Basic Vector Operations Research Articles

Hep_tables: Heterogeneous Array Programming for HEP

Array operations are one of the most concise ways of expressing common filtering and simple aggregation operations that are the hallmark of a particle physics analysis: selection, filtering, basic vector operations, and filling histograms. The High Luminosity run of the Large Hadron Collider (HL-LHC), scheduled to start in 2026, will require physicists to regularly skim datasets that are over a PB in size, and repeatedly run over datasets that are 100’s of TB’s – too big to fit in memory. Declarative programming techniques are a way of separating the intent of the physicist from the mechanics of finding the data and using distributed computing to process and make histograms. This paper describes a library that implements a declarative distributed framework based on array programming. This prototype library provides a framework for different sub-systems to cooperate in producing plots via plug-in’s. This prototype has a ServiceX data-delivery sub-system and an awkward array sub-system cooperating to generate requested data or plots. The ServiceX system runs against ATLAS xAOD data and flat ROOT TTree’s and awkward on the columnar data produced by ServiceX.

Phase retrieval algorithm for optical information security**Project supported by the National Natural Science Foundation of China (Grant Nos. 61775121, 61605165, 61307003, 61405122, and 11574311), the Key Research and Development Program of Shandong Province, China (Grant No. 2018GGX101002), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019QF006), and the Fundamental Research Funds of Shandong University, China (Grant No. 2015GN031).

As a typical technology for optical encryption, phase retrieval algorithms have been widely used in optical information encryption and authentication systems. This paper presents three applications of two-dimensional (2D) phase retrieval for optical encryption and authentication: first, a hierarchical image encryption system, by which multiple images can be hidden into cascaded multiple phase masks; second, a multilevel image authentication system, which combines (t, n) threshold secret sharing (both t and n are positive integers, and ) and phase retrieval, and provides both high-level and low-level authentication; and finally, a hierarchical multilevel authentication system that combines the secret sharing scheme based on basic vector operations and the phase retrieval, by which more certification images can be encoded into multiple cascaded phase masks of different hierarchical levels. These three phase retrieval algorithms can effectively illustrate phase-retrieval-based optical information security. The principles and features of each phase-retrieval-based optical security method are analyzed and discussed. It is hoped that this review will illustrate the current development of phase retrieval algorithms for optical information security and will also shed light on the future development of phase retrieval algorithms for optical information security.

Vector aggregation operator and score function to solve multi-criteria decision making problem in neutrosophic environment

In our real world there exist uncertain, imprecise, incomplete, and inconsistent information. Those kinds of information can be suitably handled by neutrosophic fuzzy set as it is the generalization of classic set, fuzzy set and intuitionistic fuzzy set. The uncertain, imprecise, incomplete and inconsistent information provided by several sources need to be aggregated to come to a conclusion. Aggregation and fusion of information are basic concerns for all kinds of knowledge based systems. The main purpose of this paper is to aggregate neutrosophic fuzzy information by introducing a new aggregation operator in vector approach. The new approach is simple based on basic vector operations and reliable as it will always give a meaningful result. Also a new vector score function has been defined to compare the neutrosophic fuzzy numbers and explained through geometrical interpretation. The newly proposed vector score function always gives different values for any two different neutrosophic numbers. Further, a multiple-criteria decision-making method is established on the basis of the proposed operator and newly defined score function.

Hierarchical multilevel authentication system for multiple-image based on phase retrieval and basic vector operations

A hierarchical multilevel authentication system for multiple-image based on phase retrieval and basic vector operations in the Fresnel domain is proposed, by which more certification images are iteratively encoded into multiple cascaded phase masks according to different hierarchical levels. Based on the secret sharing algorithm by basic vector decomposition and composition operations, the iterated phase distributions are split into n pairs of shadow images keys (SIKs), and then distributed to n different participants (the authenticators). During each level in the high authentication process, any 2 or more participants can be gathered to reconstruct the original meaningful certification images. While in the case of each level in the low authentication process, only one authenticator who possesses a correct pair of SIKs, will gain no significant information of certification image; however, it can result in a remarkable peak output in the nonlinear correlation coefficient of the recovered image and the standard certification image, which can successfully provide an additional authentication layer for the high-level authentication. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.

Optical image encryption based on real-valued coding and subtracting with the help of QR code

A novel optical image encryption based on real-valued coding and subtracting is proposed with the help of quick response (QR) code. In the encryption process, the original image to be encoded is firstly transformed into the corresponding QR code, and then the corresponding QR code is encoded into two phase-only masks (POMs) by using basic vector operations. Finally, the absolute values of the real or imaginary parts of the two POMs are chosen as the ciphertexts. In decryption process, the QR code can be approximately restored by recording the intensity of the subtraction between the ciphertexts, and hence the original image can be retrieved without any quality loss by scanning the restored QR code with a smartphone. Simulation results and actual smartphone collected results show that the method is feasible and has strong tolerance to noise, phase difference and ratio between intensities of the two decryption light beams.

Optical threshold secret sharing scheme based on basic vector operations and coherence superposition

We propose, to our knowledge for the first time, a simple optical algorithm for secret image sharing with the (2,n) threshold scheme based on basic vector operations and coherence superposition. The secret image to be shared is firstly divided into n shadow images by use of basic vector operations. In the reconstruction stage, the secret image can be retrieved by recording the intensity of the coherence superposition of any two shadow images. Compared with the published encryption techniques which focus narrowly on information encryption, the proposed method can realize information encryption as well as secret sharing, which further ensures the safety and integrality of the secret information and prevents power from being kept centralized and abused. The feasibility and effectiveness of the proposed method are demonstrated by numerical results.

FARMER: A novel approach to file access correlation mining and evaluation reference model

File semantic has proven effective in optimizing large scale distributed file system. As a consequence of the elaborate and rich I/O interfaces between upper layer applications and file systems, file system can provide useful and insightful information about semantic. Hence, file semantic mining has become an increasingly important practice in both engineering and research community. Unfortunately, it is a challenge to exploit file semantic knowledge because a variety of factors could affect this information exploration process. Even worse, the challenges are exacerbated due to the intricate interdependency between these factors, and make it difficult to fully exploit the potentially important correlation among various semantic knowledges. This article proposes a file access correlation miming and evaluation reference (FARMER) model, where file is treated as a multivariate vector space, and each item within the vector corresponds a separate factor of the given file. The selection of factor depends on the application, examples of factors are file path, creator and executing program. If one particular factor occurs in both files, its value is non-zero. It is clear that the extent of inter-file relationships can be measured based on the likeness of their factor values in the semantic vectors. Benefit from this model, FARMER represents files as structured vectors of identifiers, and basic vector operations can be leveraged to quantify file correlation between two file vectors. FARMER model leverages linear regression model to estimate the strength of the relationship between file correlation and a set of influencing factors so that the “bad knowledge” can be filtered out. To demonstrate the ability of new FARMER model, FARMER is incorporated into a real large-scale object-based storage system as a case study to dynamically infer file correlations. In addition FARMER-enabled optimize service for metadata prefetching algorithm and object data layout algorithm is implemented. Experimental results show that is FARMER-enabled prefetching algorithm is shown to reduce the metadata operations latency by approximately 30%–40% when compared to a state-of-the-art metadata prefetching algorithm and a commonly used replacement policy.

Image encoding based on coherent superposition and basic vector operations

A new method for image encryption based on optical coherent superposition and basic vector operations is proposed in this paper. In this encryption, the original image can be directly separated into two phase masks (PMs). One is a random phase mask (RPM) and the other is a modulation of the RPM by the original image. The mathematical calculation for obtaining the two PMs is quite simple and direct resulting from the simple principle of optical coherent superposition. The arbitrarily selected RPM can be treated as the encrypted result while the PM can be taken as the key for decryption. With this technique, the same encrypted result can be obtained for different images with the same size while the keys for decryption are different. The encryption can be performed digitally and the decryption can be performed optically or digitally. The security of the proposed method is discussed and computer simulation results are presented to verify the validity of proposed method.

A bidirectional vector associative memory architecture with application to neural networks

A bidirectional architecture for associative memory (AM) capable of vector arithmetic operations is proposed. By introducing a pair of masking and tagging mechanisms, the conventional concepts of bit-operations and word-operations in AM have been generalized to row and column operations, respectively. The proposed architecture demonstrates a symmetrical functionality such that associative processing can be performed in both column and row directions. A set of built-in vector arithmetic and logic units (VALU) is designed to perform the basic vector operations, which offers O(max{ n, m}) speed-up for vector operations over the conventional AM at an O( n + m) cost for realizing an n × m AM array. As an applicational example, an associative processing implementation for artificial neural networks is presented.

Pointing geometry for low Earth orbit auroral observations

Introduction A LGORITHMS are developed to solve the geometry required to point telescopes mounted on a low Earth-orbiting satellite at features in the aurora (at height of typically 100 km above Earth's surface). It is based on requirements for the proposed AURIO telescopes, which may be flown on a polar platform of the European Space Agency (ESA). The idea of pointing an instrument and tracking a target from space is not new and the geometry has been solved for several cases (see, e.g., Jerkovsky, Burdick et al., and Hablani). The traditional approach is to use vector notation, but at the implementation stage this method usually needs to be supported by a library of subroutines to implement the basic vector operations of addition, cross and scalar products, and rotations of vectors about the coordinate axes, which raises difficulties in a small embedded computer system. In this Note a computational method is presented to find the line-of-sight (LOS) vector in the satellite-body-attached coordinate frame. This method uses homogeneous transformation matrices (normally used in robot kinematics) to provide efficient algorithms that can readily be implemented on-board the satellite. A spherical Earth is assumed in this work as the basic model. However, the spheroidal model of Earth has been used to assess errors due to this assumption. The software coding of the pointing equations can easily be implemented in any high level programming language, and they have been tested in the occam language.

PROFIL/BIAS—A fast interval library

The interval data type is currently not supported in common programming languages. Therefore the implementation of algorithms using interval arithmetic requires special programming environments or at least special libraries. In this paper we present the C++ class library PROFIL which provides a user friendly environment for implementing interval algorithms. The main goals in the design of PROFIL were speed and portability. Therefore all interval operations in PROFIL use BIAS (Basic Interval Arithmetic Subroutines) [16]. BIAS defines a concise and portable interface for the basic scalar, vector, and matrix operations. The interface is independent of a specific interval representation or computation but permits machine specific and fast implementations. Based on this general specification we present an implementation in C using a lower/upper bound representation of intervals and directed roundings. By using few assembler instructions for switching the rounding modes and avoiding sign tests and rounding mode switches wherever possible, the computational costs of the interval operations were reduced significantly. This is especially important for RISC machines, where floating point instructions can be executed in few machine cycles. Comparisons with other interval arithmetic packages show an improvement in speed of about one order of magnitude.

A Benchmark Comparison of Three Supercomputers: Fujitsu VP-200, Hitachi S810/120, and Cray X-MP/2

The authors report on their opportunity to benchmark the VP-200 (benchmarked at the Fujitsu plant in Numazu, Japan in May 1984 and more recently in May 1985 at Amdahl); the Hitachi S810/20 (made available at the Large Scale Computation Center of Tokyo University in May 1984); and Cray Research provided time on an X-MP running COS and version 1.13 of their CFT compiler. Other X-MP benchmarks were conducted at Los Alamos. For the most part, the codes that were executed on the machines came from the Los Alamos benchmark set. The set is composed of programs that typify the Los Alamos workload. It was found that the VP-200 can be two to three times as fast as the X-MP/2 in vector mode for large vector lengths. Results from highly vectorized codes (rudimentary matrix operations and a linear equations solver) as well as the timings from basic vector operations support this conclusion. On the codes that are more indicative of the Los Alamos workload, the VP-200 and X-MP/2 are comparable. The times for BMK5 (0% vectorized) were virtually equivalent; BMK21 (0% vectorized) was executed on the VP-200 18% faster than on the X-MP; BMK1lb (62% vectorized) and BMK21a (18% vectorized) favored the VP-200 by 17% and 24%, respectively; and SIMPLE (93% vectorized) favored the X-MP by 25%. The authors suggest three reasons for the parity: (1) from the standpoint of Amdahl's Law, many of the codes are dominated by the equivalent scalar performance of the machines, (2) even in the cases of higher degrees of vectorization, vector lengths less than 100 perform equivalently, and (3) function calls prevented full vectorization on the VP-200 in some cases (for example, BMK1la). The Hitachi S810/20 does not perform as well as the other two on the benchmark codes, probably because its scalar performance and vector processor clock period are slower. Additionally, the benchmark codes could not make use of the large number of functional units in the S810/20.