Incorporating Betweenness Centrality in Compressive Sensing for Congestion Detection

This paper presents a new Compressive Sensing (CS) scheme for detecting network congested links. We focus on decreasing the required number of measurements to detect all congested links in the context of network tomography. We have expanded the LASSO objective function by adding a new term corresponding to the prior knowledge based on the relationship between the congested links and the corresponding link Betweenness Centrality (BC). The accuracy of the proposed model is verified by simulations on two real datasets. The results demonstrate that our model outperformed the state-of-the-art CS based method with significant improvements in terms of F-Score

On the H\'enon-Lane-Emden conjecture

We consider Liouville-type theorems for the following H\'{e}non-Lane-Emden system \hfill -\Delta u&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -\Delta v&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when $pq>1$, $p,q,a,b\ge0$. The main conjecture states that there is no non-trivial non-negative solution whenever $(p,q)$ is under the critical Sobolev hyperbola, i.e. $\frac{N+a}{p+1}+\frac{N+b}{q+1}>{N-2}$. We show that this is indeed the case in dimension N=3 provided the solution is also assumed to be bounded, extending a result established recently by Phan-Souplet in the scalar case. Assuming stability of the solutions, we could then prove Liouville-type theorems in higher dimensions. For the scalar cases, albeit of second order ($a=b$ and $p=q$) or of fourth order ($a\ge 0=b$ and $p>1=q$), we show that for all dimensions $N\ge 3$ in the first case (resp., $N\ge 5$ in the second case), there is no positive solution with a finite Morse index, whenever $p$ is below the corresponding critical exponent, i.e $1<p<\frac{N+2+2a}{N-2}$ (resp., $1<p<\frac{N+4+2a}{N-4}$). Finally, we show that non-negative stable solutions of the full H\'{e}non-Lane-Emden system are trivial provided \label{sysdim00} N<2+2(\frac{p(b+2)+a+2}{pq-1}) (\sqrt{\frac{pq(q+1)}{p+1}}+ \sqrt{\frac{pq(q+1)}{p+1}-\sqrt\frac{pq(q+1)}{p+1}}).Comment: Theorem 4 has been added in the new version. 23 pages, Comments are welcome. Updated version - if any - can be downloaded at http://www.birs.ca/~nassif/ or http://www.math.ubc.ca/~fazly/research.htm

Development of indole sulfonamides as cannabinoid receptor negative allosteric modulators

This Letter was supported by the Biotechnology and Biological Sciences Research Council (BBSRC) and the Scottish Universities Life Sciences Alliance (SULSA) in 2011Peer reviewedPostprin

Maximal codeword lengths in Huffman codes

The following question about Huffman coding, which is an important technique for compressing data from a discrete source, is considered. If p is the smallest source probability, how long, in terms of p, can the longest Huffman codeword be? It is shown that if p is in the range 0 less than p less than or equal to 1/2, and if K is the unique index such that 1/F(sub K+3) less than p less than or equal to 1/F(sub K+2), where F(sub K) denotes the Kth Fibonacci number, then the longest Huffman codeword for a source whose least probability is p is at most K, and no better bound is possible. Asymptotically, this implies the surprising fact that for small values of p, a Huffman code's longest codeword can be as much as 44 percent larger than that of the corresponding Shannon code