Relevant bibliographies by topics / Non-linear quantization

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Non-linear quantization'

Author: Grafiati
Published: 3 June 2025
Last updated: 7 July 2025

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Journal articles on the topic "Non-linear quantization"

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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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Dissertations / Theses on the topic "Non-linear quantization"

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Shen, Jue. "Quantization Effects Analysis on Phase Noise and Implementation of ALL Digital Phase Locked-Loop." Thesis, KTH, Skolan för informations- och kommunikationsteknik (ICT), 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-37212.

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With the advancement of CMOS process and fabrication, it has been a trend to maximize digital design while minimize analog correspondents in mixed-signal system designs. So is the case for PLL. PLL has always been a traditional mixed-signal system limited by analog part performance. Around 2000, there emerged ADPLL of which all the blocks besides oscillator are implemented in digital circuits. There have been successful examples in application of Bluetooth, and it is moving to improve results for application of WiMax and ad-hoc frequency hopping communication link. Based on the theoretic and measurement results of existing materials, ADPLL has shown advantages such as fast time-to-market, low area, low cost and better system integration; but it also showed disadvantages in frequency resolution and phase noise, etc. Also this new topic still opens questions in many researching points important to PLL such as tracking behavior and quantization effect. In this thesis, a non-linear phase domain model for all digital phase-locked loop (ADPLL) was established and validated. Based on that, we analyzed that ADPLL phase noise prediction derived from traditional linear quantization model became inaccurate in non-linear cases because its probability density of quantization error did not meet the premise assumption of linear model. The phenomena of bandwidth expansion and in-band phase noise decreasing peculiar to integer-N ADPLL were demonstrated and explained by matlab and verilog behavior level simulation test bench. The expression of threshold quantization step was defined and derived as the method to distinguish whether an integer-N ADPLL was in non-linear cases or not, and the results conformed to those of matlab simulation. A simplified approximation model for non-linear integer-N ADPLL with noise sources was established to predict in-band phase noise, and the trends of the results conformed to those of matlab simulation. Other basic analysis serving for the conclusions above covered: ADPLL loop dynamics, traditional linear theory and its quantitative limitations and numerical analysis of random number. Finally, a present measurement setup was demonstrated and the results were analyzed for future work.
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Haberichter, Mareike Katharina. "Classically spinning and isospinning non-linear σ-model solitons". Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/classically-spinning-and-isospinning-nonlinear-sigmamodel-solitons(59f1d53d-0de7-4938-ad02-85ac57f6003f).html.

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We investigate classically (iso)spinning topological soliton solutions in (2+1)- and (3+1)-dimensional models; more explicitly isospinning lump solutions in (2+1) dimensions, Skyrme solitons in (2+1) and (3+1) dimensions and Hopf soliton solutions in (3 +1) dimensions. For example, such soliton types can be used to describe quasiparticle excitations in ferromagnetic quantum Hall systems, can model spin and isospin states of nuclei and may be candidates to model glueball configurations in QCD.Unlike previous work, we do not impose any spatial symmetries on the isospinning soliton configurations and we explicitly allow the isospinning solitons to deform and break the symmetries of the static configurations. It turns out that soliton deformations clearly cannot be ignored. Depending on the topological model under investigation they can give rise to new types of instabilities, can result in new solution types which are unstable for vanishing isospin, can rearrange the spectrum of minimal energy solutions and can allow for transitions between different minimal-energy solutions in a given topological sector. Evidently, our numerical results on classically isospinning, arbitrarily deforming solitons are relevant for the quantization of classical soliton solutions.
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Hoq, Qazi Enamul. "Quantization Of Spin Direction For Solitary Waves in a Uniform Magnetic Field." Thesis, University of North Texas, 2003. https://digital.library.unt.edu/ark:/67531/metadc4210/.

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It is known that there are nonlinear wave equations with localized solitary wave solutions. Some of these solitary waves are stable (with respect to a small perturbation of initial data)and have nonzero spin (nonzero intrinsic angular momentum in the centre of momentum frame). In this paper we consider vector-valued solitary wave solutions to a nonlinear Klein-Gordon equation and investigate the behavior of these spinning solitary waves under the influence of an externally imposed uniform magnetic field. We find that the only stationary spinning solitary wave solutions have spin parallel or antiparallel to the magnetic field direction.
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SETTIMI, Alessandro. "Classical and quantum approach of quasi normal modes in linear optical regime: an application to one dimensional photonic crystals." Doctoral thesis, La Sapienza, 2005. http://hdl.handle.net/11573/916902.

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Kotousov, Gleb. "Towards the quantization of integrable non-linear sigma models." Phd thesis, 2020. http://hdl.handle.net/1885/202104.

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The class of integrable Non-Linear Sigma Models (NLSM) have many interesting applications in Quantum Field Theory, Condensed Matter Physics and String Theory. However, despite being integrable, their study still presents many challenges. In this thesis the quantization of integrable NLSM is considered within the framework of the Quantum Inverse Scattering Method. The main focus are the O(3) and O(4) NLSM and their integrable deformations. On these examples, we will encounter and discuss the long-standing conceptual challenges of quantizing NLSM in general. A key technical tool, that will allow us to make progress, is the so-called ODE/IQFT correspondence. Among the results presented in this thesis is a new approach to the problem with non-ultralocality; a study of the integrable structures in the O(3) model as well as its deformation; and a remarkable relation between the Casimir energies of the deformed O(4) model and certain solutions of the modified sinh-Gordon equation. The original obtained results of the thesis have been published in the papers, whose preprints can be found on the arXiv 1409.0449, 1706.09941, 1805.07417.
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LIN, KUAN-TING, and 林冠廷. "Architecture Design of Non-Linear Multi-Band Quantization Algorithm Using Piecewise Approximation." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/wy8p6m.

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碩士<br>國立高雄第一科技大學<br>電腦與通訊工程系碩士班<br>105<br>(Electrogardiography, ECG) is a thoracic cavity in time to record the process of heart contraction by collecting different signals on the body﹐through the sensor to complete the non-invasive detection technology that is widely used in clinical diagnosis of heart disease﹒With the development of science and technology, the ECG device combines wireless transmission and wearable devices equipped with miniaturization physiological signal sensing technology have proportion increased﹒Wireless transmission consumes large amount of power, its power consumption is positively proportional to the amount of data transmission﹐but both heart disease examinations and research require long-time records to solve problems such us storage and transmission﹔thus ECG data compression is crucial absolutely﹒ We have developed on wavelet transform-based ECG compression system with quality assurance mechanism in previous study﹒The system consists of three processing units﹐respectively : Lossless rounding of Wavelet transform, Quantization of quality assurance mechanism, Set Partitioning in Hierarchical Trees(SPIHT)﹒The core of the data compression is through Non-linear quantization of eleven bands﹐and controlled by a single parameter﹐and then through a linear prediction and error calculation module to obtain a new quantization parameters to implement quality assurance mechanism﹒ 　　Since the quantization process requires a lot of multiplication and division operations ﹐this unfavorable hardware development﹐so we proposed non-liner multi-band quantization algorithm using piecewise approximation﹒ The experiments of this study implement the hardware architecture of quantization in ECG data compression system﹐adopt the Cell-Based Design Flow as the development process of the hardware architecture﹐and use Synopsys (Verilog, Verdi, Design Compiler, Synthesis, PrimeTime®) and Cell Library (TSMC 90nm CLN90G) as a development tool and experimental process﹒
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CHU, TAI-FENG, and 朱泰峰. "Analysis and Research of Using Non-linear Quantization Strategy in Hebbian-type Associative Memories." Thesis, 2006. http://ndltd.ncl.edu.tw/handle/52333178207743016024.

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碩士<br>東海大學<br>資訊工程與科學系碩士在職專班<br>94<br>In order to widely apply Hebbian-type Associative Memories in every field, the most common way at present time is utilizing VLSI to make Hebbian-type Associative Memories. However, as pattern saving increasing, the number of times between neuron of traditional Hebbian-type Associative Memories and interconnection will increase quickly simultaneously. It comes to bottleneck when actually manufacture VLSI. There are two directions to solve this problem. One is to develop high-rank Hebbian-type Associative Memories, the other is to decrease interconnection inside of Hebbian-type Associative Memories. Although high-rank Hebbian-type Associative Memories may add to save patterns, yet, the connection inside will inevitably increase rapidly. Therefore, how to decrease interconnection is the radical solution to settle this problem once for all. Making use of quantization strategy to decrease interconnection is quite an efficient way. Chung & Tsai has focused on connection numerical quantization of Hebbian-type Associative Memories to make analysis. They found Hebbian-type Associative Memories of fairly good contractility after quantization. The strategy they applied are two-level, three-level and linear quantization. One important characteristics of Hebbian-type Associative Memories is its interconnection value owns Gauss scattering distinction. It will enhance performance of Hebbian-type Associative Memories if making use of its distinction as the strategy in applying non-linear quantization. In this research, we introduce one order and quadratic Hebbian-type Associative Memories, derive equation of probability of direct convergence from linear quantization strategy. The key-point of this research is non-linear quantization strategy is integrated by Gauss possibility density function, then, divide area according to requirements and equal every segmentation area to seek the length that every segmentation possesses on X-axis, next, calculate up & down limit value based on proportion of length of every segmentation area to the whole area. Afterwards, carry this value back to the equation of probability of direct convergence after original linear quantization and become equation of probability of direct convergence after non-linear quantization of Hebbian-type Associative Memories. Hence, We may compare which one is superior by investigating between linear & non-linear equation of probability of direct convergence Comparing experiment results between linear & non-linear quantization equation of probability of direct convergence, we may clearly observe the performance of probability of convergence in non-linear quantization strategy is far more superior than in linear quantization strategy. Therefore, when producing tip, non-linear quantization strategy owns more practically merits in Hebbian-type Associative Memories.
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lie, qiao-wen, and 劉喬溫. "Hardware Implementation of Non-Linear Quantization Algorithm for a Wavelet-based ECG Data Compress System." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/47141846326653021820.

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碩士<br>國立高雄第一科技大學<br>電腦與通訊工程所<br>95<br>Electrocardiogram (ECG) signal analysis is a non-invasive modality widely used for heart disease clinical diagnosis .The diagnosis of cardiac patients depends on the quality of the recording signal or effective real-time data transmission. ECG compression system and auto-recording signal is good choices. Associating the RROLT with the 1-D NRDPWT,1-D RRO-NRDPWT apply to ECG compression systems successfully. This non-linear quantization algorithm base on 1-D RRO-NRDPWT can obtain a superior compression performance. The algorithm have two character. First, by adjust the single quantization factor (QF). Section, this algorithm impact factor (QF) attempts to keep PRD and CR in linear relationship. And non-linear quantization algorithm make a great impact on ECG compression systems other than improving compression performance of whole system. Besides，it is based on quantization error of frequency-domain aspiration to base on quality prediction of time-domain and converge on linear error predetermination model,fast. We formulated an adaptive and real-time compression mechanism ECG compression systems architecture base on a linear error predetermination model and dynamic quantization algorithm. Quantization process of this architecture is use of integer multiplication. Component of multiplication make a great impact on quantization process performance, crucially. We proposed a novel recursive multiplier. It has error of linear and low power performance to content with portable application. The MIT-BIH arrhythmia database is used for testing signals and experimental results show that quantization scale of finite word-length between academic value can obtain CR-PRD curve to save for error of bias, only. The novel recursive multiplier can obtain a superior hardware performance over traditional recursive multiplier and the area with power consumption is improved by 39% with 32% ,respectively, but the critical path delay 3%.However, it can achieve aim of the portable quality of the recording signal.
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Machireddy, Amrutha. "Learning Non-linear Mappings from Data with Applications to Priority-based Clustering, Prediction, and Detection." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5670.

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With the volume of data generated in today's internet-of-things, learning algorithms to extract and understand the underlying relations between the various attributes of data have gained momentum. This thesis is focused on learning algorithms to extract meaningful relations from the data using both unsupervised and supervised learning algorithms. Vector quantization techniques are popularly used for applications in contextual data clustering, data visualization and high-dimensional data exploration. Existing vector quantization techniques, such as, the K-means and its variants and those derived from the self-organizing maps consider the input data vector as a whole without prioritizing over individual coordinates. Motivated by applications requiring priorities over data coordinates, we develop a theory for clustering data with different priorities over the coordinates called the data-dependent priority-based soft vector quantization. Based on the input data distribution, the priorities over the data coordinates are learnt by estimating the marginal distributions over each coordinate. The number of neurons approximating each coordinate based on the priority are determined through a reinforcement learning algorithm. Analysis on the convergence of the proposed algorithm and the probability of misclassification are presented along with simulation results on various data sets. Self-organizing maps (SOM) are popularly used for applications in learning features, vector quantization, and recalling spatial input patterns. The adaptation rule in SOMs is based on the Euclidean distance between the input vector and the neuronal weight vector along with a neighborhood function that brings in topological arrangement of the neurons in the output space. It is capable of learning the spatial correlations among the data but fails to capture temporal correlations present in a sequence of inputs. We formulate a potential function based on a spatio-temporal metric and create hierarchical vector quantization feature maps by embedding memory structures similar to long short-term memories across the feature maps to learn the spatio-temporal correlations in the data across clusters. Error correction codes such as low density parity check codes are popularly used to enhance the performance of digital communication systems. The current decoding framework relies on exchanging beliefs over a Tanner graph, which the encoder and decoder are aware of. However, this information may not be available readily, for example, in covert communication. The main idea is to build a neural network to learn the encoder mappings in the absence of knowledge of the Tanner graph. We propose a scheme to learn the mappings using the back-propagation algorithm. We investigate into the choice of different cost functions and the number of hidden neurons for learning the encoding function. The proposed scheme is capable of learning the parity check equations over a binary field towards identifying the validity of a codeword. Simulation results over synthetic data show that our algorithm is indeed capable of learning the encoder mappings. We also propose an approach to identify noisy codes using uncertainty estimation and to decode them using autoencoders. In the next work, we consider the convolutional neural networks which are widely used in natural language processing, video analysis, and image recognition. However, the popularly used max-pooling layer discards most of the data, which is a drawback in applications, such as, prediction of video frames. We propose an adaptive prediction and classification network based on a data-dependent pooling architecture. We formulate a combined cost function for minimizing the prediction and classification errors. We also detect the presence of an unseen class during testing for digit prediction in videos.
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Silva, Solange Vieira da. "Confinamento da luz num ressoador aberto." Master's thesis, 2015. http://hdl.handle.net/10316/40471.

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Books on the topic "Non-linear quantization"

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Andersson, S. I., and H. D. Doebner. Non-Linear Partial Differential Operators and Quantization Procedures: Proceedings of a Workshop Held at Clausthal, Federal Republic of Germany 1981. Springer London, Limited, 2006.

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Horing, Norman J. Morgenstern. Quantum Statistical Field Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.001.0001.

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The methods of coupled quantum field theory, which had great initial success in relativistic elementary particle physics and have subsequently played a major role in the extensive development of non-relativistic quantum many-particle theory and condensed matter physics, are at the core of this book. As an introduction to the subject, this presentation is intended to facilitate delivery of the material in an easily digestible form to students at a relatively early stage of their scientific development, specifically advanced undergraduates (rather than second or third year graduate students), who are mathematically strong physics majors. The mechanism to accomplish this is the early introduction of variational calculus with particle sources and the Schwinger Action Principle, accompanied by Green’s functions, and, in addition, a brief derivation of quantum mechanical ensemble theory introducing statistical thermodynamics. Important achievements of the theory in condensed matter and quantum statistical physics are reviewed in detail to help develop research capability. These include the derivation of coupled field Green’s function equations of motion for a model electron-hole-phonon system, extensive discussions of retarded, thermodynamic and non-equilibrium Green’s functions, and their associated spectral representations and approximation procedures. Phenomenology emerging in these discussions includes quantum plasma dynamic, nonlocal screening, plasmons, polaritons, linear electromagnetic response, excitons, polarons, phonons, magnetic Landau quantization, van der Waals interactions, chemisorption, etc. Considerable attention is also given to low-dimensional and nanostructured systems, including quantum wells, wires, dots and superlattices, as well as materials having exceptional conduction properties such as superconductors, superfluids and graphene.
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Book chapters on the topic "Non-linear quantization"

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Accardi, Luigi, Andreas Boukas, Yun-Gang Lu, and Alexander Teretenkov. "The Non–linear and Quadratic Quantization Programs." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-06170-7_1.

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Kim, Gihwan, Jemin Lee, Sihyeong Park, Yongin Kwon, and Hyungshin Kim. "Mixed Non-linear Quantization for Vision Transformers." In Lecture Notes in Computer Science. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-91979-4_10.

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Zhang, Liang, Gang Luo, and Haoyan Zhang. "Non-fragile $$ H_{\infty } $$ Controller Design for Linear Discrete-System with Quantization." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-98776-7_95.

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Bas, Patrick. "A Quantization Watermarking Technique Robust to Linear and Non-linear Valumetric Distortions Using a Fractal Set of Floating Quantizers." In Information Hiding. Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11558859_9.

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Peebles, P. J. E. "Historical Development." In Quantum Mechanics. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691209821.003.0001.

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This chapter presents the origins of quantum mechanics. The story of how people hit on the highly non-intuitive world picture of quantum mechanics, in which the physical state of a system is represented by an element in an abstract linear space and its observable properties by operators in the space, is fascinating and exceedingly complicated. The much greater change from the classical world picture of Newtonian mechanics and general relativity to the quantum world picture came in many steps taken by many people, often against the better judgment of participants. There are three major elements in the story. The first is the experimental evidence that the energy of an isolated system can only assume special discrete or quantized values. The second is the idea that the energy is proportional to the frequency of a wave function associated with the system. The third is the connection between the de Broglie relation and energy quantization through the mathematical result that a wave equation with fixed boundary conditions allows only discrete quantized values of the frequency of oscillation of the wave function (as in the fundamental and harmonics of the vibration of a violin string).
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Conference papers on the topic "Non-linear quantization"

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Alonso, Marian Temprana, Farhad Shirani, Neil Irwin Bernardo, and Yonina C. Eldar. "Non-Linear Analog Processing Gains in Task-Based Quantization." In 2024 IEEE International Symposium on Information Theory (ISIT). IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619674.

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Pankiv, Oleksandr, and Dariusz Puchala. "Neural implementation of non-linear scalar quantization." In 2023 Data Compression Conference (DCC). IEEE, 2023. http://dx.doi.org/10.1109/dcc55655.2023.00047.

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Faundez-Zanuy, Marcos. "Non-linear predictive vector quantization of speech." In 7th European Conference on Speech Communication and Technology (Eurospeech 2001). ISCA, 2001. http://dx.doi.org/10.21437/eurospeech.2001-466.

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Depoian, Arthur C., Colleen P. Bailey, Ethan Murrell, and Parthasarathy Guturu. "PCA informed non-linear channel color quantization." In Multimodal Image Exploitation and Learning 2023, edited by Sos S. Agaian, Stephen P. DelMarco, and Vijayan K. Asari. SPIE, 2023. http://dx.doi.org/10.1117/12.2664117.

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Teodoro, Sara, Adao Silva, Rui Dinis, and Atilio Gameiro. "Theoretical analysis of non-linear quantization of broadband channels." In 2015 IEEE Conference on Standards for Communications and Networking (CSCN). IEEE, 2015. http://dx.doi.org/10.1109/cscn.2015.7390463.

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Guo, Lei, Wei Chen, Yuxuan Sun, and Bo Ai. "Device-Edge Digital Semantic Communication with Trained Non-Linear Quantization." In 2023 IEEE 97th Vehicular Technology Conference (VTC2023-Spring). IEEE, 2023. http://dx.doi.org/10.1109/vtc2023-spring57618.2023.10200355.

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7

Dong, Pingcheng, Yonghao Tan, Dong Zhang, et al. "Genetic Quantization-Aware Approximation for Non-Linear Operations in Transformers." In DAC '24: 61st ACM/IEEE Design Automation Conference. ACM, 2024. http://dx.doi.org/10.1145/3649329.3657314.

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8

Sarmast, Mehdi, Saeed Bostan Manesh M., and Mahmood R. Mehran. "Sensitivity of NL-RDM to Errors in the Non-Linear Test Process." In ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2009. http://dx.doi.org/10.1115/smasis2009-1275.

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Abstract:
NL-RDM is a non-linear system identification method that combines a number of linear and non-linear system identification methods and offers a practical approach to the identification of lumped parameter and continuous systems using a classical linear modal model with additional non-linear terms. The method was started by identifying the modal parameters of the underlying linear system via the FRF, MMIF and appropriated force vector. The criteria for an ideal method are detailed in the some earlier papers, but the reality creates a limitation. This paper is divided into several sections relating to the “Nonlinear Test Process”. Error which arise from test, environmental and equipment effects, are quantization errors, input (or process) noise and measurement noise. So, the effects of these inaccuracies and possible solutions for decreasing any negative effects are considered. Then, The sensitivities to noise and quantization which could be encountered in practical applications of the NL-RDM, are discussed in concept, generated, applied and analyzed through simulation programme for two degree of freedom uncoupled and coupled examples.
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Tadic, V. B., and A. Doucet. "A simulation based algorithm for optimal quantization in non-linear/non-Gaussian state-space models." In Proceedings of the 2004 American Control Conference. IEEE, 2004. http://dx.doi.org/10.23919/acc.2004.1384713.

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Belonenko, M. B., and E. V. Demushkina. "Quantization of non-linear waves in one-dimensional system of admixture atoms." In SPIE Proceedings, edited by Vitaly V. Samartsev. SPIE, 2006. http://dx.doi.org/10.1117/12.675144.

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