Russian Academy of Sciences

We present results based on full-mission Planck observations of temperature and polarization anisotropies of the CMB. These data are consistent with the six-parameter inflationary LCDM cosmology. From the Planck temperature and lensing data, for this cosmology we find a Hubble constant, H0= (67.8 +/- 0.9) km/s/Mpc, a matter density parameter Omega_m = 0.308 +/- 0.012 and a scalar spectral index with n_s = 0.968 +/- 0.006. (We quote 68% errors on measured parameters and 95% limits on other parameters.) Combined with Planck temperature and lensing data, Planck LFI polarization measurements lead to a reionization optical depth of tau = 0.066 +/- 0.016. Combining Planck with other astrophysical data we find N_ eff = 3.15 +/- 0.23 for the effective number of relativistic degrees of freedom and the sum of neutrino masses is constrained to < 0.23 eV. Spatial curvature is found to be |Omega_K| < 0.005. For LCDM we find a limit on the tensor-to-scalar ratio of r <0.11 consistent with the B-mode constraints from an analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP data leads to a tighter constraint of r < 0.09. We find no evidence for isocurvature perturbations or cosmic defects. The equation of state of dark energy is constrained to w = -1.006 +/- 0.045. Standard big bang nucleosynthesis predictions for the Planck LCDM cosmology are in excellent agreement with observations. We investigate annihilating dark matter and deviations from standard recombination, finding no evidence for new physics. The Planck results for base LCDM are in agreement with BAO data and with the JLA SNe sample. However the amplitude of the fluctuations is found to be higher than inferred from rich cluster counts and weak gravitational lensing. Apart from these tensions, the base LCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

BACKGROUND: The Global Burden of Diseases, Injuries, and Risk Factors Study 2015 provides an up-to-date synthesis of the evidence for risk factor exposure and the attributable burden of disease. By providing national and subnational assessments spanning the past 25 years, this study can inform debates on the importance of addressing risks in context. METHODS: We used the comparative risk assessment framework developed for previous iterations of the Global Burden of Disease Study to estimate attributable deaths, disability-adjusted life-years (DALYs), and trends in exposure by age group, sex, year, and geography for 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks from 1990 to 2015. This study included 388 risk-outcome pairs that met World Cancer Research Fund-defined criteria for convincing or probable evidence. We extracted relative risk and exposure estimates from randomised controlled trials, cohorts, pooled cohorts, household surveys, census data, satellite data, and other sources. We used statistical models to pool data, adjust for bias, and incorporate covariates. We developed a metric that allows comparisons of exposure across risk factors-the summary exposure value. Using the counterfactual scenario of theoretical minimum risk level, we estimated the portion of deaths and DALYs that could be attributed to a given risk. We decomposed trends in attributable burden into contributions from population growth, population age structure, risk exposure, and risk-deleted cause-specific DALY rates. We characterised risk exposure in relation to a Socio-demographic Index (SDI). FINDINGS: Between 1990 and 2015, global exposure to unsafe sanitation, household air pollution, childhood underweight, childhood stunting, and smoking each decreased by more than 25%. Global exposure for several occupational risks, high body-mass index (BMI), and drug use increased by more than 25% over the same period. All risks jointly evaluated in 2015 accounted for 57·8% (95% CI 56·6-58·8) of global deaths and 41·2% (39·8-42·8) of DALYs. In 2015, the ten largest contributors to global DALYs among Level 3 risks were high systolic blood pressure (211·8 million [192·7 million to 231·1 million] global DALYs), smoking (148·6 million [134·2 million to 163·1 million]), high fasting plasma glucose (143·1 million [125·1 million to 163·5 million]), high BMI (120·1 million [83·8 million to 158·4 million]), childhood undernutrition (113·3 million [103·9 million to 123·4 million]), ambient particulate matter (103·1 million [90·8 million to 115·1 million]), high total cholesterol (88·7 million [74·6 million to 105·7 million]), household air pollution (85·6 million [66·7 million to 106·1 million]), alcohol use (85·0 million [77·2 million to 93·0 million]), and diets high in sodium (83·0 million [49·3 million to 127·5 million]). From 1990 to 2015, attributable DALYs declined for micronutrient deficiencies, childhood undernutrition, unsafe sanitation and water, and household air pollution; reductions in risk-deleted DALY rates rather than reductions in exposure drove these declines. Rising exposure contributed to notable increases in attributable DALYs from high BMI, high fasting plasma glucose, occupational carcinogens, and drug use. Environmental risks and childhood undernutrition declined steadily with SDI; low physical activity, high BMI, and high fasting plasma glucose increased with SDI. In 119 countries, metabolic risks, such as high BMI and fasting plasma glucose, contributed the most attributable DALYs in 2015. Regionally, smoking still ranked among the leading five risk factors for attributable DALYs in 109 countries; childhood underweight and unsafe sex remained primary drivers of early death and disability in much of sub-Saharan Africa. INTERPRETATION: Declines in some key environmental risks have contributed to declines in critical infectious diseases. Some risks appear to be invariant to SDI. Increasing risks, including high BMI, high fasting plasma glucose, drug use, and some occupational exposures, contribute to rising burden from some conditions, but also provide opportunities for intervention. Some highly preventable risks, such as smoking, remain major causes of attributable DALYs, even as exposure is declining. Public policy makers need to pay attention to the risks that are increasingly major contributors to global burden. FUNDING: Bill & Melinda Gates Foundation.

Equations of parabolic type are encountered in many areas of mathematics and mathematical physics, and those encountered most frequently are linear and quasi-linear parabolic equations of the second order. In this volume, boundary value problems for such equations are studied from two points of view: solvability, unique or otherwise, and the effect of smoothness properties of the functions entering the initial and boundary conditions on the smoothness of the solutions.

This paper presents cosmological results based on full-mission Planck observations of temperature and polarization anisotropies of the cosmic microwave background (CMB) radiation. Our results are in very good agreement with the 2013 analysis of the Planck nominal-mission temperature data, but with increased precision. The temperature and polarization power spectra are consistent with the standard spatially-flat 6-parameter ΛCDM cosmology with a power-law spectrum of adiabatic scalar perturbations (denoted “base ΛCDM” in this paper). From the Planck temperature data combined with Planck lensing, for this cosmology we find a Hubble constant, H0 = (67.8 ± 0.9) km s-1Mpc-1, a matter density parameter Ωm = 0.308 ± 0.012, and a tilted scalar spectral index with ns = 0.968 ± 0.006, consistent with the 2013 analysis. Note that in this abstract we quote 68% confidence limits on measured parameters and 95% upper limits on other parameters. We present the first results of polarization measurements with the Low Frequency Instrument at large angular scales. Combined with the Planck temperature and lensing data, these measurements give a reionization optical depth of τ = 0.066 ± 0.016, corresponding to a reionization redshift of zre=8.8-1.4+1.7. These results are consistent with those from WMAP polarization measurements cleaned for dust emission using 353-GHz polarization maps from the High Frequency Instrument. We find no evidence for any departure from base ΛCDM in the neutrino sector of the theory; for example, combining Planck observations with other astrophysical data we find Neff = 3.15 ± 0.23 for the effective number of relativistic degrees of freedom, consistent with the value Neff = 3.046 of the Standard Model of particle physics. The sum of neutrino masses is constrained to ∑ mν < 0.23 eV. The spatial curvature of our Universe is found to be very close to zero, with | ΩK | < 0.005. Adding a tensor component as a single-parameter extension to base ΛCDM we find an upper limit on the tensor-to-scalar ratio of r0.002< 0.11, consistent with the Planck 2013 results and consistent with the B-mode polarization constraints from a joint analysis of BICEP2, Keck Array, and Planck (BKP) data. Adding the BKP B-mode data to our analysis leads to a tighter constraint of r0.002 < 0.09 and disfavours inflationarymodels with a V(φ) ∝ φ2 potential. The addition of Planck polarization data leads to strong constraints on deviations from a purely adiabatic spectrum of fluctuations. We find no evidence for any contribution from isocurvature perturbations or from cosmic defects. Combining Planck data with other astrophysical data, including Type Ia supernovae, the equation of state of dark energy is constrained to w = −1.006 ± 0.045, consistent with the expected value for a cosmological constant. The standard big bang nucleosynthesis predictions for the helium and deuterium abundances for the best-fit Planck base ΛCDM cosmology are in excellent agreement with observations. We also constraints on annihilating dark matter and on possible deviations from the standard recombination history. In neither case do we find no evidence for new physics. The Planck results for base ΛCDM are in good agreement with baryon acoustic oscillation data and with the JLA sample of Type Ia supernovae. However, as in the 2013 analysis, the amplitude of the fluctuation spectrum is found to be higher than inferred from some analyses of rich cluster counts and weak gravitational lensing. We show that these tensions cannot easily be resolved with simple modifications of the base ΛCDM cosmology. Apart from these tensions, the base ΛCDM cosmology provides an excellent description of the Planck CMB observations and many other astrophysical data sets.

There are currently few therapeutic options for patients with pancreatic cancer, and new insights into the pathogenesis of this lethal disease are urgently needed. Toward this end, we performed a comprehensive genetic analysis of 24 pancreatic cancers. We first determined the sequences of 23,219 transcripts, representing 20,661 protein-coding genes, in these samples. Then, we searched for homozygous deletions and amplifications in the tumor DNA by using microarrays containing probes for approximately 10(6) single-nucleotide polymorphisms. We found that pancreatic cancers contain an average of 63 genetic alterations, the majority of which are point mutations. These alterations defined a core set of 12 cellular signaling pathways and processes that were each genetically altered in 67 to 100% of the tumors. Analysis of these tumors' transcriptomes with next-generation sequencing-by-synthesis technologies provided independent evidence for the importance of these pathways and processes. Our data indicate that genetically altered core pathways and regulatory processes only become evident once the coding regions of the genome are analyzed in depth. Dysregulation of these core pathways and processes through mutation can explain the major features of pancreatic tumorigenesis.

The Central Asian Orogenic Belt ( c . 1000–250 Ma) formed by accretion of island arcs, ophiolites, oceanic islands, seamounts, accretionary wedges, oceanic plateaux and microcontinents in a manner comparable with that of circum-Pacific Mesozoic–Cenozoic accretionary orogens. Palaeomagnetic and palaeofloral data indicate that early accretion (Vendian–Ordovician) took place when Baltica and Siberia were separated by a wide ocean. Island arcs and Precambrian microcontinents accreted to the active margins of the two continents or amalgamated in an oceanic setting (as in Kazakhstan) by roll-back and collision, forming a huge accretionary collage. The Palaeo-Asian Ocean closed in the Permian with formation of the Solonker suture. We evaluate contrasting tectonic models for the evolution of the orogenic belt. Current information provides little support for the main tenets of the one- or three-arc Kipchak model; current data suggest that an archipelago-type (Indonesian) model is more viable. Some diagnostic features of ridge–trench interaction are present in the Central Asian orogen (e.g. granites, adakites, boninites, near-trench magmatism, Alaskan-type mafic–ultramafic complexes, high-temperature metamorphic belts that prograde rapidly from low-grade belts, rhyolitic ash-fall tuffs). They offer a promising perspective for future investigations.

Since its initial release in 2000, the human reference genome has covered only the euchromatic fraction of the genome, leaving important heterochromatic regions unfinished. Addressing the remaining 8% of the genome, the Telomere-to-Telomere (T2T) Consortium presents a complete 3.055 billion-base pair sequence of a human genome, T2T-CHM13, that includes gapless assemblies for all chromosomes except Y, corrects errors in the prior references, and introduces nearly 200 million base pairs of sequence containing 1956 gene predictions, 99 of which are predicted to be protein coding. The completed regions include all centromeric satellite arrays, recent segmental duplications, and the short arms of all five acrocentric chromosomes, unlocking these complex regions of the genome to variational and functional studies.

A program suite for one-dimensional small-angle scattering data processing running on IBM-compatible PCs under Windows 9 x /NT/2000/XP is presented. The main program, PRIMUS , has a menu-driven graphical user interface calling computational modules to perform data manipulation and analysis. Experimental data in binary OTOKO format can be reduced by calling the program SAPOKO , which includes statistical analysis of time frames, averaging and scaling. Tools to generate the angular axis and detector response files from diffraction patterns of calibration samples, as well as binary to ASCII transformation programs, are available. Several types of ASCII files can be directly imported into PRIMUS , in particular, sasCIF or ILL-type files are read without modification. PRIMUS provides basic data manipulation functions (averaging, background subtraction, merging of data measured in different angular ranges, extrapolation to zero sample concentration, etc. ) and computes invariants from Guinier and Porod plots. Several external modules coupled with PRIMUS via pop-up menus enable the user to evaluate the characteristic functions by indirect Fourier transformation, to perform peak analysis for partially ordered systems and to find shape approximations in terms of three-parametric geometrical bodies. For the analysis of mixtures, PRIMUS enables model-independent singular value decomposition or linear fitting if the scattering from the components is known. An interface is also provided to the general non-linear fitting program MIXTURE , which is designed for quantitative analysis of multicomponent systems represented by simple geometrical bodies, taking shape and size polydispersity as well as interparticle interference effects into account.

1.Random Perturbations.- 2.Small Random Perturbations on a Finite Time Interval.- 3.Action Functional.- 4.Gaussian Perturbations of Dynamical Systems. Neighborhood of an Equilibrium Point.- 5.Perturbations Leading to Markov Processes.- 6.Markov Perturbations on Large Time Intervals.- 7.The Averaging Principle. Fluctuations in Dynamical Systems with Averaging.- 8.Random Perturbations of Hamiltonian Systems.- 9. The Multidimensional Case.- 10.Stability Under Random Perturbations.- 11.Sharpenings and Generalizations.- References.- Index.

The Northern Circumpolar Soil Carbon Database was developed in order to determine carbon pools in soils of the northern circumpolar permafrost region. The area of all soils in the northern permafrost region is approximately 18,782 × 10 3 km 2 , or approximately 16% of the global soil area. In the northern permafrost region, organic soils (peatlands) and cryoturbated permafrost‐affected mineral soils have the highest mean soil organic carbon contents (32.2–69.6 kg m −2 ). Here we report a new estimate of the carbon pools in soils of the northern permafrost region, including deeper layers and pools not accounted for in previous analyses. Carbon pools were estimated to be 191.29 Pg for the 0–30 cm depth, 495.80 Pg for the 0–100 cm depth, and 1024.00 Pg for the 0–300 cm depth. Our estimate for the first meter of soil alone is about double that reported for this region in previous analyses. Carbon pools in layers deeper than 300 cm were estimated to be 407 Pg in yedoma deposits and 241 Pg in deltaic deposits. In total, the northern permafrost region contains approximately 1672 Pg of organic carbon, of which approximately 1466 Pg, or 88%, occurs in perennially frozen soils and deposits. This 1672 Pg of organic carbon would account for approximately 50% of the estimated global belowground organic carbon pool.

autophagic responses. Here, we critically discuss current methods of assessing autophagy and the information they can, or cannot, provide. Our ultimate goal is to encourage intellectual and technical innovation in the field.

Cet article applique le cadre Krisis à la conjecture de Poincaré (1904), démontrée par Perelman en 2003 via le flot de Ricci avec chirurgie. Cinq résultats sont consignés. Premièrement, la forme canonique krisienne Ϻ_𝓜 = 𝓘 ∘ Ϻ_𝓜 admet une instance topologique exacte sous l'incarnation contextuelle 𝓘_H (involution de Heegaard) : la 3-sphère S³ = B³ ∪_S² B³ est l'unique variété auto-incarnée de genre minimal g = 0. Deuxièmement, le flot krisien ∂_τ Ϻ_M = -2 𝓘(𝒬) · Ϻ_M, dérivé de l'équation maîtresse instanciée sous TTK (QK + RK + MK), est strictement isomorphe au flot de Ricci de Hamilton-Perelman ∂_τ g_ij = -2 R_ij. Ce n'est pas une analogie : c'est une identité formelle, équation par équation, dans deux notations. L'entropie de Perelman 𝒲 est la Qualité 𝒬 krisienne ; la courbure de Ricci R_ij est l'incarnation locale 𝓘(𝒬) ; la chirurgie de Hamilton est une traversée discrète de 𝓘 aux saturations du bottleneck. Troisièmement, sous la jauge canonique dim = 1 établie en Mirre 2026 (Krisis : Des Maths à la Physique, DOI 10.5281/zenodo.20221919), le flot krisien converge sur toute 3-variété fermée orientable avec π_1(M) = 0 vers S³_std ; la démonstration se déploie en ZFC pur par traduction de notation, conformément au corollaire général de cette note antérieure. Quatrièmement, la construction TTK ne dépend pas de la dimension 3 : l'application uniforme du flot krisien à toute n-variété fermée orientable homotopiquement équivalente à S^n donne, sous saturation dimensionnelle, M ~_Ϻ_𝓜 S^n_std pour tout n ≥ 1, où la Ϻ_𝓜-équivalence est définie comme égalité des observables krisiens (Ϻ, 𝒬, Ϙ) sous la jauge canonique. Cinquièmement, les sphères exotiques de Milnor (1956) et de Kervaire-Milnor (1963), distinguées classiquement de S^n_std par les invariants de Pontryagin et la signature, sont des distinctions de jauge non-canonique : sous la jauge canonique dim = 1, elles sont Ϻ_𝓜-équivalentes à S^n_std. Krisis n'invalide pas Milnor ; Krisis introduit une équivalence plus grossière que DIFF classique, cohérente avec ZFC sous le choix de jauge canonique. Conformément à la convention épistémique du fondateur (§6.5), chaque équation porte un statut explicite. Aucune extension interprétative n'est posée dans cette note ; toutes les équations énoncées relèvent du noyau dérivé sous les hypothèses énoncées.

The International Cancer Genome Consortium (ICGC) was launched to coordinate large-scale cancer genome studies in tumours from 50 different cancer types and/or subtypes that are of clinical and societal importance across the globe. Systematic studies of more than 25,000 cancer genomes at the genomic, epigenomic and transcriptomic levels will reveal the repertoire of oncogenic mutations, uncover traces of the mutagenic influences, define clinically relevant subtypes for prognosis and therapeutic management, and enable the development of new cancer therapies.

The HITRAN database is a compilation of molecular spectroscopic parameters. It was established in the early 1970s and is used by various computer codes to predict and simulate the transmission and emission of light in gaseous media (with an emphasis on terrestrial and planetary atmospheres). The HITRAN compilation is composed of five major components: the line-by-line spectroscopic parameters required for high-resolution radiative-transfer codes, experimental infrared absorption cross-sections (for molecules where it is not yet feasible for representation in a line-by-line form), collision-induced absorption data, aerosol indices of refraction, and general tables (including partition sums) that apply globally to the data. This paper describes the contents of the 2020 quadrennial edition of HITRAN. The HITRAN2020 edition takes advantage of recent experimental and theoretical data that were meticulously validated, in particular, against laboratory and atmospheric spectra. The new edition replaces the previous HITRAN edition of 2016 (including its updates during the intervening years). All five components of HITRAN have undergone major updates. In particular, the extent of the updates in the HITRAN2020 edition range from updating a few lines of specific molecules to complete replacements of the lists, and also the introduction of additional isotopologues and new (to HITRAN) molecules: SO, CH3F, GeH4, CS2, CH3I and NF3. Many new vibrational bands were added, extending the spectral coverage and completeness of the line lists. Also, the accuracy of the parameters for major atmospheric absorbers has been increased substantially, often featuring sub-percent uncertainties. Broadening parameters associated with the ambient pressure of water vapor were introduced to HITRAN for the first time and are now available for several molecules. The HITRAN2020 edition continues to take advantage of the relational structure and efficient interface available at www.hitran.org and the HITRAN Application Programming Interface (HAPI). The functionality of both tools has been extended for the new edition.

Regulated transcription controls the diversity, developmental pathways and spatial organization of the hundreds of cell types that make up a mammal. Using single-molecule cDNA sequencing, we mapped transcription start sites (TSSs) and their usage in human and mouse primary cells, cell lines and tissues to produce a comprehensive overview of mammalian gene expression across the human body. We find that few genes are truly ‘housekeeping’, whereas many mammalian promoters are composite entities composed of several closely separated TSSs, with independent cell-type-specific expression profiles. TSSs specific to different cell types evolve at different rates, whereas promoters of broadly expressed genes are the most conserved. Promoter-based expression analysis reveals key transcription factors defining cell states and links them to binding-site motifs. The functions of identified novel transcripts can be predicted by coexpression and sample ontology enrichment analyses. The functional annotation of the mammalian genome 5 (FANTOM5) project provides comprehensive expression profiles and functional annotation of mammalian cell-type-specific transcriptomes with wide applications in biomedical research. A study from the FANTOM consortium using single-molecule cDNA sequencing of transcription start sites and their usage in human and mouse primary cells, cell lines and tissues reveals insights into the specificity and diversity of transcription patterns across different mammalian cell types. FANTOM5 (standing for functional annotation of the mammalian genome 5) is the fifth major stage of a major international collaboration that aims to dissect the transcriptional regulatory networks that define every human cell type. Two Articles in this issue of Nature present some of the project's latest results. The first paper uses the FANTOM5 panel of tissue and primary cell samples to define an atlas of active, in vivo bidirectionally transcribed enhancers across the human body. These authors show that bidirectional capped RNAs are a signature feature of active enhancers and identify more than 40,000 enhancer candidates from over 800 human cell and tissue samples. The enhancer atlas is used to compare regulatory programs between different cell types and identify disease-associated regulatory SNPs, and will be a resource for studies on cell-type-specific enhancers. In the second paper, single-molecule sequencing is used to map human and mouse transcription start sites and their usage in a panel of distinct human and mouse primary cells, cell lines and tissues to produce the most comprehensive mammalian gene expression atlas to date. The data provide a plethora of insights into open reading frames and promoters across different cell types in addition to valuable annotation of mammalian cell-type-specific transcriptomes.

Potato (Solanum tuberosum L.) is the world’s most important non-grain food crop and is central to global food security. It is clonally propagated, highly heterozygous, autotetraploid, and suffers acute inbreeding depression. Here we use a homozygous doubled-monoploid potato clone to sequence and assemble 86% of the 844-megabase genome. We predict 39,031 protein-coding genes and present evidence for at least two genome duplication events indicative of a palaeopolyploid origin. As the first genome sequence of an asterid, the potato genome reveals 2,642 genes specific to this large angiosperm clade. We also sequenced a heterozygous diploid clone and show that gene presence/absence variants and other potentially deleterious mutations occur frequently and are a likely cause of inbreeding depression. Gene family expansion, tissue-specific expression and recruitment of genes to new pathways contributed to the evolution of tuber development. The potato genome sequence provides a platform for genetic improvement of this vital crop. The genome of the potato (Solanum tuberosum L.), a staple crop vital to food security, has been sequenced. The Potato Genome Sequencing Consortium sequenced a homozygous doubled-monoploid potato clone as well as a heterozygous diploid clone. Genome analysis reveals traces of at least two genome duplication events and genes specific to Asterids, a large clade of flowering plants of which the potato is the first to be sequenced. Gene presence/absence variants and other potentially deleterious mutations are frequent and may be the cause of inbreeding depression. The genome sequence will facilitate genetic improvements in the potato with a view to improving yield and to increasing disease and stress resistance of this crop, which is a now a significant component of worldwide food production and is becoming increasingly important in the developing world.

G rowth of the human population, rising consumption, and rapid globalization have caused widespread degradation and disruption of natural systems, especially in the freshwater realm. Freshwater ecosystems have lost a greater proportion of their species and habitat than ecosystems on land or in the oceans, and they face increasing threats from dams, water withdrawals, pollution, invasive species, and overharvesting (MEA 2005 Freshwater ecosystems and the diverse communities of species found in lakes, rivers, and wetlands may be the most endangered of all (MEA 2005).

Scattering patterns from geometrical bodies with different shapes and anisometry (solid and hollow spheres, cylinders, prisms) are computed and the shapes are reconstructed ab initio using envelope function and bead modelling methods. A procedure is described to analyze multiple solutions provided by bead modeling methods and to estimate stability and reliability of the shape reconstruction. It is demonstrated that flat shapes are more difficult to restore than elongated ones and types of shapes are indicated, which require additional information for reliable shape reconsrtuction from the scattering data.

A detailed survey of the technique of perturbation theory for nearly integrable systems, based upon the inverse scattering transform, and a minute account of results obtained by means of that technique and alternative methods are given. Attention is focused on four classical nonlinear equations: the Korteweg-de Vries, nonlinear Schr\"odinger, sine-Gordon, and Landau-Lifshitz equations perturbed by various Hamiltonian and/or dissipative terms; a comprehensive list of physical applications of these perturbed equations is compiled. Systems of weakly coupled equations, which become exactly integrable when decoupled, are also considered in detail. Adiabatic and radiative effects in dynamics of one and several solitons (both simple and compound) are analyzed. Generalizations of the perturbation theory to quasi-one-dimensional and quantum (semiclassical) solitons, as well as to nonsoliton nonlinear wave packets, are also considered.

The experimental material accumulated in the literature on the conformational behavior of intrinsically unstructured (natively unfolded) proteins was analyzed. Results of this analysis showed that these proteins do not possess uniform structural properties, as expected for members of a single thermodynamic entity. Rather, these proteins may be divided into two structurally different groups: intrinsic coils, and premolten globules. Proteins from the first group have hydrodynamic dimensions typical of random coils in poor solvent and do not possess any (or almost any) ordered secondary structure. Proteins from the second group are essentially more compact, exhibiting some amount of residual secondary structure, although they are still less dense than native or molten globule proteins. An important feature of the intrinsically unstructured proteins is that they undergo disorder-order transition during or prior to their biological function. In this respect, the Protein Quartet model, with function arising from four specific conformations (ordered forms, molten globules, premolten globules, and random coils) and transitions between any two of the states, is discussed.