On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Induced quantum metric fluctuations and the validity of semiclassical gravity

We propose a criterion for the validity of semiclassical gravity (SCG) which is based on the stability of the solutions of SCG with respect to quantum metric fluctuations. We pay special attention to the two-point quantum correlation functions for the metric perturbations, which contain both intrinsic and induced fluctuations. These fluctuations can be described by the Einstein-Langevin equation obtained in the framework of stochastic gravity. Specifically, the Einstein-Langevin equation yields stochastic correlation functions for the metric perturbations which agree, to leading order in the large N limit, with the quantum correlation functions of the theory of gravity interacting with N matter fields. The homogeneous solutions of the Einstein-Langevin equation are equivalent to the solutions of the perturbed semiclassical equation, which describe the evolution of the expectation value of the quantum metric perturbations. The information on the intrinsic fluctuations, which are connected to the initial fluctuations of the metric perturbations, can also be retrieved entirely from the homogeneous solutions. However, the induced metric fluctuations proportional to the noise kernel can only be obtained from the Einstein-Langevin equation (the inhomogeneous term). These equations exhibit runaway solutions with exponential instabilities. A detailed discussion about different methods to deal with these instabilities is given. We illustrate our criterion by showing explicitly that flat space is stable and a description based on SCG is a valid approximation in that case.

Soliton solutions and cosmological gravitational waves

We examine plane-symmetric cosmological solutions to Einstein's equations which can be generated by the "soliton" technique, using the homogeneous Bianchi solutions as seeds and arbitrary numbers of real or complex poles. In some circumstances, these solutions can be interpreted as "incipient" gravitational waves on the Bianchi background. At early times they look like nonlinear inhomogeneities propagating at nearly the speed of light ("gravisolitons"), while at late times they look like cosmological gravitational waves.

Multisoliton solutions to Einstein's equations

We discuss a multisoliton solution to Einsteins equations in vacuum. The solution is interpreted as many gravitational solitons propagating and colliding on a homogeneous cosmological background. Following a previous letter, we characterize the solitons by their localizability and by their peculiar properties under collisions. Furthermore, we define an associated frame-dependent velocity field which illustrates the solitonic character of these gravitational solitons in the classical sense.

Optimal network topologies for local search with congestion

The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.

MORPHOLOGICAL AND MICROMORPHOLOGICAL CHANGES IN THE STRUCTURE OF A RHODIC HAPLUDOX AS A RESULT OF AGRICULTURAL MANAGEMENT

In evaluation of soil quality for agricultural use, soil structure is one of the most important properties, which is influenced not only by climate, biological activity, and management practices but also by mechanical and physico-chemical forces acting in the soil. The purpose of this study was to evaluate the influence of conventional agricultural management on the structure and microstructure of a Latossolo Vermelho distroférrico típico (Rhodic Hapludox) in an experimental area planted to maize. Soil morphology was described using the crop profile method by identifying the distinct structural volumes called Morphologically Homogeneous Units (MHUs). For comparison, we also described a profile in an adjacent area without agricultural use and under natural regrowth referred to as Memory. We took undisturbed samples from the main MHUs so as to form thin sections and blocks of soil for micromorphological and micromorphometrical analyses. Results from the application of the crop profile method showed the occurrence of the following structural types: loose (L), fragmented (F) and continuous (C) in both profiles analyzed. In the Memory soil profile, the fragmented structures were classified as Fptμ∆+tf and Fmt∆μ, whose micromorphology shows an enaulic-porphyric (porous) relative distribution with a great deal of biological activity as indicated by the presence of vughs and channels. Lower down, from 0.20 to 0.35 m, there was a continuous soil volume (sub-type C∆μ), with a subangular block microstructure and an enaulic-porphyric relative distribution, though in this case more compact and with aggregate coalescence and less biological activity. The micromorphometrical study of the soil of the Memory Plot showed the predominance of complex pores in NAM (15.03 %), Fmt∆μ (11.72 %), and Fptμ∆+tf (7.73 %), and rounded pores in C∆μ (8.21 %). In the soil under conventional agricultural management, we observed fragmented structures similar to the Memory Plot from 0.02 to 0.20 m, followed by a volume with a compact continuous structure (C∆μ), without visible porosity and with few roots. In the MHUs under conventional management, reduction in the packing pores (40 %) was observed, mainly in the continuous units (C). The microstructure had well-defined blocks, with the occurrence of planar pores and less evidence of biological activity. In conclusion, the morphological and micromorphological analyses of the soil profiles studied offered complementary information regarding soil structural quality, especially concerning the changes in pore types as result of mechanical stress undergone by the soil.

Onsager symmetry principle for a particle moving through a fluid not in equilibrium

We have shown that the mobility tensor for a particle moving through an arbitrary homogeneous stationary flow satisfies generalized Onsager symmetry relations in which the time-reversal transformation should also be applied to the external forces that keep the system in the stationary state. It is then found that the lift forces, responsible for the motion of the particle in a direction perpendicular to its velocity, have different parity than the drag forces.

A family of inhomogeneous cosmological Einstein - Rosen metrics

Some generalized soliton solutions of the cosmological EinsteinRosen type defined in the space-time region t2=z2 in terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t?8. A subset of them evolve toward isotropic FriedmannRobertsonWalker metrics.

Uniform-price assignment markets

Uniform-price assignment games are introduced as those assignment markets with the core reduced to a segment. In these games, for all active agents, competitive prices are uniform although products may be non-homogeneous. A characterization in terms of the assignment matrix is given. The only assignment markets where all submarkets are uniform are the Bohm-Bawerk horse markets. We prove that for uniform-price assignment games the kernel, or set of symmetrically-pairwise bargained allocations, either coincides with the core or reduces to the nucleolus

Complements and substitutes in multilateral assignment markets

[cat] En aquest treball provo que, en mercats d’assignació amb més de dos costats, agents de diferents sectors poden no ser complementaris mentre que agents del mateix sector poden no ser substituts. Shapley (1962) va provar que això mai pot succeïr quan el mercat d’assignació només té dos costats. No obstant, demostro que existeixen condicions suficients que garanteixen la substitutabilitat i la complementarietat entre agents en aquests tipus de mercats. A més, provo que, quan els béns al mercat son homogenis, el resultat de Shapley (1962) es manté.

Stable alpha-synuclein oligomers strongly inhibit chaperone activity of the Hsp70 system by weak interactions with J-domain co-chaperones.

α-Synuclein aggregation and accumulation in Lewy bodies are implicated in progressive loss of dopaminergic neurons in Parkinson disease and related disorders. In neurons, the Hsp70s and their Hsp40-like J-domain co-chaperones are the only known components of chaperone network that can use ATP to convert cytotoxic protein aggregates into harmless natively refolded polypeptides. Here we developed a protocol for preparing a homogeneous population of highly stable β-sheet enriched toroid-shaped α-Syn oligomers with a diameter typical of toxic pore-forming oligomers. These oligomers were partially resistant to in vitro unfolding by the bacterial Hsp70 chaperone system (DnaK, DnaJ, GrpE). Moreover, both bacterial and human Hsp70/Hsp40 unfolding/refolding activities of model chaperone substrates were strongly inhibited by the oligomers but, remarkably, not by unstructured α-Syn monomers even in large excess. The oligomers acted as a specific competitive inhibitor of the J-domain co-chaperones, indicating that J-domain co-chaperones may preferably bind to exposed bulky misfolded structures in misfolded proteins and, thus, complement Hsp70s that bind to extended segments. Together, our findings suggest that inhibition of the Hsp70/Hsp40 chaperone system by α-Syn oligomers may contribute to the disruption of protein homeostasis in dopaminergic neurons, leading to apoptosis and tissue loss in Parkinson disease and related neurodegenerative diseases.

Quantification of human adenoviruses in European recreational waters

The presence of human adenoviruses in recreational water might cause disease in the population upon exposure. Human adenoviruses detected by PCR could also serve as indicators of the virological water quality. In order to assess the applicability of human adenoviruses to the evaluation of the faecal contamination in European bathing waters, a real-time quantitative PCR assay was developed for the quantification of human adenoviruses in 132 samples collected from 24 different recreational marine and freshwater sites in nine European countries.Selected samples presenting positive nested-PCR results for human adenoviruses were analyzed using quantitative PCR and 80 samples from a total of 132 produced quantitative results with mean values of 3.2x102 10 per 100 ml of water, human adenovirus 41 being the most prevalent serotype. Human adenoviruses were quantified in samples from all 15 surveillance laboratories. Statistical analysis showed no homogeneous linear relation between humanadenoviruses and E. coli, intestinal enterococci or somatic coliphages concentrations in the tested samples when considering all the data together. Significant correlations between human adenoviruses and at least one of the other indicators were observed only when data from individual Laboratories were considered. The quantification of human adenoviruses may provide complementary information in relation to the use of bacterial standards in the control of water quality in bathing water.

Chemoconvection patterns in the Methylene-blue-glucose system: Weakly nonlinear analysis

The oxidation of solutions of glucose with methylene-blue as a catalyst in basic media can induce hydrodynamic overturning instabilities, termed chemoconvection in recognition of their similarity to convective instabilities. The phenomenon is due to gluconic acid, the marginally dense product of the reaction, which gradually builds an unstable density profile. Experiments indicate that dominant pattern wavenumbers initially increase before gradually decreasing or can even oscillate for long times. Here, we perform a weakly nonlinear analysis for an established model of the system with simple kinetics, and show that the resulting amplitude equation is analogous to that obtained in convection with insulating walls. We show that the amplitude description predicts that dominant pattern wavenumbers should decrease in the long term, but does not reproduce the aforementioned increasing wavenumber behavior in the initial stages of pattern development. We hypothesize that this is due to horizontally homogeneous steady states not being attained before pattern onset. We show that the behavior can be explained using a combination of pseudo-steady-state linear and steady-state weakly nonlinear theories. The results obtained are in qualitative agreement with the analysis of experiments.

Influence of an inert electrolyte on the morphology of quasi-two-dimensional electrodeposits

The influence of an inert electrolyte (sodium sulfate) on quasi-two-dimensional copper electrodeposition from a nondeaerated aqueous copper sulfate solution has been analyzed. The different morphologies for a fixed concentration of CuSO4 have been classified in a diagram in terms of the applied potential and the inert electrolyte concentration. The main conclusion is the extension of the well-known Ohmic model for the homogeneous growth regime for copper sulfate solutions with small amounts of sodium sulfate. Moreover, we have observed the formation of fingerlike deposits at large applied potential and inert electrolyte concentration values, before hydrogen evolution becomes the main electrode reaction.

Transient patterns in nematic liquid crystals: Domain-wall dynamics

We study the dynamics of the late stages of the Fréedericksz transition in which a periodic transient pattern decays to a final homogeneous state. A stability analysis of an unstable stationary pattern is presented, and equations for the evolution of the domain walls are obtained. Using results of previous theories, we analyze the effect that the specific dynamics of the problem, incorporating hydrodynamic couplings, has on the expected logarithmic domain growth law.