Linear Transformation Research Articles

Higher-order quantum transformations of Hamiltonian dynamics

We present a quantum algorithm to achieve higher-order transformations of Hamiltonian dynamics. Namely, the algorithm takes as input a finite number of queries to a black-box seed Hamiltonian dynamics to simulate a desired Hamiltonian. Our algorithm efficiently simulates linear transformations of any seed Hamiltonian with a bounded energy range consisting of a polynomial number of terms in system size, making use of only controlled-Pauli gates and time-correlated randomness. This algorithm is an instance of quantum functional programming, where the desired function is specified as a concatenation of higher-order quantum transformations. By way of example, we demonstrate the simulation of negative time-evolution and time-reversal, and perform a Hamiltonian learning task. Published by the American Physical Society 2024

Linear semantic transformation for semi-supervised medical image segmentation

Medical image segmentation is a focus research and foundation in developing intelligent medical systems. Recently, deep learning for medical image segmentation has become a standard process and succeeded significantly, promoting the development of reconstruction, and surgical planning of disease diagnosis. However, semantic learning is often inefficient owing to the lack of supervision of feature maps, resulting in that high-quality segmentation models always rely on numerous and accurate data annotations. Learning robust semantic representation in latent spaces remains a challenge. In this paper, we propose a novel semi-supervised learning framework to learn vital attributes in medical images, which constructs generalized representation from diverse semantics to realize medical image segmentation. We first build a self-supervised learning part that achieves context recovery by reconstructing space and intensity of medical images, which conduct semantic representation for feature maps. Subsequently, we combine semantic-rich feature maps and utilize simple linear semantic transformation to convert them into image segmentation. The proposed framework was tested using five medical segmentation datasets. Quantitative assessments indicate the highest scores of our method on IXI (73.78%), ScaF (47.50%), COVID-19-Seg (50.72%), PC-Seg (65.06%), and Brain-MR (72.63%) datasets. Finally, we compared our method with the latest semi-supervised learning methods and obtained 77.15% and 75.22% DSC values, respectively, ranking first on two representative datasets. The experimental results not only proved that the proposed linear semantic transformation was effectively applied to medical image segmentation, but also presented its simplicity and ease-of-use to pursue robust segmentation in semi-supervised learning. Our code is now open at: https://github.com/QingYunA/Linear-Semantic-Transformation-for-Semi-Supervised-Medical-Image-Segmentation.

Transductive classification via patch alignment

In this paper, a novel approach for transductive classification is proposed. Unlike existing methods that heavily rely on constructing the Laplacian matrix to capture data distribution, the proposed approach takes a unique path. It employs a linear transformation model to create local patches for each data point and then unifies them in an objective function to build the Laplacian matrix. Incorporating this Laplacian matrix into the transductive classification framework allows us to assign optimal class labels globally. The experimental results from toy data and real world databases demonstrate that the proposed approach achieves more efficient and stable performance, while this approach is insensitive to the parameters. Notably, our method exhibits robustness to parameter variations, making it highly adaptable to practical applications.

Surrogate methods for determining profiles of material properties of planar test objects with accumulation of apriori information about them

New methods for identifying the material properties of planar objects as a result of measurements by the eddy current method are proposed. The methods are based on the latest surrogate strategies and advanced optimization techniques that improve efficiency and reduce resource consumption of problem solutions, and balance computational complexity with the accuracy of the results. High-performance metamodels for global surrogate optimization are based on deep truly meaningful fully connected neural networks, serving as an additional function of accumulating apriori information about objects. High accuracy of the approximation of the multidimensional response surface, which is determined by the “exact” electrodynamic model of the testing process, is ensured by performing calculations according to the computer design of a homogeneous experiment with a low weighted symmetric centered discrepancy. The results of numerical experiments performed for full and reduced dimensional search spaces, which can be obtained by linear transformations using the principal component method, are presented. The verification of the methods proved their sufficiently high accuracy and computational performance.

A novel Dual-Branch Asymmetric Encoder–Decoder Segmentation Network for accurate colonic crypt segmentation

Colorectal cancer (CRC) is a leading cause of cancer-related deaths, with colonic crypts (CC) being crucial in its development. Accurate segmentation of CC is essential for decisions CRC and developing diagnostic strategies. However, colonic crypts’ blurred boundaries and morphological diversity bring substantial challenges for automatic segmentation. To mitigate this problem, we proposed the Dual-Branch Asymmetric Encoder–Decoder Segmentation Network (DAUNet), a novel and efficient model tailored for confocal laser endomicroscopy (CLE) CC images. In DAUNet, we crafted a dual-branch feature extraction module (DFEM), employing Focus operations and dense depth-wise separable convolution (DDSC) to extract multiscale features, boosting semantic understanding and coping with the morphological diversity of CC. We also introduced the feature fusion guided module (FFGM) to adaptively combine features from both branches using cross-group spatial and channel attention to improve the model representation in focusing on specific lesion features. These modules are seamlessly integrated into the encoder for effective multiscale information extraction and fusion, and DDSC is further introduced in the decoder to provide rich representations for precise segmentation. Moreover, the local multi-layer perceptron (LMLP) module is designed to decouple and recalibrate features through a local linear transformation that filters out the noise and refines features to provide edge-enriched representation. Experimental evaluations on two datasets demonstrate that the proposed method achieves Intersection over Union (IoU) scores of 81.54% and 84.83%, respectively, which are on par with state-of-the-art methods, exhibiting its effectiveness for CC segmentation. The proposed method holds great potential in assisting physicians with precise lesion localization and region analysis, thereby improving the diagnostic accuracy of CRC.

Energy and self-adaption in a memristive map neuron

Both capacitor and charge-controlled memristor (CCM) can regulate the inner energy levels during the release and accumulation of charges in these electronic components. Combination of inductive and capacitive components is crucial to build an oscillatory circuit, and incorporation of a nonlinear resistor is helpful to support nonlinear oscillation under continuous energy exchange between magnetic field and electric field. Relation between physical variables in neural circuits can be described by some equivalent nonlinear oscillators by applying scale transformation on the variables and parameters for the neural circuit, and the energy function becomes available from theoretical approach. In this work, a simple neural circuit coupled with a CCM is designed to obtain a memristive neuron model, and then linear transformation is applied to the sampled variables involved with time scale for time step, a new memristive map is obtained to discuss its energy characteristic and self-controllability under energy flow. The result provides guidance to measure the reliability of maps, and the new derived maps with reliable physical evidences can be further used in digital signal processing.

Frame set for Gabor systems with Haar window

We describe the full structure of the frame set for the Gabor system G(g;α,β):={e−2πimβ⋅g(⋅−nα):m,n∈Z} with the window being the Haar function g=−χ[−1/2,0)+χ[0,1/2). This is the first compactly supported window function for which the frame set is represented explicitly.The strategy of this paper is to introduce the piecewise linear transformation M on the unit circle, and to provide a complete characterization of structures for its (symmetric) maximal invariant sets. This transformation is related to the famous three gap theorem of Steinhaus which may be of independent interest. Furthermore, a classical criterion on Gabor frames is improved, which allows us to establish a necessary and sufficient condition for the Gabor system G(g;α,β) to be a frame, i.e., the symmetric invariant set of the transformation M is empty.

Innovative K-Means based machine learning method for determination of non-uniform image coordinate system in panoramic imaging: a case study with Ladybug2 camera.

Currently, the practical implementations of panoramic cameras range from vehicle navigation to space studies due to their 360-degree imaging capability in particular. In this variety of uses, it is possible to calculate three-dimensional coordinates from a panoramic image, especially using the Direct Linear Transformation (DLT) method. There are several types of omnidirectional cameras which can be classified mainly as central and non-central cameras for 360-degree imaging. The central omnidirectional cameras are those which satisfy the single-viewpoint characteristic. Multi-camera systems are usually developed for applications for which two-image stereo vision is not flexible enough to capture the environment surrounding a moving platform. Although the technology based on multi-view geometry is inexpensive, accessible, and highly customizable, multi-camera panoramic imaging systems pose a difficulty in obtaining a single projection center for the cameras. In this study, not only a defining method of the non-uniform image coordinate system is suggested by means of the K-Means algorithm for a single panoramic image, captured with a Ladybug2 panoramic camera in the panoramic calibration room but also the use of an elliptical panoramic projection coordinate system definition by Singular Value Decomposition (SVD) method in panoramic view. The results of the suggested method have been compared with the DLT algorithm for a single panoramic image which defined a conventional photogrammetric image coordinate system.

Electromagnetic Vibration and Noise Analysis of Linear Phase-Shifting Transformer

The advantages of adjustable angle phase-shifting and great expansibility make the linear phase-shifting transformer a novel type of power conversion device with a wide range of potential applications. However, during the procedure, there is a lot of noise. For the purposes of transformer design and vibration and noise reduction, it is crucial to investigate its electromagnetic vibration and noise. In this paper, the radial electromagnetic force wave considering the influence of the end effect as the source of the noise of the linear phase-shifting transformer was deduced and calculated. Based on this, the spectrum and space–time properties of the radial electromagnetic force waves were simulated and verified. Additionally, a finite element model was created using the Ansys Workbench 2022R1 platform to study the electromagnetic vibration and noise of the linear phase-shifting transformer. A joint simulation of the electromagnetic, structural, and sound fields was then performed. First, the transformer’s natural frequency was determined by modal analysis. After that, the transformer’s structure and the results of the transient electromagnetic field computation were combined and a harmonic response analysis was conducted to determine the vibration acceleration spectrum. Finally, in order to solve the sound pressure field, the transformer’s boundary vibration acceleration was coupled to the air domain. Furthermore, an analysis was conducted to determine the noise distribution surrounding the linear phase-shifting transformer. The joint simulation findings demonstrate that the linear phase-shifting transformer’s resonance, which produces larger electromagnetic vibration and noise, is indeed caused by the radial electromagnetic force. Simultaneously, the impact of the LPST core’s fixed components on the electromagnetic vibration and noise of the core was examined.

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Efficient solutions for vector optimization problem on an extended interval vector space and its application to portfolio optimization

In this paper, a generalized interval vector space is investigated and defined as an ordered relation in the form of a bijective linear transformation of its onto a real vector space. The ordered relation is utilized to formulate an interval optimization problem in the same manner as a classical multi-objective programming problem. A methodology that addresses the existence of efficient solutions for the multi-objective interval optimization problem has also been discussed. Various numerical examples are described to illustrate and substantiate all developed concepts. Furthermore, the multi-objective portfolio rebalancing problem for a time horizon is designed based on the developed interval vector optimization. An algorithm using exhaustive solution technology has been proposed to achieve an efficient investment strategy. Finally, its applicability and efficacy are analyzed using Bombay Stock Exchange India data sets.

Gabor frames on finite non-cyclic Abelian groups

We attempt to analyze Gabor frames for L2 spaces on finite non cyclic abelian groups from their natural perspectives and establish their equivalence with Gabor frames on the isomorphic product groups of finite cyclic groups by means of unitary and non unitary invertible linear transformations. Gabor frames and their canonical dual frames on finite non cyclic groups are identified as the images of the same Gabor frame on a finite product of finite cyclic groups under invertible linear transformations.

Tuberculin skin test result detection method based on CSN-II and improved OTSU method

The tuberculin skin test (TST) is an intradermal test used to diagnose Type IV hypersensitivity reactions caused by Mycobacterium tuberculosis infection. Segmentation of TST result images provides a foundation for large-scale tuberculosis screening and auxiliary diagnosis. This paper presents a specialized method for identifying TST results. Initially, a clustering approach is employed to reduce pixel complexity, followed by a linear transformation using CSN-II to enhance the original RGB space with robust color space properties. Subsequently, high-probability pixel points are located, and their Gaussian kernel convolution range is determined using the Bhattacharyya Distance. Through convolution and iterative feature amplification, the target characteristics are progressively enhanced. Finally, an improved OTSU method is proposed for segmenting TST result images. In this method, an adaptive entropy threshold is utilized to reduce the search range of the OTSU method, enhancing the relative contrast between the target and the background. Moreover, a weighted adjustment is applied to the obtained OTSU threshold to prevent drift towards backgrounds with larger intra-class variances. Experimental results demonstrate that the proposed method achieves higher segmentation accuracy and robustness in TST result image segmentation compared to traditional OTSU methods and other improved approaches, such as the neighborhood valley-emphasis method, logarithmic OTSU, and weighted OTSU, Finally, we calculate a relative value is calculated by dividing the remaining number of segmented pixels by the total number of pixels, we then classify the results based on the relative value and in reference to medical diagnostic standards our method is intended to establish an algorithmic basis for rapid screening and classification of tuberculosis on a large scale.

An on-chip microarray platform for material-temperature optimization and gas discrimination

The demand for gases detection has promoted extensive research into gas sensors. Sensor arrays can be used as electronic olfaction units for complex gas detection and identification. However, the gas sensing properties are affected by various factors. The multi-dimensional nature of those interactions is crucial for creating a sensor array with diverse responses, but it is also challenging to fabricate an array considering all these parameters, particularly in miniaturization. In this paper, we present a framework that can take multiple factors into consideration and help to fabricate an optimal array for gas identification. 32 sensors including different MOS materials (SnO2, In2O3, WO3), morphologies (microsphere, nanoparticle, nanoflake), doped/loaded metals (Pd, Pt, Ce, Ru, Rb), and operational temperatures (250℃∼370℃) are discussed. A material-temperature-analyte-response database was then established by storing their response characteristics towards low ppm concentrations of ammonia, ethyl acetate, toluene, methanol, ethanol, and acetone. An optimized array was then constructed out of 10,518,300 possible combinations of materials and operational temperatures. Results showed improvements in discrimination ability and the optimized array integrated into the chip can provide vector signals with high selectivity, completely recognizing all the 6 target gases and even for their multi-component mixture after linear discriminant analysis transformation.

Discrete Octonion Linear Canonical Transform: Definition and Properties

In this paper, the discrete octonion linear canonical transform (DOCLCT) is defined. According to the definition of the DOCLCT, some properties associated with the DOCLCT are explored, such as linearity, scaling, boundedness, Plancherel theorem, inversion transform and shift transform. Then, the relationship between the DOCLCT and the three-dimensional (3-D) discrete linear canonical transform (DLCT) is obtained. Moreover, based on a new convolution operator, we derive the convolution theorem of the DOCLCT. Finally, the correlation theorem of the DOCLCT is established.

Olsson.wl & ROC2.wl: Mathematica packages for transformations of multivariable hypergeometric functions & regions of convergence for their series representations in the two variables case

We present the Olsson.wlMathematica package which aims to find transformations for some classes of multivariable hypergeometric functions. It is based on a well-known method developed by P. O. M. Olsson [1] (1964) to derive the analytic continuations of the Appell F1 double hypergeometric series using the linear transformations of the Gauss F12 hypergeometric function. We provide a brief description of the method of Olsson and demonstrate the use of the commands of the Olsson.wl package using some examples that are presented in the text and in some ancillary Mathematica notebooks. In particular, we reproduce various results of the literature on multivariable hypergeometric functions and show practical applications of this package in the derivation of novel formulas. In the context of high energy physics, we also demonstrate how it can be used to disentangle some known results about the analytic continuation of some series representations of the one-loop pentagon in multi-Regge kinematics and D=6−2ϵ. We also provide a companion package, called ROC2.wl, which is dedicated to the derivation of the regions of convergence of double hypergeometric series. This package can be used independently of Olsson.wl. Program summaryProgram Title:Olsson.wlCPC Library link to program files:https://doi.org/10.17632/gc63xzwzz5.1Licensing provisions: GNU General Public License v3.0.Programming language: Wolfram Mathematica version 11.3 and beyond.Nature of problem: To find the transformation formulas of multivariable hypergeometric series appearing in Feynman integral calculus.Solution method: Mathematica implementation of the method of Olsson [1]. The method uses the transformation theory of lower variable hypergeometric functions to find the transformation formulas of higher variable hypergeometric functions.Companion package:ROC2.wl, which is a Mathematica package used inside Olsson.wl and can also be used as a standalone package. The package is used to find the region of convergence of double hypergeometric functions, using Horn's theorem.

A Setting Optimization Ensemble for a Distributed Power Grid Protective Relay

To ensure a stable and reliable power supply, the valid and timely response of protective relays are indispensable. Through the prevention of fault expansions, potential equipment damage or system collapse can be averted, where their setting is one vital prerequisite for such effective implementations. However, the increasing complexity of distribution power systems results in more challenges for protection tuning strategies. Ergo, this paper presents an ensemble that combines the independent factor evaluation (IFE) and quantum genetic optimization (QGO) models to further optimize the performance of relays according to their distributed tuning environment. In this ensemble, both near and far-end fault characteristics can be incorporated. In the first stage, the IFE dimensional reduction model is deployed for massive heterogeneous input data, where the statistical independence of input signals is calculated, the linear transformation matrix to decouple mixed signals is found, the linear combination of such signals is formed, and the non-Gaussian property to sort them is established. This can ameliorate the following calculation efficiency under those high-dimensional data scenarios. Subsequently, the QGO model is designed to further improve relay settings, where qubit representation is built to reduce required chromosomes, the linear superposition of the optimal solution probability in different states is implemented for a better diversity and convergence performance, and a self-adaption quantum gate is established to dynamically update the qubit chromosome groups and two-state solution combinations. Lastly, an empirical case study is presented, which validates the enhanced convergence, accuracy, and rapidity of the proposed ensemble.

Multi-distribution bi-deniable inner product encryption based on Decision-LWE

Bi-deniable Encryption scheme means that when the sender and the receiver are coerced, the coercer can obtain fake plaintext, random numbers, and secret keys. It’s a solution strategy in the case of information leakage. Compared with traditional encryption, deniable encryption can provide secret communications in situations of coercion in the Post-Quantum era. Compared with sender-deniable encryption and receiver-deniable encryption, bi-deniable encryption can achieve secret communications in the situation that both sender and receiver are coerced by the coercer. So, we propose to design a bi-deniable encryption scheme under the multi-distribution model. In our bi-deniable encryption scheme, we construct a bi-deniable encryption scheme based on the assumption of Decision-Learning With Errors (DLWE) under the multi-distribution model. Firstly, the principle of Inner Product Predicate Encryption (IPPE) is applied in our scheme. Secondly, we apply the framework of Bi-Translucent Set (BTS), combined with inner product predicate encryption. Thirdly, we construct a series of probabilistic polynomial time algorithms, which apply linear transformation between different lattice structures, and Regev dual encryption. Fourthly, the statistical indistinguishability between the sampling algorithm with discrete Gaussian sampling algorithm, and the computational indistinguishability between LWE’s ciphertext samples with uniform samples, the property of indistinguishability is applied in theorem proving, which obtain Indistinguishability under Chosen Plaintext Attacks (IND-CPA) security and the property of bi-deniability. Given the value range of the Gaussian parameter and security parameter in our scheme, the correctness of the bi-deniable encryption scheme is guaranteed. We also give the security proof of IND-CPA and bi-deniability’s property by a series of games. The ‘Inner-Product Bi-Translucent Set’ Bi-Deniable Encryption scheme under the multi-distribution model is based on Decision-LWE assumption, and can avoid quantum-resistant attacks. The bi-deniable encryption scheme is firstly constructed by the inner product with the Decision-LWE assumption, which can provide better properties of security and deniability.

A probability-exponential method of converting Z-numbers and its systematic applications in multi-attribute decision making

Z-numbers contain fuzzy restrictions, credibility measures, and probability distributions to effectively represent uncertain information. Converting Z-numbers to fuzzy numbers facilitates extensive applications (such as multi-attribute decision-making (MADM)), thus becoming valuable for research purposes. Regarding Z-number conversions, the original method never considers the association probability, while probabilistic strategies offer better informatization. Recently, a probability-driven conversion starts with a linear transformation of the centroid difference between the fuzzy restriction and probabilistic distribution. However, it has the invalidation weakness of edge information due to underlying non-normalization. To improve this probability-linear conversion, a Z-number conversion is proposed by using underlying probability-exponential descriptions, and this new method is further applied to MADM. At first, the current probability-linear conversion is analyzed based on the initial non-probabilistic conversion, and its intrinsic weakness and correctional improvement are revealed. Then, the novel probability-exponential conversion resorts to an exponential characterization of centroid difference between the restriction and distribution, and it gains information enrichment due to underlying normalization. The refined method preserves the inherent characteristics of Z-numbers more effectively, facilitating their application in subsequent engineering practices. This is especially pertinent in decision-making systems based on expert input and initial value problems. The proposed method for converting Z-numbers aims to minimize information loss in transitions between Z-numbers and classical fuzzy numbers. This approach will be further explored in future research. Furthermore, the probability-exponential conversion induces an ExpTODIM algorithm for MADM, called PE-ExpTODIM. Three Z-number conversions (i.e., the non-probabilistic, probability-linear, and probability-exponential types) and three decision algorithms (i.e., ExpTODIM, EDAS, MOORA) are combined to establish a 3 × 3 framework of Z-number-driven MADM. Finally, the systematical 9 algorithms are applied to the problem of site selection of carbon storage. They are validated by criss-cross contrast analyses and statistical significance tests. Thus, PE-ExpTODIM exhibits the desired optimization. The last technology of statistical testing is original, ingenious, and valuable for MADM.

Peristaltic transport of viscoelastic fluid in curved ducts with ciliated walls

The transport of complex rheological fluids in physiological ducts is often facilitated by the dynamic phenomenon of peristalsis. Additionally, peristaltic transport assisted by cilia plays a significant role in various natural processes such as respiration, circulation, locomotion, and reproduction. This study focuses on magnetically induced flow bounded by non-uniform curved walls, motivated by the importance of peristalsis and micro-organism motility. To characterize the complex rheology of the fluid liner, a viscoelastic model described by the constitutive equation of Jeffrey's fluid is employed. The flow problem is mathematically formulated using curvilinear coordinates. Subsequently, linear transformations and scaling factors are applied to convert the equations into dimensionless form, while considering biotic restrictions such as creeping transport and long wavelength to reduce dependent variables. By utilizing the stream function and cross-differentiation, a fourth-order equation is obtained and numerically approximated using the shooting method. The effects of various parameters on the flow are illustrated through graphs, and a physical interpretation of the graphical results is provided. It is observed that ciliated walls of the channel enhance the velocity and pumping, while trapping phenomena are more pronounced in a non-uniform channel compared to a uniform channel.