274 research outputs found
Correlations, Risk and Crisis: From Physiology to Finance
We study the dynamics of correlation and variance in systems under the load
of environmental factors. A universal effect in ensembles of similar systems
under the load of similar factors is described: in crisis, typically, even
before obvious symptoms of crisis appear, correlation increases, and, at the
same time, variance (and volatility) increases too. This effect is supported by
many experiments and observations of groups of humans, mice, trees, grassy
plants, and on financial time series.
A general approach to the explanation of the effect through dynamics of
individual adaptation of similar non-interactive individuals to a similar
system of external factors is developed. Qualitatively, this approach follows
Selye's idea about adaptation energy.Comment: 42 pages, 15 figures, misprints corrections, a proof is added,
improved journal versio
Evolution of adaptation mechanisms: adaptation energy, stress, and oscillating death
In 1938, H. Selye proposed the notion of adaptation energy and published
"Experimental evidence supporting the conception of adaptation energy".
Adaptation of an animal to different factors appears as the spending of one
resource. Adaptation energy is a hypothetical extensive quantity spent for
adaptation. This term causes much debate when one takes it literally, as a
physical quantity, i.e. a sort of energy. The controversial points of view
impede the systematic use of the notion of adaptation energy despite
experimental evidence. Nevertheless, the response to many harmful factors often
has general non-specific form and we suggest that the mechanisms of
physiological adaptation admit a very general and nonspecific description.
We aim to demonstrate that Selye's adaptation energy is the cornerstone of
the top-down approach to modelling of non-specific adaptation processes. We
analyse Selye's axioms of adaptation energy together with Goldstone's
modifications and propose a series of models for interpretation of these
axioms. {\em Adaptation energy is considered as an internal coordinate on the
`dominant path' in the model of adaptation}. The phenomena of `oscillating
death' and `oscillating remission' are predicted on the base of the dynamical
models of adaptation. Natural selection plays a key role in the evolution of
mechanisms of physiological adaptation. We use the fitness optimization
approach to study of the distribution of resources for neutralization of
harmful factors, during adaptation to a multifactor environment, and analyse
the optimal strategies for different systems of factors
Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
We provide Lyapunov-like characterizations of boundedness and convergence of
non-trivial solutions for a class of systems with unstable invariant sets.
Examples of systems to which the results may apply include interconnections of
stable subsystems with one-dimensional unstable dynamics or critically stable
dynamics. Systems of this type arise in problems of nonlinear output
regulation, parameter estimation and adaptive control.
In addition to providing boundedness and convergence criteria the results
allow to derive domains of initial conditions corresponding to solutions
leaving a given neighborhood of the origin at least once. In contrast to other
works addressing convergence issues in unstable systems, our results require
neither input-output characterizations for the stable part nor estimates of
convergence rates. The results are illustrated with examples, including the
analysis of phase synchronization of neural oscillators with heterogenous
coupling
Influence of the thermal factor on the composition of electron-beam high-entropy ALTiVCrNbMo coatings
This paper reports results of studying the element and phase compositions of electron-beam coatings based on the high-entropy alloy AlTiVCrNbMo, depending on the deposition temperature (in the range of 300...700 °С).
The high-entropy alloys were melted in an arc furnace in an atmosphere of high-purity argon. Vacuum condensates of the high-entropy alloy (AlTiVCrNbMo) with a thickness of 3–5 µm were obtained in the vacuum setup UVN-2M-1 at a working vacuum of 5·10-5 mТоrr. The alloy evaporation was performed from the water-cooled ingot mold using an electron-beam gun with a power of 5 kW. Condensation of vapors of all the elements of the alloy was performed onto copper substrates at temperatures of 300, 500, 700 °C. Based on analysis of the element composition of materials of the target made of the high-entropy six-element alloy AlTiVCrNbMo and electron-beam coatings, based on it, we established the critical parameter (specific heat of vaporization of an element) that defined a selective change in the element composition. In accordance with a characteristic change in the composition of coatings of the multi-element high-entropy alloy, 3 groups of elements were distinguished: with a specific heat of evaporation of 280...350 kJ/mol (group 1), 420…460 kJ/mol (group 2), and 590…680 kJ/mol (group 3). It was shown that the formation of a single-phase coating of the high-entropy alloy (based on BCC of the crystalline lattice) occurs at the higher deposition temperature of 500...700 °C when the coating consists of not less than 5 elements. It was established that based on the conditions for an electron-beam process of materials formation, the results obtained can be divided into two types: those determined by the condition of evaporation of the target and those determined by the conditions of coating deposition. The density of flows of elements, evaporated from the target, is determined by their specific heat of evaporation. However, the ratio of atoms in the flow, derived in this way, may not be retained in the formed coating due to the secondary evaporation of elements from the growth surface. The obtained results allow us to substantiate principles for the selection of components for achieving the optimal element and phase compositions of high-entropy alloys.На основі аналізу елементного складу матеріалів мішені з високоентропійного шестиелементного сплаву AlTiVCrNbMo і електронно-променевих покриттів на його основі встановлено критичний параметр (питома теплота випаровування елемента), який визначає селективну зміну елементного складу. Показано, що формування однофазного покриття високоентропійного сплаву відбувається, коли до складу покриття входить не менше 5 елементів. Отримані результати дозволяють обґрунтувати принципи підбору компонент для досягнення оптимальних елементного та фазового складу високоентропійних сплавів
PCA Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes
Multidimensional data distributions can have complex topologies and variable
local dimensions. To approximate complex data, we propose a new type of
low-dimensional ``principal object'': a principal cubic complex. This complex
is a generalization of linear and non-linear principal manifolds and includes
them as a particular case. To construct such an object, we combine a method of
topological grammars with the minimization of an elastic energy defined for its
embedment into multidimensional data space. The whole complex is presented as a
system of nodes and springs and as a product of one-dimensional continua
(represented by graphs), and the grammars describe how these continua transform
during the process of optimal complex construction. The simplest case of a
topological grammar (``add a node'', ``bisect an edge'') is equivalent to the
construction of ``principal trees'', an object useful in many practical
applications. We demonstrate how it can be applied to the analysis of bacterial
genomes and for visualization of cDNA microarray data using the ``metro map''
representation. The preprint is supplemented by animation: ``How the
topological grammar constructs branching principal components
(AnimatedBranchingPCA.gif)''.Comment: 19 pages, 8 figure
The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007
In special coordinates (codon position--specific nucleotide frequencies)
bacterial genomes form two straight lines in 9-dimensional space: one line for
eubacterial genomes, another for archaeal genomes. All the 348 distinct
bacterial genomes available in Genbank in April 2007, belong to these lines
with high accuracy. The main challenge now is to explain the observed high
accuracy. The new phenomenon of complementary symmetry for codon
position--specific nucleotide frequencies is observed. The results of analysis
of several codon usage models are presented. We demonstrate that the
mean--field approximation, which is also known as context--free, or complete
independence model, or Segre variety, can serve as a reasonable approximation
to the real codon usage. The first two principal components of codon usage
correlate strongly with genomic G+C content and the optimal growth temperature
respectively. The variation of codon usage along the third component is related
to the curvature of the mean-field approximation. First three eigenvalues in
codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and
archaeal genomes codon usage is clearly distributed along two third order
curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct
bacterial genomes available in Genbank in April 200
Prospects in non-invasive diagnosis of bronchial asthma-related gastroesophageal reflux disease: a single-stage open uncontrolled non-randomised observational study
Background. Respiratory symptoms of bronchial asthma (BA) comorbid with gastroesophageal reflux disease (GERD) may provoke duodenogastroesophageal reflux (DGER) via aggressive agents like pepsinogens and bilirubin.Objectives. A clinical and functional study of the saliva pepsinogen and bilirubin-associated BA-comorbid GERD for non-invasive DGER diagnosis.Methods. A total of 29 patients with an allergic BA phenotype, comorbid GERD and 50,2 ± 2,4 years mean age have been examined. Biochemical blood panel included bilirubin, C-reactive protein and allergen-specific IgE. Saliva bilirubin was estimated in colorimetry, and the pepsinogen-1, -2 content — in immunological tests. Grade A–D reflux oesophagitis (RO) in oesophagoscopy was assigned to erosive reflux disease, and grade N–M oesophageal mucosa (OM) lesions — to non-erosive reflux disease. External respiratory function (ERF) was assessed with forced expiratory volume (FEV1, L/s), forced vital capacity (FVC), Tiffeneau index (FEV1/FVC), pre- and post-berodual FEF1 and FVC dynamics.Results. The BA–GERD patients were markedly polymorbid. Cough and chest tightness associated with age, and the tight chest rate — with a higher body mass index and lower FEV1/FVC. The association between higher pepsinogen-I and lower FEV1/FVC–FVC in response to inhaled berodual, as well as between higher saliva bilirubin and lower FVC–FEV1 after berodual intake reflects a significant high-DGER effect on BA representation.Conclusion. In BA–GERD patients, saliva pepsinogen and bilirubin are biomarkers of both DGER and respiratory inflammation with bronchospasm
Elastic principal manifolds and their practical applications
Principal manifolds serve as useful tool for many practical applications.
These manifolds are defined as lines or surfaces passing through "the middle"
of data distribution. We propose an algorithm for fast construction of grid
approximations of principal manifolds with given topology. It is based on
analogy of principal manifold and elastic membrane. The first advantage of this
method is a form of the functional to be minimized which becomes quadratic at
the step of the vertices position refinement. This makes the algorithm very
effective, especially for parallel implementations. Another advantage is that
the same algorithmic kernel is applied to construct principal manifolds of
different dimensions and topologies. We demonstrate how flexibility of the
approach allows numerous adaptive strategies like principal graph constructing,
etc. The algorithm is implemented as a C++ package elmap and as a part of
stand-alone data visualization tool VidaExpert, available on the web. We
describe the approach and provide several examples of its application with
speed performance characteristics.Comment: 26 pages, 10 figures, edited final versio
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