Deflation Algorithm Research Articles

Hückel molecular orbital theory on a quantum computer: A scalable system-agnostic variational implementation with compact encoding.

Hückel molecular orbital (HMO) theory provides a semi-empirical treatment of the electronic structure in conjugated π-electronic systems. A scalable system-agnostic execution of HMO theory on a quantum computer is reported here based on a variational quantum deflation (VQD) algorithm for excited state quantum simulation. A compact encoding scheme is proposed here that provides an exponential advantage over the direct mapping and allows for quantum simulation of the HMO model for systems with up to 2n conjugated centers with n qubits. The transformation of the Hückel Hamiltonian to qubit space is achieved by two different strategies: an iterative refinement transformation and the Frobenius-inner-product-based transformation. These methods are tested on a series of linear, cyclic, and hetero-nuclear conjugated π-electronic systems. The molecular orbital energy levels and wavefunctions from the quantum simulation are in excellent agreement with the exact classical results. However, the higher excited states of large systems are found to suffer from error accumulation in the VQD simulation. This is mitigated by formulating a variant of VQD that exploits the symmetry of the Hamiltonian. This strategy has been successfully demonstrated for the quantum simulation of C60 fullerene containing 680 Pauli strings encoded on six qubits. The methods developed in this work are easily adaptable to similar problems of different complexity in other fields of research.

A numerical assembly technique for free vibration of plane frames using a shifted and deflated Newton method

A semi-analytic method, namely the Numerical Assembly Technique (NAT) is extended to compute natural frequencies of arbitrary planar frame structures. The frame structure is systematically defined by a set of nodes, beams, bearings, springs, and external loads and the corresponding boundary and interface conditions are formulated. We consider the Timoshenko-Ehrenfest beam theory and take axial, bending and shear deformations as well as linear and rotational inertia into account. Since we use the exact solutions of the governing differential equations in the NAT, the accuracy of the results is independent from the spatial discretization. However, the resulting eigenvalue problem is non-linear and requires a numerical algorithm to solve. We consider three different representations of exact homogeneous solutions and study the numerical stability of the resulting system matrix. To solve for the eigenvalues we propose a Newton method enhanced with a shifted deflation algorithm. The stability and the efficiency of this approach is illustrated in numerical examples.

Validation of the Mindray VS9 Vital Signs Monitor in a combined adult and pediatric population according to ISO Standard 81060-2:2018.

We aimed to validate the accuracy of the Mindray VS9 Vital Signs Monitor, which features the Mindray TrueBP inflation algorithm for oscillometric blood pressure (BP) measurement, to check if it complies with the International Organization for Standardization Standard (ISO 81060-2:2018) in a combined adult and pediatric population. A total of 86 participants, including both adult and pediatric subjects, were recruited. The distribution of their ages, gender, BPs and limb sizes all complied with the requirement of the ISO standard. The inflation and deflation algorithms were validated independently using the same-arm sequential BP measurement method. For each subject, the BP was first determined by two independent observers using a mercury sphygmomanometer (R1). The BP of the subject was then determined by the third observer using the test equipment (T1). Then, using a mercury sphygmomanometer, two independent observers were asked to determine the subject's BP (R2) again. R1-T1-R2 were considered a valid pair of data. This cycle continued until 3 pairs of valid data were achieved. We collected 258 pairs of valid BP data for the validation of the inflation and deflation algorithms respectively. For validation Criterion 1, the mean ± SD of the differences between the readings obtained from the test device and reference BP was 0.0 ± 6.6/-1.8 ± 7.1 mmHg (systolic/diastolic) when the deflation algorithm was used, and 2.4 ± 6.3/ 0.3 ± 6.9 mmHg (systolic/diastolic) when the inflation algorithm was used. For validation Criterion 2, the SD of the averaged BP differences between the test device and the reference BP per subject was 5.35/6.33 mmHg (systolic/diastolic) when the deflation algorithm was used, and 5.17/5.75 mmHg (systolic/diastolic) when the inflation algorithm was used. The VS9 Vital Signs Monitor fulfilled all the criteria in the ISO Standard. Moreover, the inflation algorithm had a shorter Measure Time (by 7-21 s) and lower maximum inflation pressure (by 9.7-22 mmHg). The VS9 Vital Signs Monitor fulfilled all the requirements of the ISO Standard (ISO 81060-2:2018) in a combined adult and pediatric population and is recommended for clinical use.

Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation.

In this work, we utilize the framework of many-body expansion (MBE) to decompose electronic structures into fragments by incrementing virtual orbitals, aiming to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. While our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and its generalization, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules (H2O and N2) and calculate the ground and excited state energies of three molecules (LiH, CH+, and H2O). The results demonstrate that our approach can, in principle, provide reliable descriptions in all the tests including strongly correlated systems when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.

Deflated domain decomposition method for structural problems

The paper presents a fast and stable solver algorithm for structural problems. The point is the distance between the eigenvector of the constrained stiffness matrix and the unconstrained matrix. The coarse motions are close to the kernel of the unconstrained matrix. We use lower-frequency deformation modes to construct an iterative solver algorithm through domain decomposition expressing near-rigid-body motions, deflation algorithms, and two-level algorithms. We remove the coarse space from the solution space and hand over the iteration space to the fine space. Our solver is parallelized, and the solver thus has two sets of domain decomposition. One decomposition generates the coarse space, and the other is for parallelization. The basic framework of the solver is the parallel conjugate gradient (CG) method on the fine space. We use the CG method for the basic framework instead of the (simplest) domain decomposition method. We conducted benchmark tests using elastic static analysis for thin plate models. A comparison with the standard CG solver results shows the new solver’s high-speed performance and remarkable stability.

A Compression Method for Power Quality Data

This paper presents a compression method for power quality (PQ) signals. This method consists of polynomial approximation algorithm and a lossless compression algorithm The proposed method uses the Deflate algorithm as lossless compression algorithm. The polynomial approximation is intended to decrease the entropy of the signal, thus increasing the compression ratio of the Deflate algorithm. The proposed method is characterized by high compression ratio and low computational cost, making feasible its implementation in embedded systems.

Deflation for the Symmetric Arrowhead and Diagonal-Plus-Rank-One Eigenvalue Problems

We discuss the eigenproblem for the symmetric arrowhead matrix $C = (\begin{smallmatrix} D \& {z} {z}^T & \alpha \end{smallmatrix})$, where $D \in \mathbb{R}^{n \times n}$ is diagonal, ${z} \in \mathbb{R}^n$, and $\alpha \in \mathbb{R}$, in order to examine criteria for when components of ${z}$ may be set to zero. We show that whenever two eigenvalues of $C$ are sufficiently close, some component of ${z}$ may be deflated to zero, without significantly perturbing the eigenvalues of $C$, by either substituting zero for that component or performing a Givens rotation on each side of $C$. The strategy for this deflation requires ${\mathcal{O}(n^2)}$ comparisons. Although it is too costly for many applications, when we use it as a benchmark, we can analyze the effectiveness of ${{O}(n)}$ heuristics that are more practical approaches to deflation. We show that one such ${\mathcal{O}(n)}$ heuristic finds all sets of three or more nearby eigenvalues, misses sets of two or more nearby eigenvalues under limited circumstances, and produces a reduced matrix whose eigenvalues are distinct in double the working precision. Using the ${\mathcal{O}(n)}$ heuristic, we develop a more aggressive method for finding converged eigenvalues in the symmetric Lanczos algorithm. It is shown that except for pathological exceptions, the ${\mathcal{O}(n)}$ heuristic finds nearly as much deflation as the ${\mathcal{O}(n^2)}$ algorithm that reduces an arrowhead matrix to one that cannot be deflated further. The deflation algorithms and their analysis are extended to the symmetric diagonal-plus-rank-one eigenvalue problem and lead to a better deflation strategy for the LAPACK routine dstedc.f.

MODIFIED MULTI-LEVEL STEGANOGRAPHY TO ENHANCE DATA SECURITY

Data-hiding using steganography algorithm becomes an important technique to prevent unauthorized users to have access to a secret data. In this paper, steganography algorithm has been constructed to hide a secret data in a gray and a color images, this algorithm is named deep hiding/extraction algorithm (DHEA) to modify multi-level steganography (MLS). The suggested hiding algorithm is based on modified least significant bit (MDLSB) to scatter data in a cover-image and it utilizes a number of levels; where each level perform hiding data on a gray image except the last level that applies a color image to keep secret data. Furthermore, proper randomization approach with two layers is implemented; the first layer uses random pixels selection for hiding a secret data at each level, while the second layer implements at the last level to move randomly from segment to the others. In addition, the proposed hiding algorithm implements an effective lossless image compression using DEFLATE algorithm to make it possible to hide data into a next level. Dynamic encryption algorithm based on Advanced Encryption Standard (AES) is applied at each level by changing cipher keys (Ck) from level to the next, this approach has been applied to increase the security and working against attackers. Soft computing using a meta-heuristic approach based on artificial bee colony (ABC) algorithm has been introduced to achieve smoothing on pixels of stego-image, this approach is effective to reduce the noise caused by a hidden large amount of data and to increase a stego-image quality on the last level. The experimental result demonstrates the effectiveness of the proposed algorithm with bee colony DHA-ABC to show high-performing to hide a large amount of data up to four bits per pixel (bpp) with high security in terms of hard extraction of a secret message and noise reduction of the stego-image. Moreover, using deep hiding with unlimited levels is promising to confuse attackers and to compress a deep sequence of images into one image.

A combination of least significant bit and deflate compression for image steganography

Steganography is one of the cryptography techniques where secret information can be hidden through multimedia files such as images and videos. Steganography can offer a way of exchanging secret and encrypted information in an untypical mechanism where communicating parties can only interpret the secret message. The literature has shown a great interest in the least significant bit (LSB) technique which aims at embedding the secret message bits into the most insignificant bits of the image pixels. Although LSB showed a stable performance of image steganography yet, many works should be done on the message part. This paper aims to propose a combination of LSB and Deflate compression algorithm for image steganography. The proposed Deflate algorithm utilized both LZ77 and Huffman coding. After compressing the message text, LSB has been applied to embed the text within the cover image. Using benchmark images, the proposed method demonstrated an outperformance over the state of the art. This can proof the efficacy of using Deflate as a data compression prior to the LSB embedding.

An efficient low complexity compression based optimal homomorphic encryption for secure fiber optic communication

Latest advancements in fiber optic communication have gained significant attention among researchers owing to many benefits such as high data rate, acceptable cost, bandwidth, low attenuation, etc. Fiber optic networks are found to be a commonly utilized platform to transfer data in several applications such as personal, commercial, military areas, etc. Although fiber optic networks are highly beneficial, security remains a challenging design issue. Numerous state of art works has been developed to achieve security in fiber optic communication. Among the various methods, compression then encryption is an effective way to effectively and securely transmit the data. With this motivation, this paper presents a new Low Complexity Compression Then Encryption using Optimal Homomorphic Encryption (LCCE-OHE) technique for secured fiber optic communication. The proposed LCCE-OHE technique operates on two major phases namely compression and encryption. At the first stage, low complexity compression using Neighboring Indexing Sequence (NIS) with Deflate algorithm, named Normalized Information Distance (NID) is used. Besides, in the second stage, Quasi Oppositional Sail Fish Optimizer with Homomorphic Encryption (QOSFO-HE) technique is employed. The QOSFO algorithm is derived by incorporating the quasi oppositional learning (QOBL) concept to the SFO algorithm and is applied to optimally select the encryption keys. The performance validation of the proposed model takes place on two benchmark datasets and the experimental results are examined interms of different performance measures. The experimental values highlighted the improved compression efficiency and security level of the LCCE-OHE technique over the other techniques.

Variational quantum packaged deflation for arbitrary excited states

Determining the spectral structure of molecular Hamiltonians is one of the most important and challenging research fields in quantum chemistry. In the near future, such a problem may be solvable by means of quantum simulation. However, constrained by a handful of qubits and noisy quantum gates available in the near-term quantum devices, hybrid quantum-classical algorithms based on variational methods such as variational quantum eigensolver have become a preferable choice. Here we propose an interesting variational quantum algorithm for obtaining the excited states of many-body Hamiltonians. To obtain the kth excited states, the previous variational quantum deflation algorithm requires the use of k different variational circuits, which is now reduced to only two circuits with our algorithm. The feasibility of the algorithm was numerically tested on the hydrogen molecule with and without random noise, where the chemical accuracy is reached for both cases. This algorithm is expected to significantly reduce the resource requirements of quantum simulation.

Quantum computation for predicting electron and phonon properties of solids

Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE–VQD calculations for 307 spin–orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. Also, we discuss a workflow for using VQD with lattice Green’s function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms and models also.

Applications of quantum computing for investigations of electronic transitions in phenylsulfonyl-carbazole TADF emitters

A quantum chemistry study of the first singlet (S1) and triplet (T1) excited states of phenylsulfonyl-carbazole compounds, proposed as useful thermally activated delayed fluorescence (TADF) emitters for organic light emitting diode (OLED) applications, was performed with the quantum Equation-Of-Motion Variational Quantum Eigensolver (qEOM-VQE) and Variational Quantum Deflation (VQD) algorithms on quantum simulators and devices. These quantum simulations were performed with double zeta quality basis sets on an active space comprising the highest occupied and lowest unoccupied molecular orbitals (HOMO, LUMO) of the TADF molecules. The differences in energy separations between S1 and T1 (ΔEST) predicted by calculations on quantum simulators were found to be in excellent agreement with experimental data. Differences of 17 and 88 mHa with respect to exact energies were found for excited states by using the qEOM-VQE and VQD algorithms, respectively, to perform simulations on quantum devices without error mitigation. By utilizing state tomography to purify the quantum states and correct energy values, the large errors found for unmitigated results could be improved to differences of, at most, 4 mHa with respect to exact values. Consequently, excellent agreement could be found between values of ΔEST predicted by quantum simulations and those found in experiments.

Validation of the STEP deflation algorithm of the Midmark IQvitals Zone Vital Signs Monitor: part of a novel clinical ecosystem.

ObjectivesAssess the accuracy of the Midmark IQvitals Zone Vital Signs Monitor STEP deflation algorithm according to the ANSI/AAMI/ISO 81060-2 Standard.MethodsA total of 85 subjects completed the testing protocol. All standard requirements for gender, blood pressure (BP) values, and arm circumferences were met. Manual auscultation was performed by testers blinded to the device; the manual BP values were compared to the device readings.Results:The Standard Criterion 1 data analyses showed mean ± SD device minus manual BP values of 1.22 ± 6.3 mmHg for SBP and −1.67 ± 6.09 mmHg for DBP. The SD values for criterion 2 were 5.06 mmHg (SBP) and 4.98 mmHg (DBP).ConclusionsThe device passed all Standard requirements. The Midmark IQvitals Zone device has features to improve accuracy and reduce or eliminate transcription errors and inaccuracy from improper patient positioning.

Efficient Hardware Realization of a New Variable Regularized PAST Algorithm With Multiple Deflation

This paper proposes a new variant of the projection approximation subspace tracking (PAST) algorithm with multiple deflation (MD) and its efficient hardware architecture. It extends the PAST with deflation (PAST-d) algorithm by performing multiple deflations at each step and relies on a recently introduced variable forgetting factor, and variable regularized PAST algorithm to improve the overall convergence rate, steady-state error, and numerical properties. It shares the same simple hardware structure of the PAST-d algorithm in pipeline realization but offering a more flexible tradeoff between complexity and performance. Moreover, methods for estimating the eigenvalues and the dimension of the signal subspace are proposed. Novel simplifications of the proposed variable forgetting factor (VFF) and variable regularization (VR) PAST-MD algorithm are also developed to avoid the expensive cubic root and division operations involved to facilitate its hardware implementation. Moreover, a combined data-regularization update is introduced to avoid the additional QR decomposition (QRD) update associated with the regularization, at the expense of very slight performance degradation. A novel pipelined hardware implementation of the simplified VFF-VR-PAST-MD algorithm based on the QRD and the COordinate Rotation DIgital Computer (CORDIC) is also proposed and implemented in Xilinx field programmable gate array (FPGA). Thanks to the proposed “root- and division- free” schemes, our proposed architecture can achieve around 20.2% higher working speed and save 1.9% lookup tables (LUTs), 1.8% slice register, and 22.8% digital signal processors (DSPs) over conventional implementation of the proposed architecture. Compared to the previous work, which is based on PAST-d algorithm, the proposed QRD-based algorithms offer better performance and a more flexible tradeoff between hardware resources and performance.

A Scalable Algorithm for Large-Scale Unsupervised Multi-View Partial Least Squares

We present an unsupervised multi-view partial least squares (PLS) by learning a common latent space from given multi-view data. Although PLS is a frequently used technique for analyzing relationships between two datasets, its extension to more than two views in unsupervised setting is seldom studied. In this article, we fill up the gap, and our model bears similarity to the extension of canonical correlation analysis (CCA) to more than two sets of variables and is built on the findings from analyzing PLS, CCA, and its variants. The resulting problem involves a set of orthogonality constraints on view-specific projection matrices, and is numerically challenging to existing methods that may have numerical instabilities and offer no orthogonality guarantee on view-specific projection matrices. To solve this problem, we propose a stable deflation algorithm that relies on proven numerical linear algebra techniques, can guarantee the orthogonality constraints, and simultaneously maximizes the covariance in the common space. We further adapt our algorithm to efficiently handle large-scale high-dimensional data. Extensive experiments have been conducted to evaluate the algorithm through performing two learning tasks, cross-modal retrieval, and multi-view feature extraction. The results demonstrate that the proposed algorithm outperforms the baselines and is scalable for large-scale high-dimensional datasets.

Safety and Efficacy of a Truncated Deflation Algorithm for Distal Transradial Access

PurposeTo assess safety and efficacy of a modified rapid hemostasis protocol for distal transradial access (TRA). Materials and MethodsA single-center retrospective study of patients undergoing percutaneous image-guided procedures from a distal TRA with rapid deflation hemostasis protocol was performed. Between March 2017 and August 2019, 593 procedures in 434 patients were performed. Mean patient age was 63.5 y (range, 18–94 y). ResultsThe most common procedures were transarterial chemoembolization (218; 36.8%), abdominal and pelvic embolization (116; 19.6%), yttrium-90 mapping (115; 19.4%), yttrium-90 administration (84; 14.2%), and diagnostic angiography (44; 7.4%). Mean (range) values for clotting parameters were international normalized ratio 1.2 (0.9–3.2), partial thromboplastin time 33.5 s (26–44 s), and platelets 23.4 × 109/L (37–552 × 109/L). A hematoma developed in 7 (1.2%) patients. No radial artery occlusions were encountered during follow-up. Nursing intensity was defined as the number of minutes after the procedure required for assessing and managing the access site for bleeding. The mean nursing intensity was 25.1 min (range, 25–40 min). ConclusionsThe rapid deflation hemostasis protocol for distal TRA at the anatomical snuffbox was feasible and safe. No significant difference or association was found between hematoma formation and clotting parameters after the procedure or type of vascular access equipment used.

Highly Reliable and Low-Complexity Image Compression Scheme Using Neighborhood Correlation Sequence Algorithm in WSN

Recently, the advancements in the field of wireless technologies and micro-electro-mechanical systems lead to the development of potential applications in wireless sensor networks (WSNs). The visual sensors in WSN create a significant impact on computer vision based applications such as pattern recognition and image restoration. generate a massive quantity of multimedia data. Since transmission of images consumes more computational resources, various image compression techniques have been proposed. But, most of the existing image compression techniques are not applicable for sensor nodes due to its limitations on energy, bandwidth, memory, and processing capabilities. In this article, we introduce a highly reliable and low-complexity image compression scheme using neighborhood correlation sequence (NCS) algorithm. The NCS algorithm performs the bit reduction operation and then encoded by a codec (such as PPM, Deflate, and Lempel Ziv Markov chain algorithm.) to further compress the image. The proposed NCS algorithm increases the compression performance and decreases the energy utilization of the sensor nodes with high fidelity. Moreover, it achieved a minimum end to end delay of 1074.46 ms at the average bit rate of 4.40 bpp and peak signal to noise ratio of 48.06 on the applied test images. On comparing with state-of-art methods, the proposed method maintains a better tradeoff between compression efficiency and reconstructed image quality.

7bgzf: Replacing samtools bgzip deflation for archiving and real-time compression

BackgroundGenomic sequence data are not only massive but also increasing rapidly every day; therefore, it is essential to compress such data for sharing. Though there are some specific compressors, they lack interoperability. In this study, a SAMtools bgzip variant named 7bgzf has been developed, incorporating several compression and deflation algorithms other than the widely used zlib algorithm. An extensive benchmarking study has been carried out with available data compression software. ResultsOn both x64 and ARM machines, igzip performed very rapidly. For high compression, using libdeflate on the x64 platform achieved high compression with tolerable speed loss. ConclusionsBased on appropriate algorithm selection, the proposed compression method performed better than the original bgzip method while maintaining interoperability with existing software. Therefore, this software is useful for both distribution of genomic sequence archives and real-time compression in mobile computing.

Iterative deflation algorithm, eigenvalue equations, and PLS2

AbstractPLS2 is probably the most used algorithm to perform projection to latent structures regression in the case of multivariate response. However, several criticisms pointed to the theoretical limits of its original formulation, highlighting the need of a more robust foundation within the theory of regression analysis. The iterative deflation algorithm is here introduced as a starting point to obtain a family of regression methods, which includes PLS2, principal component regression (PCR), and elastic component regression (ECR), where different eigenvalue equations are used to calculate the weight vectors. Within this framework, an original portrait of PLS2 is drawn. The main mathematical properties useful to understand what PLS2 is and how PLS2 behaves are derived. A new regression method called iterative deflation algorithm‐based regression (IDAR) is introduced to describe the limit behaviour of PLS2, PCR, and ECR. The post‐transformation method is presented as a general property of the iterative deflation algorithm. Two data sets, one simulated and the other experimental, are investigated to illustrate the main properties of PLS2.