@article{1241, abstract = {How likely is it that a population escapes extinction through adaptive evolution? The answer to this question is of great relevance in conservation biology, where we aim at species’ rescue and the maintenance of biodiversity, and in agriculture and medicine, where we seek to hamper the emergence of pesticide or drug resistance. By reshuffling the genome, recombination has two antagonistic effects on the probability of evolutionary rescue: It generates and it breaks up favorable gene combinations. Which of the two effects prevails depends on the fitness effects of mutations and on the impact of stochasticity on the allele frequencies. In this article, we analyze a mathematical model for rescue after a sudden environmental change when adaptation is contingent on mutations at two loci. The analysis reveals a complex nonlinear dependence of population survival on recombination. We moreover find that, counterintuitively, a fast eradication of the wild type can promote rescue in the presence of recombination. The model also shows that two-step rescue is not unlikely to happen and can even be more likely than single-step rescue (where adaptation relies on a single mutation), depending on the circumstances.}, author = {Uecker, Hildegard and Hermisson, Joachim}, journal = {Genetics}, number = {2}, pages = {721 -- 732}, publisher = {Genetics Society of America}, title = {{The role of recombination in evolutionary rescue}}, doi = {10.1534/genetics.115.180299}, volume = {202}, year = {2016}, } @article{12196, abstract = {SNC1 (SUPPRESSOR OF NPR1, CONSTITUTIVE 1) is one of a suite of intracellular Arabidopsis NOD-like receptor (NLR) proteins which, upon activation, result in the induction of defense responses. However, the molecular mechanisms underlying NLR activation and the subsequent provocation of immune responses are only partially characterized. To identify negative regulators of NLR-mediated immunity, a forward genetic screen was undertaken to search for enhancers of the dwarf, autoimmune gain-of-function snc1 mutant. To avoid lethality resulting from severe dwarfism, the screen was conducted using mos4 (modifier of snc1, 4) snc1 plants, which display wild-type-like morphology and resistance. M2 progeny were screened for mutant, snc1-enhancing (muse) mutants displaying a reversion to snc1-like phenotypes. The muse9 mos4 snc1 triple mutant was found to exhibit dwarf morphology, elevated expression of the pPR2-GUS defense marker reporter gene and enhanced resistance to the oomycete pathogen Hyaloperonospora arabidopsidis Noco2. Via map-based cloning and Illumina sequencing, it was determined that the muse9 mutation is in the gene encoding the SWI/SNF chromatin remodeler SYD (SPLAYED), and was thus renamed syd-10. The syd-10 single mutant has no observable alteration from wild-type-like resistance, although the syd-4 T-DNA insertion allele displays enhanced resistance to the bacterial pathogen Pseudomonas syringae pv. maculicola ES4326. Transcription of SNC1 is increased in both syd-4 and syd-10. These data suggest that SYD plays a subtle, specific role in the regulation of SNC1 expression and SNC1-mediated immunity. SYD may work with other proteins at the chromatin level to repress SNC1 transcription; such regulation is important for fine-tuning the expression of NLR-encoding genes to prevent unpropitious autoimmunity.}, author = {Johnson, Kaeli C.M. and Xia, Shitou and Feng, Xiaoqi and Li, Xin}, issn = {0032-0781}, journal = {Plant and Cell Physiology}, keywords = {Cell Biology, Plant Science, Physiology, General Medicine}, number = {8}, pages = {1616--1623}, publisher = {Oxford University Press}, title = {{The chromatin remodeler SPLAYED negatively regulates SNC1-mediated immunity}}, doi = {10.1093/pcp/pcv087}, volume = {56}, year = {2015}, } @article{12626, abstract = {Ice cliffs have been identified as a reason for higher ablation rates on debris-covered glaciers than are implied by the insulation effects of the debris. This study aims to improve our understanding of cliff backwasting, and the role of radiative fluxes in particular. An energy-balance model is forced with new data gathered in May and October 2013 on Lirung Glacier, Nepalese Himalaya. Observations show substantial variability in melt between cliffs, between locations on any cliff and between seasons. Using a high-resolution digital elevation model we calculate longwave fluxes incident to the cliff from surrounding terrain and include the effect of local shading on shortwave radiation. This is an advance over previous studies, that made simplified assumptions on cliff geometry and radiative fluxes. Measured melt rates varied between 3.25 and 8.6 cm d−1 in May and 0.18 and 1.34 cm d−1 in October. Model results reproduce the strong variability in space and time, suggesting considerable differences in radiative fluxes over one cliff. In October the model fails to reproduce stake readings, probably due to the lack of a refreezing component. Disregarding local topography can lead to overestimation of melt at the point scale by up to ∼9%.}, author = {Steiner, Jakob F. and Pellicciotti, Francesca and Buri, Pascal and Miles, Evan S. and Immerzeel, Walter W. and Reid, Tim D.}, issn = {1727-5652}, journal = {Journal of Glaciology}, number = {229}, pages = {889--907}, publisher = {International Glaciological Society}, title = {{Modelling ice-cliff backwasting on a debris-covered glacier in the Nepalese Himalaya}}, doi = {10.3189/2015jog14j194}, volume = {61}, year = {2015}, } @article{12627, abstract = {Spatial evolution of supraglacial debris cover on mountain glaciers is a largely unmonitored and poorly understood phenomenon that directly affects glacier melt. Supraglacial debris cover for 93 glaciers in the Karakoram, northern Pakistan, was mapped from Landsat imagery acquired in 1977, 1998, 2009 and 2014. Surge-type glaciers occupy 41% of the study area and were considered separately. The time series of debris-covered surface area change shows a mean value of zero or near-zero change for both surging and non-surging glaciers. An increase in debris-covered area is often associated with negative regional mass balances. We extend this logic to suggest that the stable regional mass balances in the Karakoram explain the zero or near-zero change in debris-covered area. This coupling of trends combined with our 37 year time series of data suggests the Karakoram anomaly extends further back in time than previously known.}, author = {Herreid, Sam and Pellicciotti, Francesca and Ayala, Alvaro and Chesnokova, Anna and Kienholz, Christian and Shea, Joseph and Shrestha, Arun}, issn = {1727-5652}, journal = {Journal of Glaciology}, number = {227}, pages = {524--536}, publisher = {International Glaciological Society}, title = {{Satellite observations show no net change in the percentage of supraglacial debris-covered area in northern Pakistan from 1977 to 2014}}, doi = {10.3189/2015jog14j227}, volume = {61}, year = {2015}, } @article{12628, abstract = {Thick debris cover on glaciers can significantly reduce ice melt. However, several studies have suggested that debris-covered glaciers in the Himalaya might have lost mass at a rate similar to debris-free glaciers. We reconstruct elevation and mass changes for the debris-covered glaciers of the upper Langtang valley, Nepalese Himalaya, using a digital elevation model (DEM) from 1974 stereo Hexagon satellite data and the 2000 SRTM (Shuttle Radar Topography Mission) DEM. Uncertainties are high in the accumulation areas, due to data gaps in the SRTM and difficulties with delineation of the glacier borders. Even with these uncertainties, we obtain thinning rates comparable to those of several other studies in the Himalaya. In particular, we obtain a total mass balance for the investigated debris-covered glaciers of the basin of –0.32 ± 0.18 m w.e. a−1. However, there are major spatial differences both between glaciers and within any single glacier, exhibiting a very distinct nonlinear mass-balance profile with elevation. Through analysis of surface velocities derived from Landsat ETM+ imagery, we show that thinning occurs in areas of low velocity and low slope. These areas are prone to a general, dynamic decay of surface features and to the development of supraglacial lakes and ice cliffs, which may be responsible for a considerable increase in overall glacier ablation.}, author = {Pellicciotti, Francesca and Stephan, Christa and Miles, Evan and Herreid, Sam and Immerzeel, Walter W. and Bolch, Tobias}, issn = {1727-5652}, journal = {Journal of Glaciology}, keywords = {Earth-Surface Processes}, number = {226}, pages = {373--386}, publisher = {International Glaciological Society}, title = {{Mass-balance changes of the debris-covered glaciers in the Langtang Himal, Nepal, from 1974 to 1999}}, doi = {10.3189/2015jog13j237}, volume = {61}, year = {2015}, } @article{12629, abstract = {Meteorological studies in high-mountain environments form the basis of our understanding of catchment hydrology and glacier accumulation and melt processes, yet high-altitude (>4000 m above sea level, asl) observatories are rare. This research presents meteorological data recorded between December 2012 and November 2013 at seven stations in Nepal, ranging in elevation from 3860 to 5360 m asl. Seasonal and diurnal cycles in air temperature, vapour pressure, incoming short-wave and long-wave radiation, atmospheric transmissivity, wind speed, and precipitation are compared between sites. Solar radiation strongly affects diurnal temperature and vapour pressure cycles, but local topography and valley-scale circulations alter wind speed and precipitation cycles. The observed diurnal variability in vertical temperature gradients in all seasons highlights the importance of in situ measurements for melt modelling. The monsoon signal (progressive onset and sharp end) is visible in all data-sets, and the passage of the remnants of Typhoon Phailin in mid-October 2013 provides an interesting case study on the possible effects of such storms on glaciers in the region.}, author = {Shea, J.M. and Wagnon, P. and Immerzeel, W.W. and Biron, R. and Brun, F. and Pellicciotti, Francesca}, issn = {1360-0648}, journal = {International Journal of Water Resources Development}, keywords = {Water Science and Technology, Development}, number = {2}, pages = {174--200}, publisher = {Taylor & Francis}, title = {{A comparative high-altitude meteorological analysis from three catchments in the Nepalese Himalaya}}, doi = {10.1080/07900627.2015.1020417}, volume = {31}, year = {2015}, } @article{12630, abstract = {The hydrology of high-elevation watersheds of the Hindu Kush-Himalaya region (HKH) is poorly known. The correct representation of internal states and process dynamics in glacio-hydrological models can often not be verified due to missing in situ measurements. We use a new set of detailed ground data from the upper Langtang valley in Nepal to systematically guide a state-of-the art glacio-hydrological model through a parameter assigning process with the aim to understand the hydrology of the catchment and contribution of snow and ice processes to runoff. 14 parameters are directly calculated on the basis of local data, and 13 parameters are calibrated against 5 different datasets of in situ or remote sensing data. Spatial fields of debris thickness are reconstructed through a novel approach that employs data from an Unmanned Aerial Vehicle (UAV), energy balance modeling and statistical techniques. The model is validated against measured catchment runoff (Nash–Sutcliffe efficiency 0.87) and modeled snow cover is compared to Landsat snow cover. The advanced representation of processes allowed assessing the role played by avalanching for runoff for the first time for a Himalayan catchment (5% of annual water inputs to the hydrological system are due to snow redistribution) and to quantify the hydrological significance of sub-debris ice melt (9% of annual water inputs). Snowmelt is the most important contributor to total runoff during the hydrological year 2012/2013 (representing 40% of all sources), followed by rainfall (34%) and ice melt (26%). A sensitivity analysis is used to assess the efficiency of the monitoring network and identify the timing and location of field measurements that constrain model uncertainty. The methodology to set up a glacio-hydrological model in high-elevation regions presented in this study can be regarded as a benchmark for modelers in the HKH seeking to evaluate their calibration approach, their experimental setup and thus to reduce the predictive model uncertainty. }, author = {Ragettli, S. and Pellicciotti, Francesca and Immerzeel, W.W. and Miles, E.S. and Petersen, L. and Heynen, M. and Shea, J.M. and Stumm, D. and Joshi, S. and Shrestha, A.}, issn = {0309-1708}, journal = {Advances in Water Resources}, keywords = {Water Science and Technology}, number = {4}, pages = {94--111}, publisher = {Elsevier}, title = {{Unraveling the hydrology of a Himalayan catchment through integration of high resolution in situ data and remote sensing with an advanced simulation model}}, doi = {10.1016/j.advwatres.2015.01.013}, volume = {78}, year = {2015}, } @article{12631, abstract = {Air temperature is one of the most relevant input variables for snow and ice melt calculations. However, local meteorological conditions, complex topography, and logistical concerns in glacierized regions make the measuring and modeling of air temperature a difficult task. In this study, we investigate the spatial distribution of 2 m air temperature over mountain glaciers and propose a modification to an existing model to improve its representation. Spatially distributed meteorological data from Haut Glacier d'Arolla (Switzerland), Place (Canada), and Juncal Norte (Chile) Glaciers are used to examine approximate flow line temperatures during their respective ablation seasons. During warm conditions (off-glacier temperatures well above 0°C), observed air temperatures in the upper reaches of Place Glacier and Haut Glacier d'Arolla decrease down glacier along the approximate flow line. At Juncal Norte and Haut Glacier d'Arolla, an increase in air temperature is observed over the glacier tongue. While the temperature behavior over the upper part can be explained by the cooling effect of the glacier surface, the temperature increase over the glacier tongue may be caused by several processes induced by the surrounding warm atmosphere. In order to capture the latter effect, we add an additional term to the Greuell and Böhm (GB) thermodynamic glacier wind model. For high off-glacier temperatures, the modified GB model reduces root-mean-square error up to 32% and provides a new approach for distributing air temperature over mountain glaciers as a function of off-glacier temperatures and approximate glacier flow lines.}, author = {Ayala, A. and Pellicciotti, Francesca and Shea, J. M.}, issn = {2169-8996}, journal = {Journal of Geophysical Research: Atmospheres}, keywords = {Space and Planetary Science, Earth and Planetary Sciences (miscellaneous), Atmospheric Science, Geophysics}, number = {8}, pages = {3139--3157}, publisher = {American Geophysical Union}, title = {{Modeling 2 m air temperatures over mountain glaciers: Exploring the influence of katabatic cooling and external warming}}, doi = {10.1002/2015jd023137}, volume = {120}, year = {2015}, } @inproceedings{12881, author = {Martius, Georg S and Olbrich, Eckehard}, booktitle = {Proceedings of the 13th European Conference on Artificial Life}, isbn = {9780262330275}, location = {York, United Kingdom}, pages = {78}, publisher = {MIT Press}, title = {{Quantifying self-organizing behavior of autonomous robots}}, doi = {10.7551/978-0-262-33027-5-ch018}, year = {2015}, } @article{1311, abstract = {In this paper, we develop an energy method to study finite speed of propagation and waiting time phenomena for the stochastic porous media equation with linear multiplicative noise in up to three spatial dimensions. Based on a novel iteration technique and on stochastic counterparts of weighted integral estimates used in the deterministic setting, we formulate a sufficient criterion on the growth of initial data which locally guarantees a waiting time phenomenon to occur almost surely. Up to a logarithmic factor, this criterion coincides with the optimal criterion known from the deterministic setting. Our technique can be modified to prove finite speed of propagation as well.}, author = {Julian Fischer and Grün, Günther}, journal = {SIAM Journal on Mathematical Analysis}, number = {1}, pages = {825 -- 854}, publisher = {Society for Industrial and Applied Mathematics }, title = {{Finite speed of propagation and waiting times for the stochastic porous medium equation: A unifying approach}}, doi = {10.1137/140960578}, volume = {47}, year = {2015}, } @article{1313, abstract = {We present an algorithm for the derivation of lower bounds on support propagation for a certain class of nonlinear parabolic equations. We proceed by combining the ideas in some recent papers by the author with the algorithmic construction of entropies due to Jüngel and Matthes, reducing the problem to a quantifier elimination problem. Due to its complexity, the quantifier elimination problem cannot be solved by present exact algorithms. However, by tackling the quantifier elimination problem numerically, in the case of the thin-film equation we are able to improve recent results by the author in the regime of strong slippage n ∈ (1, 2). For certain second-order doubly nonlinear parabolic equations, we are able to extend the known lower bounds on free boundary propagation to the case of irregular oscillatory initial data. Finally, we apply our method to a sixth-order quantum drift-diffusion equation, resulting in an upper bound on the time which it takes for the support to reach every point in the domain.}, author = {Julian Fischer}, journal = {Interfaces and Free Boundaries}, number = {1}, pages = {1 -- 20}, publisher = {European Mathematical Society Publishing House}, title = {{Estimates on front propagation for nonlinear higher-order parabolic equations: An algorithmic approach}}, doi = {10.4171/IFB/331}, volume = {17}, year = {2015}, } @article{1314, abstract = {We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible Navier-Stokes equation: Real fluids are never perfectly incompressible but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible Navier-Stokes equation, the pressure being a steep function of the density. We rigorously estimate the difference between an approximate solution to the incompressible Navier-Stokes equation and any weak solution to the compressible Navier-Stokes equation in the sense of Lions (without assuming any additional regularity of solutions). Heuristics and numerical results suggest that our error estimates are of optimal order in the case of "well-behaved" flows and divergence-free approximations of the velocity field. Thus, we expect our estimates to justify the idealization of fluids as perfectly incompressible also in practical situations.}, author = {Fischer, Julian L}, journal = {SIAM Journal on Numerical Analysis}, number = {5}, pages = {2178 -- 2205}, publisher = {Society for Industrial and Applied Mathematics }, title = {{A posteriori modeling error estimates for the assumption of perfect incompressibility in the Navier-Stokes equation}}, doi = {10.1137/140966654}, volume = {53}, year = {2015}, } @article{1316, abstract = {In the present work we introduce the notion of a renormalized solution for reaction–diffusion systems with entropy-dissipating reactions. We establish the global existence of renormalized solutions. In the case of integrable reaction terms our notion of a renormalized solution reduces to the usual notion of a weak solution. Our existence result in particular covers all reaction–diffusion systems involving a single reversible reaction with mass-action kinetics and (possibly species-dependent) Fick-law diffusion; more generally, it covers the case of systems of reversible reactions with mass-action kinetics which satisfy the detailed balance condition. For such equations the existence of any kind of solution in general was an open problem, thereby motivating the study of renormalized solutions.}, author = {Julian Fischer}, journal = {Archive for Rational Mechanics and Analysis}, number = {1}, pages = {553 -- 587}, publisher = {Springer}, title = {{Global existence of renormalized solutions to entropy-dissipating reaction–diffusion systems}}, doi = {10.1007/s00205-015-0866-x}, volume = {218}, year = {2015}, } @article{8242, author = {Einhorn, Lukas and Fazekas, Judit and Muhr, Martina and Schoos, Alexandra and Oida, Kumiko and Singer, Josef and Panakova, Lucia and Manzano-Szalai, Krisztina and Jensen-Jarolim, Erika}, issn = {0091-6749}, journal = {Journal of Allergy and Clinical Immunology}, number = {2}, publisher = {Elsevier}, title = {{Generation of recombinant FcεRIα of dog, cat and horse for component-resolved allergy diagnosis in veterinary patients}}, doi = {10.1016/j.jaci.2014.12.1263}, volume = {135}, year = {2015}, } @article{832, abstract = {Plants maintain capacity to form new organs such as leaves, flowers, lateral shoots and roots throughout their postembryonic lifetime. Lateral roots (LRs) originate from a few pericycle cells that acquire attributes of founder cells (FCs), undergo series of anticlinal divisions, and give rise to a few short initial cells. After initiation, coordinated cell division and differentiation occur, giving rise to lateral root primordia (LRP). Primordia continue to grow, emerge through the cortex and epidermal layers of the primary root, and finally a new apical meristem is established taking over the responsibility for growth of mature lateral roots [for detailed description of the individual stages of lateral root organogenesis see Malamy and Benfey (1997)]. To examine this highly dynamic developmental process and to investigate a role of various hormonal, genetic and environmental factors in the regulation of lateral root organogenesis, the real time imaging based analyses represent extremely powerful tools (Laskowski et al., 2008; De Smet et al., 2012; Marhavy et al., 2013 and 2014). Herein, we describe a protocol for real time lateral root primordia (LRP) analysis, which enables the monitoring of an onset of the specific gene expression and subcellular protein localization during primordia organogenesis, as well as the evaluation of the impact of genetic and environmental perturbations on LRP organogenesis.}, author = {Peter Marhavy and Eva Benková}, journal = {Bio-protocol}, number = {8}, publisher = {Bio-protocol LLC}, title = {{Real time analysis of lateral root organogenesis in arabidopsis}}, doi = {10.21769/BioProtoc.1446}, volume = {5}, year = {2015}, } @article{8456, abstract = {The large majority of three-dimensional structures of biological macromolecules have been determined by X-ray diffraction of crystalline samples. High-resolution structure determination crucially depends on the homogeneity of the protein crystal. Overall ‘rocking’ motion of molecules in the crystal is expected to influence diffraction quality, and such motion may therefore affect the process of solving crystal structures. Yet, so far overall molecular motion has not directly been observed in protein crystals, and the timescale of such dynamics remains unclear. Here we use solid-state NMR, X-ray diffraction methods and μs-long molecular dynamics simulations to directly characterize the rigid-body motion of a protein in different crystal forms. For ubiquitin crystals investigated in this study we determine the range of possible correlation times of rocking motion, 0.1–100 μs. The amplitude of rocking varies from one crystal form to another and is correlated with the resolution obtainable in X-ray diffraction experiments.}, author = {Ma, Peixiang and Xue, Yi and Coquelle, Nicolas and Haller, Jens D. and Yuwen, Tairan and Ayala, Isabel and Mikhailovskii, Oleg and Willbold, Dieter and Colletier, Jacques-Philippe and Skrynnikov, Nikolai R. and Schanda, Paul}, issn = {2041-1723}, journal = {Nature Communications}, keywords = {General Biochemistry, Genetics and Molecular Biology, General Physics and Astronomy, General Chemistry}, publisher = {Springer Nature}, title = {{Observing the overall rocking motion of a protein in a crystal}}, doi = {10.1038/ncomms9361}, volume = {6}, year = {2015}, } @article{8457, abstract = {We review recent advances in methodologies to study microseconds‐to‐milliseconds exchange processes in biological molecules using magic‐angle spinning solid‐state nuclear magnetic resonance (MAS ssNMR) spectroscopy. The particularities of MAS ssNMR, as compared to solution‐state NMR, are elucidated using numerical simulations and experimental data. These simulations reveal the potential of MAS NMR to provide detailed insight into short‐lived conformations of biological molecules. Recent studies of conformational exchange dynamics in microcrystalline ubiquitin are discussed.}, author = {Ma, Peixiang and Schanda, Paul}, isbn = {9780470034590}, journal = {eMagRes}, number = {3}, pages = {699--708}, publisher = {Wiley}, title = {{Conformational exchange processes in biological systems: Detection by solid-state NMR}}, doi = {10.1002/9780470034590.emrstm1418}, volume = {4}, year = {2015}, } @article{848, abstract = {The nature of factors governing the tempo and mode of protein evolution is a fundamental issue in evolutionary biology. Specifically, whether or not interactions between different sites, or epistasis, are important in directing the course of evolution became one of the central questions. Several recent reports have scrutinized patterns of long-term protein evolution claiming them to be compatible only with an epistatic fitness landscape. However, these claims have not yet been substantiated with a formal model of protein evolution. Here, we formulate a simple covarion-like model of protein evolution focusing on the rate at which the fitness impact of amino acids at a site changes with time. We then apply the model to the data on convergent and divergent protein evolution to test whether or not the incorporation of epistatic interactions is necessary to explain the data. We find that convergent evolution cannot be explained without the incorporation of epistasis and the rate at which an amino acid state switches from being acceptable at a site to being deleterious is faster than the rate of amino acid substitution. Specifically, for proteins that have persisted in modern prokaryotic organisms since the last universal common ancestor for one amino acid substitution approximately ten amino acid states switch from being accessible to being deleterious, or vice versa. Thus, molecular evolution can only be perceived in the context of rapid turnover of which amino acids are available for evolution.}, author = {Usmanova, Dinara and Ferretti, Luca and Povolotskaya, Inna and Vlasov, Peter and Kondrashov, Fyodor}, journal = {Molecular Biology and Evolution}, number = {2}, pages = {542 -- 554}, publisher = {Oxford University Press}, title = {{A model of substitution trajectories in sequence space and long-term protein evolution}}, doi = {10.1093/molbev/msu318}, volume = {32}, year = {2015}, } @article{8495, abstract = {In this note, we consider the dynamics associated to a perturbation of an integrable Hamiltonian system in action-angle coordinates in any number of degrees of freedom and we prove the following result of ``micro-diffusion'': under generic assumptions on $ h$ and $ f$, there exists an orbit of the system for which the drift of its action variables is at least of order $ \sqrt {\varepsilon }$, after a time of order $ \sqrt {\varepsilon }^{-1}$. The assumptions, which are essentially minimal, are that there exists a resonant point for $ h$ and that the corresponding averaged perturbation is non-constant. The conclusions, although very weak when compared to usual instability phenomena, are also essentially optimal within this setting.}, author = {Bounemoura, Abed and Kaloshin, Vadim}, issn = {0002-9939}, journal = {Proceedings of the American Mathematical Society}, number = {4}, pages = {1553--1560}, publisher = {American Mathematical Society}, title = {{A note on micro-instability for Hamiltonian systems close to integrable}}, doi = {10.1090/proc/12796}, volume = {144}, year = {2015}, } @article{8498, abstract = {In the present note we announce a proof of a strong form of Arnold diffusion for smooth convex Hamiltonian systems. Let ${\mathbb T}^2$ be a 2-dimensional torus and B2 be the unit ball around the origin in ${\mathbb R}^2$ . Fix ρ > 0. Our main result says that for a 'generic' time-periodic perturbation of an integrable system of two degrees of freedom $H_0(p)+\varepsilon H_1(\theta,p,t),\quad \ \theta\in {\mathbb T}^2,\ p\in B^2,\ t\in {\mathbb T}={\mathbb R}/{\mathbb Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in ${\mathbb T}^2 \times B^2 \times {\mathbb T}$ , namely, a ρ-neighborhood of the orbit contains ${\mathbb T}^2 \times B^2 \times {\mathbb T}$ . Our proof is a combination of geometric and variational methods. The fundamental elements of the construction are the usage of crumpled normally hyperbolic invariant cylinders from [9], flower and simple normally hyperbolic invariant manifolds from [36] as well as their kissing property at a strong double resonance. This allows us to build a 'connected' net of three-dimensional normally hyperbolic invariant manifolds. To construct diffusing orbits along this net we employ a version of the Mather variational method [41] equipped with weak KAM theory [28], proposed by Bernard in [7].}, author = {Kaloshin, Vadim and Zhang, K}, issn = {0951-7715}, journal = {Nonlinearity}, keywords = {Mathematical Physics, General Physics and Astronomy, Applied Mathematics, Statistical and Nonlinear Physics}, number = {8}, pages = {2699--2720}, publisher = {IOP Publishing}, title = {{Arnold diffusion for smooth convex systems of two and a half degrees of freedom}}, doi = {10.1088/0951-7715/28/8/2699}, volume = {28}, year = {2015}, }