An Efficient Analytical Solution to Thwart DDoS Attacks in Public Domain

In this paper, an analytical model for DDoS attacks detection is proposed, in which propagation of abrupt traffic changes inside public domain is monitored to detect a wide range of DDoS attacks. Although, various statistical measures can be used to construct profile of the traffic normally seen in the network to identify anomalies whenever traffic goes out of profile, we have selected volume and flow measure. Consideration of varying tolerance factors make proposed detection system scalable to the varying network conditions and attack loads in real time. NS-2 network simulator on Linux platform is used as simulation testbed. Simulation results show that our proposed solution gives a drastic improvement in terms of detection rate and false positive rate. However, the mammoth volume generated by DDoS attacks pose the biggest challenge in terms of memory and computational overheads as far as monitoring and analysis of traffic at single point connecting victim is concerned. To address this problem, a distributed cooperative technique is proposed that distributes memory and computational overheads to all edge routers for detecting a wide range of DDoS attacks at early stage.Comment: arXiv admin note: substantial text overlap with arXiv:1203.240

Persistence in q-state Potts model: A Mean-Field approach

We study the Persistence properties of the T=0 coarsening dynamics of one dimensional $q$-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating spins with different Potts states is ignored, but the correct time dependence of the mean density $P(t)$ of persistent spins is imposed. For this model, it is known that $P(t)$ follows a power-law decay with time, $P(t)\sim t^{-\theta(q)}$ where $\theta(q)$ is the $q$-dependent persistence exponent. We study the spatial structure of the persistent region within the MMFA. We show that the persistent site pair correlation function $P_{2}(r,t)$ has the scaling form $P_{2}(r,t)=P(t)^{2}f(r/t^{{1/2}})$ for all values of the persistence exponent $\theta(q)$. The scaling function has the limiting behaviour $f(x)\sim x^{-2\theta}$ ($x\ll 1$) and $f(x)\to 1$ ($x\gg 1$). We then show within the Independent Interval Approximation (IIA) that the distribution $n(k,t)$ of separation $k$ between two consecutive persistent spins at time $t$ has the asymptotic scaling form $n(k,t)=t^{-2\phi}g(t,\frac{k}{t^{\phi}})$ where the dynamical exponent has the form $\phi$=max(${1/2},\theta$). The behaviour of the scaling function for large and small values of the arguments is found analytically. We find that for small separations $k\ll t^{\phi}, n(k,t)\sim P(t)k^{-\tau}$ where $\tau$=max($2(1-\theta),2\theta$), while for large separations $k\gg t^{\phi}$, $g(t,x)$ decays exponentially with $x$. The unusual dynamical scaling form and the behaviour of the scaling function is supported by numerical simulations.Comment: 11 pages in RevTeX, 10 figures, submitted to Phys. Rev.

Cosmology and thermodynamics of FRW universe with bulk viscous stiff fluid

We consider a cosmological model dominated by stiff fluid with a constant bulk viscosity. We classify all the possible cases of the universe predicted by the model and analyzing the scale factor, density as well as the curvature scalar. We find that when the dimensionless constant bulk viscous parameter is in the range $0 < \bar\zeta <6$ the model began with a Big Bang, and make a transition form the decelerating expansion epoch to an accelerating epoch, then tends to the de Sitter phase as $t\to \infty$. The transition into the accelerating epoch would be in the recent past, when $4<\bar\zeta<6.$ For $\bar\zeta>6$ the model doesn't have a Big Bang and suffered an increase in the fluid density and scalar curvature as the universe expands, which are eventually saturates as the scale factor $a \to \infty$ in the future. We have analyzed the model with statefinder diagnostics and find that the model is different from $\Lambda$CDM model but approaches $\Lambda$CDM point as $a \to \infty.$ We have also analyzed the status of the generalized second law of thermodynamics with apparent horizon as the boundary of the universe and found that the law is generally satisfied when $0 \leq \bar\zeta <6$ and for $\bar\zeta >6$ the law is satisfied when the scale factor is larger than a minimum value

Automorphisms of abelian group extensions

Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.Comment: 11 page