On three-dimensional Gerstner-like equatorial water waves Henry, D.
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
01/2018, Letnik:
376, Številka:
2111
Journal Article
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This paper reviews some recent mathematical research activity in the field of nonlinear geophysical water waves. In particular, we survey a number of exact Gerstner-like solutions which have been ...derived to model various geophysical oceanic waves, and wave-current interactions, in the equatorial region. These solutions are nonlinear, three-dimensional and explicit in terms of Lagrangian variables.
This article is part of the theme issue ‘Nonlinear water waves’.
We propose a new machine-learning approach for fiber-optic communication systems whose signal propagation is governed by the nonlinear Schrödinger equation (NLSE). Our main observation is that the ...popular split-step method (SSM) for numerically solving the NLSE has essentially the same functional form as a deep multi-layer neural network; in both cases, one alternates linear steps and pointwise nonlinearities. We exploit this connection by parameterizing the SSM and viewing the linear steps as general linear functions, similar to the weight matrices in a neural network. The resulting physics-based machine-learning model has several advantages over "black-box" function approximators. For example, it allows us to examine and interpret the learned solutions in order to understand why they perform well. As an application, low-complexity nonlinear equalization is considered, where the task is to efficiently invert the NLSE. This is commonly referred to as digital backpropagation (DBP). Rather than employing neural networks, the proposed algorithm, dubbed learned DBP (LDBP), uses the physics-based model with trainable filters in each step and its complexity is reduced by progressively pruning filter taps during gradient descent. Our main finding is that the filters can be pruned to remarkably short lengths-as few as 3 taps/step-without sacrificing performance. As a result, the complexity can be reduced by orders of magnitude in comparison to prior work. By inspecting the filter responses, an additional theoretical justification for the learned parameter configurations is provided. Our work illustrates that combining data-driven optimization with existing domain knowledge can generate new insights into old communications problems.
Summary Background The relation between platelet reactivity and stent thrombosis, major bleeding, and other adverse events after coronary artery implantation of drug-eluting stents has been ...incompletely characterised. We aimed to determine the relation between platelet reactivity during dual therapy with aspirin and clopidogrel and clinical outcomes after successful coronary drug-eluting stent implantation. Methods ADAPT-DES was a prospective, multicentre registry of patients successfully treated with one or more drug-eluting stents and given aspirin and clopidogrel at 10–15 US and European hospitals. We assessed platelet reactivity in those patients after successful percutaneous coronary intervention using VerifyNow point-of-care assays, and assigned different cutoffs to define high platelet reactivity. The primary endpoint was definite or probable stent thrombosis; other endpoints were all-cause mortality, myocardial infarction, and clinically relevant bleeding. We did a propensity-adjusted multivariable analysis to determine the relation between platelet reactivity and subsequent adverse events. This study is registered with ClinicalTrials.gov , number NCT00638794. Findings Between Jan 7, 2008, and Sept 16, 2010, 8665 patients were prospectively enrolled at 11 sites, of which 8582 were eligible. At 1-year follow-up, stent thrombosis had occurred in 70 (0·8%) patients, myocardial infarction in 269 (3·1%), clinically relevant bleeding in 531 (6·2%), and death in 161 (1·9%) patients. High platelet reactivity on clopidogrel was strongly related to stent thrombosis (adjusted HR 2·49 95% CI 1·43–4·31, p=0·001) and myocardial infarction (adjusted HR 1·42 1·09–1·86, p=0·01), was inversely related to bleeding (adjusted HR 0·73 0·61–0·89, p=0·002), but was not related to mortality (adjusted HR 1·20 0·85–1·70, p=0·30). High platelet reactivity on aspirin was not significantly associated with stent thrombosis (adjusted HR 1·46 0·58–3·64, p=0·42), myocardial infarction, or death, but was inversely related to bleeding (adjusted HR 0·65 0·43–0·99, p=0·04). Interpretation The findings from this study emphasise the counter-balancing effects of haemorrhagic and ischaemic complications after stent implantation, and suggest that safer drugs or tailored strategies for the use of more potent agents must be developed if the benefits of greater platelet inhibition in patients with cardiovascular disease are to be realised. Funding Boston Scientific, Abbott Vascular, Medtronic, Cordis, Biosensors, The Medicines Company, Daiichi-Sankyo, Eli Lilly, Volcano, and Accumetrics
We formulate an equivalence between machine learning and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number ...in a feedforward artificial network setting is the analog of time in the data assimilation setting. This connection has been noted in the machine learning literature. We add a perspective that expands on how methods from statistical physics and aspects of Lagrangian and Hamiltonian dynamics play a role in how networks can be trained and designed. Within the discussion of this equivalence, we show that adding more layers (making the network deeper) is analogous to adding temporal resolution in a data assimilation framework. Extending this equivalence to recurrent networks is also discussed.
We explore how one can find a candidate for the global minimum of the cost functions in the machine learning context using a method from data assimilation. Calculations on simple models from both sides of the equivalence are reported.
Also discussed is a framework in which the time or layer label is taken to be continuous, providing a differential equation, the Euler-Lagrange equation and its boundary conditions, as a necessary condition for a minimum of the cost function. This shows that the problem being solved is a two-point boundary value problem familiar in the discussion of variational methods. The use of continuous layers is denoted “deepest learning.”
These problems respect a symplectic symmetry in continuous layer phase space. Both Lagrangian versions and Hamiltonian versions of these problems are presented. Their well-studied implementation in a discrete time/layer, while respecting the symplectic structure, is addressed. The Hamiltonian version provides a direct rationale for backpropagation as a solution method for a certain two-point boundary value problem.
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Dostopno za:
DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, SIK, UILJ, UKNU, UL, UM, UPUK
Earth's forests face grave challenges in the Anthropocene, including hotter droughts increasingly associated with widespread forest die-off events. But despite the vital importance of forests to ...global ecosystem services, their fates in a warming world remain highly uncertain. Lacking is quantitative determination of commonality in climate anomalies associated with pulses of tree mortality-from published, field-documented mortality events-required for understanding the role of extreme climate events in overall global tree die-off patterns. Here we established a geo-referenced global database documenting climate-induced mortality events spanning all tree-supporting biomes and continents, from 154 peer-reviewed studies since 1970. Our analysis quantifies a global "hotter-drought fingerprint" from these tree-mortality sites-effectively a hotter and drier climate signal for tree mortality-across 675 locations encompassing 1,303 plots. Frequency of these observed mortality-year climate conditions strongly increases nonlinearly under projected warming. Our database also provides initial footing for further community-developed, quantitative, ground-based monitoring of global tree mortality.
Tau pathology is a hallmark of Alzheimer’s disease (AD) but also occurs in normal cognitive aging. Using the tau PET agent 18F-AV-1451, we examined retention patterns in cognitively normal older ...people in relation to young controls and AD patients. Age and β-amyloid (measured using PiB PET) were differentially associated with tau tracer retention in healthy aging. Older age was related to increased tracer retention in regions of the medial temporal lobe, which predicted worse episodic memory performance. PET detection of tau in other isocortical regions required the presence of cortical β-amyloid and was associated with decline in global cognition. Furthermore, patterns of tracer retention corresponded well with Braak staging of neurofibrillary tau pathology. The present study defined patterns of tau tracer retention in normal aging in relation to age, cognition, and β-amyloid deposition.
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•AV-1451 PET imaging allows in vivo Braak tau staging based on tracer uptake•Age and β-amyloid are associated with different patterns of tau tracer retention•Medial temporal tau tracer retention relates to episodic memory decline in aging
Schöll, Lockhart, et al. examined tau pathology in vivo using 18F-AV-1451 (tau) PET in healthy aging and found relationships with cognitive function. Confirming neuropathologically established patterns, they also detected different effects of age and β-amyloid on patterns of tau deposition.
In order to take the full advantage of the high-temperature SiC and GaN operating devices, package materials able to withstand high-temperature storage and large thermal cycles have been ...investigated. The temperature under consideration here are higher than 200 °C. Such temperatures are required for several potential applications such as down-hole oil and gas industry for well logging, aircrafts, automotive, and space exploration. This review focuses on the reliability of a selection of potential components or materials used in the package assembly as the substrates, the die attaches, the interconnections, and the encapsulation materials. It reveals that, substrates with low coefficient of thermal expansion (CTE) conductors or with higher fracture resistant ceramics are potential candidates for high temperatures. Die attaches and interconnections reliable solutions are also available with the use of compatible metallization schemes. At this level, the reliability can also be improved by reducing the CTE mismatch between assembled materials. The encapsulation remains the most limiting packaging component since hard materials present thermomechanical reliability issues, while soft materials have low degradation temperatures. The review allows identifying reliable components and materials for high-temperature wide bandgap semiconductors and is expected to be very useful for researchers working for the development on high-temperature electronics.
The influence of large (
>
1
μ
m
diameter) particles on the recrystallization behaviour of magnesium alloys deformed in plane strain compression has been studied. Deformation zones characterized by a ...misorientation gradient were observed surrounding large particles, which were similar to those seen in other alloys where particle-stimulated nucleation (PSN) of recrystallization occurs. During annealing, new grains formed by PSN, but only at a small fraction of the coarse particles. Recrystallization was instead dominated by growth of existing dynamically recrystallized grains and nucleation of new grains from the deformed grain mantle region.
Product codes (PCs) protect a 2-D array of bits using short component codes. Assuming transmission over the binary symmetric channel, the decoding is commonly performed by iteratively applying ...bounded-distance decoding to the component codes. For this coding scheme, undetected errors in the component decoding-also known as miscorrections-significantly degrade the performance. In this paper, we propose a novel iterative decoding algorithm for PCs which can detect and avoid most miscorrections. The algorithm can also be used to decode many recently proposed classes of generalized PCs, such as staircase, braided, and half-product codes. Depending on the component code parameters, our algorithm significantly outperforms the conventional iterative decoding method. As an example, for double-error-correcting Bose-Chaudhuri-Hocquenghem component codes, the net coding gain can be increased by up to 0.4 dB. Moreover, the error floor can be lowered by orders of magnitude, up to the point where the decoder performs virtually identical to a genie-aided decoder that avoids all miscorrections. We also discuss post-processing techniques that can be used to reduce the error floor even further.
It has been argued that children who possess an advanced theory of mind (ToM) are more likely to act prosocially, yet the empirical findings are mixed. To address this issue definitively, a ...meta-analytic integration of all prior literature that met appropriate inclusion criteria was conducted. In total, 76 studies including 6,432 children between 2 and 12 years of age contributed to these analyses. Collapsed across all studies, a significant association emerged (r = .19), indicating that children with higher ToM scores also received higher scores on concurrent measures of prosocial behavior. The magnitude of this effect was similar across ToM assessments requiring identification of others' cognitions versus emotions, and it existed irrespective of whether the ToM measure imposed demands on false belief reasoning or not. The association with ToM was also evident for different subtypes of prosocial behavior (helping, cooperating, comforting). ToM had a similar effect for boys and girls, but was slightly stronger in children aged 6 years or older, relative to their younger peers. Taken together, these findings provide the strongest evidence to date that being able to explicitly consider what other people are thinking and feeling is related to children's tendencies to act prosocially, although the magnitude of the association is relatively weak.
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