Vector Addition Research Articles

All-Optical Aggregation and De-Aggregation of 4×BPSK-16QAM Using Nonlinear Wave Mixing for Flexible Optical Network

A scheme is proposed for all-optical aggregation from four 10 Gbps binary-phase-shift-keying (BPSK) signals into one 40 Gbps 16-ary quadrature amplitude modulation (16QAM) signal by applying the coherent addition of optical vectors, and de-aggregation for the 16QAM signal to recover the data of four original BPSK signals in high nonlinear fiber (HNLF) without information loss or redundancy using self-phase modulation (SPM) and four-wave mixing (FWM). The simulation results show that the error-vector-magnitude (EVM) curves of BPSK signal before aggregation and the 16QAM signal almost coincide with each other, as well as after the de-aggregation it has about 20% degradation at most. The bit error rate (BER) performance of BPSK signals indicates that when the OSNR of BPSK before aggregation is greater than 21.0 dB, then the wrong code of BPSK signal after de-aggregation can be corrected at the receiving end. Additionally, the expanded methods are also proposed for the aggregation of 8PSK signal and 64QAM signal by employing the similar principle. This proposed method provides a new way for realizing the flexible optical transmission and reception of advanced modulation format signals, and suits for the future dynamically reconfigurable optical network at the gateway nodes between different transmission networks.

Theoretical and experimental verification of a fast two‐dimensional Gaussian beam mode analysis method

In quasi-optical systems, the beam distortion and the cross-polarisation caused by the offset reflectors get a lot of attention. Also, the distortion was thoroughly studied in previous works. In this study, the authors give the detailed derivations of exact and approximate expressions of cross-polarisation and some simple explanations about energy conversion between co- and cross-polarisations in two-dimensional multi-reflector systems based on Gaussian beam mode analysis (GBMA). In addition two dual-reflector systems with different structures are used to verify the correctness and accuracy of GBMA comparing with physical optics (PO) in commercial software GRASP10. Furthermore, the authors fabricate one of these two systems and give experimental results. Then, they propose a fast analysis algorithm based on the vector addition method to reduce the computation time by eliminating the redundant modes. The efficiency of the proposed fast algorithm is illustrated by the number of modes and the calculation time for each reflection in a tri-reflector system. In addition, the authors also present the computation time of PO in GRASP10 as a reference. With the application of the fast algorithm, the computational efficiency is improved and increases with the number of reflections.

Facial expression animation through action units transfer in latent space

Automatic animation synthesis has attracted much attention from the community. As most existing methods take a small number of discrete expressions rather than continuous expressions, their integrity and reality of the facial expressions is often compromised. In addition, the easy manipulation with simple inputs and unsupervised processing, although being important to the automatic facial expression animation applications, is relatively less concerned. To address these issues, we propose an unsupervised continuous automatic facial expression animation approach through action units (AU) transfer in the latent space of generative adversarial networks. The expression descriptor which is depicted with AU vector is transferred into the input image without the need of labeled pairs of images and even without their expressions and further network training. We also propose a new approach to quickly generate input image's latent code and cluster the boundaries of different AU attributes with their latent codes. Two latent code operators, vector addition and continuous interpolation, are leveraged for facial expression animation simulating align with the boundaries in the latent space. Experiments have shown that the proposed approach is effective on facial expression translation and animation synthesis.

Enhanced growth and β-galactosidase production on Escherichia coli using oxygen vectors

The addition of n-dodecane (between 1-3%) to the Escherichia coli fermentation broth in a mechanically agitated and aerated bioreactor revealed improved DO (dissolved oxygen) levels induced during fermentation which lead to an increase in biomass productivity and faster glucose consumption. The maximum values for enzyme activity (increased with 43% compared with the control) and k L a (the volumetric mass transfer coefficient) were obtained for the addition of 2% v/v n-dodecane in the bioreactor, due to the fact that oxygen limitation during the exponential growth phase of the bacterium can repress β-galactosidase production. The oxygen vector addition increased the available dissolved oxygen and activated a redox-sensitive regulation and an elevated intracellular oxidative metabolism that lead to the enhancement in E. coli biomass accumulation and a more accurate protein folding of β-galactosidase that would increase its activity. In addition to the experimental analysis, a complex model, developed using an improved version of Bacterial Foraging Algorithm and Artificial Neural Networks, was proposed, with a good average absolute value (6.2% in the training phase and 7.28% in the testing phase) between the process dynamic and the predictions generated by the model.

Model for identification of the background emission of Universe microwaves

This article discusses the identification of digital images in the map of the background emission of Universe microwaves developed on the basis of data from the European Space Agency telescope Planck upon applying a simulation of parameter z from the Doppler effect formula and the theory of covariance functions. The value of the Doppler parameter z shows an approximate mutual speed of two digital images (objects) with respect to the speed of light in vacuum. For a calculation of values of parameter z, vectors transformed by digital images and the pixels intensity of the white solar spectrum were used. The values of parameter z enabled calculation of the mutual speed of the digital images and the speeds of their movement with respect to the solar system. For calculation of estimates of the covariance functions, the algebraic additions of vectors transformed by the digital images and single vectors were applied. While varying the scale of a digital image, the frequencies of single pixel colours do not change, that is, they remain constant and no impact of the scale variation expresses itself in the calculation procedure of covariance functions. For the identification of images, the spectrum of RGB format was used. The average values of parameter z in the Doppler formula were calculated according to the formula created on the basis of expressions of cross-covariance functions of the algebraic addition of relevant transformed vectors and single vectors. The mutual speed of the movement of images of a part of the Universe was established. The calculation data were obtained using MATLAB-based computer programmes.

Path integration in large-scale space and with novel geometries: Comparing vector addition and encoding-error models.

Path integration is thought to rely on vestibular and proprioceptive cues yet most studies in humans involve primarily visual input, providing limited insight into their respective contributions. We developed a paradigm involving walking in an omnidirectional treadmill in which participants were guided on two sides of a triangle and then found their back way to origin. In Experiment 1, we tested a range of different triangle types while keeping the distance of the unguided side constant to determine the influence of spatial geometry. Participants overshot the angle they needed to turn and undershot the distance they needed to walk, with no consistent effect of triangle type. In Experiment 2, we manipulated distance while keeping angle constant to determine how path integration operated over both shorter and longer distances. Participants underestimated the distance they needed to walk to the origin, with error increasing as a function of the walked distance. To attempt to account for our findings, we developed configural-based computational models involving vector addition, the second of which included terms for the influence of past trials on the current one. We compared against a previously developed configural model of human path integration, the Encoding-Error model. We found that the vector addition models captured the tendency of participants to under-encode guided sides of the triangles and an influence of past trials on current trials. Together, our findings expand our understanding of body-based contributions to human path integration, further suggesting the value of vector addition models in understanding these important components of human navigation.

A note on the generator subgraph of a graph

Graphs considered in this paper are finite simple undirected graphs. Let G = ( V ( G ), E ( G )) be a graph with E ( G ) = {e 1 , e 2 ,..., e m }, for some positive integer m . The edge space of G , denoted by ℰ( G ), is a vector space over the field ℤ 2 . The elements of ℰ( G ) are all the subsets of E ( G ). Vector addition is defined as X + Y = X ∆ Y , the symmetric difference of sets X and Y , for X , Y ∈ ℰ( G ). Scalar multiplication is defined as 1. X = X and 0. X = ∅ for X ∈ ℰ( G ). Let H be a subgraph of G . The uniform set of H with respect to G , denoted by E H ( G ), is the set of all elements of ℰ( G ) that induces a subgraph isomorphic to H . The subspace of ℰ( G ) generated by ℰ H ( G ) shall be denoted by ℰ H ( G ). If E H ( G ) is a generating set, that is ℰ H ( G )= ℰ( G ), then H is called a generator subgraph of G . This study determines the dimension of subspace generated by the set of all subsets of E ( G ) with even cardinality and the subspace generated by the set of all k -subsets of E ( G ), for some positive integer k , 1 ≤ k ≤ m . Moreover, this paper determines all the generator subgraphs of star graphs. Furthermore, it gives a characterization for a graph G so that star is a generator subgraph of G .

Taking the fear out of vector addition by concentrating on the superimposed axes

Introductory physics students often express fears regarding graphical vector addition. To ameliorate student trepidation of possibly making a mistake when moving the second vector to its new position at the head of the first vector before being added, as is most often advised by physics teachers, an alternative method is detailed here. This subtly different method instead concentrates student effort on using ‘sensing personification’ to identify a ‘center of the universe’ position that shifts for each vector by considering the initial axes choice when drawing the first vector, then superimposing a new axes for the second vector onto the same graph at the head of the first vector before drawing in the second vector. The vector is then drawn to-scale onto the new axes. This process then allows students to render the vector correctly without worry of inadvertent error of vector rotation and/or accidental elongation or truncation of the vector. A simple example is given to demonstrate this alternative method and how it also better aligns with analytical vector addition which uses vector equations. Use of sensing personification in vector addition can also set the stage for its use in other physics problems the student will encounter later, such as remembered experiences on amusement park rides.

The ideal view on Rackoff's coverability technique

Well-structured transition systems form a large class of infinite-state systems, for which safety verification is decidable thanks to a generic backward coverability algorithm. However, for several classes of systems, the generic upper bounds one can extract from the algorithm are far from optimal. In particular, in the case of vector addition systems (VAS) and several of their extensions, the known tight upper bounds were rather derived thanks to ad-hoc arguments based on Rackoff's small witness property.We show how to derive the same bounds directly on the computations of the VAS instantiation of the generic backward coverability algorithm. This relies on a dual view of the algorithm using ideal decompositions of downwards-closed sets, which exhibits a key structural invariant in the VAS case. This reasoning offers a uniform setting for all well-structured transition systems, including branching ones, and we further apply it to several VAS extensions, deriving optimal upper bounds.

Methanol production by polymer-encapsulated methanotrophs from simulated biogas in the presence of methane vector

Type I (Methylomicrobium album) and II (Methyloferula stellata) methanotrophs were encapsulated by alginate and polyvinyl alcohol (PVA) to improve methanol production from simulated biogas [methane (CH4) and carbon dioxide (CO2)] in the presence of CH4 vector. Polymeric matrix alginate (2%) and PVA (10%) were found to be optimum for the immobilization of both the methanotrophs, with a relative efficiency of methanol production up to 80.6 and 88.7%, respectively. The stability of methanol production by immobilized cells was improved up to 13.2-fold under repeated batch-culture over free cells. The addition of CH4 vectors showed 1.7-fold higher methanol production on using simulated biogas than in the control. The maximum methanol production of 7.46 and 7.14 mmol/L was noted for PVA-encapsulated M. album and M. stellata, respectively. This study successfully established the beneficial effects of CH4 vectors on methanol production by methanotrophs from greenhouse gases that can be applied for real biogas feedstock.

Superposition of vectors and electric fields: a study using structured inquiry tutorial lessons with upper secondary level students

Tutorials in introductory physics (TIP) are a well known resource for use in third level insititutions for developing students’ understanding of physics concepts. However, this resource is only sparingly used at second level. This study presents an adaptation of the approach taken in TIP to enhance the understanding of vector addition of a group of upper secondary students. The results present qualitative evidence of the development of the students’ understanding of vector addition. Issues surrounding the application of their understanding to an electrostatics context are also examined. Our results indicate that the approach taken in TIP can improve student learning at second level, and contribute to the small body of literature on this topic.

Quantum versus classical angular momentum

Angular momentum in classical mechanics is given by a vector. The plane perpendicular to this vector, in accordance to central field theory, determines the space in which particle motion takes place. No such simple picture exists in quantum mechanics. The states of a particle in a central field are proportional to spherical harmonics which do not define any plane of motion. In the first part of this paper we discuss the angular distribution of particle position and compare it to the classical probabilistic approach. In the second part, the matter of addition of angular momenta is discussed. In classical mechanics this means addition of vectors, while in quantum mechanics Clebsch–Gordan coefficients have to be used. We have found classical approximations to quantum coefficients and the limit of their applicability. This analysis gives a basis for the so-called ‘vector addition model’ used in some elementary textbooks on atomic physics. It can help to better understand the addition of angular momenta in quantum mechanics.

Novel efficient lattice-based IBE schemes with CPK for fog computing.

The data security of fog computing is a key problem for the Internet of things. Identity-based encryption (IBE) from lattices is extremely suitable for fog computing. It is able to not only simplify certificate management, but also resist quantum attacks. In this paper, firstly, we construct a novel efficient lattice-based IBE scheme with Combined Public Key (CPK) technique by keeping from consumptive trapdoor generation algorithm and preimage sampling algorithm, which is required by the existing lattice-based IBE schemes based on learning with errors (LWE). In addition, its key storage cost is lower and it is IND-ID-CPA secure in the random oracle model. Furthermore, based on this, an enhanced lattice-based IBE scheme with IND-ID-CCA security is developed by employing strong one-time signature. Our schemes only need O(n3/log n) additions of vectors, while the existing schemes need at least O(n3) of additions and multiplications in Setup and Extract phase.

Predefined-Time Polynomial-Function-Based Synchronization of Chaotic Systems via a Novel Sliding Mode Control

In the context of chaotic secure communication, this paper is concerned with the predefined-time polynomial-function-based synchronization of chaotic systems via sliding mode control. Firstly, a novel hybrid synchronization scheme among multiple chaotic systems based on polynomial function is defined. Subsequently, based on a new predefined-time stability criterion, a novel multi-power integral terminal sliding mode control algorithm is designed to realize the predefined-time polynomial-function-based synchronization. Finally, the secure communication simulation is presented to verify the feasibility and efficiency of the proposed synchronization scheme. The polynomial-function-based synchronization not only uses the addition and subtraction of vectors, but also uses the power multiplication of vectors, which makes the nonlinear structure of the composed drive system more complex, so that the communication scheme is more secure. Applying the sliding mode control algorithm designed in this work, the synchronization time can be preset off-line without estimation, moreover, the ratio between the formation time and the convergence time of sliding mode can also be distributed in advance, which is more flexible.

Predictive models for identification of parameters of seismic vibrations by applying the theory of covariance functions

The paper analyses an opportunity to develop predictive models for identification of parameters of seismic vibrations by applying statistical processing of measurement data. The calculations used measurement data arrays according to vectors E, N and Z obtained from four seismic stations (India EVBH, Indonesia LUWIBH, Italy CERABN and Turkey BNHBH). The Doppler method and the theory of covariance functions were applied for analysing the measurement data arrays. The trend of seismic vibration intensity vectors was estimated by applying the least-squares method. In addition, the said procedure partially eliminates random errors of the measurement data from the stations. Using the intensity variation of seismic vibration vectors E, N and Z on the timescale, the estimates of autocovariance and cross-covariance functions of seismic vibration vectors were calculated by changing the quantised interval on the time scale. The average values of parameter z in the Doppler formula were calculated according to the created formula by applying the expressions of cross-covariance functions of the algebraic addition of the relevant vectors and a single vector. By applying the values of parameter z from the Doppler formula, the approximate value of the velocity of reciprocal movement of seismic vectors was calculated. In the calculations, the software developed on the basis of the MATLAB program package operators was applied.

Incorporating Semantic Word Representations into Query Expansion for Microblog Information Retrieval

Microblog information retrieval has attracted much attention of researchers to capture the desired information in daily communications on social networks. Since the contents of microblogs are always non-standardized and flexible, including many popular Internet expressions, the retrieval accuracy of microblogs has much room for improvement. To enhance microblog information retrieval, we propose a novel query expansion method to enrich user queries with semantic word representations. In our method, we use a neural network model to map each word in the corpus to a low-dimensional vector representation. The mapped word vectors satisfy the algebraic vector addition operation, and the new vector obtained by the addition operation can express some common attributes of the two words. In this sense, we represent keywords in user queries as vectors, sum all the keyword vectors, and use the obtained query vectors to select the expansion words. In addition, we also combine the traditional pseudo-relevance feedback query expansion method with the proposed query expansion method. Experimental results show that the proposed method is effective and reduces noises in the expanded query, which improves the accuracy of microblog retrieval.

Examination of Thai freshmen’s understanding on vectors using a model analysis technique

This study focused on an investigation of Thai students’ comprehension of vectors using the model analysis technique, which is based on the matrix representation of quantum physics. This technique displays students’ knowledge states and the probability of applying each mental model to solve a given vector concept. A well-known vector concept test in physics education research named the Test of Understanding of Vectors (TUV) was translated into Thai language and validated by a group of physics lecturers. It was administered to 651 first-year engineering students at Prince of Songkla University via the online system at the beginning of the first semester. The three common mental states of vectors were identified as correct, popular incorrect, and other models. Model estimation of the model analysis revealed that although 54% of the students correctly answered vector addition, they still had difficulty with vector subtraction. Theoretically, both topics are considered as identical concepts. The students had inconsistent ideas on vector subtraction as reported by eigenvalues < 0.65. Moreover, they demonstrated equal distribution in using the three mental models to solve the dot product of vectors. The most common incorrect idea was that a dot product resultant was a vector quantity. The initial knowledge states of the cross product were in an incorrect model region involving confusion between calculating magnitudes of the cross product and the dot product, and incorrectly applying the right-hand rule to locate a direction of the cross product. Overall, the findings will guide instructors which common vector ideas should be revised and how. The vector concept plays an important role in physics learning since it is embedded in several physics topics as a learning mechanism.

In-Memory Low-Cost Bit-Serial Addition Using Commodity DRAM Technology

In-memory computing architectures present a promising solution to address the memory- and the power-wall challenges by mitigating the bottleneck between processing units and storage. Such architectures incorporate computing functionalities inside memory arrays to make better use of the large internal memory bandwidth, thereby, avoiding frequent data movements. In-DRAM computing architectures offer high throughput and energy improvements in accelerating modern data-intensive applications like machine learning etc . In this manuscript, we propose a vector addition methodology inside DRAM arrays through functional read enabled on local word-lines. The proposed primitive performs majority-based addition operations by storing data in transposed manner. Majority functions are achieved in DRAM cells by activating odd number of rows simultaneously. The proposed majority based bit-serial addition enables huge parallelism and high throughput. We validate the robustness of the proposed in-DRAM computing methodology under process variations to ascertain its reliability. Energy evaluation of the proposed scheme shows 21.7X improvement compared to normal data read operations in standard DDR3-1333 interface. Moreover, compared to state-of-the-art in-DRAM compute proposals, the proposed scheme provides one of the fastest addition mechanisms with low area overhead ( ${k}$ -Nearest Neighbor ( ${k}$ NN) algorithm on the MNIST handwritten digit classification dataset shows 11.5X performance improvement compared to a conventional von-Neumann machine.

Normed Interval Space and Its Topological Structure

Based on the natural vector addition and scalar multiplication, the set of all bounded and closed intervals in R cannot form a vector space. This is mainly because the zero element does not exist. In this paper, we endow a norm to the interval space in which the axioms are almost the same as the axioms of conventional norm by involving the concept of null set. Under this consideration, we shall propose two different concepts of open balls. Based on the open balls, we shall also propose the different types of open sets, which can generate many different topologies.

Co-Finiteness and Co-Emptiness of Reachability Sets in Vector Addition Systems with States

The coverability and boundedness problems are well-known exponential-space complete problems for vector addition systems with states (or Petri nets). The boundedness problem asks if the reachability set (for a given initial configuration) is finite. Here we consider a dual problem, the co-finiteness problem that asks if the complement of the reachability set is finite; by restricting the question we get the co-emptiness (or universality) problem that asks if all configurations are reachable.