International Journal of Mathematical Sciences and Computing

Cover page and Table of Contents. Vol. 3 No. 2, 2017, IJMSC

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Cover page and Table of Contents. Vol. 8 No. 1, 2022, IJMSC

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Optimal bounding function for GNR-enumeration

Gholam Reza Moghissi, Ali Payandeh

Статья научная

The proposed pruning technique by Gama-Nguyen-Regev for enumeration function makes this pruned enumeration (GNR-enumeration) as a claimant practical solver for SVP. The total cost of GNR-enumeration over a specific input lattice block with pre-defined enumeration radius and success probability would be minimized, just if this enumeration uses an optimal bounding function for pruning. Unfortunately, the running time of the original proposed algorithm of searching optimal bounding function by the work of Chen-Nguyen (in 2011) is not analyzed at all, so our work in this paper tries to introduce some efficient searching algorithms with exact analysis of their time/space complexity. In fact, this paper proposes a global search algorithm to generate the optimal bounding function by a greedy idea. Then, by using our greedy strategy and defining the searching steps based on success probability, a practical search algorithm is introduced, while it’s time-complexity can be determined accurately. Main superiorities of our algorithm include: complexity analysis, using high-performance version of each sub-function in designing search algorithm, jumping from local optimums, simple heuristics to guide the search, trade-off between quality of output and running time by tuning parameters. Also by using the building blocks in our practical search algorithm, a high-quality and fast algorithm is designed to approximate the optimal bounding function.

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Application of Differential Geometry on a Chemical Dynamical Model via Flow Curvature Method

A.K.M. Nazimuddin, Md. Showkat Ali

Статья научная

Slow invariant manifolds can contribute major rules in many slow-fast dynamical systems. This slow manifold can be obtained by eliminating the fast mode from the slow-fast system and allows us to reduce the dimension of the system where the asymptotic dynamics of the system occurs on that slow manifold and a low dimensional slow invariant manifold can reduce the computational cost. This article considers a trimolecular chemical dynamical Brusselator model of the mixture of two components that represents a chemical reaction-diffusion system. We convert this system of two-dimensional partial differential equations into four-dimensional ordinary differential equations by considering the new wave variable and obtain a new system of chemical Brusselator flow model. We observe that the onset of the chemical instability does not depend on the flow rate. We particularly study the slow manifold of the four-dimensional Brusselator flow model at zero flow speed. We apply the flow curvature method to the dynamical Brusselator flow model and acquire the analytical equation of the flow curvature manifold. Then we prove the invariance of this slow manifold equation with respect to the flow by using the Darboux invariance theorem. Finally, we find the osculating plane equation by using the flow curvature manifold.

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A Multi-channel Character Relationship Classification Model Based on Attention Mechanism

Yuhao Zhao, Hang Li, Shoulin Yin

Статья научная

Relation classification is an important semantic processing task in the field of natural language processing. The deep learning technology, which combines Convolutional Neural Network and Recurrent Neural Network with attention mechanism, has always been the mainstream and state-of-art method. The LSTM model based on recurrent neural network dynamically controls the weight by gating, which can better extract the context state information in time series and effectively solve the long-standing problem of recurrent neural network. The pre-trained model BERT has also achieved excellent results in many natural language processing tasks. This paper proposes a multi-channel character relationship classification model of BERT and LSTM based on attention mechanism. Through the attention mechanism, the semantic information of the two models is fused to get the final classification result. Using this model to process the text, we can extract and classify the relationship between the characters, and finally get the relationship between the characters included in this paper. Experimental results show that the proposed method performs better than the previous deep learning model on the SemEval-2010 task 8 dataset and the COAE-2016-Task3 dataset.

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Emoji Prediction Using Emerging Machine Learning Classifiers for Text-based Communication

Sayan Saha, Kakelli Anil Kumar

Статья научная

We aim to extract emotional components within statements to identify the emotional state of the writer and assigning emoji related to the emotion. Emojis have become a staple part of everyday text-based communication. It is normal and common to construct an entire response with the sole use of emoji. It comes as no surprise, therefore, that effort is being put into the automatic prediction and selection of emoji appropriate for a text message. Major companies like Apple and Google have made immense strides in this, and have already deployed such systems into production (for example, the Google Gboard). The proposed work is focused on the problem of automatic emoji selection for a given text message using machine learning classification algorithms to categorize the tone of a message which is further segregated through n-gram into one of seven distinct categories. Based on the output of the classifier, select one of the more appropriate emoji from a predefined list using natural language processing (NLP) and sentimental analysis techniques. The corpus is extracted from Twitter. The result is a boring text message made lively after being annotated with appropriate text messages

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