Learning Stable Koopman Models for Identification and Control of Dynamical Systems

Learning models of dynamical systems from data is a widely-studied problem in control theory and machine learning. One recent approach for modelling nonlinear systems considers the class of Koopman models, which embeds the nonlinear dynamics in a higher-dimensional linear subspace. Learning a Koopman embedding would allow for the analysis and control of nonlinear systems using tools from linear systems theory. Many recent methods have been proposed for data-driven learning of such Koopman embeddings, but most of these methods do not consider the stability of the Koopman model. Stability is an important and desirable property for models of dynamical systems. Unstable models tend to be non-robust to input perturbations and can produce unbounded outputs, which are both undesirable when the model is used for prediction and control. In addition, recent work has shown that stability guarantees may act as a regularizer for model fitting. As such, a natural direction would be to construct Koopman models with inherent stability guarantees. Two new classes of Koopman models are proposed that bridge the gap between Koopman-based methods and learning stable nonlinear models. The first model class is guaranteed to be stable, while the second is guaranteed to be stabilizable with an explicit stabilizing controller that renders the model stable in closed-loop. Furthermore, these models are unconstrained in their parameter sets, thereby enabling efficient optimization via gradient-based methods. Theoretical connections between the stability of Koopman models and forms of nonlinear stability such as contraction are established. To demonstrate the effect of the stability guarantees, the stable Koopman model is applied to a system identification problem, while the stabilizable model is applied to an imitation learning problem. Experimental results show empirically that the proposed models achieve better performance over prior methods without stability guarantees

Lepton Models for TeV Emission from SNR RX J1713.7-3946

(Aims.) SNR RX J1713.7-3946 is perhaps one of the best observed shell-type supernova remnants with emissions dominated by energetic particles accelerated near the shock front. The nature of the TeV emission, however, is an issue still open to investigation. (Methods.) We carry out a systematic study of four lepton models for the TeV emission with the Markov chain Monte Carlo method. (Results.) It is shown that current data already give good constraints on the model parameters. Two commonly used parametric models do not appear to fit the observed radio, X-ray, and gamma-ray spectra. Models motivated by diffusive shock acceleration and by stochastic acceleration by compressive waves in the shock downstream give comparably good fits. The former has a sharper spectral cutoff in the hard X-ray band than the latter. Future observations with the HXMT and NuSTAR may distinguish these two models.Comment: 4 pages, 2 figures, accepted by A&A Lette

Convolutional Neural Net Learning Can Achieve Production-Level Brain Segmentation in Structural Magnetic Resonance Imaging

Deep learning implementations using convolutional neural nets have recently demonstrated promise in many areas of medical imaging. In this article we lay out the methods by which we have achieved consistently high quality, high throughput computation of intra-cranial segmentation from whole head magnetic resonance images, an essential but typically time-consuming bottleneck for brain image analysis. We refer to this output as “production-level” because it is suitable for routine use in processing pipelines. Training and testing with an extremely large archive of structural images, our segmentation algorithm performs uniformly well over a wide variety of separate national imaging cohorts, giving Dice metric scores exceeding those of other recent deep learning brain extractions. We describe the components involved to achieve this performance, including size, variety and quality of ground truth, and appropriate neural net architecture. We demonstrate the crucial role of appropriately large and varied datasets, suggesting a less prominent role for algorithm development beyond a threshold of capability

Multiscale and Multiphysics Modeling of Additive Manufacturing of Advanced Materials

The objective of this proposed project is to research and develop a prediction tool for advanced additive manufacturing (AAM) processes for advanced materials and develop experimental methods to provide fundamental properties and establish validation data. Aircraft structures and engines demand materials that are stronger, useable at much higher temperatures, provide less acoustic transmission, and enable more aeroelastic tailoring than those currently used. Significant improvements in properties can only be achieved by processing the materials under nonequilibrium conditions, such as AAM processes. AAM processes encompass a class of processes that use a focused heat source to create a melt pool on a substrate. Examples include Electron Beam Freeform Fabrication and Direct Metal Deposition. These types of additive processes enable fabrication of parts directly from CAD drawings. To achieve the desired material properties and geometries of the final structure, assessing the impact of process parameters and predicting optimized conditions with numerical modeling as an effective prediction tool is necessary. The targets for the processing are multiple and at different spatial scales, and the physical phenomena associated occur in multiphysics and multiscale. In this project, the research work has been developed to model AAM processes in a multiscale and multiphysics approach. A macroscale model was developed to investigate the residual stresses and distortion in AAM processes. A sequentially coupled, thermomechanical, finite element model was developed and validated experimentally. The results showed the temperature distribution, residual stress, and deformation within the formed deposits and substrates. A mesoscale model was developed to include heat transfer, phase change with mushy zone, incompressible free surface flow, solute redistribution, and surface tension. Because of excessive computing time needed, a parallel computing approach was also tested. In addition, after investigating various methods, a Smoothed Particle Hydrodynamics Model (SPH Model) was developed to model wire feeding process. Its computational efficiency and simple architecture makes it more robust and flexible than other models. More research on material properties may be needed to realistically model the AAM processes. A microscale model was developed to investigate heterogeneous nucleation, dendritic grain growth, epitaxial growth of columnar grains, columnar-to-equiaxed transition, grain transport in melt, and other properties. The orientations of the columnar grains were almost perpendicular to the laser motion's direction. Compared to the similar studies in the literature, the multiple grain morphology modeling result is in the same order of magnitude as optical morphologies in the experiment. Experimental work was conducted to validate different models. An infrared camera was incorporated as a process monitoring and validating tool to identify the solidus and mushy zones during deposition. The images were successfully processed to identify these regions. This research project has investigated multiscale and multiphysics of the complex AAM processes thus leading to advanced understanding of these processes. The project has also developed several modeling tools and experimental validation tools that will be very critical in the future of AAM process qualification and certification

Multi-colour optical monitoring of eight red blazars

We present the observational results of multi-colour optical monitoring of eight red blazars from 2003 September to 2004 February. The aim of our monitoring is to investigate the spectral variability as well as the flux variations at short and long time scales. The observations were carried out using the 1.0 m robotic telescope of Mt. Lemmon Optical Astronomy Observatory, in Arizona, USA, the 0.6 m telescope of Sobaeksan Optical Astronomy Observatory and the 1.8 m telescope of Bohyunsan Optical Astronomy Observatory, in the Republic of Korea. During the observations, all sources show strong flux variations with amplitudes of larger than 0.5 mag. Variations with amplitudes of over 1 mag are found in four sources. Intraday variations with amplitudes larger than 0.15 mag, and a rapid brightness increase with a rate of ~0.2 mag per day in four days, are detected in S5 0716+71. We investigate the relationship between the colour index and source brightness for each source. We find that two out of three FSRQs tend to be redder when they are brighter, and, conversely, all BL Lac objects tend to be bluer. In particular, we find a significant anti-correlation between the V-I colour index and R magnitude for 3C 454.3. This implies that the spectrum became steeper when the source was brighter, which is opposite to the common trend for blazars. In contrast, significant positive correlations are found in 3C 66A, S5 0716+71, and BL Lac. However, there are only very weak correlations for PKS 0735+17 and OJ 287. We propose that the different relative contributions of the thermal versus non-thermal radiation to the optical emission may be responsible for the different trends of the colour index with brightness in FSRQs and BL Lac objects.Comment: 15 pages, 12 figures. Accepted for publication in A&

Blood Purification by Non-Selective Hemoadsorption Prevents Death after Traumatic Brain Injury and Hemorrhagic Shock in Rats

Background Patients who sustain traumatic brain injury (TBI) and concomitant hemorrhagic shock (HS) are at high risk of high-magnitude inflammation which can lead to poor outcomes and death. Blood purification by hemoadsorption (HA) offers an alternative intervention to reduce inflammation after injury. We tested the hypothesis that HA would reduce mortality in a rat model of TBI and HS. Methods Male Sprague Dawley rats were subjected to a combined injury of a controlled cortical impact (CCI) to their brain and pressure-controlled hemorrhagic shock (HS). Animals were subsequently instrumented with an extracorporeal blood circuit that passed through a cartridge for sham or experimental treatment. In experimental animals, the treatment cartridge was filled with proprietary beads (Cytosorbents; Monmouth Junction, NJ) that removed circulating molecules between 5 KDa and 60 KDa. Sham rats had equivalent circulation but no blood purification. Serial blood samples were analyzed with multiplex technology to quantify changes in a trauma-relevant panel of immunologic mediators. The primary outcome was survival to 96hr post-injury. Results HA improved survival from 47% in sham treated rats to 86% in HA treated rats. There were no treatment-related changes in histologic appearance. HA affected biomarker concentrations both during the treatment and over the ensuing four days after injury. Distinct changes in biomarker concentrations were also measured in survivor and non-survivor rats from the entire cohort of rats indicating biomarker patterns associated with survival and death after injury. Conclusions Blood purification by non-selective HA is an effective intervention to prevent death in a combined TBI/HS rat model. HA changed circulating concentrations of multiple inmmunologically active mediators during the treatment time frame and after treatment. HA has been safely implemented in human patients with sepsis and may be a treatment option after injury

Partially-erupting prominences: a comparison between observations and model-predicted observables

<p><b>Aims:</b> We investigate several partially-erupting prominences to study their relationship with other CME-associated phenomena and compare these observations with observables predicted by a model of partially-expelled-flux-ropes (Gibson & Fan 2006a, ApJ, 637, L65; 2006b, J. Geophys. Res., 111, 12103).</p> <p><b>Methods:</b> We studied 6 selected events with partially-erupting prominences using multi-wavelength observations recorded by the Extreme-ultraviolet Imaging Telescope (EIT), Transition Region and Coronal Explorer (TRACE), Mauna Loa Solar Observatory (MLSO), Big Bear Solar Observatory (BBSO), and Soft X-ray Telescope (SXT). The observational features associated with partially-erupting prominences were then compared with the predicted observables from the model.</p> <p><b>Results:</b> The partially-expelled-flux-rope (PEFR) model can explain the partial eruption of these prominences, and in addition predicts a variety of other CME-related observables that provide evidence of internal reconnection during eruption. We find that all of the partially-erupting prominences studied in this paper exhibit indirect evidence of internal reconnection. Moreover, all cases showed evidence of at least one observable unique to the PEFR model, e.g., dimmings external to the source region and/or a soft X-ray cusp overlying a reformed sigmoid.</p> <p><b>Conclusions:</b> The PEFR model provides a plausible mechanism to explain the observed evolution of partially-erupting-prominence-associated CMEs in our study.</p&gt

Four patients with a history of acute exacerbations of COPD: implementing the CHEST/Canadian Thoracic Society guidelines for preventing exacerbations

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Ab-initio study of the stability and electronic properties of wurtzite and zinc-blende BeS nanowires

In this work we study the structural stability and electronic properties of the Beryllium sulphide nanowires (NWs) in both zinc blende (ZB) and wurtzite (WZ) phases with triangle and hexagonal cross section, using first principle calculations within plane-wave pseudopotential method. A phenomenological model is used to explain the role of dangling bonds in the stability of the NWs. In contrast to the bulk phase, ZB-NWs with diameter less than 133.3 (angstrom) are found to be less favorable over WZ-NWs, in which the surface dangling bonds (DBs) on the NW facets play an important role to stabilize the NWs. Furthermore, both ZB and WZ NWs are predicted to be semiconductor and the values of the band gaps are dependent on the surface DBs as well as the size and shape of NWs. Finally, we performed atom projected density-of states (PDOSs) analysis by calculating the localized density of states on the surface atoms, as well as on the core and edge atoms.Comment: 9 Pages, 6 Figure