Kazan Federal University

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.

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.

Autophagy is a core molecular pathway for the preservation of cellular and organismal homeostasis. Pharmacological and genetic interventions impairing autophagy responses promote or aggravate disease in a plethora of experimental models. Consistently, mutations in autophagy-related processes cause severe human pathologies. Here, we review and discuss preclinical data linking autophagy dysfunction to the pathogenesis of major human disorders including cancer as well as cardiovascular, neurodegenerative, metabolic, pulmonary, renal, infectious, musculoskeletal, and ocular disorders.

The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14 May 2009 and has been scanning the microwave and submillimetre sky continuously since 12 August 2009. In March 2013, ESA and the Planck Collaboration released the initial cosmology products based on the first 15.5 months of Planck data, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the mission and its performance, the processing, analysis, and characteristics of the data, the scientific results, and the science data products and papers in the release. The science products include maps of the cosmic microwave background (CMB) and diffuse extragalactic foregrounds, a catalogue of compact Galactic and extragalactic sources, and a list of sources detected through the Sunyaev-Zeldovich effect. The likelihood code used to assess cosmological models against the Planck data and a lensing likelihood are described. Scientific results include robust support for the standard six-parameter ΛCDM model of cosmology and improved measurements of its parameters, including a highly significant deviation from scale invariance of the primordial power spectrum. The Planck values for these parameters and others derived from them are significantly different from those previously determined. Several large-scale anomalies in the temperature distribution of the CMB, first detected by WMAP, are confirmed with higher confidence. Planck sets new limits on the number and mass of neutrinos, and has measured gravitational lensing of CMB anisotropies at greater than 25σ. Planck finds no evidence for non-Gaussianity in the CMB. Planck's results agree well with results from the measurements of baryon acoustic oscillations. Planck finds a lower Hubble constant than found in some more local measures. Some tension is also present between the amplitude of matter fluctuations (σ8) derived from CMB data and that derived from Sunyaev-Zeldovich data. The Planck and WMAP power spectra are offset from each other by an average level of about 2% around the first acoustic peak. Analysis of Planck polarization data is not yet mature, therefore polarization results are not released, although the robust detection of E-mode polarization around CMB hot and cold spots is shown graphically. © 2014 ESO.

We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey, which includes more than twice the integration time of the nominal survey used for the 2013 release papers. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be n s = 0.968 0.006 and tightly constrain its scale dependence to dn s /dln k = -0.003 0.007 when combined with the Planck lensing likelihood. When the Planck high-polarization data are included, the results are consistent and uncertainties are further reduced. The upper bound on the tensor-to-scalar ratio is r 0.002 < 0.11 (95% CL). This upper limit is consistent with the B-mode polarization constraint r < 0.12 (95% CL) obtained from a joint analysis of the BICEP2/Keck Array and Planck data. These results imply that V() 2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R 2 inflation. We search for several physically motivated deviations from a simple power-law spectrum of curvature perturbations, including those motivated by a reconstruction of the inflaton potential not relying on the slow-roll approximation. We find that such models are not preferred, either according to a Bayesian model comparison or according to a frequentist simulation-based analysis. Three independent methods reconstructing the primordial power spectrum consistently recover a featureless and smooth P R (k) over the range of scales 0.008 Mpc -1 < k < 0.1 Mpc -1 . At large scales, each method finds deviations from a power law, connected to a deficit at multipoles 20-40 in the temperature power spectrum, but at an uncompelling statistical significance owing to the large cosmic variance present at these multipoles. By combining power spectrum and non-Gaussianity bounds, we constrain models with generalized Lagrangians, including Galileon models and axion monodromy models. The Planck data are consistent with adiabatic primordial perturbations, and the estimated values for the parameters of the base cold dark matter (CDM) model are not significantly altered when more general initial conditions are admitted. In correlated mixed adiabatic and isocurvature models, the 95% CL upper bound for the non-adiabatic contribution to the observed CMB temperature variance is | non-adi | < 1.9%, 4.0%, and 2.9% for CDM, neutrino density, and neutrino velocity isocurvature modes, respectively. We have tested inflationary models producing an anisotropic modulation of the primordial curvature power spectrum finding that the dipolar modulation in the CMB temperature field induced by a CDM isocurvature perturbation is not preferred at a statistically significant level. We also establish tight constraints on a possible quadrupolar modulation of the curvature perturbation. These results are consistent with the Planck 2013 analysis based on the nominal mission data and further constrain slow-roll single-field inflationary models, as expected from the increased precision of Planck data using the full set of observations.

The sol‐gel process is a more chemical method (wet chemical method) for the synthesis of various nanostructures, especially metal oxide nanoparticles. In this method, the molecular precursor (usually metal alkoxide) is dissolved in water or alcohol and converted to gel by heating and stirring by hydrolysis/alcoholysis. Since the gel obtained from the hydrolysis/alcoholysis process is wet or damp, it should be dried using appropriate methods depending on the desired properties and application of the gel. For example, if it is an alcoholic solution, the drying process is done by burning alcohol. After the drying stage, the produced gels are powdered and then calcined. The sol‐gel method is a cost‐effective method and due to the low reaction temperature there is good control over the chemical composition of the products. The sol‐gel method can be used in the process of making ceramics as a molding material and can be used as an intermediate between thin films of metal oxides in various applications. The materials obtained from the sol‐gel method are used in various optical, electronic, energy, surface engineering, biosensors, and pharmaceutical and separation technologies (such as chromatography). The sol‐gel method is a conventional and industrial method for the synthesis of nanoparticles with different chemical composition. The basis of the sol‐gel method is the production of a homogeneous sol from the precursors and its conversion into a gel. The solvent in the gel is then removed from the gel structure and the remaining gel is dried. The properties of the dried gel depend significantly on the drying method. In other words, the “removing solvent method” is selected according to the application in which the gel will be used. Dried gels in various ways are used in industries such as surface coating, building insulation, and the production of special clothing. It is worth mentioning that, by grinding the gel by special mills, it is possible to achieve nanoparticles.

The design and use of materials in the nanoscale size range for addressing medical and health-related issues continues to receive increasing interest. Research in nanomedicine spans a multitude of areas, including drug delivery, vaccine development, antibacterial, diagnosis and imaging tools, wearable devices, implants, high-throughput screening platforms, etc. using biological, nonbiological, biomimetic, or hybrid materials. Many of these developments are starting to be translated into viable clinical products. Here, we provide an overview of recent developments in nanomedicine and highlight the current challenges and upcoming opportunities for the field and translation to the clinic.

Abstract The stability and decomposition of biochar are fundamental to understand its persistence in soil, its contribution to carbon (C) sequestration, and thus its role in the global C cycle. Our current knowledge about the degradability of biochar, however, is limited. Using 128 observations of biochar‐derived CO 2 from 24 studies with stable ( 13 C) and radioactive ( 14 C) carbon isotopes, we meta‐analyzed the biochar decomposition in soil and estimated its mean residence time ( MRT ). The decomposed amount of biochar increased logarithmically with experimental duration, and the decomposition rate decreased with time. The biochar decomposition rate varied significantly with experimental duration, feedstock, pyrolysis temperature, and soil clay content. The MRT s of labile and recalcitrant biochar C pools were estimated to be about 108 days and 556 years with pool sizes of 3% and 97%, respectively. These results show that only a small part of biochar is bioavailable and that the remaining 97% contribute directly to long‐term C sequestration in soil. The second database (116 observations from 21 studies) was used to evaluate the priming effects after biochar addition. Biochar slightly retarded the mineralization of soil organic matter ( SOM ; overall mean: −3.8%, 95% CI = −8.1–0.8%) compared to the soil without biochar addition. Significant negative priming was common for studies with a duration shorter than half a year (−8.6%), crop‐derived biochar (−20.3%), fast pyrolysis (−18.9%), the lowest pyrolysis temperature (−18.5%), and small application amounts (−11.9%). In contrast, biochar addition to sandy soils strongly stimulated SOM mineralization by 20.8%. This indicates that biochar stimulates microbial activities especially in soils with low fertility. Furthermore, abiotic and biotic processes, as well as the characteristics of biochar and soils, affecting biochar decomposition are discussed. We conclude that biochar can persist in soils on a centennial scale and that it has a positive effect on SOM dynamics and thus on C sequestration.

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky surveyof galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data sets, and is the first SZ-selected cluster survey containing >103 confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the estimates of the SZ strength parameter Y5R500are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical, and X-ray data sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under-luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.

This study provided a content analysis of studies aiming to disclose how artificial intelligence (AI) has been applied to the education sector and explore the potential research trends and challenges of AI in education. A total of 100 papers including 63 empirical papers (74 studies) and 37 analytic papers were selected from the education and educational research category of Social Sciences Citation Index database from 2010 to 2020. The content analysis showed that the research questions could be classified into development layer (classification, matching, recommendation, and deep learning), application layer (feedback, reasoning, and adaptive learning), and integration layer (affection computing, role‐playing, immersive learning, and gamification). Moreover, four research trends, including Internet of Things, swarm intelligence, deep learning, and neuroscience, as well as an assessment of AI in education, were suggested for further investigation. However, we also proposed the challenges in education may be caused by AI with regard to inappropriate use of AI techniques, changing roles of teachers and students, as well as social and ethical issues. The results provide insights into an overview of the AI used for education domain, which helps to strengthen the theoretical foundation of AI in education and provides a promising channel for educators and AI engineers to carry out further collaborative research.

The European Space Agency’s Planck satellite, which is dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013. In February 2015, ESA and the Planck Collaboration released the second set of cosmology products based ondata from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The data products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing uncertainties and the performance of the analysis methods. The likelihood code used to assess cosmological models against the Planck data is described, along with a CMB lensing likelihood. Scientific results include cosmological parameters derived from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity, and new results on low-frequency Galactic foregrounds.

Abstract Despite its fundamental role for carbon (C) and nutrient cycling, rhizodeposition remains ‘the hidden half of the hidden half ’: it is highly dynamic and rhizodeposits are rapidly incorporated into microorganisms, soil organic matter, and decomposed to CO 2 . Therefore, rhizodeposition is rarely quantified and remains the most uncertain part of the soil C cycle and of C fluxes in terrestrial ecosystems. This review synthesizes and generalizes the literature on C inputs by rhizodeposition under crops and grasslands (281 data sets). The allocation dynamics of assimilated C (after 13 C‐ CO 2 or 14 C‐ CO 2 labeling of plants) were quantified within shoots, shoot respiration, roots, net rhizodeposition (i.e., C remaining in soil for longer periods), root‐derived CO 2 , and microorganisms. Partitioning of C pools and fluxes were used to extrapolate belowground C inputs via rhizodeposition to ecosystem level. Allocation from shoots to roots reaches a maximum within the first day after C assimilation. Annual crops retained more C (45% of assimilated 13 C or 14 C) in shoots than grasses (34%), mainly perennials, and allocated 1.5 times less C belowground. For crops, belowground C allocation was maximal during the first 1–2 months of growth and decreased very fast thereafter. For grasses, it peaked after 2–4 months and remained very high within the second year causing much longer allocation periods. Despite higher belowground C allocation by grasses (33%) than crops (21%), its distribution between various belowground pools remains very similar. Hence, the total C allocated belowground depends on the plant species, but its further fate is species independent. This review demonstrates that C partitioning can be used in various approaches, e.g., root sampling, CO 2 flux measurements, to assess rhizodeposits’ pools and fluxes at pot, plot, field and ecosystem scale and so, to close the most uncertain gap of the terrestrial C cycle.

Abstract We synthesized 20 years of research to explain the interrelated processes that determine soil and plant responses to biochar. The properties of biochar and its effects within agricultural ecosystems largely depend on feedstock and pyrolysis conditions. We describe three stages of reactions of biochar in soil: dissolution (1–3 weeks); reactive surface development (1–6 months); and aging (beyond 6 months). As biochar ages, it is incorporated into soil aggregates, protecting the biochar carbon and promoting the stabilization of rhizodeposits and microbial products. Biochar carbon persists in soil for hundreds to thousands of years. By increasing pH, porosity, and water availability, biochars can create favorable conditions for root development and microbial functions. Biochars can catalyze biotic and abiotic reactions, particularly in the rhizosphere, that increase nutrient supply and uptake by plants, reduce phytotoxins, stimulate plant development, and increase resilience to disease and environmental stressors. Meta‐analyses found that, on average, biochars increase P availability by a factor of 4.6; decrease plant tissue concentration of heavy metals by 17%–39%; build soil organic carbon through negative priming by 3.8% (range −21% to +20%); and reduce non‐CO 2 greenhouse gas emissions from soil by 12%–50%. Meta‐analyses show average crop yield increases of 10%–42% with biochar addition, with greatest increases in low‐nutrient P‐sorbing acidic soils (common in the tropics), and in sandy soils in drylands due to increase in nutrient retention and water holding capacity. Studies report a wide range of plant responses to biochars due to the diversity of biochars and contexts in which biochars have been applied. Crop yields increase strongly if site‐specific soil constraints and nutrient and water limitations are mitigated by appropriate biochar formulations. Biochars can be tailored to address site constraints through feedstock selection, by modifying pyrolysis conditions, through pre‐ or post‐production treatments, or co‐application with organic or mineral fertilizers. We demonstrate how, when used wisely, biochar mitigates climate change and supports food security and the circular economy.

Halloysite is an alumosilicate tubular clay with a diameter of 50 nm, an inner lumen of 15 nm and a length of 600-900 nm. It is a natural biocompatible nanomaterial available in thousands of tons at low price, which makes it a good candidate for nanoarchitectural composites. The inner lumen of halloysite may be adjusted by etching to 20-30% of the tube volume and loading with functional agents (antioxidants, anticorrosion agents, flame-retardant agents, drugs, or proteins) allowing for formulations with sustained release tuned by the tube end-stoppers for hours and days. Clogging the tube ends in polymeric composites allows further extension of the release time. Thus, antioxidant-loaded halloysite doped into rubber enhances anti-aging properties for at least 12 months. The addition of 3-5 wt% of halloysite increases the strength of polymeric materials, and the possibility of the tube's orientation promises a gradient of properties. Halloysite nanotubes are a promising mesoporous media for catalytic nanoparticles that may be seeded on the tube surface or synthesized exclusively in the lumens, providing enhanced catalytic properties, especially at high temperatures. In vitro and in vivo studies on biological cells and worms indicate the safety of halloysite, and tests for efficient adsorption of mycotoxins in animals' stomachs are also carried out.

Acute myocardial infarction (AMI) and the heart failure that often follows, are major causes of death and disability worldwide. As such, new therapies are required to limit myocardial infarct (MI) size, prevent adverse left ventricular (LV) remodeling, and reduce the onset of heart failure following AMI. The inflammatory response to AMI, plays a critical role in determining MI size, and a persistent pro-inflammatory reaction can contribute to adverse post-MI LV remodeling, making inflammation an important therapeutic target for improving outcomes following AMI. In this article, we provide an overview of the multiple players (and their dynamic roles) involved in the complex inflammatory response to AMI and subsequent LV remodeling, and highlight future opportunities for targeting inflammation as a therapeutic strategy for limiting MI size, preventing adverse LV remodeling, and reducing heart failure in AMI patients.

Arabidopsis thaliana is a long established model species for plant molecular biology, genetics and genomics, and studies of A. thaliana gene function provide the basis for formulating hypotheses and designing experiments involving other plants, including economically important species. A comprehensive understanding of the A. thaliana genome and a detailed and accurate understanding of the expression of its associated genes is therefore of great importance for both fundamental research and practical applications. Such goal is reliant on the development of new genetic and genomic resources, involving new methods of data acquisition and analysis. We present here the genome-wide analysis of A. thaliana gene expression profiles across different organs and developmental stages using high-throughput transcriptome sequencing. The expression of 25 706 protein-coding genes, as well as their stability and their spatiotemporal specificity, was assessed in 79 organs and developmental stages. A search for alternative splicing events identified 37 873 previously unreported splice junctions, approximately 30% of them occurred in intergenic regions. These potentially represent novel spliced genes that are not included in the TAIR10 database. These data are housed in an open-access web-based database, TraVA (Transcriptome Variation Analysis, http://travadb.org/), which allows visualization and analysis of gene expression profiles and differential gene expression between organs and developmental stages.

Abstract The grand challenges of contemporary fundamental physics—dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem—all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. This write-up is an initiative taken within the framework of the European Action on ‘Black holes, Gravitational waves and Fundamental Physics’.

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlation functions of the cosmic microwave background (CMB) temperature and polarization fluctuations that account for relevant uncertainties, both instrumental and astrophysical in nature. They are based on the same hybrid approach used for the previous release, i.e., a pixel-based likelihood at low multipoles ( < 30) and a Gaussian approximation to the distribution of cross-power spectra at higher multipoles. The main improvements are the use of more and better processed data and of Planck polarization information, along with more detailed models of foregrounds and instrumental uncertainties. The increased redundancy brought by more than doubling the amount of data analysed enables further consistency checks and enhanced immunity to systematic effects. It also improves the constraining power of Planck, in particular with regard to small-scale foreground properties. Progress in the modelling of foreground emission enables the retention of a larger fraction of the sky to determine the properties of the CMB, which also contributes to the enhanced precision of the spectra. Improvements in data processing and instrumental modelling further reduce uncertainties. Extensive tests establish the robustness and accuracy of the likelihood results, from temperature alone, from polarization alone, and from their combination. For temperature, we also perform a full likelihood analysis of realistic end-to-end simulations of the instrumental response to the sky, which were fed into the actual data processing pipeline; this does not reveal biases from residual low-level instrumental systematics. Even with the increase in precision and robustness, the CDM cosmological model continues to offer a very good fit to the Planck data. The slope of the primordial scalar fluctuations, n s , is confirmed smaller than unity at more than 5 from Planck alone. We further validate the robustness of the likelihood results against specific extensions to the baseline cosmology, which are particularly sensitive to data at high multipoles. For instance, the effective number of neutrino species remains compatible with the canonical value of 3.046. For this first detailed analysis of Planck polarization spectra, we concentrate at high multipoles on the E modes, leaving the analysis of the weaker B modes to future work. At low multipoles we use temperature maps at all Planck frequencies along with a subset of polarization data. These data take advantage of Planck's wide frequency coverage to improve the separation of CMB and foreground emission. Within the baseline CDM cosmology this requires = 0.078 0.019 for the reionization optical depth, which is significantly lower than estimates without the use of high-frequency data for explicit monitoring of dust emission. At high multipoles we detect residual systematic errors in E polarization, typically at the K 2 level; we therefore choose to retain temperature information alone for high multipoles as the recommended baseline, in particular for testing non-minimal models. Nevertheless, the high-multipole polarization spectra from Planck are already good enough to enable a separate high-precision determination of the parameters of the CDM model, showing consistency with those established independently from temperature information alone.

We present cluster counts and corresponding cosmological constraints from the Planck full mission data set. Our catalogue consists of 439 clusters detected via their Sunyaev-Zeldovich (SZ) signal down to a signal-to-noise ratio of 6, and is more than a factor of 2 larger than the 2013 Planck cluster cosmology sample. The counts are consistent with those from 2013 and yield compatible constraints under the same modelling assumptions. Taking advantage of the larger catalogue, we extend our analysis to the two-dimensional distribution in redshift and signal-to-noise. We use mass estimates from two recent studies of gravitational lensing of background galaxies by Planck clusters to provide priors on the hydrostatic bias parameter, (1b). In addition, we use lensing of cosmic microwave background (CMB) temperature fluctuations by Planck clusters as an independent constraint on this parameter. These various calibrations imply constraints on the present-day amplitude of matter fluctuations in varying degrees of tension with those from the Planck analysis of primary fluctuations in the CMB; for the lowest estimated values of (1b) the tension is mild, only a little over one standard deviation, while it remains substantial (3.7) for the largest estimated value. We also examine constraints on extensions to the base flat CDM model by combining the cluster and CMB constraints. The combination appears to favour non-minimal neutrino masses, but this possibility does little to relieve the overall tension because it simultaneously lowers the implied value of the Hubble parameter, thereby exacerbating the discrepancy with most current astrophysical estimates. Improving the precision of cluster mass calibrations from the current 10%-level to 1% would significantly strengthen these combined analyses and provide a stringent test of the base CDM model.

Abstract It is shown that in a medium representing an example of “Koch's tree”‐type fractional structure the diffusion process is described by a generalized transfer equation in partial derivations. Such a structure can serve as a model of a porous medium where the diffusion process takes place. The geometry of an inhomogeneous medium can serve as the dicisive factor in the explanation of the “universal response” phenomenon. A range of frequencies is found where such “superslow” diffusion process can be observed.