Model Checking of Statechart Models: Survey and Research Directions

We survey existing approaches to the formal verification of statecharts using model checking. Although the semantics and subset of statecharts used in each approach varies considerably, along with the model checkers and their specification languages, most approaches rely on translating the hierarchical structure into the flat representation of the input language of the model checker. This makes model checking difficult to scale to industrial models, as the state space grows exponentially with flattening. We look at current approaches to model checking hierarchical structures and find that their semantics is significantly different from statecharts. We propose to address the problem of state space explosion using a combination of techniques, which are proposed as directions for further research

Perturbation of closed range operators and Moore-Penrose inverse

Let $H_1,H_2$ be complex Hilbert spaces and $T:H_1\rightarrow H_2$ be a densely defined closed operator with domain $D(T)\subseteq H_1$ and $T^{\dagger}$ be the Moore-Penrose inverse of $T$. Let $S:H_1\rightarrow H_2$ be a bounded operator. In this article we focus our attention on the following questions: $1.$ Under what conditions closedness of range of $T$ will imply the closedness of range of $T+S$? $2.$ What is the relation between $T^{\dagger}$ and $(T+S)^{\dagger}$? $3.$ What is the relation between $T^{\dagger}$ and $S^{\dagger}$?

Operators that attain the reduced minimum

Let $H_1, H_2$ be complex Hilbert spaces and $T$ be a densely defined closed linear operator from its domain $D(T)$, a dense subspace of $H_1$, into $H_2$. Let $N(T)$ denote the null space of $T$ and $R(T)$ denote the range of $T$. Recall that $C(T) := D(T) \cap N(T)^{\perp}$ is called the {\it carrier space of} $T$ and the {\it reduced minimum modulus } $\gamma(T)$ of $T$ is defined as: $$\gamma(T) := \inf \{\|T(x)\| : x \in C(T), \|x\| = 1 \} .$$ Further, we say that $T$ {\it attains its reduced minimum modulus} if there exists $x_0 \in C(T)$ such that $\|x_0\| = 1$ and $\|T(x_0)\| = \gamma(T)$. We discuss some properties of operators that attain reduced minimum modulus. In particular, the following results are proved.Comment: submitted to a journal. arXiv admin note: text overlap with arXiv:1606.05736, arXiv:1609.06869. Deleted the last section from the earlier versio

On the Convergence of Quasilinear Viscous Approximations Using Compensated Compactness

Method of compensated compactness is used to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of {\it Bardos et.al}\cite{MR542510}) of the corresponding scalar conservation laws in a bounded domain in $\mathbb{R}^{d}$, where the viscous term is of the form $\varepsilon div\left(B(u^{\varepsilon})\nabla u^{\varepsilon}\right)$

Medical Image Compression using Wavelet Decomposition for Prediction Method

In this paper offers a simple and lossless compression method for compression of medical images. Method is based on wavelet decomposition of the medical images followed by the correlation analysis of coefficients. The correlation analyses are the basis of prediction equation for each sub band. Predictor variable selection is performed through coefficient graphic method to avoid multicollinearity problem and to achieve high prediction accuracy and compression rate. The method is applied on MRI and CT images. Results show that the proposed approach gives a high compression rate for MRI and CT images comparing with state of the art methods.Comment: IEEE format, International Journal of Computer Science and Information Security, IJCSIS January 2010, ISSN 1947 5500, http://sites.google.com/site/ijcsis

On the convergence of quasilinear viscous approximations with BV initial data

We show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of {\it Bardos-Leroux-Nedelec}) of the corresponding scalar conservation laws on a bounded domain in $\mathbb{R}^{d}$ whenever the initial data is essentially bounded and a function of bounded variation

Black Hole Paradoxes

We propose here that the well-known black hole paradoxes such as the information loss and teleological nature of the event horizon are restricted to a particular idealized case, which is the homogeneous dust collapse model. In this case, the event horizon, which defines the boundary of the black hole, forms initially, and the singularity in the interior of the black hole at a later time. We show that, in contrast, gravitational collapse from physically more realistic initial conditions typically leads to the scenario in which the event horizon and space-time singularity form simultaneously. We point out that this apparently simple modification can mitigate the causality and teleological paradoxes, and also lends support to two recently suggested solutions to the information paradox, namely, the `firewall' and `classical chaos' proposals.Comment: Revised version; minor corrections and title change

CRLB Calculations for Joint AoA, AoD and Multipath Gain Estimation in Millimeter Wave Wireless Networks

In this report we present an analysis of the non-random and the Bayesian Cramer-Rao lower bound (CRLB) for the joint estimation of angle-of-arrival (AoA), angle-of-departure (AoD), and the multipath amplitudes, for the millimeter-wave (mmWave) wireless networks. Our analysis is applicable to multipath channels with Gaussian noise and independent path parameters. Numerical results based on uniform AoA and AoD in $[0,\pi)$, and Rician fading path amplitudes, reveal that the Bayesian CRLB decreases monotonically with an increase in the Rice factor. Further, the CRLB obtained by using beamforming and combining code books generated by quantizing directly the domain of AoA and AoD was found to be lower than those obtained with other types of beamforming and combining code books

Energy distribution of solar flare events

Observational evidence of the braiding of magnetic field lines has been reported. The magnetic reconnection within the loop (nanoflares) and with other loops (microflares) disentangle the field. The coronal field then reorganizes itself to attain a force-free field configuration. We have evaluated the power law index of the energy distribution $f(E)=f_0 E^{-\alpha}$ by using a model of relaxation incorporating different profile functions of winding number distribution $f(w)$ based on braided topologies. We study the radio signatures that occur in the solar corona using the radio data obtained from the Gauribidanur Radio Observatory (IIA) and extract the power law index by using the Statistic-sensitive nonlinear iterative peak clipping (SNIP) algorithm. We see that the power law index obtained from the model is in good agreement with the calculated value from the radio data observation.Comment: 2 pages, 1 figure; to appear in proceedings of IAU Symposium 340: Long-term datasets for the understanding of solar and stellar magnetic cycle

An Intelligent Call Admission Control Decision Mechanism for Wireless Networks

The Call admission control (CAC) is one of the Radio Resource Management (RRM) techniques plays instrumental role in ensuring the desired Quality of Service (QoS) to the users working on different applications which have diversified nature of QoS requirements. This paper proposes a fuzzy neural approach for call admission control in a multi class traffic based Next Generation Wireless Networks (NGWN). The proposed Fuzzy Neural Call Admission Control (FNCAC) scheme is an integrated CAC module that combines the linguistic control capabilities of the fuzzy logic controller and the learning capabilities of the neural networks .The model is based on Recurrent Radial Basis Function Networks (RRBFN) which have better learning and adaptability that can be used to develop the intelligent system to handle the incoming traffic in the heterogeneous network environment. The proposed FNCAC can achieve reduced call blocking probability keeping the resource utilisation at an optimal level. In the proposed algorithm we have considered three classes of traffic having different QoS requirements. We have considered the heterogeneous network environment which can effectively handle this traffic. The traffic classes taken for the study are Conversational traffic, Interactive traffic and back ground traffic which are with varied QoS parameters. The paper also presents the analytical model for the CAC .The paper compares the call blocking probabilities for all the three types of traffic in both the models. The simulation results indicate that compared to Fuzzy logic based CAC, Conventional CAC, The simulation results are optimistic and indicates that the proposed FNCAC algorithm performs better where the call blocking probability is minimal when compared to other two methods.Comment: Journal of Computing online at https://sites.google.com/site/journalofcomputing