arXiv subjects
Publications and source records attributed to Abdul Basit.
We show that there exists an absolute constant $c > 0$, such that, for any finite set $A$ of quaternions, \[ \max\{|A+A, |AA| \} \gtrsim |A|^{4/3 + c}. \] This generalizes a sum-product bound for real numbers proved by Konyagin and Shkredov.
A bipartite graph $H = \left(V_1, V_2; E \right)$ with $|V_1| + |V_2| = n$ is semilinear if $V_i \subseteq \mathbb{R}^{d_i}$ for some $d_i$ and the edge relation $E$ consists of the pairs of points $(x_1, x_2) \in V_1 \times V_2$ satisfying a fixed Boolean combination of $s$ linear equalities and inequalities in $d_1 + d_2$ variables for some $s$. We show that for a fixed $k$, the number of edges in a $K_{k,k}$-free semilinear $H$ is almost linear in $n$, namely $|E| = O_{s,k,\varepsilon}(n^{1+\varepsilon})$ for any $\varepsilon > 0$; and more generally, $|E| = O_{s,k,r,\varepsilon}(n^{r-1 + \varepsilon})$ for a $K_{k, \ldots,k}$-free semilinear $r$-partite $r$-uniform hypergraph. As an application, we obtain the following incidence bound: given $n_1$ points and $n_2$ open boxes with axis parallel sides in $\mathbb{R}^d$ such that their incidence graph is $K_{k,k}$-free, there can be at most $O_{k,\varepsilon}(n^{1+\varepsilon})$ incidences. The same bound holds if instead of boxes one takes polytopes cut out by the translates of an arbitrary fixed finite set of halfspaces. We also obtain matching upper and (superlinear) lower bounds in the case of dyadic boxes on the plane, and point out some connections to the model-theoretic trichotomy in $o$-minimal structures (showing that the failure of an almost linear bound for some definable graph allows one to recover the field operations from that graph in a definable manner).
Alavi, Malde, Schwenk and Erdős asked whether the independent set sequence of every tree is unimodal. Here we make some observations about this question. We show that for the uniformly random (labelled) tree, asymptotically almost surely (a.a.s.) the initial approximately 49.5\% of the sequence is increasing while the terminal approximately 38.8\% is decreasing. Our approach uses the Matrix Tree Theorem, combined with computation. We also present a generalization of a result of Levit and Mandrescu, concerning the final one-third of the independent set sequence of a König-Egerváry graph.
Visual identification of gunmen in a crowd is a challenging problem, that requires resolving the association of a person with an object (firearm). We present a novel approach to address this problem, by defining human-object interaction (and non-interaction) bounding boxes. In a given image, human and firearms are separately detected. Each detected human is paired with each detected firearm, allowing us to create a paired bounding box that contains both object and the human. A network is trained to classify these paired-bounding-boxes into human carrying the identified firearm or not. Extensive experiments were performed to evaluate effectiveness of the algorithm, including exploiting full pose of the human, hand key-points, and their association with the firearm. The knowledge of spatially localized features is key to success of our method by using multi-size proposals with adaptive average pooling. We have also extended a previously firearm detection dataset, by adding more images and tagging in extended dataset the human-firearm pairs (including bounding boxes for firearms and gunmen). The experimental results ($AP_{hold} = 78.5$) demonstrate effectiveness of the proposed method.
A churn prediction system guides telecom service providers to reduce revenue loss. However, the development of a churn prediction system for a telecom industry is a challenging task, mainly due to the large size of the data, high dimensional features, and imbalanced distribution of the data. In this paper, we present a solution to the inherent problems of churn prediction, using the concept of Transfer Learning (TL) and Ensemble-based Meta-Classification. The proposed method TL-DeepE is applied in two stages. The first stage employs TL by fine-tuning multiple pre-trained Deep Convolution Neural Networks (CNNs). Telecom datasets are normally in vector form, which is converted into 2D images because Deep CNNs have high learning capacity on images. In the second stage, predictions from these Deep CNNs are appended to the original feature vector and thus are used to build a final feature vector for the high-level Genetic Programming (GP) and AdaBoost based ensemble classifier. Thus, the experiments are conducted using various CNNs as base classifiers and the GP-AdaBoost as a meta-classifier. By using 10-fold cross-validation, the performance of the proposed TL-DeepE system is compared with existing techniques, for two standard telecommunication datasets; Orange and Cell2cell. Performing experiments on Orange and Cell2cell datasets, the prediction accuracy obtained was 75.4% and 68.2%, while the area under the curve was 0.83 and 0.74, respectively.
Designing a technique for the automatic analysis of different actions in videos in order to detect the presence of interested activities is of high significance nowadays. In this paper, we explore a robust and dynamic appearance technique for the purpose of identifying different action activities. We also exploit a low-rank and structured sparse matrix decomposition (LSMD) method to better model these activities.. Our method is effective in encoding localized spatio-temporal features which enables the analysis of local motion taking place in the video. Our proposed model use adjacent frame differences as the input to the method thereby forcing it to capture the changes occurring in the video. The performance of our model is tested on a benchmark dataset in terms of detection accuracy. Results achieved with our model showed the promising capability of our model in detecting action activities.
Because of lack of infrastructure and Central Authority(CA), secure communication is a challenging job in MANETs. A lightweight security solution is needed in MANET to balance its nodes resource tightness and mobility feature. The role of CA should be decentralized in MANET because the network is managed by the nodes themselves without any fixed infrastructure and centralized authority. In this paper, we created a distributed Public Key Infrastructure (PKI) using Shamir secret sharing mechanism which allows the nodes of the MANET to have a share of its private key. The traditional PKI protocols require centralized authority and heavy computing power to manage public and private keys, thus making them not suitable for MANETs. To establish a secure communication for the MANET nodes, we proposed a lightweight crypto protocol which requires limited resources, making it suitable for MANETs.
In this paper, we discuss an attempt to develop an automatic language identification system for 5 closely-related Indo-Aryan languages of India, Awadhi, Bhojpuri, Braj, Hindi and Magahi. We have compiled a comparable corpora of varying length for these languages from various resources. We discuss the method of creation of these corpora in detail. Using these corpora, a language identification system was developed, which currently gives state of the art accuracy of 96.48\%. We also used these corpora to study the similarity between the 5 languages at the lexical level, which is the first data-based study of the extent of closeness of these languages.
Authenticating a node in mobile ad-hoc networks is a challenging task due to their dynamic and resource constraint infrastructure. For this purpose, MANETS adopt two kinds of approaches Public key cryptography and identity-based cryptography. In Public Key Infrastructure (PKI), Certificate Authority (CA) is responsible for key management. In order to adapt it to MANET, the job of the CA must be distributed. The master secret key is shared among the nodes of the MANET, to self-organize the network without a central authority.The key is shared based on Shamir secret sharing scheme with bivariate polynomial to make the MANET fully self-managed by nodes.In this paper, we considered PKI based scenario and proposed a new scheme to authenticate a node using BLS signature which is light weight compared to the existing schemes thus making it suitable for MANET.