and quantization properties of stationary solutions of the system in R 4. [ABSTRACT FROM AUTHOR]

We discuss the problems of dynamics of the gravitational field and try to solve them according to quantum field theory by suggesting canonical states for the gravitational field and its conjugate field. To solve the problem of quantization of gravitational field, we assume that the quantum gravitational field eI changes the geometry of curved spacetime xµ, and relate this changing to quantization of the gravitational field. We introduce a field πI and consider it as a canonical momentum conjugates to a canonical gravitational field e-I. We use them in deriving the path integral of the gravitational field according to quantum field theory, we get Lagrangian with dependence only on the covariant derivative of the gravitational field eI, similarly to Lagrangian of scalar field in curved spacetime. Then, we discuss the case of free gravitational field. We find that this case takes place only in background spacetime approximation of low matter density; weak gravity. Similarly, we study the Plebanski two form complex field Σi and derive its Lagrangian with dependence only on the covariant derivative of Σi, which is represented in selfdual representation |Σi. Then, we try to combine the gravitational and Plebanski fields into one field: Kµi. Finally, we derive the static potential of exchanging gravitons between particles of scalar and spinor fields; the Newtonian gravitational potential. [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]

Sampled-data based quantisation control for Takagi-Sugeno (T-S) fuzzy switched systems with actuator failures under asynchronous switching is studied. By the T-S fuzzy model, sampled-data based asynchronous control is extended into switched non-linear systems. An improved functional method is introduced. Applying this method, improved Lyapunov functionals are constructed. These functionals are mode dependent and piecewise continuous; not every term of these functionals is required to be positive definite; sampling states at both sides of sampling intervals are introduced into these functionals. More useful information with respect to system states is reflected in constructing functionals. Combining these functionals with the averaged dwell time technique, stabilisation conditions are relaxed, and improved exponential stabilisation criteria are obtained with less conservatism. In addition, variation ranges of membership functions are taken into account to reduce conservatism. Then, a sampled-data based fuzzy quantisation controller is designed. Simulation examples are given to illustrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Abstract Promoting recycling is one of the best effective measures to relieve contradictions such as “waste siege” and resource shortage in China. To do that, quantifying and recognizing the recycling potential (RCP) of recyclable waste (RCW) are foundations. This study quantifies the RCP of RCW (RCP-RCW) in Suzhou, a typical developed city in East China, based on a systematic tracking survey for one week in each season and in different districts starting from the summer of 2011 to the spring of 2017. Results show that Suzhou's RCP-RCW was 92.7 (89.3–96.0), with a 90% confidence interval percentage, among which, recyclable organics and recyclable material (RCM) accounted for 55.1% and 37.6%, respectively. In RCMs, a high RCM recovery value and low RCM recovery value accounted for 64.8% and 26.0%, respectively. RCW generation was 242.4 thousand tons in 2016 and is expected to reach 738.8 thousand tons in 2030. Moreover, spatiotemporal variation of RCW was characterized. Factors, such as local customs and culture, dietary habits, residential lifestyles and consumption structure influence the RCW stream generation. All the obtained results can improve the knowledge base for effectively promote recycling, and contribute to making governmental policy and the recycling industry's business development in Suzhou and other Chinese cities. Graphical abstract Image 1 Highlights • Recycling potential of recyclable waste (RCW) were quantitated. • RCWs generation trends were estimated. • Recommendations for recycling were proposed. [ABSTRACT FROM AUTHOR]

Abstract The gluon propagator plays a central role in determining the dynamics of QCD. In this work we demonstrate for BRST quantised QCD that the Dyson–Schwinger equation imposes significant analytic constraints on the structure of this propagator. In particular, we find that these constraints control the appearance of massless components in the gluon spectral density. [ABSTRACT FROM AUTHOR]

Abstract We show a possibility for the charge quantization of the standard model (SM) particles. If a global symmetry makes the three copies of a generation and supersymmetry (SUSY) relates the Higgs boson to a lepton, all the charges of the SM particles can be quantized through gauge-anomaly cancellation. In the minimal model realizing the possibility, the gravitino mass around the Planck-scale is needed to generate the SM couplings through (quantum) supergravity. Much below the Planck-scale, the SM with non-vanishing neutrino masses is obtained as the effective theory. As extensions of the SM with this quantization mechanism, millicharged particles can exist without introducing massless hidden photons. [ABSTRACT FROM AUTHOR]

Abstract The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes. We apply the same idea of its derivation in LQC to the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson–Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian. [ABSTRACT FROM AUTHOR]