Signature Vector Research Articles

Generative vs. Non-Generative Models in Engineering Shape Optimization

Generative models offer design diversity but tend to be computationally expensive, while non-generative models are computationally cost-effective but produce less diverse and often invalid designs. However, the limitations of non-generative models can be overcome with the introduction of augmented shape signature vectors (SSVs) to represent both geometric and physical information. This recent advancement has inspired a systematic comparison of the effectiveness and efficiency of generative and non-generative models in constructing design spaces for novel and efficient design exploration and shape optimization, which is demonstrated in this work. These models are showcased in airfoil/hydrofoil design, and a comparison of the resulting design spaces is conducted in this work. A conventional generative adversarial network (GAN) and a state-of-the-art generative model, the performance-augmented diverse generative adversarial network (PaDGAN), are juxtaposed with a linear non-generative model based on the coupling of the Karhunen–Loève Expansion and a physics-informed shape signature vector (SSV-KLE). The comparison demonstrates that, with an appropriate shape encoding and a physics-augmented design space, non-generative models have the potential to cost-effectively generate high-performing valid designs with enhanced coverage of the design space. In this work, both approaches were applied to two large foil profile datasets comprising real-world and artificial designs generated through either a profile-generating parametric model or a deep-learning approach. These datasets were further enriched with integral properties of their members’ shapes, as well as physics-informed parameters. The obtained results illustrate that the design spaces constructed by the non-generative model outperform the generative model in terms of design validity, generating robust latent spaces with no or significantly fewer invalid designs when compared to generative models. The performance and diversity of the generated designs were compared to provide further insights about the quality of the resulting spaces. These findings can aid the engineering design community in making informed decisions when constructing design spaces for shape optimization, as it has been demonstrated that, under certain conditions, computationally inexpensive approaches can closely match or even outperform state-of-the art generative models.

Determining the optimal design for complex systems using a reliability signature

In reliability analysis, the structure-function is a commonly used mathematical representation of the studied system. A signature vector is used for systems with independently and identically distributed (i.i.d.) component lifetimes. Each element in the signature represents the probability that the failure of the corresponding component will fail the entire system. This paper aims to provide a comprehensive understanding of assessing the performance of two complex systems for optimal communication design. The study compares two systems with the same components using signatures, expected cost rate, survival signature, and sensitivity to determine which system is preferred. It also provides several sufficient conditions for comparing the lifetimes of two systems based on the usual stochastic order. The results are applied to two communication systems that have the same components. The mathematical properties presented in the study have been proven to enable efficient weighting of the optimal design.

A Physicist’s View on Partial 3D Shape Matching

A new algorithm is presented to compute nonrigid, possibly partial comparisons of shapes defined by unstructured triangulations of their surfaces. The algorithm takes as input a pair of surfaces with each surface given by a distinct and unrelated triangulation. Its goal is to define a possibly partial correspondence between the vertices of the two triangulations, with a cost associated with this correspondence that can serve as a measure of the similarity of the two shapes. To find this correspondence, the vertices in each triangulation are characterized by a signature vector of features. We tested both the LD-SIFT signatures, based on the concept of spin images, and the wave kernel signatures obtained by solving the Shrödinger equation on the triangulation. A cost matrix C is constructed such that C(k,l) is the norm of the difference of the signature vectors of vertices k and l. The correspondence between the triangulations is then computed as the transport plan that solves the optimal transport or optimal partial transport problem between their sets of vertices. We use a statistical physics approach to solve these problems. The presentation of the proposed algorithm is complemented with examples that illustrate its effectiveness and manageable computing cost.

Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces

A class of zipper fractal functions is more versatile than corresponding classes of traditional and fractal interpolants due to a binary vector called a signature. A zipper fractal function constructed through a zipper iterated function system (IFS) allows one to use negative and positive horizontal scalings. In contrast, a fractal function constructed with an IFS uses positive horizontal scalings only. This article introduces some novel classes of continuously differentiable convexity-preserving zipper fractal interpolation curves and surfaces. First, we construct zipper fractal interpolation curves for the given univariate Hermite interpolation data. Then, we generate zipper fractal interpolation surfaces over a rectangular grid without using any additional knots. These surface interpolants converge uniformly to a continuously differentiable bivariate data-generating function. For a given Hermite bivariate dataset and a fixed choice of scaling and shape parameters, one can obtain a wide variety of zipper fractal surfaces by varying signature vectors in both the x direction and y direction. Some numerical illustrations are given to verify the theoretical convexity results.

Combined m-Consecutive-k-Out-of-n: F and Consecutive kc-Out-of-n: F Structures with Cold Standby Redundancy

In the present work, we study the combined m-consecutive-k-out-of-n: F and kc-out-of-n: F reliability systems, which consist of independent and identically distributed components. Two different redundancy policies are considered, and their general frameworks are described and illustrated. The main objective of the paper refers to the investigation of the effect of adding cold standby redundancy to the system at the the system level and the component level. Exact formulae for determining the crucial characteristics of the enhanced structure, such as its survival function, the mean time to failure and the mean residual lifetime, are provided. All formulae proved in the present manuscript are explicit expressions which are based on the signature vector of the resulting reliability schemes. An extensive numerical investigation is carried out to shed light on the performance of the combined m-consecutive-k-out-of-n: F and consecutive kc-out-of-n: F reliability systems with cold standby redundancy. Some concluding remarks and comments are provided upon the determination of the optimal design parameters.

On the Uncertainty Properties of the Conditional Distribution of the Past Life Time.

For a given system observed at time t, the past entropy serves as an uncertainty measure about the past life-time of the distribution. We consider a coherent system in which there are n components that have all failed at time t. To assess the predictability of the life-time of such a system, we use the signature vector to determine the entropy of its past life-time. We explore various analytical results, including expressions, bounds, and order properties, for this measure. Our results provide valuable insight into the predictability of the coherent system's life-time, which may be useful in a number of practical applications.

Quantum similarity and QSPR in Euclidean-, and Minkowskian–Banach spaces

This paper describes first how Euclidian- and Minkowskian–Banach spaces are related via the definition of a metric or signature vector. Also, it is discussed later on how these spaces can be generated using homothecies of the unit sphere or shell. Such possibility allows for proposing a process aiming at the dimension condensation in such spaces. The condensation of dimensions permits the account of the incompleteness of classical QSPR procedures, independently of whether the algorithm used is statistical bound or AI-neural network related. Next, a quantum QSPR framework within Minkowskian vector spaces is discussed. Then, a well-defined set of general isometric vectors is proposed, and connected to the set of molecular density functions generating the quantum similarity metric matrix. A convenient quantum QSPR algorithm emerges from this Minkowskian mathematical structure and isometry.

Transform Waveforms Into Signature Vectors for General-Purpose Incipient Fault Detection

Power system equipment presents special signatures at the incipient stage of faults. As more renewables are integrated into the systems, these signatures are harder to detect. If faults are detected at an early stage, economical losses and power outages can be avoided in modern power grids. Many researchers and power engineers have proposed a series of signature-specific methods for one type of equipment’s waveform abnormality. However, conventional methods are not designed to identify multiple types of incipient faults (IFs) signatures at the same time. Therefore, we develop a general-purpose IF detection method that detects waveform abnormality stemming from multiple types of devices. To avoid the computational burden of the general-purpose IF detection method, we embed the abnormality signatures into a vector and develop a pre-training model (PTM) for machine understanding. In the PTM, signal “words,” “sentences,” and “dictionaries” are designed and proposed. Through the comparison with a machine learning classifier and a simple probabilistic language model, the results show a superior detection performance and reveal that the training radius is highly related to the size of abnormal waveforms.

Discussion of signature‐based models of preventive maintenance

Discussion of signature‐based models of preventive maintenance

Discussion of signature‐based models of preventive maintenance

Discussion of signature‐based models of preventive maintenance

Shape-supervised Dimension Reduction: Extracting Geometry and Physics Associated Features with Geometric Moments

In shape optimisation problems, subspaces generated with conventional dimension reduction approaches often fail to extract the intrinsic geometric features of the shape that would allow the exploration of diverse but valid candidate solutions. More importantly, they also lack incorporation of any notion of physics against which shape is optimised. This work proposes a shape-supervised dimension reduction approach. To simultaneously tackle these deficiencies, it uses higher-level information about the shape in terms of its geometric integral properties, such as geometric moments and their invariants. Their usage is based on the fact that moments of a shape are intrinsic features of its geometry, and they provide a unifying medium between geometry and physics. To enrich the subspace with latent features associated with shape’s geometrical features and physics, we also evaluate a set of composite geometric moments, using the divergence theorem, for appropriate shape decomposition. These moments are combined with the shape modification function to form a Shape Signature Vector (SSV) uniquely representing a shape. Afterwards, the generalised Karhunen–Loève expansion is applied to SSV, embedded in a generalised (disjoint) Hilbert space, which results in a basis of the shape-supervised subspace retaining the highest geometric and physical variance. Validation experiments are performed for a three-dimensional wing and a ship hull model. Our results demonstrate a significant reduction of the original design space’s dimensionality for both test cases while maintaining a high representation capacity and a large percentage of valid geometries that facilitate fast convergence to the optimal solution. The code developed to implement this approach is available at https://github.com/shahrozkhan66/SSDR.git . • Shape signature vector (SSV) comprises a shape modification vector and geometric moments (GM). • Karhunen–Loève expansion of SSV results in a shape-supervised space (SSS). • GM can induce the notion of physics resulting in a physics-informed SSS. • SSS retains higher geometric variance with fewer latent variables. • SSS is robust and compact, providing accelerated optimisation convergence.

Signature-Based Analysis of the Weighted-r-within-Consecutive-k-out-of-n: F Systems

In the present paper, we deliver a reliability study of the weighted-r-consecutive-k-out-of-n: F reliability systems consisting of independent and identically distributed components. The signature vector of the structures is arithmetically determined by the aid of an appropriate Monte-Carlo simulation scheme. Several conclusions for the corresponding reliability polynomials are also drawn. An extensive numerical investigation is carried out to evaluate the performance of the weighted-r-consecutive-k-out-of-n: F reliability systems. Some stochastic signature-based comparisons among several members of the underlying family of reliability structures are also discussed.

A Linear Algebraic Threshold Essential Secret Image Sharing Scheme

A secret sharing scheme allocates to each participant a share of a secret in such a way that authorized subsets of participants can reconstruct the secret, while shares of unauthorized subsets of participants provide no useful information about the secret. For positive integers r,s,t,n with r⩽s⩽t⩽n, an (r,s,t,n)–threshold essential secret sharing scheme is an algorithm that decomposes a secret S into n shares, s of which are essential, in a way that authorized subsets are precisely those with at least t members, at least r of whom are essential. This work proposes a lossless linear algebraic (r,s,t,n)–threshold essential secret image sharing scheme that decomposes the secret, S, into equally-sized shares, each of size 1/t the size of S. For each block, B, of S, the scheme assigns to the n participants distinct signature vectors v1,v2,…,vn in the vector space F2αt, where α is a suitable positive integer, typically between 2 and 5, inclusive. These signature vectors must adhere to some admissibility conditions in order to satisfy the secret sharing threshold properties. The decomposition of B into n shares is obtained by partitioning B into t vectors, then computing the share yj of the jth participant (1≤j≤n), as a linear combination of these parts with coefficients from the signature vj. The presented simulations showcase the effectiveness and robustness of the proposed scheme against standard statistical and security attacks. They further demonstrate its superiority with respect to existing schemes.

Multiple access interference suppression for CDMA systems via [formula omitted]-minimization

A key problem in code-division multiple access (CDMA) system is to mitigate the multiple access interference (MAI) from other users while detecting the desired user. The performance of the conventional minimum output energy (MOE) multiuser detector for CDMA system significantly degrades in the presence of signature waveform distortions induced by multipath propagation or timing asynchronism. In this paper, a robust linear programming (ROLP) algorithm for blind multiuser detection is proposed. Different from the existing MOE-based multiuser detection techniques, the proposed ROLP minimizes the ℓ∞-norm of the output to exploit the non-Gaussianity of the communication signals. To achieve robustness against signature waveform mismatch, the proposed method constrains the magnitude response of any signature vector within a specified uncertainty set to exceed unity. The uncertainty set is modeled as a rhombus, which differs from the spherical uncertainty region widely taken in the existing robust multiuser detectors. The resulting optimization problem is reformulated into a linear programming program and hence can be solved efficiently. The proposed ROLP is computationally simpler than its robust counterparts that requires solving a second-order cone programming. Simulation results demonstrate the superiority of the ROLP over several robust detectors, which indicate that its performance approaches the optimal performance bound.

A Heuristic Boolean NPN Equivalent Matching Verification Method Based on Shannon Decomposition

In this paper, we describe a new verification method to accelerate the input negation and/or input permutation and/or output negation (NPN) Boolean matching for a single-output completely specified Boolean function. Through research on the Boolean Shannon decomposition binary tree, we prove that the signature vectors of the left child node and right child node are complementary relative to the signature vector of the parent node. We introduce an independent variable check to speed up the detection of candidate transformation. The proposed approach utilises this complementarity, a symmetry check, an independent variable check and a phase collision check, which can quickly verify whether the candidate transformation obtained in the detection of the candidate transformation of the Boolean matching process is accurate. We perform experiments on two types of Boolean function sets. One type consists of Boolean functions from randomly generated circuits. The other is exported from the Microelectronics Center of North Carolina (MCNC) benchmark. The experimental results show that the average runtime of our algorithm is 68.8% faster than those in Zhang et al. (2019) on two randomly generated circuits and 51% faster than those in Zhang et al. (2019) when tested on the MCNC benchmark circuit set. Therefore, the experimental results demonstrate the effectiveness of the proposed method.

Reproducible families of codes and cryptographic applications

Abstract Structured linear block codes such as cyclic, quasi-cyclic and quasi-dyadic codes have gained an increasing role in recent years both in the context of error control and in that of code-based cryptography. Some well known families of structured linear block codes have been separately and intensively studied, without searching for possible bridges between them. In this article, we start from well known examples of this type and generalize them into a wider class of codes that we call ℱ-reproducible codes. Some families of ℱ-reproducible codes have the property that they can be entirely generated from a small number of signature vectors, and consequently admit matrices that can be described in a very compact way. We denote these codes as compactly reproducible codes and show that they encompass known families of compactly describable codes such as quasi-cyclic and quasi-dyadic codes. We then consider some cryptographic applications of codes of this type and show that their use can be advantageous for hindering some current attacks against cryptosystems relying on structured codes. This suggests that the general framework we introduce may enable future developments of code-based cryptography.

On the Closure of Aging Classes Under the Formation of Coherent Structures

In this paper, we study the closure property of the Increasing Failure Rate (IFR) class under the formation of coherent systems. Sufficient conditions for the nonpreservation of the IFRattribute for reliability structures consisting of [Formula: see text] independent and identically distributed ([Formula: see text] components are provided. More precisely, we deal with the IFR preservation (or nonpreservation) under the formation of structures with two common failure criteria by the aid of their signature vectors.

An algorithm for computing the t-signature of two-state networks

Due to the importance of the signature vector in studying the reliability of networks, some methods have been proposed by researchers to obtain the signature. The notion of signature is used when at most one link may fail at each time instant. It is more realistic to consider the case where none of the components, one component, or more than one component of the network may be destroyed at each time. Motivated by this, the concept of t-signature has been recently defined to get the reliability of such a network. The t-signature is a probability vector and depends only on the network structure. In this article, we propose an algorithm to compute the t-signature. The performance of the proposed algorithm is evaluated for some networks.

Developing Software Signature Search Engines Using Paragraph Vector Model: A Triage Approach for Digital Forensics

Today, with the growth of information and communication technology, digital crimes have also spread. Advanced storage technologies and their low cost have led to a significant increase in their use. Therefore, the high volume of digital data to be analyzed is a challenge facing digital forensic investigators. Digital forensic triage solutions aim to alleviate the forensic backlog. A promising triage technique is to quickly find the software packages run on the target system to narrow down the search space. In this paper, we propose a software signature search engine (S3E) to identify software on the system under investigation. The document collection of this search engine consists of software signatures, and the query is the features extracted from the system’s hard disk. We propose a forensic differential analysis model to build software signatures. Besides, we use the paragraph vector model to construct the corresponding vectors of each software signature and find similarities between the query vector and the signature vectors. Different design parameters are involved in making software signature search engines, and distinct values of these parameters lead to different models. We have measured the performance of these S3E models against several controlled systems and some pseudo-real systems. The experimental results on both datasets show that some S3E models achieve perfect recall, and many of them have a recall of more than 90%. Besides, we find that the recall rate of the S3E models in both datasets is higher than the averaged word2vec model and the TF-IDF model.

EKG ve SKG Sinyallerinin Temel Tanım ve Zarf Vektörleriyle Modellenmesi

Seismocardiogram (SCG) is a low-cost monitoring method to collect precordial vibrations of sternum due to heartbeats and evaluate cardiac activity. It is mostly used as an auxiliary measurement to the other monitoring methods; however, it carries significant patterns reflecting current cardiovascular health status of subjects. If it is properly collected within a non-clinical environment, it might be able to present preliminary data to physicians before clinic. SCG signals are morphologically noisy. These signals store excessive amount of data. Extracting significant information corresponding to heartbeat complexes is so important. Previously, the method called compressed sensing (CS) had been applied to weed up the redundant information by taking the advantage of sparsity feature in a study. This compressed sensing is based on storing significant signals below the Nyquist rate which suffice for medical diagnosis. It has been feasible to compress SCG signals with 3:1 compression rate at least while maintaining accurate signal reconstruction. Nevertheless, higher compression rates lead to the formation of artifacts on reconstructed signals. This limits a more aggressive compression to reduce the amount of data. The requirement of a different approach which will allow higher compression rates and lower loss of information arises. The purpose of this study is to obtain more competent results by using a method called predefined signature and envelope vector sets (PSEVS) which has been satisfyingly applied to electrocardiogram (ECG) and speech signals. In the study, simultaneously recorded ECG and SCG signals were modeled with the method called PSEVS. The reconstructed signals were compared to the original signals so as to investigate the efficacy of signature-based modeling methods in constructing medically remarkable biosignals for clinical use. After examining the components of reconstructed signals called frame-scaling coefficient, signature and envelope vectors, it has been seen that the error function values of envelope vectors differ from expected values. We concluded that reconstructed SCG signals were not adequate for medical diagnosis.