One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula

In \cite{Mul} one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane $\mathbb{E}^2$ were obtained. Moreover, the relations between the Complex velocities one-parameter motion in the Complex plane were provided by \cite{Mul}. One-parameter planar homothetic motion was defined in the Complex plane, \cite{Kur}. In this paper, analogous to homothetic motion in the Complex plane given by \cite{Kur}, one-parameter planar homothetic motion is defined in the Hyperbolic plane. Some characteristic properties about the velocity vectors, the acceleration vectors and the pole curves are given. Moreover, in the case of homothetic scale $h$ identically equal to 1, the results given in \cite{Yuc} are obtained as a special case. In addition, three hyperbolic planes, of which two are moving and the other one is fixed, are taken into consideration and a canonical relative system for one-parameter planar hyperbolic homothetic motion is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, is obtained with the help of this relative system

Landscape statistics of the low autocorrelated binary string problem

The statistical properties of the energy landscape of the low autocorrelated binary string problem (LABSP) are studied numerically and compared with those of several classic disordered models. Using two global measures of landscape structure which have been introduced in the Simulated Annealing literature, namely, depth and difficulty, we find that the landscape of LABSP, except perhaps for a very large degeneracy of the local minima energies, is qualitatively similar to some well-known landscapes such as that of the mean-field 2-spin glass model. Furthermore, we consider a mean-field approximation to the pure model proposed by Bouchaud and Mezard (1994, J. Physique I France 4 1109) and show both analytically and numerically that it describes extremely well the statistical properties of LABSP

Inter-individual differences in foraging tactics of a colonial raptor : consistency, weather effects, and fitness correlates

Background: Consistent inter-individual differences in behavioural phenotypes may entail differences in energy efficiency and expenditure, with different fitness payoffs. In colonial-breeding species, inter-individual differences in foraging behaviour may evolve to reduce resource use overlap among conspecifics exploiting shared foraging areas. Furthermore, individual differences in foraging behaviour may covary with individual characteristics, such as sex or physiological conditions. Methods: We investigated individual differences in foraging tactics of a colonial raptor, the lesser kestrel (Falco naumanni). We tracked foraging trips of breeding individuals using miniaturized biologgers. We classified behaviours from GPS data and identified tactics at the foraging trip level by cluster analysis. We then estimated energy expenditure associated to each tactic from tri-axial accelerometer data. Results: We obtained 489 foraging trips by 36 individuals. Two clusters of trips were identified, one (SF) characterized by more static foraging behaviour and the other (DF) by more dynamic foraging behaviour, with a higher proportion of flying activity and a higher energy expenditure compared to SF. Lesser kestrels showed consistent inter-individual differences in foraging tactics across weather condition gradients, favouring DF trips as solar radiation and crosswind intensity increased. DF trips were more frequent during the nestling-rearing than during the egg incubation stage. Nestlings whose tracked parent was more prone to perform DF trips experienced higher daily mass increase, irrespective of nestling feeding rates. Conclusions: Our study provided evidence that breeding lesser kestrels flexibly adopted different foraging tactics according to contingent weather landscapes, with birds showing consistent inter-individual differences in the tendency to adopt a given tactic. The positive correlation between the tendency to perform more energy-demanding DF trips and nestling growth suggests that individual differences in foraging behaviour may play a role in maintaining key life-history trade-offs between reproduction and self-maintenance

Cytosine methylation at CpCpG sites triggers accumulation of non-CpG methylation in gene bodies

Methylation of cytosine is an epigenetic mark involved in the regulation of transcription, usually associated with transcriptional repression. In mammals, methylated cytosines are found predominantly in CpGs but in plants non-CpG methylation (in the CpHpG or CpHpH contexts, where H is A, C or T) is also present and is associated with the transcriptional silencing of transposable elements. In addition, CpG methylation is found in coding regions of active genes. In the absence of the demethylase of lysine 9 of histone 3 (IBM1), a subset of body-methylated genes acquires non-CpG methylation. This was shown to alter their expression and affect plant development. It is not clear why only certain body-methylated genes gain non-CpG methylation in the absence of IBM1 and others do not. Here we describe a link between CpG methylation and the establishment of methylation in the CpHpG context that explains the two classes of body-methylated genes. We provide evidence that external cytosines of CpCpG sites can only be methylated when internal cytosines are methylated. CpCpG sites methylated in both cytosines promote spreading of methylation in the CpHpG context in genes protected by IBM1. In contrast, CpCpG sites remain unmethylated in IBM1-independent genes and do not promote spread of CpHpG methylation.European Research Council [322621]; Gatsby Foundation [AT3273/GLE]. Funding for open access charge: Gatsby Foundation [AT3273/GLE]

Phase transition and landscape statistics of the number partitioning problem

The phase transition in the number partitioning problem (NPP), i.e., the transition from a region in the space of control parameters in which almost all instances have many solutions to a region in which almost all instances have no solution, is investigated by examining the energy landscape of this classic optimization problem. This is achieved by coding the information about the minimum energy paths connecting pairs of minima into a tree structure, termed a barrier tree, the leaves and internal nodes of which represent, respectively, the minima and the lowest energy saddles connecting those minima. Here we apply several measures of shape (balance and symmetry) as well as of branch lengths (barrier heights) to the barrier trees that result from the landscape of the NPP, aiming at identifying traces of the easy/hard transition. We find that it is not possible to tell the easy regime from the hard one by visual inspection of the trees or by measuring the barrier heights. Only the {\it difficulty} measure, given by the maximum value of the ratio between the barrier height and the energy surplus of local minima, succeeded in detecting traces of the phase transition in the tree. In adddition, we show that the barrier trees associated with the NPP are very similar to random trees, contrasting dramatically with trees associated with the $p$ spin-glass and random energy models. We also examine critically a recent conjecture on the equivalence between the NPP and a truncated random energy model

A split-GFP tool reveals differences in the sub-mitochondrial distribution of wt and mutant alpha-synuclein

Parkinson's disease (PD), the second most common neurodegenerative disorder, is characterized by dopaminergic neuronal loss that initiates in the substantia nigra pars compacta and by the formation of intracellular inclusions mainly constituted by aberrant \u3b1-synuclein (\u3b1-syn) deposits known as Lewy bodies. Most cases of PD are sporadic, but about 10% are familial, among them those caused by mutations in SNCA gene have an autosomal dominant transmission. SNCA encodes \u3b1-syn, a small 140-amino acids protein that, under physiological conditions, is mainly localized at the presynaptic terminals. It is prevalently cytosolic, but its presence has been reported in the nucleus, in the mitochondria and, more recently, in the mitochondria-associated ER membranes (MAMs). Whether different cellular localizations may reflect specific \u3b1-syn activities is presently unclear and its action at mitochondrial level is still a matter of debate. Mounting evidence supports a role for \u3b1-syn in several mitochondria-derived activities, among which maintenance of mitochondrial morphology and modulation of complex I and ATP synthase activity. \u3b1-syn has been proposed to localize at the outer membrane (OMM), in the intermembrane space (IMS), at the inner membrane (IMM) and in the mitochondrial matrix, but a clear and comparative analysis of the sub-mitochondrial localization of WT and mutant \u3b1-syn is missing. Furthermore, the reasons for this spread sub-mitochondrial localization under physiological and pathological circumstances remain elusive. In this context, we decided to selectively monitor the sub-mitochondrial distribution of the WT and PD-related \u3b1-syn mutants A53T and A30P by taking advantage from a bimolecular fluorescence complementation (BiFC) approach. We also investigated whether cell stress could trigger \u3b1-syn translocation within the different mitochondrial sub-compartments and whether PD-related mutations could impinge on it. Interestingly, the artificial targeting of \u3b1-syn WT (but not of the mutants) to the mitochondrial matrix impacts on ATP production, suggesting a potential role within this compartment

Last passage percolation and traveling fronts

We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped and move like a traveling wave, subject to discretization and driven by a random noise. As N increases, we obtain estimates for the speed of the front and its profile, for different laws of the driving noise. The Gumbel distribution plays a central role for the particle jumps, and we show that the scaling limit is a L\'evy process in this case. The case of bounded jumps yields a completely different behavior

Semantic technologies for the production and publication of open data in ACI - Automobile club d’Italia

Semantic technologies combine knowledge representation techniques with artificial intelligence in order to achieve a more effective management of enterprise knowledge bases, thanks to the separation of the conceptual level of the applications from the logical and physical ones, and to the automatic reasoning services they deploy for data access and control. In this context, Ontology-based Data Management (OBDM) [3] has consolidated itself as a paradigm for data integration and governance, based on a three-tier architecture: the ontology, the data sources, and the mappings, which declaratively link the ontology predicates to the data in the sources. In this talk1 we present a joint project by Sapienza University of Rome, the Automobile Club d’Italia (ACI), and OKKAM S.r.l.2, a spinoff of the University of Trento. The objectives of the project were the definition of an ontology of ACI’s Public Vehicle Register (PRA) and car tax domains, the development of an OBDM system to access the data through such ontology, and the creation of a web portal for the publication of ACI’s car parc data in Linked Open format

Higher spin quaternion waves in the Klein-Gordon theory

Electromagnetic interactions are discussed in the context of the Klein-Gordon fermion equation. The Mott scattering amplitude is derived in leading order perturbation theory and the result of the Dirac theory is reproduced except for an overall factor of sixteen. The discrepancy is not resolved as the study points into another direction. The vertex structures involved in the scattering calculations indicate the relevance of a modified Klein-Gordon equation, which takes into account the number of polarization states of the considered quantum field. In this equation the d'Alembertian is acting on quaternion-like plane waves, which can be generalized to representations of arbitrary spin. The method provides the same relation between mass and spin that has been found previously by Majorana, Gelfand, and Yaglom in infinite spin theories

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities