The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions

We consider a large class of self-adjoint elliptic problem associated with the second derivative acting on a space of vector-valued functions. We present two different approaches to the study of the associated eigenvalues problems. The first, more general one allows to replace a secular equation (which is well-known in some special cases) by an abstract rank condition. The latter seems to apply particularly well to a specific boundary condition, sometimes dubbed "anti-Kirchhoff" in the literature, that arise in the theory of differential operators on graphs; it also permits to discuss interesting and more direct connections between the spectrum of the differential operator and some graph theoretical quantities. In either case our results yield, among other, some results on the symmetry of the spectrum

Paris'te Yahya Kemal

Taha Toros Arşivi, Dosya No: 182-Yahya Kemal Beyatlı. Not: Ekteki belgede Eric von Post'un "Bir Mayıs gecesinde" başlıklı yazısı bulunmaktadır.İstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Effective Theories for Circuits and Automata

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.Comment: 11 pages, 9 figure

Large-time asymptotic equivalence for a class of non-autonomous semilinear parabolic equations

AbstractIn this article we prove new results concerning the long-time behavior of solutions to a class of non-autonomous semilinear parabolic Neumann boundary-value problems defined on open bounded connected subsets Ω of RN. The nature of the equations that we investigate leads us to consider two complementary situations, according to whether the time-dependent lower order terms in the equations possess recurrence properties. If the lower order terms are recurrent, we prove that every solution stabilizes around a spatially homogeneous and recurrent solution of the same Neumann problem in the C1 (Ω)-topology. In contrast, if the lower order terms are not recurrent, the asymptotic states need not be solutions to the original problem and we prove that every solution stabilizes around such an asymptotic state again in the C1 (Ω)-topology. In all cases the dynamics of the asymptotic solutions are governed by a compact and connected set of scalar ordinary differential equations, which are thereby asymptotically equivalent to the original Neumann problem for large times. A major difficulty to be bypassed in the proofs of our theorems stems from the fact that we allow the nonlinearitics to depend explicitly on the gradient of the unknown function. Our method of proof rests upon the use of comparison principles and upon the existence of exponential dichotomies for the family of evolution operators associated with the principal part of the equations. It is also based on ideas that stem for the classic reduction methods for non-autonomous finite-dimentional dynamical systems originally devised by Miller, Strauss-Yorke and Sell

Evaluating approaches for estimating peat depth

Estimates of peat depth are required to inform understanding of peatland development, functioning, and ecosystem services such as carbon storage. However, there is a considerable lack of peat depth data at local, national, and global scales. Recent studies have attempted to address this knowledge deficit by using manual probing and ground-penetrating radar (GPR) to estimate depth. Despite increasing application, little consideration has been given to the accuracy of either of these techniques. This study examines the accuracy of probing and GPR for measuring peat depth. Corresponding GPR and probing surveys were carried out at a catchment scale in a blanket peatland. GPR depth estimations, calibrated using common midpoint (CMP) surveys, were found to be on average 35% greater than probe measurements. The source of disagreement was found to be predominantly caused by depth probes becoming obstructed by artifacts within the peat body, although occasionally probing rods also penetrated sediments underlying the peat. Using the Complex Refractive Index Model, it was found that applying a single velocity of 0.036 m ns−1 across a single site may also result in −8 to +17% error in estimation of peat depth due to spatial variability in water content and porosity. It is suggested that GPR calibrated at each site using CMP surveys may provide a more accurate method for measuring peat depth

Healthy aims: developing new medical implants and diagnostic equipment

Healthy Aims is a €23-million, four-year project, funded under the EU’s Information Society Technology Sixth Framework program to develop intelligent medical implants and diagnostic systems (www.healthyaims.org). The project has 25 partners from 10 countries, including commercial, clinical, and research groups. This consortium represents a combination of disciplines to design and fabricate new medical devices and components as well as to test them in laboratories and subsequent clinical trials. The project focuses on medical implants for nerve stimulation and diagnostic equipment based on straingauge technology

The permafrost carbon inventory on the Tibetan Plateau : a new evaluation using deep sediment cores

Acknowledgements We are grateful for Dr. Jens Strauss and the other two anonymous reviewers for their insightful comments on an earlier version of this MS, and appreciate members of the IBCAS Sampling Campaign Teams for their assistance in field investigation. This work was supported by the National Basic Research Program of China on Global Change (2014CB954001 and 2015CB954201), National Natural Science Foundation of China (31322011 and 41371213), and the Thousand Young Talents Program.Peer reviewedPostprin

Long-Term Vegetation Dynamics in a Megadiverse Hotspot: The Ice-Age Record of a Pre-montane Forest of Central Ecuador.

Tropical ecosystems play a key role in many aspects of Earth system dynamics currently of global concern, including carbon sequestration and biodiversity. To accurately understand complex tropical systems it is necessary to parameterise key ecological aspects, such as rates of change (RoC), species turnover, dynamism, resilience, or stability. To obtain a long-term (>50 years) perspective on these ecological aspects we must turn to the fossil record. However, compared to temperate zones, collecting continuous sedimentary archives in the lowland tropics is often difficult due to the active landscape processes, with potentially frequent volcanic, tectonic, and/or fluvial events confounding sediment deposition, preservation, and recovery. Consequently, the nature, and drivers, of vegetation dynamics during the last glacial are barely known from many non-montane tropical landscapes. One of the first lowland Amazonian locations from which palaeoecological data were obtained was an outcrop near Mera (Ecuador). Mera was discovered, and analysed, by Paul Colinvaux in the 1980s, but his interpretation of the data as indicative of a forested glacial period were criticised based on the ecology and age control. Here we present new palaeoecological data from a lake located less than 10 km away from Mera. Sediment cores raised from Laguna Pindo (1250 masl; 1°27'S, 78°05'W) have been shown to span the late last glacial period [50-13 cal kyr BP (calibrated kiloyears before present)]. The palaeoecological information obtained from Laguna Pindo indicate that the region was characterised by a relatively stable plant community, formed by taxa nowadays common at both mid and high elevations. was the dominant taxon until around 30 cal kyr BP, when it was replaced by , Asteraceae and among other taxa. Heat intolerant taxa including , , and peaked around the onset of the Last Glacial Maximum (c. 21 cal kyr BP). The results obtained from Laguna Pindo support Colinvaux's hypothesis that glacial cooling resulted in a reshuffling of taxa in the region but did not lead to a loss of the forest structure. Wide tolerances of the plant species occurring to glacial temperature range and cloud formation have been suggested to explain Pindo forest stability. This scenario is radically different than the present situation, so vulnerability of the tropical pre-montane forest is highlighted to be increased in the next decades