Low Storage Requirements Research Articles

Efficient and Reliable Algorithms for the Computation of Non-Twist Invariant Circles

This paper presents a methodology to study non-twist invariant circles and their bifurcations for area preserving maps, which is supported on the theoretical framework developed in Gonzalez-Enriquez et al. (Mem. Amer. Math. Soc. 227:vi+115, 2014). We recall that non-twist invariant circles are characterized not only by being invariant, but also by having some specified normal behavior. The normal behavior may endow them with extra stability properties (e.g., against external noise), and hence, they appear as design goals in some applications, e.g., in plasma physics, astrodynamics and oceanography. The methodology leads to efficient algorithms to compute and continue, with respect to parameters, non-twist invariant circles. The algorithms are quadratically convergent and, when implemented using FFT, have low storage requirement and low operations count per step. Furthermore, the algorithms are backed up by rigorous a posteriori theorems, proved and discussed in detail in Gonzalez-Enriquez et al. (Mem. Amer. Math. Soc. 227:vi+115, 2014), which give sufficient conditions guaranteeing the existence of a true non-twist invariant circle, provided an approximate invariant circle is known. Hence, one can compute confidently even very close to breakdown. With some extra effort, the calculations could be turned into computer-assisted proofs, see Figueras et al. (Found. Comput. Math. 17:1123–1193, 2017) for examples of the latter. The algorithms are also guaranteed to converge up to the breakdown of the invariant circles, and then, they are suitable to compute regions of parameters where the non-twist invariant circles exist. The calculations involved in the computation of the boundary of these regions are very robust, and they do not require symmetries and can run without continuous manual adjustments, largely improving methods based on the computation of very long period periodic orbits to approximate invariant circles. This paper contains a detailed description of our algorithms, the corresponding implementation and some numerical results, obtained by running the computer programs. In particular, we include calculations for two-dimensional parameter regions where non-twist invariant circles (with a prescribed frequency) exist. Indeed, we present systematic results in systems that do not contain symmetry lines, which seem to be unaccessible for previous methods. These numerical explorations lead to some open questions, also included here.

Comparison of Pairwise Similarity Distance Methods for Effective Hashing

Content-based image retrieval (CBIR) methods search for points with the most similar content to query features from within a large dataset. The most notable approach for this purpose is an approximate nearest neighbor (ANN) searching. The main properties expected from a retrieval system can be listed as follows; low storage requirement, high retrieve speed, and high average precision. Hashing, which can generate discriminative and low-dimensional binary codes, is one of today’s most effective ANN searching methods. Although there are various hashing approaches in the literature, almost all hashing approaches consist of low-dimension feature representation and binarization sections. This study focuses on the low-dimension feature representation. Hand-crafted or deep learning based approaches are used for feature extraction in hashing methods. These features are the main components that affect the performance in creating binary codes. Contrastive loss is often used in the literature to update the learnable parameters of these feature extraction algorithms. The distance parameter of these data points critical to calculating contrastive loss. In this study, contrastive loss performance is tested using five different distance methods (Euclidean, Manhattan, Cosine, Minkowski, Chebyshev) for more effective feature representation. Retrieval performance is tested using low-dimensional feature vectors produced by these methods in MNIST and CIFAR-10 datasets. It is thought that the information obtained from this study is very useful for new researchers.

PRP-like algorithm for monotone operator equations

Many studies have been devoted to develop and improve the iterative methods for solving convex constraint nonlinear equations problem (CCP). Based on the projection technique, we introduce a derivative-free method for approximating the solution of CCP. The proposed method is suitable for solving large-scale nonlinear equations due to its lower storage requirements. The directions generated by the proposed method at every iteration are bounded. Under some mild conditions, we establish the global convergence result of the proposed method. Numerical experiments are provided to show the efficiency of the method in solving CCP. Moreover, we tested the capability of the method in solving the monotone nonlinear operator equation equivalent to the $$\ell _1$$ -norm regularized minimization problem.

Multilevel CC2 and CCSD in Reduced Orbital Spaces: Electronic Excitations in Large Molecular Systems.

We present efficient implementations of the multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) models. As the system size increases, MLCC2 and MLCCSD exhibit the scaling of the lower-level coupled cluster model. To treat large systems, we combine MLCC2 and MLCCSD with a reduced-space approach in which the multilevel coupled cluster calculation is performed in a significantly truncated molecular orbital basis. The truncation scheme is based on the selection of an active region of the molecular system and the subsequent construction of localized Hartree–Fock orbitals. These orbitals are used in the multilevel coupled cluster calculation. The electron repulsion integrals are Cholesky decomposed using a screening protocol that guarantees accuracy in the truncated molecular orbital basis and reduces computational cost. The Cholesky factors are constructed directly in the truncated basis, ensuring low storage requirements. Systems for which Hartree–Fock is too expensive can be treated by using a multilevel Hartree–Fock reference. With the reduced-space approach, we can handle systems with more than a thousand atoms. This is demonstrated for paranitroaniline in aqueous solution.

Fast kNN Search in Weighted Hamming Space With Multiple Tables.

Hashing methods have been widely used in Approximate Nearest Neighbor (ANN) search for big data due to low storage requirements and high search efficiency. These methods usually map the ANN search for big data into the k -Nearest Neighbor ( k NN) search problem in Hamming space. However, Hamming distance calculation ignores the bit-level distinction, leading to confusing ranking. In order to further increase search accuracy, various bit-level weights have been proposed to rank hash codes in weighted Hamming space. Nevertheless, existing ranking methods in weighted Hamming space are almost based on exhaustive linear scan, which is time consuming and not suitable for large datasets. Although Multi-Index hashing that is a sub-linear search method has been proposed, it relies on Hamming distance rather than weighted Hamming distance. To address this issue, we propose an exact k NN search approach with Multiple Tables in Weighted Hamming space named WHMT, in which the distribution of bit-level weights is incorporated into the multi-index building. By WHMT, we can get the optimal candidate set for exact k NN search in weighted Hamming space without exhaustive linear scan. Experimental results show that WHMT can achieve dramatic speedup up to 69.8 times over linear scan baseline without losing accuracy in weighted Hamming space.

Transformerless Stacked Active Bridge Converters: Analysis, Properties, and Synthesis

This article presents analysis, properties, and systematic synthesis of a new class of hybrid dc–dc converters named transformerless stacked active bridge (TSAB) converters. The TSAB converters, which are obtained from switched-capacitor (SC) converters by insertion of small ac inductors, inherit advantages of parent SC converters together with conversion and control characteristics similar to transformer-isolated dual-active-bridge (DAB) dc–dc converters. Features of TSAB converters include soft charging and discharging of capacitors, zero voltage switching, low peak and rms current stresses, low energy storage requirement of magnetic components, and regulation capabilities using simple phase-shift control. Based on a network-theoretic approach, an algebraic representation of TSAB converters yields general results for dc characteristics and component stresses. Furthermore, a systematic synthesis approach is formulated allowing construction of TSAB converter topologies starting from various two-phase SC converters. Synthesis results are presented for TSAB converters with two inductors obtained from well-known SC parent topologies, including Dickson, ladder, stacked-ladder, doubler, and Fibonacci. Experimental results are summarized for 48-to-12 V doubler, 48-to-12 V Dickson, and 36-to-12 V ladder TSAB prototypes. It is shown how the TSAB prototypes use small ac inductors (tens to hundreds of nanohenries) while operating at relatively low switching frequencies (150–200 kHz) and have measured efficiency above 98% over wide load range.

Pseudonym Changing Strategy with Mix Zones Based Authentication Protocol for Location Privacy in Road Networks

A great advancement has been made in intelligent transportation system and communication technologies in order to exchange secure information between automobiles, facilities provider have led an frame over road network. The intelligent transportation system provides an efficient traffic system for drivers, so that there must be less risk to users. In order to design a secure communication protocol among V & V and V & I is a challenging problem. In order to reduce the chance of attacks and increase privacy level, crypto graphic tools provides the feasible solution. In this paper, we proposed pseudonym changing strategy with mix zones (1) Anonymous authentication: the message should be authenticated by issuer due to mix zone and cryptographic tools secure message without any attack. (2) Privacy: Communication contents are confidential due to encrypted messages during communications also improving the scalability through address configuration scheme to reduce computational cost. (3) Efficiency: low storage requirements, The velocity and distance factors may also consider secure measurement, message delivery, overhead and coverage,packet delivery rate, reduce latency and overhead not only by computation cost and time but also compared our scheme, fast delivery rate, low latency and maximum coverage in order to enhance privacy against malicious attacks.

A Derivative-Free Liu–Storey Method for Solving Large-Scale Nonlinear Systems of Equations

In this paper, a descent Liu–Storey conjugate gradient method is extended to solve large-scale nonlinear systems of equations. Based on certain assumptions, the global convergence property is obtained with a nonmonotone line search. The proposed method is suitable to solve large-scale problems for the low-storage requirement. Numerical experiment results show that the new method is practically effective.

BLOCKCHAIN: A NEW DATA STANDARD IN ORAL AND MAXILLOFACIAL RADIOLOGY?

<h3>Background</h3> Despite the Health Insurance Portability and Accountability Act (HIPAA) efforts, protected health information (PHI) and patient's privacy and safety are still under risk. With exposure of greater than 200 million patients' records for the period 2009–2019, the U.S. government is wondering if enough is being done to keep data safe. Blockchain is becoming a gold standard in health care data management because of its trusted, autonomous, immutable, and secured distributed ledger properties. <h3>Objective</h3> The goals of this retrospective, randomized, double-blind study were to assess (1) the effectiveness of Blockchain patient data conversion, (2) backup storage requirements, and (3) HIPAA compliance, compared with the current data storing and sharing methods and the feasibility of the use of Blockchain in Oral and Maxillofacial Radiology (OMR). <h3>Materials and Methods</h3> Head and neck computed tomography (CT) scans (n = 92,903 files) from the Cancer Imaging Archive (Blockchain folder n=46,465 and Monitoring folder n=46,438) and deidentified PHI were randomly assigned by 1 operator. Data were then converted into cryptographic Blockchain hashes via syncing the CBCT scans database folder with the DDSBlockchain (Charlotte, NC, 28,277) folder into the Hyperledger private Blockchain platform by a second operator. Data conversion percentage was assessed, and an F-test Two-Samples for Variances was conducted to quantify data upload speed (<i>P</i> < .05). Storing sizes of the original data and the Blockchain data were compared, and sharing privacy and safety were corroborated through the HIPAA compliance checklist by a third operator within the private Blockchain platform. <h3>Results</h3> One hundred percent of data uploaded were converted into Blockchain. Blockchain conversion had an average speed of 0.617 files per second. No statistical difference (<i>P</i> = .562) was found when comparing the 2 folders upload speed (average 26 hours, 11 minutes, and 5 seconds). The Blockchain data report storage size was 1.22 MB, whereas the original data folder storage size was 5.36 GB. No HIPAA breach was found during the data upload, conversion, sharing, and storage processes. <h3>Discussion</h3> The Blockchain private platform promises to become a gold standard in OMR PHI data backup because of its data conversion effectiveness, low storage requirements, and trusted, autonomous, immutable, and secured distributed ledger capabilities for keeping data private and safe. Preliminary study results indicated the feasibility of adopting Blockchain in OMR as a new data backup management method.

A data estimation for failing nodes using fuzzy logic with integrated microcontroller in wireless sensor networks

Continuous data transmission in wireless sensor networks (WSNs) is one of the most important characteristics which makes sensors prone to failure. a backup strategy needs to co-exist with the infrastructure of the network to assure that no data is missing. The proposed system relies on a backup strategy of building a history file that stores all collected data from these nodes. This file is used later on by fuzzy logic to estimate missing data in case of failure. An easily programmable microcontroller unit is equipped with a data storage mechanism used as cost worthy storage media for these data. An error in estimation is calculated constantly and used for updating a reference “optimal table” that is used in the estimation of missing data. The error values also assure that the system doesn’t go into an incremental error state. This paper presents a system integrated of optimal data table, microcontroller, and fuzzy logic to estimate missing data of failing sensors. The adapted approach is guided by the minimum error calculated from previously collected data. Experimental findings show that the system has great potentials of continuing to function with a failing node, with very low processing capabilities and storage requirements.

A Projection Hestenes–Stiefel Method with Spectral Parameter for Nonlinear Monotone Equations and Signal Processing

A number of practical problems in science and engineering can be converted into a system of nonlinear equations and therefore, it is imperative to develop efficient methods for solving such equations. Due to their nice convergence properties and low storage requirements, conjugate gradient methods are considered among the most efficient for solving large-scale nonlinear equations. In this paper, a modified conjugate gradient method is proposed based on a projection technique and a suitable line search strategy. The proposed method is matrix-free and its sequence of search directions satisfies sufficient descent condition. Under the assumption that the underlying function is monotone and Lipschitzian continuous, the global convergence of the proposed method is established. The method is applied to solve some benchmark monotone nonlinear equations and also extended to solve ℓ 1 -norm regularized problems to reconstruct a sparse signal in compressive sensing. Numerical comparison with some existing methods shows that the proposed method is competitive, efficient and promising.

Learning discriminative hashing codes for cross-modal retrieval based on multi-view features

Hashing techniques have been applied broadly in retrieval tasks due to their low storage requirements and high speed of processing. Many hashing methods based on a single view have been extensively studied for information retrieval. However, the representation capacity of a single view is insufficient and some discriminative information is not captured, which results in limited improvement. In this paper, we employ multiple views to represent images and texts for enriching the feature information. Our framework exploits the complementary information among multiple views to better learn the discriminative compact hash codes. A discrete hashing learning framework that jointly performs classifier learning and subspace learning is proposed to complete multiple search tasks simultaneously. Our framework includes two stages, namely a kernelization process and a quantization process. Kernelization aims to find a common subspace where multi-view features can be fused. The quantization stage is designed to learn discriminative unified hashing codes. Extensive experiments are performed on single-label datasets (WiKi and MMED) and multi-label datasets (MIRFlickr and NUS-WIDE), and the experimental results indicate the superiority of our method compared with the state-of-the-art methods.

Whiskered Tori for Presymplectic Dynamical Systems

We prove persistence result of whiskered tori for the dynamical system which preserves an exact presymplectic form. The results are given in an a-posteriori format. Given an approximate solution of an invariance equation which satisfies some non-degeneracy assumptions, we conclude that there is a true solution close by. The proof is based on certain iterative procedure by which the accuracy of the approximate solutions of the invariance equation can be improved. The iterative procedure is not based on transformation theory, which is cumbersome for presymplectic systems, but on finding corrections to the solutions of the invariance equation. This iterative procedure takes advantage of identities that come from the preservation of the geometric structure and leads to a very efficient numerical method which has low storage requirements, low operator count per step and it is quadratically convergent. We note that a particular case of presymplectic systems is symplectic perturbed by quasi-periodic systems.

A Kalman filtering based adaptive threshold algorithm for QRS complex detection

This work presents an adaptive threshold algorithm in electrocardiogram signal feature extraction by introducing Kalman filtering theory. Low computational cost, low storage requirement and fast response feature are achieved by applying two sets of adaptive threshold systems in different conditions. Also, double-threshold peak detection design dramatically decreases the false detection conditions resulting from noise. As a proof of concept, the proposed algorithm is verified in Matlab and implemented on field programmable gate arrays (FPGA) using MIT/BIH database. The experimental results demonstrate proposed algorithm consumes low resource of FPGA and exhibits 99.30 % detection sensitivity and 99.31 % positive prediction in average, respectively. With the self-adjusting system, proposed algorithm can rapidly adapt different individuals in satisfied detection accuracy.

Implementation of harmonically mapped averaging in LAMMPS, and effect of potential truncation on anharmonic properties.

Implementation of the harmonically mapped averaging (HMA) framework in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is presented for on-the-fly computations of the energy, pressure, and heat capacity of crystalline systems during canonical molecular dynamics simulations. HMA has a low central processing unit and storage requirements and is straightforward to use. As a case study, the properties of the Lennard-Jones and embedded-atom model (parameterized for nickel) crystals are computed. The results demonstrate the higher efficiency of the new class compared to the inbuilt LAMMPS classes for calculating these properties. However, HMA loses its effectiveness in systems where diffusion occurs in the crystal, and an example is presented to allow this behavior to be recognized. In addition to its improved precision, HMA is less affected by small errors introduced by having a larger time step in molecular dynamics simulations. We also present an analysis of the effect of potential truncation on anharmonic properties, and show that artifacts of truncation on the HMA averages can be eliminated simply by shifting the potential energy to zero at the truncation radius. Full properties can be obtained by adding easily computed values for the lattice and harmonic properties using the untruncated potential.

A Modified Conjugate Descent Projection Method for Monotone Nonlinear Equations and Image Restoration

In this article, we propose a modified conjugate descent (CD) projection algorithm for solving system of nonlinear monotone equations with convex constraints. The search direction in this algorithm use a convex combination of the steepest descent algorithm and the well-known CD method. The algorithm proves to be quite efficient for solving large scale monotone nonlinear equations, as it has low storage requirement and does not need the computation of Jacobian matrix. We prove the convergence of the algorithm using some conditions, and perform numerical experiments on some test problems. In order to show the efficiency of our proposed algorithm, the numerical performance is compared with some existing algorithms. Finally, by reformulating l 2 regularized problem into monotone equation, we successfully apply the algorithm to restore some blurred images. The numerical results obtained prove that the algorithm can be used as an efficient and qualitative solver for image restoration problems.

Relaxation Runge--Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier--Stokes Equations

The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Product Norms}, SIAM Journal on Numerical Analysis, 2019) is extended to general convex quantities. Conservation, dissipation, or other solution properties with respect to any convex functional are enforced by the addition of a {\em relaxation parameter} that multiplies the Runge-Kutta update at each step. Moreover, other desirable stability (such as strong stability preservation) and efficiency (such as low storage requirements) properties are preserved. The technique can be applied to both explicit and implicit Runge-Kutta methods and requires only a small modification to existing implementations. The computational cost at each step is the solution of one additional scalar algebraic equation for which a good initial guess is available. The effectiveness of this approach is proved analytically and demonstrated in several numerical examples, including applications to high-order entropy-conservative and entropy-stable semi-discretizations on unstructured grids for the compressible Euler and Navier-Stokes equations.

Adaptive reversible data hiding scheme for AMBTC compressed images

Protecting the security of information transmission over the Internet has become a critical contemporary issue. Compressed images are now widely used in mobile devices and the Internet cloud due to low storage requirements; therefore, many researchers have treated compressed images as a popular carrier in studies of studied reversible data hiding (RDH) schemes. However, the hiding capacity and image quality offered by the reversible data hiding schemes designed for a compression domain are all still limited. To reverse this situation, this paper presents an adaptive reversible data hiding scheme for absolute moment block truncation coding (AMBTC) compressed image using a pixel-value adjusting strategy. Experimental results confirm that the proposed scheme outperforms in both hiding capacity and image quality compared with prior AMBCT-based RDH schemes.

Derivative Free Conjugate Gradient Method via Broyden’s Update for solving symmetric systems of nonlinear equations

The applications of mathematics in many areas of computing, scientific and engineering research mostly give rise to a systems of nonlinear equations. Various iterative methods have been developed to solve such equations, this includes Newton method, Quasi-Newton’s etc. Over the years, there has been significant theoretical study on quasi-Newton methods for solving such systems, but unfortunately the methods suffers setback. To overcome such problems, a Derivative free Method for Solving Symmetric Systems of Nonlinear Equations Using Broyden’s Update is presented. The modification is achieved by simply approximating the inverse Hessian matrix to with (δk and I represents acceleration parameter and an identity matrix respectively) without computing any derivative. The method uses the symmetric structure of the system sufficiently and the generalized classical Broyden’s update method for unconstrained optimization problems. The squared norm merit function is used, both the direction and the line search technique are derivative-free, this attractive feature of the proposed method makes it to have a very low storage requirement thereby solving large scale problems successfully. In an effort to solve nonlinear problems of the form F(x) = 0, 0, x ∈ Rn different initial starting points were used on a set of benchmark test problems, the output is based on number of iterations and CPU time. A comparison between the proposed method and the classical methods were made and found that the proposed method is efficient, robust and outperformed the existing method.

A NEW THREE-TERM CONJUGATE GRADIENT-BASED PROJECTION METHOD FOR SOLVING LARGE-SCALE NONLINEAR MONOTONE EQUATIONS

A new three-term conjugate gradient-based projection method is presented in this paper for solving large-scale nonlinear monotone equations. This method is derivative-free and it is suitable for solving large-scale nonlinear monotone equations due to its lower storage requirements. The method satisfies the sufficient descent condition FTkdk ≤ −τ‖Fk‖2, where τ &gt; 0 is a constant, and its global convergence is also established. Numerical results show that the method is efficient and promising.