Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...

In supersymmetric models the lightest Higgs boson may decay with a sizable branching ratio into a pair of light neutralinos. We analyze such decays within the context of the minimal supersymmetric standard model with R-parity violation, where the neutralino itself is unstable and decays into Standard Model fermions. We show that the R-parity violating couplings induce novel Higgs decay signals ...

We propose a method for upper bounding the general adversary bound for certain boolean functions. Due to the the tightness of query complexity and the general adversary bound [5], this gives an upper bound on the quantum query complexity of those functions. We give an example where this upper bound is smaller than the query complexity of any known quantum algorithm.

In this paper we derive high probability lower and upper bounds on the excess risk of stochastic optimization of exponentially concave loss functions. Exponentially concave loss functions encompass several fundamental problems in machine learning such as squared loss in linear regression, logistic loss in classification, and negative logarithm loss in portfolio management. We demonstrate an O(d...

This paper proposes a new MIMO-OFDM precoding technique that aims to minimize a bit error rate (BER) upper bound of the maximum likelihood detection (MLD) in mobile radio communications. Using a steepest descent algorithm, the proposed method estimates linear precoding matrices that can minimize the upper bound of BER under power constraints. Since the upper bound is derived from all the pairwi...

The worst-case position error provides valuable information for efficiently designing location based services in wireless networks. In this study, a technique based on a geometric approach is investigated for deriving a reasonable upper bound on the position error in bearingonly target localization. Assuming bounded measurement errors, it is first observed that the target node location belongs ...

We study two random walks on a group of upper triangular matrices. In each case, we give upper bound on the mixing time by using a stopping time technique.