Modification of Algorithm of Directed Graph Paths Decomposition with Schedule

This study aims to refinement of the oriented graph paths decomposition algorithm. An additional constraint on the balance parameter is considered to take into account the locomotive departure schedule. Also new rule to compute Ns parameters is given. An example of the operation of the oriented graph paths decomposition algorithm with the schedule is given. The scientific and practical novelty of the work lies in a significant reduction in the dimension of the original problem, which is especially important in the conditions of transport networks of complex topology.

Escape and evolution of Titan’s N2 atmosphere constrained by 14N/15N isotope ratios

ABSTRACT We apply a 1D upper atmosphere model to study thermal escape of nitrogen over Titan’s history. Significant thermal escape should have occurred very early for solar extreme ultraviolet (EUV) fluxes 100–400 times higher than today with escape rates as high as ≈1.5 × 1028 s−1 and ≈4.5 × 1029 s−1, respectively, while today it is ≈7.5 × 1017 s−1. Depending on whether the Sun originated as a slow, moderate, or fast rotator, thermal escape was the dominant escape process for the first 100–1000 Myr after the formation of the Solar system. If Titan’s atmosphere originated that early, it could have lost between $\approx0.5\,\, \mathrm{ and}\,\, 16$ times its present atmospheric mass depending on the Sun’s rotational evolution. We also investigated the mass-balance parameter space for an outgassing of Titan’s nitrogen through decomposition of NH3-ices in its deep interior. Our study indicates that, if Titan’s atmosphere originated at the beginning, it could have only survived until today if the Sun was a slow rotator. In other cases, the escape would have been too strong for the degassed nitrogen to survive until present day, implying later outgassing or an additional nitrogen source. An endogenic origin of Titan’s nitrogen partially through NH3-ices is consistent with its initial fractionation of 14N/15N ≈ 166–172, or lower if photochemical removal was relevant for longer than the last ≈ 1000 Myr. Since this ratio is slightly above the ratio of cometary ammonia, some of Titan’s nitrogen might have originated from refractory organics.

Gradient Method for Continuous Influence Maximization with Budget-Saving Considerations

Continuous influence maximization (CIM) generalizes the original influence maximization by incorporating general marketing strategies: a marketing strategy mix is a vector x = (x1, …, xd) such that for each node v in a social network, v could be activated as a seed of diffusion with probability hv(x), where hv is a strategy activation function satisfying DR-submodularity. CIM is the task of selecting a strategy mix x with constraint ∑ixi ≤ k where k is a budget constraint, such that the total number of activated nodes after the diffusion process, called influence spread and denoted as g(x), is maximized. In this paper, we extend CIM to consider budget saving, that is, each strategy mix x has a cost c(x) where c is a convex cost function, and we want to maximize the balanced sum g(x) + λ(k − c(x)) where λ is a balance parameter, subject to the constraint of c(x) ≤ k. We denote this problem as CIM-BS. The objective function of CIM-BS is neither monotone, nor DR-submodular or concave, and thus neither the greedy algorithm nor the standard result on gradient method could be directly applied. Our key innovation is the combination of the gradient method with reverse influence sampling to design algorithms that solve CIM-BS: For the general case, we give an algorithm that achieves (½ − ε)-approximation, and for the case of independent strategy activations, we present an algorithm that achieves (1 − 1/e − ε) approximation.

Full Likelihood Inference from the Site Frequency Spectrum based on the Optimal Tree Resolution

We develop a novel importance sampler to compute the full likelihood function of a demographic or structural scenario given the site frequency spectrum (SFS) at a locus free of intra-locus recombination. This sampler, instead of representing the hidden genealogy of a sample of individuals by a labelled binary tree, uses the minimal level of information about such a tree that is needed for the likelihood of the SFS and thus takes advantage of the huge reduction in the size of the state space that needs to be integrated. We assume that the population may have demographically changed and may be non-panmictically structured, as reflected by the branch lengths and the topology of the genealogical tree of the sample, respectively. We also assume that mutations conform to the infinitely-many-sites model. We achieve this by a controlled Markov process that generates ‘particles’ in the hidden space of SFS histories which are always compatible with the observed SFS.To produce the particles, we use Aldous’ Beta-splitting model for a one parameter family of prior distributions over genealogical topologies or shapes (including that of the Kingman coalescent) and allow the branch lengths or epoch times to have a parametric family of priors specified by a model of demography (including exponential growth and bottleneck models). Assuming independence across unlinked loci, we can estimate the likelihood of a population scenario based on a large collection of independent SFS by an importance sampling scheme, using the (unconditional) distribution of the genealogies under this scenario when the latter is available. When it is not available, we instead compute the joint likelihood of the tree balance parameter β assuming that the tree topology follows Aldous’ Beta-splitting model, and of the demographic scenario determining the distribution of the inter-coalescence times or epoch times in the genealogy of a sample, in order to at least distinguish different equivalence classes of population scenarios leading to different tree balances and epoch times. Simulation studies are conducted to demonstrate the capabilities of the approach with publicly available code.

EFFECTS OF VESTIBULAR EXERCISES ON POSTURAL BALANCE FOR CHILDREN

The balance is one of the most important skills of the postural control and ability to move. The data are gained during the research that was supported by National Research Program "Innovative solutions in social rehabilitation in Latvian schools in the context of inclusive education". The balance sway index (SI) was tested by digital platform BioSway. The research group included 8 boys and 7 girls in the 12-14 years age range with vestibular function insufficiency. The aim of the study was to examine the immediate effect of vestibular exercises and to evaluate the degree of postural balance parameter changes after vestibular exercises complex applications. Vestibular exercise with head rotation 20 seconds with 3 repetitions caused statistically significant (p- 0.03) increasing of SI. The statistically significant (p- 0.025) improvement of SI was set after vestibular rehabilitation exercises complex application during 6 weeks (10-15 minutes a day).