Non-singular circulant graphs and digraphs

We give necessary and sufficient conditions for a few classes of known circulant graphs and/or digraphs to be singular. The above graph classes are generalized to $(r,s,t)$-digraphs for non-negative integers $r,s$ and $t$, and the digraph $C_n^{i,j,k,l}$, with certain restrictions. We also obtain a necessary and sufficient condition for the digraphs $C_n^{i,j,k,l}$ to be singular. Some necessary conditions are given under which the $(r,s,t)$-digraphs are singular.Comment: 12 page

Representation of Cyclotomic Fields and Their Subfields

Let \K be a finite extension of a characteristic zero field \F. We say that the pair of $n\times n$ matrices $(A,B)$ over \F represents \K if \K \cong \F[A]/ where \F[A] denotes the smallest subalgebra of M_n(\F) containing $A$ and $$ is an ideal in \F[A] generated by $B$. In particular, $A$ is said to represent the field \K if there exists an irreducible polynomial q(x)\in \F[x] which divides the minimal polynomial of $A$ and \K \cong \F[A]/. In this paper, we identify the smallest circulant-matrix representation for any subfield of a cyclotomic field. Furthermore, if $p$ is any prime and \K is a subfield of the $p$-th cyclotomic field, then we obtain a zero-one circulant matrix $A$ of size $p\times p$ such that (A,\J) represents \K, where \J is the matrix with all entries 1. In case, the integer $n$ has at most two distinct prime factors, we find the smallest 0-1 companion-matrix that represents the $n$-th cyclotomic field. We also find bounds on the size of such companion matrices when $n$ has more than two prime factors.Comment: 17 page

Bulk viscosity of spin-one color superconducting strange quark matter

The bulk viscosity in spin-one color-superconducting strange quark matter is calculated by taking into account the interplay between the nonleptonic and semi-leptonic week processes. In agreement with previous studies, it is found that the inclusion of the semi-leptonic processes may result in non-negligible corrections to the bulk viscosity in a narrow window of temperatures. The effect is generally more pronounced for pulsars with longer periods. Compared to the normal phase, however, this effect due to the semi-leptonic processes is less pronounced in spin-one color superconductors. Assuming that the critical temperature of the phase transition is much larger than 40 keV, the main effect of spin-one color superconductivity in a wide range of temperatures is an overall increase of the bulk viscosity with respect to the normal phase. The corresponding enhancement factor reaches up to about 9 in the polar and A-phases, about 25 in the planar phase and about 29 in the CSL phase. This factor is determined by the suppression of the nonleptonic rate in color-superconducting matter and, therefore, may be even larger if all quark quasiparticles happen to be gapped.Comment: 10 pages, 4 multi-panel figures, including one new in the final versio

Flooding attacks to internet threat monitors (ITM): Modeling and counter measures using botnet and honeypots

The Internet Threat Monitoring (ITM),is a globally scoped Internet monitoring system whose goal is to measure, detect, characterize, and track threats such as distribute denial of service(DDoS) attacks and worms. To block the monitoring system in the internet the attackers are targeted the ITM system. In this paper we address flooding attack against ITM system in which the attacker attempt to exhaust the network and ITM's resources, such as network bandwidth, computing power, or operating system data structures by sending the malicious traffic. We propose an information-theoretic frame work that models the flooding attacks using Botnet on ITM. Based on this model we generalize the flooding attacks and propose an effective attack detection using Honeypots

X-ray properties of UV-selected star forming galaxies at z~1 in the Hubble Deep Field North

We present an analysis of the X-ray emission from a large sample of ultraviolet (UV) selected, star forming galaxies with 0.74<z<1.32 in the Hubble Deep Field North (HDF-N) region. By excluding all sources with significant detected X-ray emission in the 2 Ms Chandra observation we are able to examine the properties of galaxies for which the emission in both UV and X-ray is expected to be predominantly due to star formation. Stacking the X-ray flux from 216 galaxies in the soft and hard bands produces significant detections. The derived mean 2-10 keV rest-frame luminosity is 2.97+/-0.26x10^(40) erg/s, corresponding to an X-ray derived star formation rate (SFR) of 6.0+/-0.6 Msolar/yr. Comparing the X-ray value with the mean UV derived SFR, uncorrected for attenuation, we find that the average UV attenuation correction factor is \~3. By binning the galaxy sample according to UV magnitude and colour, correlations between UV and X-ray emission are also examined. We find a strong positive correlation between X-ray emission and rest-frame UV emission. A correlation between the ratio of X-ray-to-UV emission and UV colour is also seen, such that L(X)/L(UV) increases for redder galaxies. Given that X-ray emission offers a view of star formation regions that is relatively unaffected by extinction, results such as these can be used to evaluate the effects of dust on the UV emission from high-z galaxies. For instance we derive a relationship for estimating UV attenuation corrections as a function of colour excess. The observed relation is inconsistent with the Calzetti et al. (2000) reddening law which over predicts the range in UV attenuation corrections by a factor of ~100 for the UV selected z~1 galaxies in this sample (abridged).Comment: 10 pages, 7 figures, accepted for publication in MNRA