Diagonal Correlation Research Articles

Quantum encryption of healthcare images: Enhancing security and confidentiality in e‐health systems

AbstractEnsuring the security and privacy of patient data in e‐healthcare systems that rely on cloud computation is of utmost importance. Traditional encryption is no longer resistant to quantum attacks and safeguards sensitive medical images. To tackle this issue, robust security countermeasures are proposed by integrating quantum encryption with a cloud‐based healthcare system. The encryption scheme utilizes the Generalized Novel Enhancement Quantum Representation (GNEQR) and the Novel Enhancement Quantum Representation (NEQR) to provide a framework for representing color and grayscale healthcare images. The proposed quantum algorithm uses quantum logic for image scrambling, which is combined with the encryption key by the Xor quantum gate. The encryption key is generated by 9D chaotic and permutated before encryption. Finally, channel re‐ordering is applied for color images. The simulation results for 15 medical tests with an encryption key space >2600 on a developed e‐healthcare system demonstrate the effectiveness and reliability of the proposed work where the average number of pixels change rates was 99.82, while the unified average change intensity rate was 33.51, entropy was 7.9, the horizontal, vertical, and diagonal correlation coefficients averaged 0.000533333, 0.000706667, and 0.00076, respectively. Finally, the mean squared error (MSE) between the original and encrypted images was 10203.72. These findings improve digital healthcare by revealing the solutions' performance, security, and efficacy.

QCD sum rule study on the fully strange tetraquark states of JPC = 2++

We apply the QCD sum rule method to systematically study the fully strange tetraquark states with the quantum number JPC = 2++. We construct both the diquark–antidiquark and mesonic–mesonic currents and calculate both their diagonal and off-diagonal correlation functions. Based on the obtained results, we further construct three mixing currents that are nearly non-correlated. We use one mixing current to extract the mass of the lowest-lying state to be 2.03−0.15+0.16 GeV, which can be used to explain f2(2010) as a fully strange tetraquark state of JPC = 2++. This state was observed by BESIII in the ϕϕ channel, and we propose to confirm it in the η(′)η(′) channel.

Multivariate Garch Models Comparison in Terms of the Symmetric and Asymmetric Models

Modelling the Multivariate Generalised Autoregressive Conditional Heteroscedasticity (GARCH) model included both symmetric and asymmetric processes. The information includes monthly data for the Consumer Price Index, Crude Oil Price, Exchange Rate, and Inflation Rate from January 2005 to December 2021. For the analysis, E-view Statistical software was employed. The aforementioned four macroeconomic variables show a tendency for volatility to cluster across time. Both symmetrical and asymmetrical processes had the volatility condition. The residual recursive plot was used to analyse the structural fluctuation in the series. The plot showed continual movement in the inflation rate as well as a downward and upward movement in the consumer price index, exchange rate, and crude oil price. The Akaike Information Criterion (AIC), Hannan-Quinn Information Criterion (HQIC), and Schwarz Information Criterion were chosen as the best models based on information criteria (SIC). Symmetric and asymmetric modelling techniques were used to create the Economic Variables Multivariate GARCH (M-GARCH) models. To calculate the covariance and correlation between the four variables, M-GARCH models were utilised. The main finding of the estimation of all M-GARCH models is that the symmetric models (Diagonal BEKK and Constant Conditional Correlation, or "CCC") have the lowest values of the model information criteria compared to the asymmetric models (Diagonal BEKK and CCC), while the asymmetric models (Diagonal VECH) have the lowest values of the model information criteria compared to the symmetric models (Diagonal VECH). Based on the findings, it was discovered that while analysing the interaction between the four economic variables returns series, the Symmetric Diagonal BEKK and CCC model outperformed the Asymmetric Diagonal VECH model.

Optimal Linear Discriminant Analysis for High-Dimensional Functional Data

Most of existing methods of functional data classification deal with one or a few processes. In this work we tackle classification of high-dimensional functional data, in which each observation is potentially associated with a large number of functional processes, p, which is comparable to or even much larger than the sample size n. The challenge arises from the complex inter-correlation structures among multiple functional processes, instead of a diagonal correlation for a single process. Since truncation is often needed for approximation in functional data, another difficulty stems from the fact that the discriminant set of the infinite-dimensional optimal classifier may be different from that of the truncated optimal classifier, when multiple (especially a large number of) processes are involved. We bridge the gap by proposing a penalized classifier that achieves both near-perfect classification that is unique to functional data, and discriminant set inclusion consistency in the sense that the classification-responsible functional predictors include those of the underlying optimal classifier. Simulation study and real data application are carried out to demonstrate its favorable performance. Supplementary materials for this article are available online.

A Novel 2D Hyperchaotic with a Complex Dynamic Behavior for Color Image Encryption

The generation method of the key stream and the structure of the algorithm determine the security of the cryptosystem. The classical chaotic map has simple dynamic behavior and few control parameters, so it is not suitable for modern cryptography. In this paper, we design a new 2D hyperchaotic system called 2D simple structure and complex dynamic behavior map (2D-SSCDB). The 2D-SSCDB has a simple structure but has complex dynamic behavior. The Lyapunov exponent verifies that the 2D-SSCDB has hyperchaotic behavior, and the parameter space in the hyperchaotic state is extensive and continuous. Trajectory analysis and some randomness tests verify that the 2D-SSCDB can generate random sequences with good performance. Next, to verify the excellent performance of the 2D-SSCDB, we use the 2D-SSCDB to generate a keystream for color image encryption. In the encryption algorithm, the encryption algorithm scrambles and diffuses simultaneously, increasing the cryptographic system’s security. The horizontal correlation, vertical correlation, and diagonal correlation of ciphertext are −0.0004, −0.0004 and 0.0007, respectively. The average information entropy of the ciphertext is 7.9993. In addition, the designed encryption algorithm reduces the correlation between the three channels of the color image. Security analysis shows that the color image encryption algorithm designed using 2D-SSCDB has good security, can resist standard attack methods, and has high efficiency.

A Unified Framework for Correlation Mining in Ultra-High Dimension

Many applications benefit from theory relevant to the identification of variables having large correlations or partial correlations in high dimension. Recently there has been progress in the ultra-high dimensional setting when the sample size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is fixed and the dimension <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> tends to infinity. Despite these advances, the correlation screening framework suffers from practical, methodological and theoretical deficiencies. For instance, previous correlation screening theory requires that the population covariance matrix be sparse and block diagonal. This block sparsity assumption is however restrictive in practical applications. As a second example, correlation and partial correlation screening requires the estimation of dependence measures, which can be computationally prohibitive. In this paper, we propose a unifying approach to correlation and partial correlation mining that is not restricted to block diagonal correlation structure, thus yielding a methodology that is suitable for modern applications. By making connections to random geometric graphs, the number of highly correlated or partial correlated variables are shown to have compound Poisson finite-sample characterizations, which hold for both the finite <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> case and when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> tends to infinity. The unifying framework also demonstrates a duality between correlation and partial correlation screening with theoretical and practical consequences.

Symmetries of Non-Linear ODEs: Lambda Extensions of the Ising Correlations

This paper provides several illustrations of the numerous remarkable properties of the lambda extensions of the two-point correlation functions of the Ising model, shedding some light on the non-linear ODEs of the Painlevé type they satisfy. We first show that this concept also exists for the factors of the two-point correlation functions focusing, for pedagogical reasons, on two examples, namely C(0,5) and C(2,5) at ν=−k. We then display, in a learn-by-example approach, some of the puzzling properties and structures of these lambda extensions: for an infinite set of (algebraic) values of λ these power series become algebraic functions, and for a finite set of (rational) values of lambda they become D-finite functions, more precisely polynomials (of different degrees) in the complete elliptic integrals of the first and second kind K and E. For generic values of λ these power series are not D-finite, they are differentially algebraic. For an infinite number of other (rational) values of λ these power series are globally bounded series, thus providing an example of an infinite number of globally bounded differentially algebraic series. Finally, taking the example of a product of two diagonal two-point correlation functions, we suggest that many more families of non-linear ODEs of the Painlevé type remain to be discovered on the two-dimensional Ising model, as well as their structures, and in particular their associated lambda extensions. The question of their possible reduction, after complicated transformations, to Okamoto sigma forms of Painlevé VI remains an extremely difficult challenge.

Highly excited and exotic fully-strange tetraquark states

Some hadrons have the exotic quantum numbers that the traditional bar{q} q mesons and qqq baryons can not reach, such as J^{PC} = 0^{--}/0^{+-}/1^{-+}/2^{+-}/3^{-+}/4^{+-}, etc. We investigate for the first time the exotic quantum number J^{PC}=4^{+-}, and study the fully-strange tetraquark states with such an exotic quantum number. We systematically construct all the diquark–antidiquark interpolating currents, and apply the method of QCD sum rules to calculate both the diagonal and off-diagonal correlation functions. The obtained results are used to construct three mixing currents that are nearly non-correlated, and we use one of them to extract the mass of the lowest-lying state to be 2.85^{+0.19}_{-0.22} GeV. We apply the Fierz rearrangement to transform this mixing current to be the combination of three meson–meson currents, and the obtained Fierz identity suggests that this state dominantly decays into the P-wave phi (1020) f_2^prime (1525) channel. This fully-strange tetraquark state of J^{PC}=4^{+-} is a purely exotic hadron to be potentially observed in future particle experiments.

On general-n coefficients in series expansions for row spin–spin correlation functions in the two-dimensional Ising model

We consider spin–spin correlation functions for spins along a row, R n = ⟨σ 0,0 σ n,0⟩, in the two-dimensional Ising model. We discuss a method for calculating general-n expressions for coefficients in high-temperature and low-temperature series expansions of R n and apply it to obtain such expressions for several higher-order coefficients. In addition to their intrinsic interest, these results could be useful in the continuing quest for a nonlinear ordinary differential equation whose solution would determine R n , analogous to the known nonlinear ordinary differential equation whose solution determines the diagonal correlation function ⟨σ 0,0 σ n,n ⟩ in this model.

A New Chaotic-Based RGB Image Encryption Technique Using a Nonlinear Rotational 16 × 16 DNA Playfair Matrix

Due to great interest in the secure storage and transmission of color images, the necessity for an efficient and robust RGB image encryption technique has grown. RGB image encryption ensures the confidentiality of color images during storage and transmission. In the literature, a large number of chaotic-based image encryption techniques have been proposed, but there is still a need for a robust, efficient and secure technique against different kinds of attacks. In this paper, a novel RGB image encryption technique is proposed for encrypting individual pixels of RGB images using chaotic systems and 16 rounds of DNA encoding, transpositions and substitutions. First, round keys are generated randomly using a logistic chaotic function. Then, these keys are used across different rounds to alter individual pixels using a nonlinear randomly generated 16×16 DNA Playfair matrix. Experimental results show the robustness of the proposed technique against most attacks while reducing the consumed time for encryption and decryption. The quantitative metrics show the ability of the proposed technique to maintain reference evaluation values while resisting statistical and differential attacks. The obtained horizontal, vertical and diagonal correlation is less than 0.01, and the NPCR and UACI are larger than 0.99 and 0.33, respectively. Finally, NIST analysis is presented to evaluate the randomness of the proposed technique.

A Novel Random Error Approximate Adder-Based Lightweight Medical Image Encryption Scheme for Secure Remote Monitoring of Health Data

In the present global scenario, social distancing is an inevitable one. The need for social distancing and advancements of technology to facilitate the patients and doctors around the world mandated the telemedicine and remote monitoring of patience details as the pivotal way to diagnose the disease. In this, it is essential to transmit the patient’s information such as X-ray and scan images of them to the doctor in the remote location. Preventing the medical data from the technological adversaries is the need of the hour. Infinitesimal attacks in medical images may cost human lives. This work proposes a lightweight, secure medical image encryption scheme for the remote monitoring of health data. The proposed encryption scheme uses computationally less complex weighted shift approximate adder (WSAA)–based encryption logic. The scheme uses a 256-bit key for the encryption process that strengthens the encryption and robust against various attacks. The proposed encryption scheme deploys the WSAA for diffusing the pixel values. A unique way of key distribution for pixel-wise encryption within the image is proposed that avoids the need for separate logic for the pixel-wise confusion. The proposed Encryption scheme is evaluated for its entropy and horizontal, vertical, diagonal correlation, histogram, key space, and sensitivity. Experimental results affirm that the proposed scheme significantly good with less computational complexity. The peak signal-to-noise ratio (PSNR) value of the decrypted image is infinity, and this matches the ideal requirement of the medical encryption scheme.

Diagonal Degree Correlations vs. Epidemic Threshold in Scale-Free Networks

We prove that the presence of a diagonal assortative degree correlation, even if small, has the effect of dramatically lowering the epidemic threshold of large scale-free networks. The correlation matrix considered is P h | k = 1 − r P h k U + r δ h k , where P U is uncorrelated and r (the Newman assortativity coefficient) can be very small. The effect is uniform in the scale exponent γ if the network size is measured by the largest degree n . We also prove that it is possible to construct, via the Porto–Weber method, correlation matrices which have the same k n n as the P h | k above, but very different elements and spectra, and thus lead to different epidemic diffusion and threshold. Moreover, we study a subset of the admissible transformations of the form P h | k ⟶ P h | k + Φ h , k with Φ h , k depending on a parameter which leaves k n n invariant. Such transformations affect in general the epidemic threshold. We find, however, that this does not happen when they act between networks with constant k n n , i.e., networks in which the average neighbor degree is independent from the degree itself (a wider class than that of strictly uncorrelated networks).

QCD sum rules for parameters of the B -meson distribution amplitudes

We obtain new estimates for the parameters $\lambda_{E}^2$, $\lambda_H^2$ and their ratio $\mathcal{R} = \lambda_{E}^2/\lambda_H^2$, which appear in the second moments of the $B$-meson light-cone distribution amplitudes defined in the heavy-quark effective field theory. The computation is based on two-point QCD sum rules for the diagonal correlation function and includes all contributions up to mass dimension seven in the operator-product expansion. For the ratio we get $\mathcal{R} = (0.1 \pm 0.1)$ with $\lambda_H^2 = (0.15 \pm 0.05) \, \text{GeV}^2$ and $\lambda_E^2 = (0.01 \pm 0.01) \, \text{GeV}^2$.

How to account for temporal correlations with a diagonal correlation model in a nonlinear functional model: a plane fitting with simulated and real TLS measurements

To avoid computational burden, diagonal variance covariance matrices (VCM) are preferred to describe the stochasticity of terrestrial laser scanner (TLS) measurements. This simplification neglects correlations and affects least-squares (LS) estimates that are trustworthy with minimal variance, if the correct stochastic model is used. When a linearization of the LS functional model is performed, a bias of the parameters to be estimated and their dispersions occur, which can be investigated using a second-order Taylor expansion. Both the computation of the second-order solution and the account for correlations are linked to computational burden. In this contribution, we study the impact of an enhanced stochastic model on that bias to weight the corresponding benefits against the improvements. To that aim, we model the temporal correlations of TLS measurements using the Matérn covariance function, combined with an intensity model for the variance. We study further how the scanning configuration influences the solution. Because neglecting correlations may be tempting to avoid VCM inversions and multiplications, we quantify the impact of such a reduction and propose an innovative yet simple way to account for correlations with a “diagonal VCM.” Originally developed for GPS measurements and linear LS, this model is extended and validated for TLS range and called the diagonal correlation model (DCM).

Chaotic Cryptosystem for Selective Encryption of Faces in Photographs

In this article, a safe communication system is proposed that implements one or more portable devices denominated SBC (single-board computers), with which photographs are taken and that later utilizes the OpenCV Library for the detection and identification of the faces that appear in them. Subsequently, it consults the information in a stored database, whether locally in SBC or in a remote server, to verify that the faces should be coded, and it encrypts these, implementing a new cryptosystem that executes mathematical models to generate chaotic orbits, one of which is used for application on two occasions the technique of diffusion with the purpose of carrying out a small change in one of the pixels of the image, generating very different cryptograms. In addition, in order to make a safer system, it implements other chaotic orbits during the technique of confusion. With the purpose of verifying the robustness of the encryption algorithm, a statistical analysis is performed employing histograms, horizontal, vertical, and diagonal correlation diagrams, entropy, number of pixel change rate (NPCR), unified average change intensity (UACI), sensitivity of the key, encryption quality analysis, and the avalanche effect. The cryptosystem is very robust in that it generates highly disordered cryptograms, supports differential attacks, and in addition is highly sensitive to changes in the pixels as well as in the encrypted keys.

A new image encryption scheme based on hybrid chaotic maps

In this paper, a novel grayscale image cryptosystem based on hybrid chaotic maps is proposed. The scheme employs both confusion phase to scramble the location of pixels and diffusion phase for changing the content of pixels in consecutive manner. In this scheme, Arnold’s cat map is introduced to perform confusion operation and the principle of diffusion is achieved by using the proper selection of combined Sine map, Logistic map, and Tent map. Furthermore, exclusive OR (XOR), exchange, and transform operations are used to enhance the efficiency of diffusion phase. Accordingly, the use of chaotic maps and XOR operation provides a dual layer of security. Depending on the average absolute value of horizontal, vertical, and diagonal correlation coefficient of plain image as well as bifurcation properties of chaotic maps, one of the mentioned chaotic maps is selected for diffusion phase. First, original gray scale image matrix is extended to square matrix by adding the sequences generated with proper chaotic maps to implement the first step of diffusion phase. Then the Arnold’s cat map changes pixels location of new extended matrix by means of certain equation as confusion phase. The encrypted image is generated after applying XOR, exchange and transform operations on the content of pixels as second step of diffusion phase. Thus the system is able to build several more complicated chaotic structures. In addition the encryption and decryption processing time directly depend on the value of correlation coefficient of original image. Plain images with less correlation coefficient have less encryption and decryption processing time, and vice versa. Compared with several existing methods, the proposed scheme has more better properties, including wider chaotic ranges and more complex chaotic behavior. Experimental results show that the proposed system has proper encryption and decryption processing time, unified average changing intensity (UACI), number of pixel change rate (NPCR), and extensive security analysis for kind of images.

Modeling of Nuclear Reactions with Langevin Calculations

The mass angle distribution shows a strong correlation between mass and angle when quasifission events are dominant. Therefore, as long as quasifission events are dominant, the mass angle distribution is characterized in that diagonal correlation appears. This diagonal correlation could not be reproduced in our previous model that is before introducing $${{f}_{{{\text{ina}}}}}$$ and $$\gamma _{t}^{0}$$ model parameters. In this study, we clarify the indeterminate parameters included in the model to reproduce the diagonal correlation appearing in the mass angle distribution in the 48Ti + 186W reaction system. As a result, $${{f}_{{{\text{ina}}}}}$$ and $$\gamma _{t}^{0}$$ of model parameters found to be key parameters for MAD. it was also found that the balance between $${{f}_{{{\text{ina}}}}}$$ and $$\gamma _{t}^{0}$$ parameters values is important for the strong correlation between mass and angle.

Color multiple image encryption scheme based on 3D-chaotic maps

In many research areas, production of images is increasing with every day. These days, the prime focus of researchers is on the security of digital images. Motivated by gray multiple image encryption algorithms, this paper suggests a novel Chaos-based color multiple image encryption technique. A 3D histogram equalization method has been applied to equalize the chaotic sequences histograms of Lorenz system. Confusion/diffusion of image data has been implemented by using sequences generated by histogram equalized Lorenz and Rossler system. In confusion stage, the input image colored pixels have been scrambled. Then in diffusion stage, pixel replacement is done by scrambled images and sequences of Rossler system. The proposed scheme efficiency is validated via key sensitivity, key space, entropy, horizontal, vertical, diagonal correlation, UACI and NPCR tests. Furthermore, the overall security analysis and experimental results show that the proposed encryption technique has achieved confidentiality and have resistance against classical attacks.

Banks’ equity performance and the term structure of interest rates

AbstractUsing an extensive global sample, this paper investigates the impact of the term structure of interest rates on bank equity returns. Decomposing the yield curve to its three constituents (level, slope and curvature), the paper evaluates the time‐varying sensitivity of the bank's equity returns to these constituents by using a diagonal dynamic conditional correlation multivariate GARCH framework. Evidence reveals that the empirical proxies for the three factors explain the variations in equity returns above and beyond the market‐wide effect. More specifically, shocks to the long‐term (level) and short‐term (slope) factors have a statistically significant impact on equity returns, while those on the medium‐term (curvature) factor are less clear‐cut. Bank size plays an important role in the sense that exposures are higher for SIFIs and large banks compared to medium and small banks. Moreover, banks exhibit greater sensitivities to all risk factors during the crisis and post‐crisis periods compared to the pre‐crisis period; though these sensitivities do not differ for market‐oriented and bank‐oriented financial systems.

Analytical solution of three-dimensional Fourier transform frequency spectrum for three-level potassium atomic gas

With the development of laser technology in the field of optics, ultra-fast optics has become an important research field. Compared with the traditional technology, ultrafast optics can be realized not only under shorter pulse function, but also on a smaller scale, which can more quickly reflect the dynamic process. We present an analytical calculation of the full three-dimensional (3D) coherent spectrum with a finite duration two-dimensional (2D) Gaussian pulse envelope. Our starting point is the solution of the optical Bloch equations for three-level potassium atomic gas in the 3D time domain by using the projection-slice theorem, error function and Fourier-shift theorem of 3D Fourier transform. These principles are used to calculate and simplify the third-order polarization equation generated by the device, and the analytical calculation of three-dimensional Fourier transform frequency spectrum at &lt;i&gt;T&lt;/i&gt; = 0 is obtained. We simulate the analytic solution by using mathematics software. By comparing the simulations with the experimental results, with the homogeneous line-width fixed, we can obtain the relationship among the in-homogeneous broadening, the correlation diagonal coefficients and the three-dimensional spectrum characteristics, which can be identified quantitatively by fitting the slices of three-dimensional Fourier transform spectrum peaks in an appropriate direction. The results show that the three-dimensional Fourier transform spectrum will extend along the diagonal direction with the increasing of the in-homogeneous broadening, and the spectrogram progressively becomes a circle with the increasing of the diagonal correlation coefficient, and the amplitude also gradually turns smaller. According to the analytical solution, we give a complete two-dimensional spectrum of the &lt;i&gt;T&lt;/i&gt; = 0 interface. The results can be fit to the experimental 3D coherent spectrum for arbitrary inhomogeneity.