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Journal articles on the topic 'Non-linear quantization'

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Published: 3 June 2025

Last updated: 20 July 2025

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Accardi, Luigi, and Ameur Dhahri. "C*-Non-Linear Second Quantization." Annales Henri Poincaré 17, no. 7 (2015): 1883–907. http://dx.doi.org/10.1007/s00023-015-0439-4.

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ALDAYA, VICTOR, MANUEL CALIXTO, JULIO GUERRERO, and FRANCISCO F. LOPEZ-RUIZ. "JET-GAUGE GROUPS AS BASIC SYMMETRIES OF NON-LINEAR SIGMA AND YANG–MILLS MODELS AND QUANTIZATION." International Journal of Geometric Methods in Modern Physics 09, no. 02 (2012): 1260006. http://dx.doi.org/10.1142/s0219887812600067.

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The quantum description of non-linear systems finds a deep obstruction in the Canonical Quantization framework and Non-Linear Sigma Models constitute the best representatives. In this paper, we face the quantization of such systems on the grounds of a Group Approach to Quantization, and extend the algorithm to the specific case of massive Non-Abelian gauge theories. The basic geometric structures behind are the so-called "jet-gauge groups".

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ALDAYA, V., M. CALIXTO, J. GUERRERO, and F. F. LÓPEZ-RUIZ. "SYMMETRIES OF NON-LINEAR SYSTEMS: GROUP APPROACH TO THEIR QUANTIZATION." International Journal of Geometric Methods in Modern Physics 08, no. 06 (2011): 1329–54. http://dx.doi.org/10.1142/s0219887811005713.

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We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically non-perturbative, is primarily intended for non-linear systems, although needless to say that finding the basic symmetry associated with a given (quantum) physical problem is in general a difficult task, which many times nearly emulates the complexity of finding the actual (classical) solutions. Apart from some interesting examples related to the electromagnetic and gravitational particle interactions, where an algebraic version of the Equivalence Principle naturally arises, we attempt to the quantum description of non-linear sigma models. In particular, we present the actual quantization of the partial-trace non-linear SU (2) sigma model as a representative case of non-linear quantum field theory.

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MATSCHULL, H. J., and H. NICOLAI. "CANONICAL TREATMENT OF COSET SPACE SIGMA MODELS." International Journal of Modern Physics D 03, no. 01 (1994): 81–91. http://dx.doi.org/10.1142/s0218271894000095.

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Brjuhanov, Jurij. "Oscillations in first-order non-linear recursive digital circuits under constant external influence." Izvestiya VUZ. Applied Nonlinear Dynamics 7, no. 4 (1999): 29–34. http://dx.doi.org/10.18500/0869-6632-1999-7-4-29-34.

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Dynamics of first—order recursive circuits without quantization effects is investigated. Filter adder has characteristic of two types: saturation and overflow. Linear regime boundaries are determined. Relation of magnitude of external influence, parasitic oscillations period and circuit parameter is defermined. Range of initial conditions of parasitic oscillation origin is refrieved.

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Wang, Yuhuan, Jianguo Li, Neng Ye, and Xiangyuan Bu. "Novel Low Complexity BP Decoding Algorithms for Polar Codes: Simplifying on Non-Linear Operations." Electronics 11, no. 1 (2021): 93. http://dx.doi.org/10.3390/electronics11010093.

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The parallel nature of the belief propagation (BP) decoding algorithm for polar codes opens up a real possibility of high throughput and low decoding latency during hardware implementation. To address the problem that the BP decoding algorithm introduces high-complexity non-linear operations in the iterative messages update process, this paper proposes to simplify these operations and develops two novel low complexity BP decoding algorithms, namely, exponential BP (Exp-BP) decoding algorithm and quantization function BP (QF-BP) decoding algorithm. The proposed algorithms simplify the compound hyperbolic tangent function by using probability distribution fitting techniques. Specifically, the Exp-BP algorithm simplifies two types of non-linear operations into single non-linear operation using the piece-wise exponential model function, which can approximate the hyperbolic tangent function in the updating formula. The QF-BP algorithm eliminates non-linear operations using the non-uniform quantization in the updating formula, which is effective in reducing computational complexity. According to the simulation results, the proposed algorithms can reduce the computational complexity up to 50% in each iteration with a loss of less than 0.1 dB compared with the BP decoding algorithm, which can facilitate the hardware implementation.

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Hasso, Alaaldin, and Karwan Jacksi. "Effects of Rounding and Truncating Methods of Quantization Error and SQNR for Sine Signal." Journal of Applied Science and Technology Trends 1, no. 1 (2020): 08–12. http://dx.doi.org/10.38094/jastt113.

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Within the Analog to Digital Conversion (ADC), quantization noise is a duplicate of a Quantization Error (QE) which is introduced by quantization. In signal processing and telecommunication systems, the noise is non-linear and depends on the signal type. During the analog, Sine signal converts to the digital (ADC) process, the two methods are used Rounding and Truncating in-order to eliminate the error produced in the digitization process. The rounding method quantize assigns each sample of sine signal to the nearest quantization level. However, making the Truncating would have assigned each sample of sine signal to the quantization level below it. This paper compares the rounding and truncating methods of QE for sine signal, signal to quantization noise ratio, correlation coefficient, and regression equation of a line for both methods. Then, it calculates the residual sum of squares and compares it to the regression equations of the lines.

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Svozil, Karl. "On the Complete Description of Entangled Systems Part II: The (Meta)Physical Status and Semantic Aspects." Entropy 24, no. 12 (2022): 1724. http://dx.doi.org/10.3390/e24121724.

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We review some semantical aspects of probability bounds from Boole’s “conditions on possible experience” violated by quantum mechanics. We also speculate about emerging space-time categories as an epiphenomenon of quantization and the resulting breakdown of relativity theory by non-unitary and non-linear processes.

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KAHNG, BYUNG-JAY. "DEFORMATION QUANTIZATION OF CERTAIN NONLINEAR POISSON STRUCTURES." International Journal of Mathematics 09, no. 05 (1998): 599–621. http://dx.doi.org/10.1142/s0129167x98000269.

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As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain nonlinear Poisson brackets which are "cocycle perturbations" of the linear Poisson bracket. We show that these special Poisson brackets are equivalent to Poisson brackets of central extension type, which resemble the central extensions of an ordinary Lie bracket via Lie algebra cocycles. We are able to formulate (strict) deformation quantizations of these Poisson brackets by means of twisted group C*-algebras. We also indicate that these deformation quantizations can be used to construct some specific non-compact quantum groups.

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Kraus, Elizabeth, and Klaus Sibold. "Yang-Mills theories in a non-linear gauge: Quantization and gauge independence." Nuclear Physics B 331, no. 2 (1990): 350–74. http://dx.doi.org/10.1016/0550-3213(90)90212-v.

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Liu, Qing Quan. "Observer-Based Quantized Feedback Control via Noisy Communication Channels." Advanced Materials Research 433-440 (January 2012): 6242–49. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.6242.

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This paper investigates the input and output quantized control problem for stochastic linear systems with unbounded and possibly non-Gaussian process disturbance, where sensors, controllers and plants are connected by a noisy digital communication channel. Due to the unbounded process disturbance, a dynamic, logarithmic quantization scheme is proposed. An observer-based control policy is presented to stabilize the unstable plant in the mean square sense. Simulation results show the validity of the proposed quantization and control policy.

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Lagunas, Miguel A., Ana Perez-Neira, and José Rubio. "NDM: 1-Bit Delta-Sigma Converter with Non-Linear Loop." MATEC Web of Conferences 292 (2019): 04005. http://dx.doi.org/10.1051/matecconf/201929204005.

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In this paper we propose to introduce a new processing scheme in the basic loop of a Delta Sigma (ΔΣ) analog-to-digital converter. This processing confers extra gains of the converter over both the quantization error and the channel noise. This is an advance with respect to all cases found in the literature, where the desired signal is not protected against channel noise. Also, the proposed processing is simple and contrasts with the existing architectures, which produce better quality at the expense of sensitivity to implementation imperfections due to the presence of multiples loops in the corresponding architecture. Furthermore, the in-phase/quadrature components structure of a band pass signal has not been used to improve the performance of ΔΣ converters.

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Joan, C. Micó, Caselles Antonio, and Amigó Salvador. "Avances en la interpretación mecanocuántica de la dinámica del cerebro." Revista Internacional de Sistemas 16 (December 15, 2008): 74–82. https://doi.org/10.5281/zenodo.1137624.

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From a non-linear Schrödinger equation to describe the space-time dynamics of brain in absence of stimuli, we demonstrate that the wave function cannot be interpreted as a probability density, such as it happens in the non-relativistic Quantum Mechanics. The analytical solution of this equation is obtained, which depends on two integral constants. The boundary conditions are applied to a “box brain” model that has a parallelepiped shape. We deduce that there are not solutions for an isolated “box brain”. However, the boundary condition of null value for the wave function in the walls of the “box brain” provides the quantization of brain speed propagation. In addition, the periodicity of the wave function gives also the quantization of brain frequency and wave longitude. The frequency quantization is tested experimentally.

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Huang, Chenglong, Nuo Xu, Wenqing Wang, Yihong Hu, and Liang Fang. "Conductance-Aware Quantization Based on Minimum Error Substitution for Non-Linear-Conductance-State Tolerance in Neural Computing Systems." Micromachines 13, no. 5 (2022): 667. http://dx.doi.org/10.3390/mi13050667.

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Emerging resistive random-access memory (ReRAM) has demonstrated great potential in the achievement of the in-memory computing paradigm to overcome the well-known “memory wall” in current von Neumann architecture. The ReRAM crossbar array (RCA) is a promising circuit structure to accelerate the vital multiplication-and-accumulation (MAC) operations in deep neural networks (DNN). However, due to the nonlinear distribution of conductance levels in ReRAM, a large deviation exists in the mapping process when the trained weights that are quantized by linear relationships are directly mapped to the nonlinear conductance values from the realistic ReRAM device. This deviation degrades the inference accuracy of the RCA-based DNN. In this paper, we propose a minimum error substitution based on a conductance-aware quantization method to eliminate the deviation in the mapping process from the weights to the actual conductance values. The method is suitable for multiple ReRAM devices with different non-linear conductance distribution and is also immune to the device variation. The simulation results on LeNet5, AlexNet and VGG16 demonstrate that this method can vastly rescue the accuracy degradation from the non-linear resistance distribution of ReRAM devices compared to the linear quantization method.

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Baskin, Chaim, Natan Liss, Eli Schwartz, et al. "UNIQ." ACM Transactions on Computer Systems 37, no. 1-4 (2021): 1–15. http://dx.doi.org/10.1145/3444943.

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We present a novel method for neural network quantization. Our method, named UNIQ , emulates a non-uniform k -quantile quantizer and adapts the model to perform well with quantized weights by injecting noise to the weights at training time. As a by-product of injecting noise to weights, we find that activations can also be quantized to as low as 8-bit with only a minor accuracy degradation. Our non-uniform quantization approach provides a novel alternative to the existing uniform quantization techniques for neural networks. We further propose a novel complexity metric of number of bit operations performed (BOPs), and we show that this metric has a linear relation with logic utilization and power. We suggest evaluating the trade-off of accuracy vs. complexity (BOPs). The proposed method, when evaluated on ResNet18/34/50 and MobileNet on ImageNet, outperforms the prior state of the art both in the low-complexity regime and the high accuracy regime. We demonstrate the practical applicability of this approach, by implementing our non-uniformly quantized CNN on FPGA.

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Monkewitz, Peter A., Patrick Huerre, and Jean-Marc Chomaz. "Global linear stability analysis of weakly non-parallel shear flows." Journal of Fluid Mechanics 251 (June 1993): 1–20. http://dx.doi.org/10.1017/s0022112093003313.

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The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e. that its streamwise development is slow on the scale of a typical instability wavelength. This implies the general study of the temporal evolution of global modes, which are time-harmonic solutions of the linear disturbance equations, subject to homogeneous boundary conditions in all space directions. Flow domains of both doubly infinite and semi-infinite streamwise extent are considered and complete solutions are obtained within the framework of asymptotically matched WKBJ approximations. In both cases the global eigenfrequency is given, to leading order in the WKBJ parameter, by the absolute frequency ω0(Xt) at the dominant turning pointXtof the WKBJ approximation, while its quantization is provided by the connection of solutions acrossXt. Within the context of the present analysis, global modes can therefore only become time-amplified or self-excited if the basic flow contains a region of absolute instability.

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Liu, Peng, Congduan Li, Nanfeng Zhang, Jingfeng Yang, and Li Wang. "Efficient Integer Quantization for Compressed DETR Models." Entropy 27, no. 4 (2025): 422. https://doi.org/10.3390/e27040422.

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The Transformer-based target detection model, DETR, has powerful feature extraction and recognition capabilities, but its high computational and storage requirements limit its deployment on resource-constrained devices. To solve this problem, we first replace the ResNet-50 backbone network in DETR with Swin-T, which realizes the unification of the backbone network with the Transformer encoder and decoder under the same Transformer processing paradigm. On this basis, we propose a quantized inference scheme based entirely on integers, which effectively serves as a data compression method for reducing memory occupation and computational complexity. Unlike previous approaches that only quantize the linear layer of DETR, we further apply integer approximation to all non-linear operational layers (e.g., Sigmoid, Softmax, LayerNorm, GELU), thus realizing the execution of the entire inference process in the integer domain. Experimental results show that our method reduces the computation and storage to 6.3% and 25% of the original model, respectively, while the average accuracy decreases by only 1.1%, which validates the effectiveness of the method as an efficient and hardware-friendly solution for target detection.

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Hoyos, Fredy E., John E. Candelo-Becerra, and Carlos I. Hoyos Velasco. "Application of Zero Average Dynamics and Fixed Point Induction Control Techniques to Control the Speed of a DC Motor with a Buck Converter." Applied Sciences 10, no. 5 (2020): 1807. http://dx.doi.org/10.3390/app10051807.

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Several technological applications require well-designed control systems to induce a desired speed in direct current (DC) motors. Some controllers present saturation in the duty cycle, which generates variable switching frequency and subharmonics. The zero average dynamics and fixed point induction control (ZAD-FPIC) techniques have been shown to reduce these problems; however, little research has been done for DC motors, considering fixed switching frequency, quantization effects, and delays. Therefore, this paper presents the speed control of a DC motor by using a buck converter controlled with the ZAD-FPIC techniques. A fourth-order, non-linear mathematical model is used to describe the system dynamics, which combines electrical and electromechanical physical models. The dynamic response and non-linear system dynamics are studied for different scenarios where the control parameters are changed. Results show that the speed of the motor is successfully controlled when using ZAD-FPIC, with a non-saturated duty cycle presenting fixed switching frequency. Simulation and experimental tests show that the controlled system presents a good performance for different quantization levels, which makes it robust to the resolution for the measurement and type of sensor.

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Stosic, Biljana. "Coefficient quantization effects on new filters based on Chebyshev fourth-kind polynomials." Facta universitatis - series: Electronics and Energetics 34, no. 2 (2021): 291–305. http://dx.doi.org/10.2298/fuee2102291s.

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The aim of this paper is to construct non-recursive filters, extensively used type of digital filters in digital signal processing applications, based on Chebyshev orthogonal polynomials. The paper proposes the use of the fourth-kind Chebyshev polynomials as functions in generating new filters. In this kind, low-pass filters with linear phase responses are obtained. Comprenhansive study of the frequency response characteristics of the generated filter functions is presented. The effects of coefficient quantization as one type of quantization that influences a filter characteristic are investigated here also. The quantized-coefficient errors are considered based on the number of bits and the implementation algorithms.

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Masumoto, Tomoyuki, Misuzu Baba, and Norio Baba. "PM-07A non-linear discrete reconstruction method based on the gray-level quantization unit." Microscopy 65, suppl 1 (2016): i35.1—i35. http://dx.doi.org/10.1093/jmicro/dfw070.

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Sanjuan, J., and M. Nofrarias. "Non-linear quantization error reduction for the temperature measurement subsystem on-board LISA Pathfinder." Review of Scientific Instruments 89, no. 4 (2018): 045004. http://dx.doi.org/10.1063/1.5012692.

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Sun, Yanzhi, Muqing Wu, Qilin Guo, Feng Zheng, and Chunxiu Xu. "Robust Non-linear Precoder for Multiuser MISO Systems Based on Delay and Channel Quantization." Wireless Personal Communications 72, no. 4 (2013): 1993–2014. http://dx.doi.org/10.1007/s11277-013-1117-9.

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Juan Esteban Sereno Mesa, Antonio Ferramosca, Alejandro H. González, and Agustina D' Jorge. "IMPACTS OF QUANTIFYING SOCIAL DISTANCING MEASURES ON MPC PERFORMANCE FOR SIR-TYPE SYSTEMS." Latin American Applied Research - An international journal 53, no. 4 (2023): 417–22. http://dx.doi.org/10.52292/j.laar.2023.3278.

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Currently, there has been a sharp increase in epidemic control research as a result of recent epidemic outbreaks. Several strategies aiming to minimize the Epidemic Final Size and/or to keep the Infected Peak Prevalence under a specific value were proposed. However, not many strategies focused on analyzing the impact of applying quantified measures instead of continuous control action. This analysis is a crucial aspect since policymakers design their non-pharmaceutical intervention based on a discrete scale of intensity, from mask-wearing to hard lockdown. In this work, we present a quantized-input non-linear Model Predictive Control strategy to manage non-pharmaceutical interventions during an epidemic outbreak. The impact of quantifying the social distancing measure is computed through several simulations based on a COVID-19 epidemic model and considering different quantization levels of the non-pharmaceutical intervention. Finally, the control performance in each quantization level is evaluated with the computation of four epidemic indices.

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Zheng, Yong, Haigang Yang, Yiping Jia, and Zhihong Huang. "PermLSTM: A High Energy-Efficiency LSTM Accelerator Architecture." Electronics 10, no. 8 (2021): 882. http://dx.doi.org/10.3390/electronics10080882.

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Pruning and quantization are two commonly used approaches to accelerate the LSTM (Long Short-Term Memory) model. However, the traditional linear quantization usually suffers from the problem of gradient vanishing, and the existing pruning methods all have the problem of producing undesired irregular sparsity or large indexing overhead. To alleviate the problem of vanishing gradient, this work proposed a normalized linear quantization approach, which first normalize operands regionally and then quantize them in a local mix-max range. To overcome the problem of irregular sparsity and large indexing overhead, this work adopts the permuted block diagonal mask matrices to generate the sparse model. Due to the sparse model being highly regular, the position of non-zero weights can be obtained by a simple calculation, thus avoiding the large indexing overhead. Based on the sparse LSTM model generated from the permuted block diagonal mask matrices, this paper also proposed a high energy-efficiency accelerator, PermLSTM that comprehensively exploits the sparsity of weights, activations, and products regarding the matrix–vector multiplications, resulting in a 55.1% reduction in power consumption. The accelerator has been realized on Arria-10 FPGAs running at 150 MHz and achieved 2.19×∼24.4× energy efficiency compared with the other FPGA-based LSTM accelerators previously reported.

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Mandal, Ipsita. "Effect of Interactions on the Quantization of the Chiral Photocurrent for Double-Weyl Semimetals." Symmetry 12, no. 6 (2020): 919. http://dx.doi.org/10.3390/sym12060919.

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The circular photogalvanic effect (CPGE) is the photocurrent generated in an optically active material in response to an applied AC electric field, and it changes sign depending on the chirality of the incident circularly polarized light. It is a non-linear DC current as it is second order in the applied electric field, and for a certain range of low frequencies, takes on a quantized value proportional to the topological charge for a system which is a source of non-zero Berry flux. We show that for a non-interacting double-Weyl node, the CPGE is proportional to two quanta of Berry flux. On examining the effect of short-ranged Hubbard interactions up to first-order corrections, we find that this quantization is destroyed. This implies that unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in topological semimetals is not protected.

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Kijowski, Jerzy. "Geometric structure of the arrival time operator." International Journal of Geometric Methods in Modern Physics 11, no. 07 (2014): 1460021. http://dx.doi.org/10.1142/s0219887814600214.

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Uniqueness of the construction of the quantum arrival time operator, proposed by me in 1974, follows from the uniqueness of the "quantization through Lie derivative" which applies to any observable linear in momenta. Arguments given by Wolfgang Pauli against the "quantum time operator" are shown to be equivalent to the non-completeness of the constant vector field on the real half-line ℝ+.

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Yu, Jimin, Liangsheng Nan, Xiaoming Tang, and Ping Wang. "Model predictive control of non-linear systems over networks with data quantization and packet loss." ISA Transactions 59 (November 2015): 1–9. http://dx.doi.org/10.1016/j.isatra.2015.06.014.

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Beneduci, Roberto, Emmanuel Frion, and Jean-Pierre Gazeau. "Quantum description of angles in the plane." Acta Polytechnica 62, no. 1 (2022): 8–15. http://dx.doi.org/10.14311/ap.2022.62.0008.

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The real plane with its set of orientations or angles in [0, π) is the simplest non trivial example of a (projective) Hilbert space and provides nice illustrations of quantum formalism. We present some of them, namely covariant integral quantization, linear polarisation of light as a quantum measurement, interpretation of entanglement leading to the violation of Bell inequalities, and spin one-half coherent states viewed as two entangled angles.

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Guo, Xuan, Danyu Wu, Lei Zhou, Huasen Liu, Jin Wu, and Xinyu Liu. "High speed high resolution direct digital frequency synthesizer with non-linear DAC coarse quantization and ROM-based piecewise linear interpolation." Analog Integrated Circuits and Signal Processing 90, no. 1 (2016): 263–72. http://dx.doi.org/10.1007/s10470-016-0882-2.

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Brjuhanov, Jurij, and Evgenii Myasnikov. "Parameters of limit cycle in recursive second-order digital system with one quantizer." Izvestiya VUZ. Applied Nonlinear Dynamics 8, no. 1 (2000): 21–28. http://dx.doi.org/10.18500/0869-6632-2000-8-1-21-28.

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Parameters of limit cycles in second—order digital system with non—linear adder are investigated. Two kinds of quantization way are considered: rounding and value truncation. New analytical and computer aimed methods are proposed for investigation of limit cycles parameters dependencies upon the system coefficients. Upper bounds of limit cycles amplitudes are obtained by the first method. These bounds are rational functions of system coefficients and are verified by the second method.

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GALAPON, ERIC A. "THEORY OF QUANTUM FIRST TIME OF ARRIVAL VIA SPATIAL CONFINEMENT I: CONFINED TIME OF ARRIVAL OPERATORS FOR CONTINUOUS POTENTIALS." International Journal of Modern Physics A 21, no. 31 (2006): 6351–81. http://dx.doi.org/10.1142/s0217751x06034215.

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The constructions of two classes of self-adjoint and compact first time of arrival operators for confined systems under arbitrary, everywhere continuous potential are detailed, extending in the interacting case the concept of confined quantum time of arrival operators first developed for the free particle. One class is the quantized confined time of arrival operators and another is the class of algebra preserving confined time of arrival operators. The former is the projection of the quantization of the classical time of arrival, and is constructed by solving the quantization problem of the multiple-valued and non-everywhere-real-valued classical time of arrival for arbitrary potential. The later arises to address the nonconjugacy with the Hamiltonian of the entire class of the quantized confined time of arrival operators, and is constructed by solving the obstruction to quantization present in Euclidean space. These two sets of operators coincide for linear systems; but differ for nonlinear systems, with the former as the leading term of the latter. The confined time of arrival operators for potentials representative of linear and nonlinear systems are numerically investigated and demonstrated to have the same dynamical behaviors as those of the free confined time of arrival operators. In particular, the eigenfunctions evolve according to Schrödinger equation such that the corresponding probabilities of locating the quantum particle in the neighborhood of the arrival point are maximum at their respective eigenvalues.

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Yamasaki, Toshihiko, and Kiyoharu Aizawa. "Error Evaluation Model for 3Dc-Based Normal Map Compression and Its Application to Non-Linear Quantization." Journal of The Institute of Image Information and Television Engineers 62, no. 9 (2008): 1427–34. http://dx.doi.org/10.3169/itej.62.1427.

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Okano, Keisuke, and Lothar Schülke. "Renormalization and renormalization group behaviour of the O(N) non-linear sigma-model in stochastic quantization." Nuclear Physics B 295, no. 1 (1988): 105–22. http://dx.doi.org/10.1016/0550-3213(88)90230-1.

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Aldaya, Victor, Julio Guerrero, and Francisco F. López-Ruiz. "Sharing symmetries in non-linear systems: Generalized Heisenberg–Weyl algebra on the de Sitter space-time out of the sphere S3." International Journal of Geometric Methods in Modern Physics 18, no. 05 (2021): 2150074. http://dx.doi.org/10.1142/s0219887821500742.

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In this paper, we exploit the formal equivalence of the Solution Manifold of two distinct physical systems to create enough symmetries so as to characterize them by Noether Invariants, thus favoring their future quantization. In so doing, we somehow generalize the Arnold Transformation for non-necessarily linear systems. Very particularly, this algorithm applies to the case of the motion on the de Sitter space-time providing a finite-dimensional algebra generalizing the Heisenberg–Weyl algebra globally. In this case, the basic (contact) symmetry is imported from the motion of a (non-relativistic) particle on the sphere [Formula: see text].

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Chen, Gong, and Peter J. Olver. "Dispersion of discontinuous periodic waves." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2149 (2013): 20120407. http://dx.doi.org/10.1098/rspa.2012.0407.

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The dynamic evolution of linearly dispersive waves on periodic domains with discontinuous initial profiles is shown to depend remarkedly upon the asymptotics of the dispersion relation at large wavenumbers. Asymptotically linear or sublinear dispersion relations produce slowly changing waves, while those with polynomial growth exhibit dispersive quantization, a.k.a. the Talbot effect, being (approximately) quantized at rational times, but a non-differentiable fractal at irrational times. Numerical experiments suggest that such effects persist into the nonlinear regime, for both integrable and non-integrable systems. Implications for the successful modelling of wave phenomena on bounded domains and numerical challenges are discussed.

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AÇIKTEPE, T., K. G. AKDENIZ, A. O. BARUT, and J. KALAYCI. "CONFORMALLY COVARIANT COUPLED NON-LINEAR FIELD THEORY ON THE HYPERCONE: VACUUM SOLUTIONS AND QUANTIZATION OF NORMAL MODES." Modern Physics Letters A 03, no. 02 (1988): 161–65. http://dx.doi.org/10.1142/s0217732388000192.

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For the conformally covariant coupled non-linear spinor-scalar fields of the σ -model type we show that the non-trivial vacuum instanton solutions have a geometric meaning as constant spinors on the five-dimensional hypercone. The quantized fields around these solutions correspond to the normal modes of the hypercone. A connection is thus established between field theory, particle spectrum of the fields and quantized excitations of a geometry (the hypercone).

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Zhu, Xiaolong, Sitong Xiang, and Jianguo Yang. "Novel thermal error modeling method for machining centers." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 8 (2014): 1500–1508. http://dx.doi.org/10.1177/0954406214545661.

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Thermal deformation is one of the main contributors to machining errors in machine tools. In this paper, a novel approach to build an effective thermal error model for a machining center is proposed. Adaptive vector quantization network clustering algorithm is conducted to identify the temperature variables, and then one temperature variable is selected from each cluster to represent the same cluster. Furthermore, a non-linear model based on output-hidden feedback Elman neural network is adopted to establish the relationship between thermal error and temperature variables. The output-hidden feedback Elman network is adopted to predict the thermal deformation of the machining center. Back propagation (BP) neural network is introduced for comparison. A verification experiment on the machining center is carried out to validate the efficiency of the newly proposed method. Experimental verification shows that the adaptive vector quantization network clustering algorithm and output-hidden feedback Elman neural network is an accurate and effective method.

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Zhao, Ruiyong, Zhenghui Gong, Yulan Liu, and Jing Chen. "A High-Precision Voltage-Quantization-Based Current-Mode Computing-in-Memory SRAM." Micromachines 14, no. 12 (2023): 2180. http://dx.doi.org/10.3390/mi14122180.

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Non-linear distortion of signals is a serious problem in computing-in-memory SRAM (CIM-SRAM) circuits in current mode. This problem greatly limits the performance of calculations and directly affects the computing power of the CIM-SRAM. In this study, the causes of non-linearity and inconsistency were investigated. Based on detailed analyses, we proposed a high-precision, fully dynamic range IV (HFIV) conversion circuit. The HFIV circuit was added to each bit line (BL) for voltage clamping and proportionally mirroring the read current. We applied the structure to numerous prior studies and evaluated them using the 55 nm complementary metal-oxide semiconductor process. The results showed the proposed HFIV circuit could increase the CIM-SRAM’s calculation linearity to 99.92% (8~32 SRAM bit-cells) and 99.8% (32~64 SRAM bit-cells) with a 1.2 V supply.

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Li, Zhuo, and Jin Jun Xia. "A Quantitative Method on Formative Elements Optimization of Car Styling Design." Advanced Materials Research 118-120 (June 2010): 748–52. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.748.

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According to the basic principles of Kansei Engineering and BP neural network, the article establishes a non-linear relationship between the user’s perceptual evaluation and the car’s formative element. It also builds a strong anti-interference black box model, which may work out the precise value of the formative elements by the perceptual evaluations. The paper also discusses the model with deductive method, and the results show that the quantization and transformation in body design can be effectively solved by the method based on BP neural network and Kansei Engineering.

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CALIXTO, M., and V. ALDAYA. "GAUGE TRANSFORMATION PROPERTIES OF VECTOR AND TENSOR POTENTIALS REVISITED: A GROUP QUANTIZATION APPROACH." International Journal of Modern Physics A 15, no. 11 (2000): 1661–83. http://dx.doi.org/10.1142/s0217751x00000744.

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The possibility of nontrivial representations of the gauge group on wave functionals of a gauge invariant quantum field theory leads to a generation of mass for intermediate vector and tensor bosons. The mass parameters m show up as central charges in the algebra of constraints, which then become of second-class nature. The gauge group coordinates acquire dynamics outside the null-mass shell and provide the longitudinal field degrees of freedom that massless bosons need to form massive bosons. This is a non-Higgs mechanism that could provide new clues for the best understanding of the symmetry breaking mechanism in unified field theories. A unified quantization of massless and massive non-Abelian Yang–Mills, linear gravity and Abelian two-form gauge field theories are fully developed from this new approach, where a cohomological origin of mass is pointed out.

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Zuo, Yixin, Jiayi Guo, Yueting Zhang, Bin Lei, Yuxin Hu, and Mingzhi Wang. "A Deep Vector Quantization Clustering Method for Polarimetric SAR Images." Remote Sensing 13, no. 11 (2021): 2127. http://dx.doi.org/10.3390/rs13112127.

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Convolutional Neural Network (CNN) models are widely used in supervised Polarimetric Synthetic Aperture Radar (PolSAR) image classification. They are powerful tools to capture the non-linear dependency between adjacent pixels and outperform traditional methods on various benchmarks. On the contrary, research works investigating unsupervised PolSAR classification are quite rare, because most CNN models need to be trained with labeled data. In this paper, we propose a completely unsupervised model by fusing the Convolutional Autoencoder (CAE) with Vector Quantization (VQ). An auxiliary Gaussian smoothing loss is adopted for better semantic consistency in the output classification map. Qualitative and quantitative experiments are carried out on satellite and airborne full polarization data (RadarSat2/E-SAR, AIRSAR). The proposed model achieves 91.87%, 83.58% and 96.93% overall accuracy (OA) on the three datasets, which are much higher than the traditional H/alpha-Wishart method, and it exhibits better visual quality as well.

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Zhao, Xinggui, Bo Meng, and Zhen Wang. "Event-triggered integral sliding mode control for uncertain networked linear control systems with quantization." Mathematical Biosciences and Engineering 20, no. 9 (2023): 16705–24. http://dx.doi.org/10.3934/mbe.2023744.

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<abstract><p>In this paper, the integral sliding mode (ISM, SM) controller is designed to address the problem of implementing non-periodic sampled data for a class of networked linear systems with matched and unmatched uncertainties. Due to the redesigned gain of the nominal controller, the feedback control used by the nominal controller guarantees the asymptotic stability of the uncertain networked linear system. The discontinuous control uses intermittent control based on the reaching law to achieve the finite-time reachability of practical SM band. Based on the defined measurement error, the event-triggered (ET) condition can be derived, and furthermore, it guarantees a sufficient condition for the existence of the actual SM. On this basis, a quantization scheme is added to further decrease the network transmission burden of the linear system. No Zeno behavior occurs in the system owing to the existence of a positive lower bound of inter-event time. Compared with the conventional integral sliding mode control (ISMC, SMC), the proposed control law can not only relieve the network burden, but also decrease the transmission energy loss. Finally, simulation results of a numerical example and a mass-spring damping system demonstrate the effectiveness of the proposed method.</p></abstract>

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Chen, Shuo-Tsung, Ren-Jie Ye, Tsung-Hsien Wu, et al. "Patient Confidential Data Hiding and Transmission System Using Amplitude Quantization in the Frequency Domain of ECG Signals." Sensors 23, no. 22 (2023): 9199. http://dx.doi.org/10.3390/s23229199.

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The transform domain provides a useful tool in the field of confidential data hiding and protection. In order to protect and transmit patients’ information and competence, this study develops an amplitude quantization system in a transform domain by hiding patients’ information in an electrocardiogram (ECG). In this system, we first consider a non-linear model with a hiding state switch to enhance the quality of the hidden ECG signals. Next, we utilize particle swarm optimization (PSO) to solve the non-linear model so as to have a good signal-to-noise ratio (SNR), root mean square error (RMSE), and relative root mean square error (rRMSE). Accordingly, the distortion of the shape in each ECG signal is tiny, while the hidden information can fulfill the needs of physiological diagnostics. The extraction of hidden information is reversely similar to a hiding procedure without primary ECG signals. Preliminary outcomes confirm the effectiveness of our proposed method, especially an Amplitude Similarity of almost 1, an Interval RMSE of almost 0, and SNRs all above 30.

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Li, Zhimin, Chengming Lu, and Hongyu Wang. "Non-Fragile Fuzzy Tracking Control for Nonlinear Networked Systems with Dynamic Quantization and Randomly Occurring Gain Variations." Mathematics 11, no. 5 (2023): 1116. http://dx.doi.org/10.3390/math11051116.

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This paper investigates the observer-based non-fragile output feedback tracking control problem for nonlinear networked systems with randomly occurring gain variations. The considered nonlinear networked systems are represented by a Takagi–Sugeno (T–S) fuzzy model. The dynamical quantization methodology is employed to achieve the reasonable and efficacious utilization of the limited communication resources. The objective is to design the observer-based non-fragile output feedback tracking controller, such that the resulting system is mean-square asymptotically stable with the given H∞ tracking performance. Based on the descriptor representation strategy combined with the S-procedure, sufficient conditions for the existence of the desired dynamic quantizers and observer-based non-fragile tracking controller are proposed in the form of linear matrix inequalities. Finally, simulation results are provided to show the effectiveness of the proposed design method

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Das, P. K., J. Pal, M. Debbarma, and K. P. Ghatak. "The Magneto Electron Statistics in Heavily Doped N Type-Intrinsic-P Type-Intrinsic Structures." Journal of Nanoscience and Nanotechnology 21, no. 12 (2021): 6183–87. http://dx.doi.org/10.1166/jnn.2021.19539.

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In this paper we study the Electron Statistics in Heavily Doped N Type-Intrinsic-P Type-Intrinsic structures of non-linear optical, tetragonal and opto-electronic materials in the presence of magnetic quantization. It is found taking such heavily doped structures of Cd3As2, CdGeAs2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y as examples that the Fermi energy (EF) oscillates with inverse quantizing magnetic field (1/B) and increases with increasing electron concentration with different numerical magnitudes which is the signature of respective band structure. The numerical value of the Fermi energy is different in different cases due to the different values of the energy band constants.

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Pistellato, Mara, Filippo Bergamasco, Gianluca Bigaglia, et al. "Quantization-Aware NN Layers with High-throughput FPGA Implementation for Edge AI." Sensors 23, no. 10 (2023): 4667. http://dx.doi.org/10.3390/s23104667.

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Over the past few years, several applications have been extensively exploiting the advantages of deep learning, in particular when using convolutional neural networks (CNNs). The intrinsic flexibility of such models makes them widely adopted in a variety of practical applications, from medical to industrial. In this latter scenario, however, using consumer Personal Computer (PC) hardware is not always suitable for the potential harsh conditions of the working environment and the strict timing that industrial applications typically have. Therefore, the design of custom FPGA (Field Programmable Gate Array) solutions for network inference is gaining massive attention from researchers and companies as well. In this paper, we propose a family of network architectures composed of three kinds of custom layers working with integer arithmetic with a customizable precision (down to just two bits). Such layers are designed to be effectively trained on classical GPUs (Graphics Processing Units) and then synthesized to FPGA hardware for real-time inference. The idea is to provide a trainable quantization layer, called Requantizer, acting both as a non-linear activation for neurons and a value rescaler to match the desired bit precision. This way, the training is not only quantization-aware, but also capable of estimating the optimal scaling coefficients to accommodate both the non-linear nature of the activations and the constraints imposed by the limited precision. In the experimental section, we test the performance of this kind of model while working both on classical PC hardware and a case-study implementation of a signal peak detection device running on a real FPGA. We employ TensorFlow Lite for training and comparison, and use Xilinx FPGAs and Vivado for synthesis and implementation. The results show an accuracy of the quantized networks close to the floating point version, without the need for representative data for calibration as in other approaches, and performance that is better than dedicated peak detection algorithms. The FPGA implementation is able to run in real time at a rate of four gigapixels per second with moderate hardware resources, while achieving a sustained efficiency of 0.5 TOPS/W (tera operations per second per watt), in line with custom integrated hardware accelerators.

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Martins, Rachel A. D. "A perspective on non-commutative quantum gravity." International Journal of Geometric Methods in Modern Physics 12, no. 08 (2015): 1560021. http://dx.doi.org/10.1142/s021988781560021x.

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In this paper, we present some of the concepts underlying a program of non-commutative quantum gravity and recall some of the results. This program includes a novel approach to spectral triple categorification and also a precise connection between Fell bundles and Connes' non-commutative geometry. Motivated by topics in quantization of the non-commutative standard model and introduction of algebraic techniques and concepts into quantum gravity (following for example Crane, Baez and Barrett), we define spectral C*-categories, which are deformed spectral triples in a sense made precise. This definition gives to representations of a C*-category on a small category of Hilbert spaces and bounded linear maps, the interpretation of a topological quantum field theory. The construction passes two mandatory tests: (i) there is a classical limit theorem reproducing a Riemannian spin manifold manifesting Connes' and Schücker's non-commutative counterpart of Einstein's equivalence principle, and (ii) there is consistency with the experimental fermion mass matrix. We also present an algebra invariant taking the form of a partition function arising from a C*-bundle dynamical system in connection with C*-subalgebra theory.

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Gharab, Saddam, Vicente Feliu-Batlle, and Raul Rivas-Perez. "A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System." Entropy 21, no. 3 (2019): 309. http://dx.doi.org/10.3390/e21030309.

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This article addresses the identification of the nonlinear dynamics of the main pool of a laboratory hydraulic canal installed in the University of Castilla La Mancha. A new dynamic model has been developed by taking into account the measurement errors caused by the different parts of our experimental setup: (a) the nonlinearity associated to the input signal, which is caused by the movements of the upstream gate, is avoided by using a nonlinear equivalent upstream gate model, (b) the nonlinearity associated to the output signal, caused by the sensor’s resolution, is avoided by using a quantization model in the identification process, and (c) the nonlinear behaviour of the canal, which is related to the working flow regime, is taken into account considering two completely different models in function of the operating regime: the free and the submerged flows. The proposed technique of identification is based on the time-domain data. An input pseudo-random binary signal (PRBS) is designed depending on the parameters of an initially estimated linear model that was obtained by using a fundamental technique of identification. Fractional and integer order plus time delay models are used to approximate the responses of the main pool of the canal in its different flow regimes. An accurate model has been obtained, which is composed of two submodels: a first order plus time delay submodel that accurately describes the dynamics of the free flow and a fractional-order plus time delay submodel that properly describes the dynamics of the submerged flow.

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Cremaschini, Claudio, and Massimo Tessarotto. "Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity." Symmetry 10, no. 7 (2018): 287. http://dx.doi.org/10.3390/sym10070287.

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Space-time quantum contributions to the classical Einstein equations of General Relativity are determined. The theoretical background is provided by the non-perturbative theory of manifestly-covariant quantum gravity and the trajectory-based representation of the related quantum wave equation in terms of the Generalized Lagrangian path formalism. To reach the target an extended functional setting is introduced, permitting the treatment of a non-stationary background metric tensor allowed to depend on both space-time coordinates and a suitably-defined invariant proper-time parameter. Based on the Hamiltonian representation of the corresponding quantum hydrodynamic equations occurring in such a context, the quantum-modified Einstein field equations are obtained. As an application, the quantum origin of the cosmological constant is investigated. This is shown to be ascribed to the non-linear Bohm quantum interaction of the gravitational field with itself in vacuum and to depend generally also on the realization of the quantum probability density for the quantum gravitational field tensor. The emerging physical picture predicts a generally non-stationary quantum cosmological constant which originates from fluctuations (i.e., gradients) of vacuum quantum gravitational energy density and is consistent with the existence of quantum massive gravitons.

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Deva Koresh, Mr H. James. "Quantization with Perception for Performance Improvement in HEVC for HDR Content." Journal of Innovative Image Processing 2, no. 1 (2020): 55–64. http://dx.doi.org/10.36548/jiip.2020.1.006.

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Human eye always reveals a non –linear understanding, for the disturbances caused by the lossy image and video coding. This is mainly because of the masking capability of the human eye to conceal the attributes such as contrast, luminous, spatial and temporal frequencies. To have a distortion less and efficient video encoding for the high dynamic video range content by eluding the invisible messages in the video that causes disturbances the paper puts forth the quantization with perception utilizing the luminous masking. The methodology utilized, computes the tone mapping to scale every frames in the HDR and later quantizes on unit basis with perception tuning. For this purpose the mechanism put forth incorporates the reference model of the HEVC with the extension range of the HEVC. The proposed model was validated by evaluating the reduction incurred in each rate of bit compared to the HDR range extension. The results acquired proved to have an enhancement in terms of the savings endured in the bit rate compared to the High efficient video coding that relied on the high dynamic range visible difference predictor-II

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