Continuous Functional Calculus for Quaternionic Bounded Normal Operators

In this article we give an approach to define continuous functional calculus for bounded quaternionic normal operators defined on a right quaternionic Hilbert space.Comment: Submitted to a journal. There was a gap in the previous version. We have corrected it and stated all the results for bounded cas

An Effective Private Data storage and Retrieval System using Secret sharing scheme based on Secure Multi-party Computation

Privacy of the outsourced data is one of the major challenge.Insecurity of the network environment and untrustworthiness of the service providers are obstacles of making the database as a service.Collection and storage of personally identifiable information is a major privacy concern.On-line public databases and resources pose a significant risk to user privacy, since a malicious database owner may monitor user queries and infer useful information about the customer.The challenge in data privacy is to share data with third-party and at the same time securing the valuable information from unauthorized access and use by third party.A Private Information Retrieval(PIR) scheme allows a user to query database while hiding the identity of the data retrieved.The naive solution for confidentiality is to encrypt data before outsourcing.Query execution,key management and statistical inference are major challenges in this case.The proposed system suggests a mechanism for secure storage and retrieval of private data using the secret sharing technique.The idea is to develop a mechanism to store private information with a highly available storage provider which could be accessed from anywhere using queries while hiding the actual data values from the storage provider.The private information retrieval system is implemented using Secure Multi-party Computation(SMC) technique which is based on secret sharing. Multi-party Computation enable parties to compute some joint function over their private inputs.The query results are obtained by performing a secure computation on the shares owned by the different servers.Comment: Data Science & Engineering (ICDSE), 2014 International Conference, CUSA

On the polar decomposition of right linear operators in quaternionic Hilbert spaces

In this article we prove the existence of the polar decomposition for densely defined closed right linear operators in quaternionic Hilbert spaces: If $T$ is a densely defined closed right linear operator in a quaternionic Hilbert space $H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. In fact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separable and $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$ if and only if either $N(T) = \{0\}$ or $R(T)^{\bot} = \{0\}$.Comment: 17 page

Identification of Association between Prescription Drugs and Side Effects by Analyzing Social Network Messages

In this world of internet and social media all people have started discussing about their health information and treatment procedures in the health forums and social media like twitter. Researches are now being focused towards identifying hazardous effects of the prescription drugs and the treatment process through mining this information posted over the internet. Specifically, Twitter can be considered as an important source of information for the detection of such as Adverse Drug Reaction (ADR). The mining or analysis of Twitter messages is not easy because they are of short length, unstructured and almost in informal form. The twitter messages related to drugs prescribed for cardio vascular and diabetes were considered and collected to form the initial dataset. Later they are preprocessed to remove redundancy and improve the further classification process. A set of feature like Semantic, Z-Score, lexicon related features were extracted from the collected tweets to from the training dataset. Next the feature selection is performed using the Pointwise Mutual Information (PMI) approach. Finally, the selected feature set is utilized to train the Support Vector Machine (SVM). The SVM is validated with a test dataset and its performance was found satisfactory when linear function is used as the kernel. This model can be utilized further to identify the association between prescribed drugs and adverse effects from the Tweets and other messages of health forums