Statistics of Cycles: How Loopy is your Network?

We study the distribution of cycles of length h in large networks (of size N>>1) and find it to be an excellent ergodic estimator, even in the extreme inhomogeneous case of scale-free networks. The distribution is sharply peaked around a characteristic cycle length, h* ~ N^a. Our results suggest that h* and the exponent a might usefully characterize broad families of networks. In addition to an exact counting of cycles in hierarchical nets, we present a Monte-Carlo sampling algorithm for approximately locating h* and reliably determining a. Our empirical results indicate that for small random scale-free nets of degree exponent g, a=1/(g-1), and a grows as the nets become larger.Comment: Further work presented and conclusions revised, following referee report

Languages cool as they expand: Allometric scaling and the decreasing need for new words

We analyze the occurrence frequencies of over 15 million words recorded in millions of books published during the past two centuries in seven different languages. For all languages and chronological subsets of the data we confirm that two scaling regimes characterize the word frequency distributions, with only the more common words obeying the classic Zipf law. Using corpora of unprecedented size, we test the allometric scaling relation between the corpus size and the vocabulary size of growing languages to demonstrate a decreasing marginal need for new words, a feature that is likely related to the underlying correlations between words. We calculate the annual growth fluctuations of word use which has a decreasing trend as the corpus size increases, indicating a slowdown in linguistic evolution following language expansion. This ‘‘cooling pattern’’ forms the basis of a third statistical regularity, which unlike the Zipf and the Heaps law, is dynamical in nature

Invariants of Lie algebras extended over commutative algebras without unit

We establish results about the second cohomology with coefficients in the trivial module, symmetric invariant bilinear forms and derivations of a Lie algebra extended over a commutative associative algebra without unit. These results provide a simple unified approach to a number of questions treated earlier in completely separated ways: periodization of semisimple Lie algebras (Anna Larsson), derivation algebras, with prescribed semisimple part, of nilpotent Lie algebras (Benoist), and presentations of affine Kac-Moody algebras.Comment: v3: added a footnote on p.10 about a wrong derivation of the correct statemen

Unified Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Five Dimensions

Unified N=2 Maxwell-Einstein supergravity theories (MESGTs) are supergravity theories in which all the vector fields, including the graviphoton, transform in an irreducible representation of a simple global symmetry group of the Lagrangian. As was established long time ago, in five dimensions there exist only four unified Maxwell-Einstein supergravity theories whose target manifolds are symmetric spaces. These theories are defined by the four simple Euclidean Jordan algebras of degree three. In this paper, we show that, in addition to these four unified MESGTs with symmetric target spaces, there exist three infinite families of unified MESGTs as well as another exceptional one. These novel unified MESGTs are defined by non-compact (Minkowskian) Jordan algebras, and their target spaces are in general neither symmetric nor homogeneous. The members of one of these three infinite families can be gauged in such a way as to obtain an infinite family of unified N=2 Yang-Mills-Einstein supergravity theories, in which all vector fields transform in the adjoint representation of a simple gauge group of the type SU(N,1). The corresponding gaugings in the other two infinite families lead to Yang-Mills-Einstein supergravity theories coupled to tensor multiplets.Comment: Latex 2e, 28 pages. v2: reference added, footnote 14 enlarge

Two Novel Mutations in the EYS Gene Are Possible Major Causes of Autosomal Recessive Retinitis Pigmentosa in the Japanese Population

Retinitis pigmentosa (RP) is a highly heterogeneous genetic disease including autosomal recessive (ar), autosomal dominant (ad), and X-linked inheritance. Recently, arRP has been associated with mutations in EYS (Eyes shut homolog), which is a major causative gene for this disease. This study was conducted to determine the spectrum and frequency of EYS mutations in 100 Japanese arRP patients. To determine the prevalence of EYS mutations, all EYS exons were screened for mutations by polymerase chain reaction amplification, and sequence analysis was performed. We detected 67 sequence alterations in EYS, of which 21 were novel. Of these, 7 were very likely pathogenic mutations, 6 were possible pathogenic mutations, and 54 were predicted non-pathogenic sequence alterations. The minimum observed prevalence of distinct EYS mutations in our study was 18% (18/100, comprising 9 patients with 2 very likely pathogenic mutations and the remaining 9 with only one such mutation). Among these mutations, 2 novel truncating mutations, c.4957_4958insA (p.S1653KfsX2) and c.8868C>A (p.Y2956X), were identified in 16 patients and accounted for 57.1% (20/35 alleles) of the mutated alleles. Although these 2 truncating mutations were not detected in Japanese patients with adRP or Leber's congenital amaurosis, we detected them in Korean arRP patients. Similar to Japanese arRP results, the c.4957_4958insA mutation was more frequently detected than the c.8868C>A mutation. The 18% estimated prevalence of very likely pathogenic mutations in our study suggests a major involvement of EYS in the pathogenesis of arRP in the Japanese population. Mutation spectrum of EYS in 100 Japanese patients, including 13 distinct very likely and possible pathogenic mutations, was largely different from the previously reported spectrum in patients from non-Asian populations. Screening for c.4957_4958insA and c.8868C>A mutations in the EYS gene may therefore be very effective for the genetic testing and counseling of RP patients in Japan

In vivo

Rectal balloons are used in external beam prostate radiotherapy to provide reproducible anatomy and rectal dose reductions. This is an investigation into the combination of a MOSFET radiation detector with a rectal balloon for realtime in vivo rectal wall dosimetry. The MOSFET used in the study is a radiation detector that provides a water equivalent depth of measurement of 70 μm. Two MOSFETs were combined in a face-to-face orientation. The reproducibility, sensitivity and angular dependence were measured for the dual MOSFET in a 6 MV photon beam. The dual MOSFET was combined with a rectal balloon and irradiated with hypothetical prostate treatments in a phantom. The anterior rectal wall dose was measured in real time and compared with the planning system calculated dose. The dual MOSFET showed angular dependence within ±2.5% in the azimuth and +2.5%/−4% in the polar axes. When compared with an ion chamber measurement in a phantom, the dual MOSFET agreed within 2.5% for a range of radiation path lengths and incident angles. The dual MOSFET had reproducible sensitivity for fraction sizes of 2–10 Gy. For the hypothetical prostate treatments the measured anterior rectal wall dose was 2.6 and 3.2% lower than the calculated dose for 3DCRT and IMRT plans. This was expected due to limitations of the dose calculation method used at the balloon cavity interface. A dual MOSFET combined with a commercial rectal balloon was shown to provide reproducible measurements of the anterior rectal wall dose in real time. The measured anterior rectal wall dose agreed with the expected dose from the treatment plan for 3DCRT and IMRT plans. The dual MOSFET could be read out in real time during the irradiation, providing the capability for real-time dose monitoring of the rectal wall dose during treatment

Impact of Single Links in Competitive Percolation -- How complex networks grow under competition

How a complex network is connected crucially impacts its dynamics and function. Percolation, the transition to extensive connectedness upon gradual addition of links, was long believed to be continuous but recent numerical evidence on "explosive percolation" suggests that it might as well be discontinuous if links compete for addition. Here we analyze the microscopic mechanisms underlying discontinuous percolation processes and reveal a strong impact of single link additions. We show that in generic competitive percolation processes, including those displaying explosive percolation, single links do not induce a discontinuous gap in the largest cluster size in the thermodynamic limit. Nevertheless, our results highlight that for large finite systems single links may still induce observable gaps because gap sizes scale weakly algebraically with system size. Several essentially macroscopic clusters coexist immediately before the transition, thus announcing discontinuous percolation. These results explain how single links may drastically change macroscopic connectivity in networks where links add competitively.Comment: non-final version, for final see Nature Physics homepag

Palaeoclimatic conditions in the Mediterranean explain genetic diversity of Posidonia oceanica seagrass meadows

Past environmental conditions in the Mediterranean Sea have been proposed as main drivers of the current patterns of distribution of genetic structure of the seagrass Posidonia oceanica, the foundation species of one of the most important ecosystems in the Mediterranean Sea. Yet, the location of cold climate refugia (persistence regions) for this species during the Last Glacial Maximum (LGM) is not clear, precluding the understanding of its biogeographical history. We used Ecological Niche Modelling together with existing phylogeographic data to locate Pleistocene refugia in the Mediterranean Sea and to develop a hypothetical past biogeographical distribution able to explain the genetic diversity presently found in P. oceanica meadows. To do that, we used an ensemble approach of six predictive algorithms and two Ocean General Circulation Models. The minimum SST in winter and the maximum SST in summer allowed us to hindcast the species range during the LGM. We found separate glacial refugia in each Mediterranean basin and in the Central region. Altogether, the results suggest that the Central region of the Mediterranean Sea was the most relevant cold climate refugium, supporting the hypothesis that long-term persistence there allowed the region to develop and retain its presently high proportion of the global genetic diversity of P. oceanica.Fundacao para a Ciencia e a Tecnologia (FCT, Portugal) [SFRH/BPD/85040/2012]; FCT [UID/Multi/04326/2013, FCT-BIODIVERSA/004/2015]; Pew foundation (USA)info:eu-repo/semantics/publishedVersio

High Tumour Cannabinoid CB1 Receptor Immunoreactivity Negatively Impacts Disease-Specific Survival in Stage II Microsatellite Stable Colorectal Cancer

BACKGROUND: There is good evidence in the literature that the cannabinoid system is disturbed in colorectal cancer. In the present study, we have investigated whether CB(1) receptor immunoreactive intensity (CB(1)IR intensity) is associated with disease severity and outcome. METHODOLOGY/PRINCIPAL FINDINGS: CB(1)IR was assessed in formalin-fixed, paraffin-embedded specimens collected with a consecutive intent during primary tumour surgical resection from a series of cases diagnosed with colorectal cancer. Tumour centre (n = 483) and invasive front (n = 486) CB(1)IR was scored from 0 (absent) to 3 (intense staining) and the data was analysed as a median split i.e. CB(1)IR <2 and ≥2. In microsatellite stable, but not microsatellite instable tumours (as adjudged on the basis of immunohistochemical determination of four mismatch repair proteins), there was a significant positive association of the tumour grade with the CB(1)IR intensity. The difference between the microsatellite stable and instable tumours for this association of CB(1)IR was related to the CpG island methylation status of the cases. Cox proportional hazards regression analyses indicated a significant contribution of CB(1)IR to disease-specific survival in the microsatellite stable tumours when adjusting for tumour stage. For the cases with stage II microsatellite stable tumours, there was a significant effect of both tumour centre and front CB(1)IR upon disease specific survival. The 5 year probabilities of event-free survival were: 85±5 and 66±8%; tumour interior, 86±4% and 63±8% for the CB(1)IR<2 and CB(1)IR≥2 groups, respectively. CONCLUSIONS/SIGNIFICANCE: The level of CB(1) receptor expression in colorectal cancer is associated with the tumour grade in a manner dependent upon the degree of CpG hypermethylation. A high CB(1)IR is indicative of a poorer prognosis in stage II microsatellite stable tumour patients