Cliques and duplication-divergence network growth

A population of complete subgraphs or cliques in a network evolving via duplication-divergence is considered. We find that a number of cliques of each size scales linearly with the size of the network. We also derive a clique population distribution that is in perfect agreement with both the simulation results and the clique statistic of the protein-protein binding network of the fruit fly. In addition, we show that such features as fat-tail degree distribution, various rates of average degree growth and non-averaging, revealed recently for only the particular case of a completely asymmetric divergence, are present in a general case of arbitrary divergence.Comment: 7 pages, 6 figure

Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter $q$. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter $q$. Interestingly, we show that by adjusting $q$, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from `large' to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.Comment: 7 pages, 3 figures, definitive version accepted for publication in EPJ

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

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

Mobility and stochastic resonance in spatially inhomogeneous system

The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same periodicity but have a phase difference, the mobility shows many interesting features as a function of the applied force, the temperature, etc. The mobility shows stochastic resonance even for constant applied force, an issue of much recent interest. The mobility also exhibits a resonance like phenomenon as a function of the field strength and noise induced slowing down of the particle in an appropriate parameter regime.Comment: 14 pages, 12 figures. Submitted to Phys. Rev.

Receptor Heteromerization Expands the Repertoire of Cannabinoid Signaling in Rodent Neurons

A fundamental question in G protein coupled receptor biology is how a single ligand acting at a specific receptor is able to induce a range of signaling that results in a variety of physiological responses. We focused on Type 1 cannabinoid receptor (CB1R) as a model GPCR involved in a variety of processes spanning from analgesia and euphoria to neuronal development, survival and differentiation. We examined receptor dimerization as a possible mechanism underlying expanded signaling responses by a single ligand and focused on interactions between CB1R and delta opioid receptor (DOR). Using co-immunoprecipitation assays as well as analysis of changes in receptor subcellular localization upon co-expression, we show that CB1R and DOR form receptor heteromers. We find that heteromerization affects receptor signaling since the potency of the CB1R ligand to stimulate G-protein activity is increased in the absence of DOR, suggesting that the decrease in CB1R activity in the presence of DOR could, at least in part, be due to heteromerization. We also find that the decrease in activity is associated with enhanced PLC-dependent recruitment of arrestin3 to the CB1R-DOR complex, suggesting that interaction with DOR enhances arrestin-mediated CB1R desensitization. Additionally, presence of DOR facilitates signaling via a new CB1R-mediated anti-apoptotic pathway leading to enhanced neuronal survival. Taken together, these results support a role for CB1R-DOR heteromerization in diversification of endocannabinoid signaling and highlight the importance of heteromer-directed signal trafficking in enhancing the repertoire of GPCR signaling

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

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