Proper Representations Research Articles

Estimates for representation numbers of binary quadratic forms and Apollonian circle packings

Fix a primitive, positive definite binary quadratic form g with integer coefficients. We prove asymptotic formulas for sums of the form ∑rg(n)β and ∑rg⁎(n)β, where β≥0 and rg(n), resp. rg⁎(n), denote the number of inequivalent representations, resp. proper inequivalent representations, of n by g. These estimates generalize a previous result by Blomer and Granville (2006) by allowing for non-fundamental discriminants and also clarify some details in the proof of the positive density conjecture for integral Apollonian circle packings by Bourgain and Fuchs (2011).

QMwebJS—An Open Source Software Tool to Visualize and Share Time-Evolving Three-Dimensional Wavefunctions

Numerical simulation experiments are of great importance for research and education in Physics. They can be greatly aided by proper graphical representations, especially for spatio-temporal dynamics. In this contribution, we describe and provide a novel Javascript-based library and cloud microservice—QMwebJS—for the visualization of the temporal evolution of three-dimensional distributions. It is an easy to use, web-based library for creating, editing, and exporting 3D models based on the particle sampling method. Accessible from any standard browser, it does not require downloads or installations. Users can directly share their work with other students, teachers or researchers by keeping their models in the cloud and allowing for interactive viewing of the spatio-temporal solutions. This software tool was developed to support quantum mechanics teaching at an undergraduate level by plotting the spatial probability density distribution given by the wavefunction, but it can be useful in different contexts including the study of nonlinear waves.

Improving Sentence Representations via Component Focusing

The efficiency of natural language processing (NLP) tasks, such as text classification and information retrieval, can be significantly improved with proper sentence representations. Neural networks such as convolutional neural network (CNN) and recurrent neural network (RNN) are gradually applied to learn the representations of sentences and are suitable for processing sequences. Recently, bidirectional encoder representations from transformers (BERT) has attracted much attention because it achieves state-of-the-art performance on various NLP tasks. However, these standard models do not adequately address a general linguistic fact, that is, different sentence components serve diverse roles in the meaning of a sentence. In general, the subject, predicate, and object serve the most crucial roles as they represent the primary meaning of a sentence. Additionally, words in a sentence are also related to each other by syntactic relations. To emphasize on these issues, we propose a sentence representation model, a modification of the pre-trained bidirectional encoder representations from transformers (BERT) network via component focusing (CF-BERT). The sentence representation consists of a basic part which refers to the complete sentence, and a component-enhanced part, which focuses on subject, predicate, object, and their relations. For the best performance, a weight factor is introduced to adjust the ratio of both parts. We evaluate CF-BERT on two different tasks: semantic textual similarity and entailment classification. Results show that CF-BERT yields a significant performance gain compared to other sentence representation methods.

Time-Frequency Representations: Spectrogram, Cochleogram and Correlogram

In recent years, the advancement in computer vision with deep learning based convolutional neural network (CNN) has raised many research interest. Multi-resolution time-frequency (T-F) representation of acoustic signal (speech/music or sound) as an input to CNN is one of them. A convolutional layer of CNN processes an image of speech or sound (spectrogram or any other T-F representation). Besides conventional spectrogram, many more multi-resolution T-F representations exist, in which, cochleogram and correlogram are the prime representative. The main issue which has emerged from this wide scope of research is that, the making selection of choice of the proper representations for better processing with increased accuracy. As, the T-F representation includes various rich features of the speech or sound content, and to make a selection for representations, which one is more useful than another, and which one is perceptually or psycho-physically relevant to auditory, is a very challenging task. This task pays more attraction with recent research attention towards the writing of this article. The aim of this article is to give a chronological, systematic and critical review of the existing literature on the spectrogram, cochleogram and correlogram consequences of speech/sound analysis of acoustic/auditory models and discuss the significances of our findings for their interrelation.

Decision support for offshore asset construction using expert judgments for supply disruptions risk

Offshore asset construction is a complex and costly process that is subject to various uncertainties within the entire supply chain. Hence, both the construction management optimization and the reduction of deployment expenditures should be supported by automated decision support models which include proper representations of predominant uncertainties. One of these is the supply disruption risk that is often ignored in existing models. Therefore, this article proposes a methodology to properly take this construction risk into account. An algorithm to model this risk was developed and a study was conducted to obtain the required probability distributions of disruption delays using real data and expert judgments for an offshore wind farm construction application. The simulation of a realistic test case with an appropriately modified stochastic simulation tool showed that it is important to consider this risk in order to make optimal decisions for different offshore wind farm construction strategies. © 2019 Elsevier B.V.

Structural and Functional Abnormalities in the Olfactory System of Fragile X Syndrome Models.

Fragile X Syndrome (FXS) is the most common inherited form of intellectual disability. It is produced by mutation of the Fmr1 gene that encodes for the Fragile Mental Retardation Protein (FMRP), an important RNA-binding protein that regulates the expression of multiple proteins located in neuronal synapses. Individuals with FXS exhibit abnormal sensory information processing frequently leading to hypersensitivity across sensory modalities and consequently a wide array of behavioral symptoms. Insects and mammals engage primarily their sense of smell to create proper representations of the external world and guide adequate decision-making processes. This feature in combination with the exquisitely organized neuronal circuits found throughout the olfactory system (OS) and the wide expression of FMRP in brain regions that process olfactory information makes it an ideal model to study sensory alterations in FXS models. In the last decade several groups have taken advantage of these features and have used the OS of fruit fly and rodents to understand neuronal alteration giving rise to sensory perception issues. In this review article, we will discuss molecular, morphological and physiological aspects of the olfactory information processing in FXS models. We will highlight the decreased inhibitory/excitatory synaptic balance and the diminished synaptic plasticity found in this system resulting in behavioral alteration of individuals in the presence of odorant stimuli.

Regular Cartan groupoids and longitudinal representations

With the intent of laying the groundwork for a program that aims at explicitly describing the space of Cartan (i.e. multiplicative) connections on a general proper Lie groupoid, we begin to investigate the space of such connections in the regular case. We point out that there is a close relationship between Cartan connections on a proper regular groupoid and representations of the groupoid on its own longitudinal bundle (i.e. on the vector distribution tangent to its orbits). This observation enables us to reduce the original problem to a simpler one. We carry out a prospective study of the latter problem, and apply the resulting analysis to produce a number of examples in rank two which serve to illustrate the diversity of the possible obstructions to the existence of multiplicative connections.

Deciphering the Microstructure and Energy-Level Splitting of Tm3+-Doped Yttrium Aluminum Garnet.

Thulium-doped yttrium aluminum garnet (Tm:YAG) is an important solid-state laser crystal. The energy-level splitting within it is still an unresolved problem. Here, we perform a theoretical study on the microstructure of Tm3+-doped YAG using the CALYPSO structure search method in conjunction with first-principles calculations. The calculated results show that the 4.16% doping concentration of Tm3+ impurity causes an obvious structural distortion of YAG crystal, forming an orthorhombic phase in C222 symmetry. On the basis of our developed WEPMD method, we obtain a new and complete set of free-ion and crystal field parameters by a good fit (with proper irreducible representations) to 69 observed energy levels and determine the exact energy-level splitting of Tm3+ in YAG. The calculated Stark levels and electric dipole transitions are in excellent agreement with the measured data and similar theoretical calculations. Some promising emission lines between 3F3, 3F2, 1D2, and 1I6 states are presented. These findings offer fundamental insights and practical tools for further exploration of the structural and electronic properties of other transition-metal-doped YAG crystal.

Feature Representation and Data Augmentation for Human Activity Classification Based on Wearable IMU Sensor Data Using a Deep LSTM Neural Network.

Wearable inertial measurement unit (IMU) sensors are powerful enablers for acquisition of motion data. Specifically, in human activity recognition (HAR), IMU sensor data collected from human motion are categorically combined to formulate datasets that can be used for learning human activities. However, successful learning of human activities from motion data involves the design and use of proper feature representations of IMU sensor data and suitable classifiers. Furthermore, the scarcity of labelled data is an impeding factor in the process of understanding the performance capabilities of data-driven learning models. To tackle these challenges, two primary contributions are in this article: first; by using raw IMU sensor data, a spectrogram-based feature extraction approach is proposed. Second, an ensemble of data augmentations in feature space is proposed to take care of the data scarcity problem. Performance tests were conducted on a deep long term short term memory (LSTM) neural network architecture to explore the influence of feature representations and the augmentations on activity recognition accuracy. The proposed feature extraction approach combined with the data augmentation ensemble produces state-of-the-art accuracy results in HAR. A performance evaluation of each augmentation approach is performed to show the influence on classification accuracy. Finally, in addition to using our own dataset, the proposed data augmentation technique is evaluated against the University of California, Irvine (UCI) public online HAR dataset and yields state-of-the-art accuracy results at various learning rates.

Optimization of Microblog Representation Using Deep Learning Approach

Microblogging, as a new form of online communication in which users talk about their daily lives, to gather real-time news, opinion about people or share information by short posts, has become one of the most popular social networking services today, e.g. to stay in touch with friends . Finding proper representations of microblog texts is a challenging issue. The overview of microblog included how to extract information from microblog, also discuss about Microblogging and Twitter. This paper included existing research on Optimization of Microblog Representation by using existing techniques and methods as well as microblogging services.Current approaches, for microblog reduction are single indexing. In this work, we have proposed double indexing method for microblog reduction. We have used our own generated dataset for microblog reduction. We have collected tweets from real time twitter for both single and double indexing technique. Also, we have use LDA with Semantic Similarity algorithm. We compared our results with single indexing. Experimental results shows that double indexing gives better performance than single indexing. This may happen because we will show both original and reduced tweets, so it will be known to user which tweet are removed and relevant part shows as output. We have also compared our results with the state-of-art. The proposed double indexing gives better performance than existing 1-ROCA of improved online SVM technique.

Dependency-based Siamese long short-term memory network for learning sentence representations.

Textual representations play an important role in the field of natural language processing (NLP). The efficiency of NLP tasks, such as text comprehension and information extraction, can be significantly improved with proper textual representations. As neural networks are gradually applied to learn the representation of words and phrases, fairly efficient models of learning short text representations have been developed, such as the continuous bag of words (CBOW) and skip-gram models, and they have been extensively employed in a variety of NLP tasks. Because of the complex structure generated by the longer text lengths, such as sentences, algorithms appropriate for learning short textual representations are not applicable for learning long textual representations. One method of learning long textual representations is the Long Short-Term Memory (LSTM) network, which is suitable for processing sequences. However, the standard LSTM does not adequately address the primary sentence structure (subject, predicate and object), which is an important factor for producing appropriate sentence representations. To resolve this issue, this paper proposes the dependency-based LSTM model (D-LSTM). The D-LSTM divides a sentence representation into two parts: a basic component and a supporting component. The D-LSTM uses a pre-trained dependency parser to obtain the primary sentence information and generate supporting components, and it also uses a standard LSTM model to generate the basic sentence components. A weight factor that can adjust the ratio of the basic and supporting components in a sentence is introduced to generate the sentence representation. Compared with the representation learned by the standard LSTM, the sentence representation learned by the D-LSTM contains a greater amount of useful information. The experimental results show that the D-LSTM is superior to the standard LSTM for sentences involving compositional knowledge (SICK) data.

Variational principle and time-space finite element method for dynamic thermoelasticity based on mixed convolved action

Abstract A new variational formulation is proposed for time-domain analysis of initial/boundary value problems of dynamic thermoelasticity. By using the concept of mixed convolved action, the difficulties with dissipative phenomena and proper representations of the temporal end point conditions can be overcome to create a true stationary variational principle. After an elementary illustrative development for a lumped parameter thermoelastic model, the convolved action functional for linear thermoelastic continuum is written directly in terms of mixed variables, which include displacements and the impulses of stress, temperature and heat flux. Unlike previous variational approaches, based for example upon a generalization of Hamilton's principle , the present mixed convolved action formulation allows direct application of finite element methodology in both space and time. Here, simple linear shape functions are employed for the temporal representations. Meanwhile, standard three-noded triangular elements are used in the present two-dimensional numerical implementation. Several computational examples are considered to test this original approach and to investigate interesting aspects of coupled dynamic thermoelastic response.

Joint Learning of Distance Metric and Query Model for Posteriorgram-Based Keyword Search

In this paper, we propose a novel approach to keyword search (KWS) in low-resource languages, which provides an alternative method for retrieving the terms of interest, especially for the out of vocabulary (OOV) ones. Our system incorporates the techniques of query-by-example retrieval tasks into KWS and conducts the search by means of the subsequence dynamic time warping (sDTW) algorithm. For this, text queries are modeled as sequences of feature vectors and used as templates in the search. A Siamese neural network-based model is trained to learn a frame-level distance metric to be used in sDTW and the proper query model frame representations for this learned distance. Experiments conducted on Intelligence Advanced Research Projects Activity Babel Program's Turkish, Pashto, and Zulu datasets demonstrate the effectiveness of our approach. In each of the languages, the proposed system outperforms the large vocabulary continuous speech recognition (LVCSR) based baseline for OOV terms. Furthermore, the fusion of the proposed system with the baseline system provides an average relative actual term weighted value (ATWV) improvement of 13.9% on all terms and, more significantly, the fusion yields an average relative ATWV improvement of 154.5% on OOV terms. We show that this new method can be used as an alternative to conventional LVCSR-based KWS systems, or in combination with them, to achieve the goal of closing the gap between OOV and in-vocabulary retrieval performances.

Survey on deep learning methods in human action recognition

A study on one of the most important issues in a human action recognition task, i.e. how to create proper data representations with a high‐level abstraction from large dimensional noisy video data, is carried out. Most of the recent successful studies in this area are mainly focused on deep learning. Deep learning methods have gained superiority to other approaches in the field of image recognition. In this survey, the authors first investigate the role of deep learning in both image and video processing and recognition. Owing to the variety and plenty of deep learning methods, the authors discuss them in a comparative form. For this purpose, the authors present an analytical framework to classify and to evaluate these methods based on some important functional measures. Furthermore, a categorisation of the state‐of‐the‐art approaches in deep learning for human action recognition is presented. The authors summarise the significantly related works in each approach and discuss their performance.

SPATIOTEMPORAL VISUALIZATION OF TSUNAMI WAVES USING KML ON GOOGLE EARTH

Abstract. Disaster risk is a function of hazard and vulnerability. Risk is defined as the expected losses, including lives, personal injuries, property damages, and economic disruptions, due to a particular hazard for a given area and time period. Risk assessment is one of the key elements of a natural disaster management strategy as it allows for better disaster mitigation and preparation. It provides input for informed decision making, and increases risk awareness among decision makers and other stakeholders. Virtual globes such as Google Earth can be used as a visualization tool. Proper spatiotemporal graphical representations of the concerned risk significantly reduces the amount of effort to visualize the impact of the risk and improves the efficiency of the decision-making process to mitigate the impact of the risk. The spatiotemporal visualization of tsunami waves for disaster management process is an attractive topic in geosciences to assist investigation of areas at tsunami risk. In this paper, a method for coupling virtual globes with tsunami wave arrival time models is presented. In this process we have shown 2D+Time of tsunami waves for propagation and inundation of tsunami waves, both coastal line deformation, and the flooded areas. In addition, the worst case scenario of tsunami on Chabahar port derived from tsunami modelling is also presented using KML on google earth.

Poincaré section analysis of the electroencephalogram in autism spectrum disorder using complement plots

PurposeThis paper aims to explain, first of all, signal modeling steps using Poincaré, and then considering the occurred events, concept of information applying Poincaré section and information approach, the brain pattern variations in autism spectrum disorder (ASD) cases will be diagnosed. A kind of representation of electroencephalogram (EEG) signal, namely, complementary plot, in which the main characteristic is special attention to asymmetry and symmetry coexist in natural and human processes, is introduced. In this paper, a new model is provided whose variations of patterns are similar to EEG’s when the transformation parameter is changed. A significant difference between ASD and healthy cases was also observed, which could be used to distinguish between various types of systems.Design/methodology/approachComplementary plot method is one of the most proper representations for Poincaré section of complex dynamics, because, as it was said about its characteristics, it has a qualitative approach toward signal (Sabelli, 2000, 2001, 2003, 2008, 2005, Sabelli et al., 2011). Considering the special conditions of this representation, here, intersection with a circle y2 + x2 = r2 will be used; the important fact is, on the contrary to previous representations in which circular section had energy concept, here circular section considers phases. For finding trajectory intersection points, after calculating the sin and cosine of each term of EEG, plotting them in XY plane and drawing a chord between successive points of presentation transitions, then its intersections with the assumed circle are determined. But considering the sampling frequency, chords and Poincaré section, in this space, a minimum error – as the threshold – should be assumed in the program.FindingsNatural and human processes are biotic (life-like) and creative (Sabelli and Galilei), and studying coexisting opposites by calculating the sine and cosine of each term in heartbeat intervals, weather variables and integer biotic series or random walk reveals an astonishingly regular mandala pattern; these patterns are not generated by random, periodic or chaotic series (Sabelli, 2005). This paper shows that in EEG of ASD children, mandala-like patterns of concentric rings are emergent in all situations (baseline – watching animation with voice and without voice) and electrode site (C3 and C4), but not in healthy individuals. The authors take the relation between sine and cosine functions as a mathematical model for complementary opposition, because it involves reciprocity and orthogonality sine and cosine are natural models for information. In fact, trigonometric analyses of empirical data to be described in this paper suggest expanding the concept of co-creative opposition to include uncorrelated opposites and partial opposites, i.e. partial agonists and partial antagonists that are neither linear nor orthogonal. Using Poincaré sections, it is shown that the difference in information and creativity of the data is the distinctive characteristic in ASD and healthy cases. Creation is the generation of novelty, diversity and complexity in complex systems.Originality/valueThis paper is an original paper based on cybernetic approaches for studying the variations of ASD children.

Material modeling of 6016-O and 6016-T4 aluminum alloy sheets and application to hole expansion forming simulation

This study investigates the influence of heat treatment on the anisotropic plastic deformation behaviors of 6016-O and 6016-T4 aluminum alloy sheets. The two material samples were fabricated from the same lot and, therefore, have the same grain size and crystallographic texture. Biaxial tensile tests using both cruciform and tubular specimens are performed for many proportional stress paths in the first quadrant of stress space. The test results reveal that the degree of differential hardening (DH) is much larger in 6016-T4 than in 6016-O. It is shown that the work contour shape of 6016-O is controlled by crystallographic texture, whereas that of 6016-T4 presumably depends on GP-zones as well. From the biaxial stress test data, an appropriate yield function for each material is determined and employed in the finite element analysis of the hole expansion forming process. It was found that the Yld2000-2d yield function provides proper material representations of the plastic behavior of both material samples in the sense that it correctly predicts the fracture or localized neck locations, which occurs in the hole edge vicinity. For 6016-O, the thickness strain profile predicted with the Yld2000-2d yield function, which accounts for the DH of the material, is in better agreement with the experimental results than that obtained with the isotropic hardening model. For 6016-T4, the Yld2000-2d yield function with an exponent of 8 with the isotropic hardening assumption leads to a fair prediction of the experimental data. In order to enhance the accuracy of forming simulations for 6016-T4, it is necessary to develop a material model that is capable of reproducing the significant DH resulting from the GP-zones.

Microblog Dimensionality Reduction—A Deep Learning Approach

Exploring potentially useful information from huge amount of textual data produced by microblogging services has attracted much attention in recent years. An important preprocessing step of microblog text mining is to convert natural language texts into proper numerical representations. Due to the short-length characteristics of microblog texts, using term frequency vectors to represent microblog texts will cause “sparse data” problem. Finding proper representations of microblog texts is a challenging issue. In this paper, we apply deep networks to map the high-dimensional representations of microblog texts to low-dimensional representations. To improve the result of dimensionality reduction, we take advantage of the semantic similarity derived from two types of microblogspecific information, namely the retweet relationship and hashtags. Two types of approaches, including modifying training data and modifying the training objective of deep networks, are proposed to make use of microblog-specific information. Experiment results show that the deep models perform better than traditional dimensionality reduction methods such as latent semantic analysis and latent Dirichlet allocation topic model, and the use of microblog-specific information can help to learn better representations.

Proper representations of (multivariate) linear differential systems

A proper representation of a linear differential system is a representation with no singularity at infinity. It is shown that such a representation always exists. It turns out that for proper representations having minimal number of rows is equivalent to having minimal total row degree. One is led therefore to a natural definition of the notion of minimality. What is remarkable is that a minimal proper representation is uniquely determined up to premultiplication by a unimodular polynomial matrix of special form. This uniqueness result allows, in particular, to introduce important integer invariants.

Extending Partial Representations of Proper and Unit Interval Graphs

The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire graph. In this paper, we give a linear-time algorithm for extending proper interval representations and an almost quadratic-time algorithm for extending unit interval representations. We also introduce the more general problem of bounded representations of unit interval graphs, where the input constrains the positions of some intervals by lower and upper bounds. We show that this problem is NP-complete for disconnected input graphs and give a polynomial-time algorithm for the special class of instances, where the ordering of the connected components of the input graph along the real line is prescribed. This includes the case of partial representation extension. The hardness result sharply contrasts the recent polynomial-time algorithm for bounded representations of proper interval graphs (Balko et al. in 2013). So unless $${\textsf {P}} = {\textsf {NP}}$$P=NP, proper and unit interval representations have vastly different structure. This explains why partial representation extension problems for these different types of representations require substantially different techniques.