Traceroute sampling makes random graphs appear to have power law degree distributions

The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is scale-free; however, many of these measurements have relied on sampling traceroutes from a small number of sources. It was recently argued that sampling in this way can introduce a fundamental bias in the degree distribution, for instance, causing random (Erdos-Renyi) graphs to appear to have power law degree distributions. We explain this phenomenon analytically using differential equations to model the growth of a breadth-first tree in a random graph G(n,p=c/n) of average degree c, and show that sampling from a single source gives an apparent power law degree distribution P(k) ~ 1/k for k < c

Transition Property for α\alpha-Power Free Languages with α≥2\alpha\geq 2 and k≥3k\geq 3 Letters

In 1985, Restivo and Salemi presented a list of five problems concerning power free languages. Problem $4$ states: Given $\alpha$-power-free words $u$ and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$ states: Given $\alpha$-power-free words $u$ and $v$, find a transition word $w$, if it exists. Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denote the $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$ is a rational number or a rational "number with $+$". If $\alpha$ is a "number with $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" a number then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We show that: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and $v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a (transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show a construction of the word $w$

Modulation of microglial activation by adenosine A2a receptor in animal models of perinatal brain injury

Neuroinflammation has a key role in the pathogenesis of perinatal brain injury. Caffeine, a nonspecific antagonist of adenosine receptors (ARs), is widely used to treat apnea of prematurity and has been linked to a decrease in the incidence of cerebral palsy in premature infants. The mechanisms explaining its neuroprotective effect have not yet been elucidated. The objective of this study was to characterize the expression of adenosine and ARs in two neonatal rat models of neuroinflammation and to determine the effect of A2aR blockade on microglial activation assessed through inflammatory cytokine gene expression. We have used two rat models of microglial activation: the gestational low protein diet (LPD) model, associated with chronic brain injury, and postnatal ibotenate intracerebral injections, responsible for acute excitotoxicity injury. Adenosine blood levels have been measured by Tandem Mass Spectrometry. The expression of ARs in vivo was assessed using qPCR and immunohistochemistry. In vivo models have been replicated in vitro on primary microglial cell cultures exposed to A2aR agonist CGS-21680 or antagonist SCH-58261. The effects of these treatments have been assessed on the M1/M2 cytokine expressions measured by RT-qPCR. LPD during pregnancy was associated with higher adenosine levels in pups at postnatal day 1 and 4. A2aR mRNA expression was significantly increased in both cortex and magnetically sorted microglial cells from LPD animals compared to controls. CD73 expression, responsible for extracellular production of brain adenosine, was significantly increased in LPD cortex and sorted microglia cells. Moreover, CD73 protein level was increased in ibotenate treated animals. In vitro experiments confirmed that LPD or control microglial cells exposed to ibotenate display an increased expression, at both protein and molecular levels, of A2aR and M1 markers (IL-1\u3b2, IL-6, iNOS, TNF\u3b1). This pro-inflammatory profile was significantly reduced by SCH-58261, which reduces M1 markers in both LPD and ibotenate-exposed cells, with no effect on control cells. In the same experimental conditions, a partial increased of M1 cytokines was observed in response to A2aR agonist CGS-21680. These results support the involvement of adenosine and particularly of its receptor A2aR in the regulation of microglia in two different animal models of neuroinflammation

A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Bias reduction in traceroute sampling: towards a more accurate map of the Internet

Traceroute sampling is an important technique in exploring the internet router graph and the autonomous system graph. Although it is one of the primary techniques used in calculating statistics about the internet, it can introduce bias that corrupts these estimates. This paper reports on a theoretical and experimental investigation of a new technique to reduce the bias of traceroute sampling when estimating the degree distribution. We develop a new estimator for the degree of a node in a traceroute-sampled graph; validate the estimator theoretically in Erdos-Renyi graphs and, through computer experiments, for a wider range of graphs; and apply it to produce a new picture of the degree distribution of the autonomous system graph.Comment: 12 pages, 3 figure

Periodic points in random substitution subshifts

We study various aspects of periodic points for random substitution subshifts. In order to do so, we introduce a new property for random substitutions called the disjoint images condition. We provide a procedure for determining the property for compatible random substitutions—random substitutions for which a well-defined abelianisation exists. We find some simple necessary criteria for primitive, compatible random substitutions to admit periodic points in their subshifts. In the case that the random substitution further has disjoint images and is of constant length, we provide a stronger criterion. A method is outlined for enumerating periodic points of any specified length in a random substitution subshift

Melatonin Promotes Oligodendroglial Maturation of Injured White Matter in Neonatal Rats

OBJECTIVE:To investigate the effects of melatonin treatment in a rat model of white matter damage (WMD) in the developing brain. Additionally, we aim to delineate the cellular mechanisms of melatonin effect on the oligodendroglial cell lineage. METHODS:A unilateral ligation of the uterine artery in pregnant rat at the embryonic day 17 induces fetal hypoxia and subsequent growth restriction (GR) in neonatal pups. GR and control pups received a daily intra-peritoneal injection of melatonin from birth to post-natal day (P) 3. RESULTS:Melatonin administration was associated with a dramatic decrease in microglial activation and astroglial reaction compared to untreated GR pups. At P14, melatonin prevented white matter myelination defects with an increased number of mature oligodendrocytes (APC-immunoreactive) in treated GR pups. Conversely, melatonin was not found to be associated with an increased density of total oligodendrocytes (Olig2-immunoreactive), suggesting that melatonin is able to promote oligodendrocyte maturation but not proliferation. These effects appear to be melatonin-receptor dependent and were reproduced in vitro. INTERPRETATION:These data suggest that melatonin has a strong protective effect on developing damaged white matter through decreased microglial activation and oligodendroglial maturation leading to a normalization of the myelination process. Consequently, melatonin should be a considered as an effective neuroprotective candidate not only in perinatal brain damage but also in inflammatory and demyelinating diseases observed in adults

Neuroprotective Effect of Inhaled Nitric Oxide on Excitotoxic-Induced Brain Damage in Neonatal Rat

BACKGROUND: Inhaled nitric oxide (iNO) is one of the most promising therapies used in neonates. However, little information is known about its impact on the developing brain submitted to excitotoxic challenge. METHODOLOGY/PRINCIPAL FINDINGS: We investigated here the effect of iNO in a neonatal model of excitotoxic brain lesions. Rat pups and their dams were placed in a chamber containing 20 ppm NO during the first week of life. At postnatal day (P)5, rat pups were submitted to intracranial injection of glutamate agonists. At P10, rat pups exposed to iNO exhibited a significant decrease of lesion size in both the white matter and cortical plate compared to controls. Microglia activation and astrogliosis were found significantly decreased in NO-exposed animals. This neuroprotective effect was associated with a significant decrease of several glutamate receptor subunits expression at P5. iNO was associated with an early (P1) downregulation of pCREB/pAkt expression and induced an increase in pAkt protein concentration in response to excitotoxic challenge (P7). CONCLUSION: This study is the first describe and investigate the neuroprotective effect of iNO in neonatal excitotoxic-induced brain damage. This effect may be mediated through CREB pathway and subsequent modulation of glutamate receptor subunits expression