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Abstract Loss functions with a large number of saddle points are one of the major obstacles for training modern machine learning (ML) models efficiently. First-order methods such as gradient descent (GD) are usually the methods of choice for training ML models. However, these methods converge to saddle points for certain choices of initial guesses. In this paper, we propose a modification of the recently proposed Laplacian smoothing gradient descent (LSGD) [Osher et al., arXiv:1806.06317 ], called modified LSGD (mLSGD), and demonstrate its potential to avoid saddle points without sacrificing the convergence rate. Our analysis is based on the attraction region, formed by all starting points for which the considered numerical scheme converges to a saddle point. We investigate the attraction region’s dimension both analytically and numerically. For a canonical class of quadratic functions, we show that the dimension of the attraction region for mLSGD is $\lfloor (n-1)/2\rfloor$ , and hence it is significantly smaller than that of GD whose dimension is $n-1$ .

In this paper, we propose MetaMobi, a novel spatio-temporal multi-dots connectivity-aware modeling and Meta model update approach for crowd Mobility learning. MetaMobi analyzes real-world Wi-Fi association data collected from our campus wireless infrastructure, with the goal towards enabling a smart connected campus. Specifically, MetaMobi aims at addressing the following two major challenges with existing crowd mobility sensing system designs: (a) how to handle the spatially, temporally, and contextually varying features in large-scale human crowd mobility distributions; and (b) how to adapt to the impacts of such crowd mobility patterns as well as the dynamic changes in crowd sensing infrastructures. To handle the first challenge, we design a novel multi-dots connectivity-aware learning approach, which jointly learns the crowd flow time series of multiple buildings with fusion of spatial graph connectivities and temporal attention mechanisms. Furthermore, to overcome the adaptivity issues due to changes in the crowd sensing infrastructures (e.g., installation of new ac- cess points), we further design a novel meta model update approach with Bernoulli dropout, which mitigates the over- fitting behaviors of the model given few-shot distributions of new crowd mobility datasets. Extensive experimental evaluations based on the real-world campus wireless dataset (including over 76 million Wi-Fi association andmore »disassociation records) demonstrate the accuracy, effectiveness, and adaptivity of MetaMobi in forecasting the campus crowd flows, with 30% higher accuracy compared to the state-of-the-art approaches.« less

The shape of the heliosphere is currently under active debate. Energetic neutral atoms (ENAs) offer the best method for investigating the global structure of the heliosphere. To date, the Interstellar Boundary Explorer (IBEX) and the Ion and Neutral Camera (INCA) that was on board Cassini provide the only global ENA observations of the heliosphere. While extensive modeling has been done at IBEX-Hi energies (0.52–6 keV), no global ENA modeling has been conducted for INCA energies (5.2–55 keV). Here, we use an ENA model of the heliosphere based on hybrid results that capture the heating and acceleration of pickup ions (PUIs) at the termination shock to compare modeled global ENA results with IBEX-Hi and INCA observations using both a long- and short-tail model of the heliosphere. We find that the modeled ENA results for the two heliotail configurations produce similar results from the IBEX-Hi through the INCA energies. We conclude from our modeled ENAs, which only include PUI acceleration at the termination shock, that ENA observations in currently available energy ranges are insufficient for probing the shape and length of the heliotail. However, as a prediction for the future IMAP-Ultra mission (3–300 keV) we present modeled ENA maps at 80more »keV, where the cooling length (∼600 au) is greater than the distance where the long- and short-heliotail models differ (∼400 au), and find that IMAP-Ultra should be able to identify the shape of the heliotail, predicting differences in the north lobe to downwind flux ratio between the models at 48%.

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Aims. On the Sun, jets in light bridges (LBs) are frequently observed with high-resolution instruments. The respective roles played by convection and the magnetic field in triggering such jets are not yet clear. Methods. We report a small fan-shaped jet along a LB observed by the 1.6m Goode Solar Telescope (GST) with the TiO Broadband Filter Imager (BFI), the Visible Imaging Spectrometer (VIS) in H α , and the Near-InfraRed Imaging Spectropolarimeter (NIRIS), along with the Stokes parameters. The high spatial and temporal resolution of those instruments allowed us to analyze the features identified during the jet event. By constructing the H α Dopplergrams, we found that the plasma is first moving upward, whereas during the second phase of the jet, the plasma is flowing back. Working with time slice diagrams, we investigated the propagation-projected speed of the fan and its bright base. Results. The fan-shaped jet developed within a few minutes, with diverging beams. At its base, a bright point was slipping along the LB and ultimately invaded the umbra of the sunspot. The H α profiles of the bright points enhanced the intensity in the wings, similarly to the case of Ellerman bombs. Co-temporally, the extreme ultraviolet (EUV)more »brightenings developed at the front of the dark material jet and moved at the same speed as the fan, leading us to propose that the fan-shaped jet material compressed and heated the ambient plasma at its extremities in the corona. Conclusions. Our multi-wavelength analysis indicates that the fan-shaped jet could result from magnetic reconnection across the highly diverging field low in the chromosphere, leading to an apparent slipping motion of the jet material along the LB. However, we did not find any opposite magnetic polarity at the jet base, as would typically be expected in such a configuration. We therefore discuss other plausible physical mechanisms, based on waves and convection, that may have triggered the event.« less

Abstract The structure of shocks and turbulence are strongly modified during the acceleration of cosmic rays (CRs) at a shock wave. The pressure and the collisionless viscous stress decelerate the incoming thermal gas and thus modify the shock structure. A CR streaming instability ahead of the shock generates the turbulence on which CRs scatter. The turbulent magnetic field in turn determines the CR diffusion coefficient and further affects the CR energy spectrum and pressure distribution. The dissipation of turbulence contributes to heating the thermal gas. Within a multicomponent fluid framework, CRs and thermal gas are treated as fluids and are closely coupled to the turbulence. The system equations comprise the gas dynamic equations, the CR pressure evolution equation, and the turbulence transport equations, and we adopt typical parameters for the hot ionized interstellar medium. It is shown that the shock has no discontinuity but possesses a narrow but smooth transition. The self-generated turbulent magnetic field is much stronger than both the large-scale magnetic field and the preexisting turbulent magnetic field. The resulting CR diffusion coefficient is substantially suppressed and is more than three orders smaller near the shock than it is far upstream. The results are qualitatively consistent with certainmore »observations.« less

Abstract Zank et al. developed models describing the transport of low-frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order-unity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as amore »check on the validity and correctness of the turbulence transport models and also provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications.« less

Convolutional neural networks (CNNs), a class of deep learning models, have experienced recent success in modeling sensory cortices and retinal circuits through optimizing performance on machine learning tasks, otherwise known as task optimization. Previous research has shown task-optimized CNNs to be capable of providing explanations as to why the retina efficiently encodes natural stimuli and how certain retinal cell types are involved in efficient encoding. In our work, we sought to use task-optimized CNNs as a means of explaining computational mechanisms responsible for motion-selective retinal circuits. We designed a biologically constrained CNN and optimized its performance on a motion-classification task. We drew inspiration from psychophysics, deep learning, and systems neuroscience literature to develop a toolbox of methods to reverse engineer the computational mechanisms learned in our model. Through reverse engineering our model, we proposed a computational mechanism in which direction-selective ganglion cells and starburst amacrine cells, both experimentally observed retinal cell types, emerge in our model to discriminate among moving stimuli. This emergence suggests that direction-selective circuits in the retina are ecologically designed to robustly discriminate among moving stimuli. Our results and methods also provide a framework for how to build more interpretable deep learning models and how to understandmore »them.« less

Water is ubiquitous in many thermal treatments and reaction conditions involving zeolite catalysts, but the potential impacts are complex. The different types of water interaction with zeolites have profound consequences in the stability, structure/ composition, and reactivity of these important catalysts. This review analyzes the current knowledge about the mechanistic aspects of water adsorption and nucleation on zeolites surfaces and the concomitant role of zeolite defects, cations and extra framework species. Examples of experimental and computational studies of water interaction with zeolites of varying Si/Al ratios, topologies, and level of silanol defects are reviewed and analyzed. The different steps associated with the process of steaming, including the Al-O-Si bond hydrolysis and subsequent structural modifications, such as dealumination, mesopore formation, and amorphization, are evaluated in light of recent DFT calculations, as well as SS NMR and other spectroscopic studies. Differences between the mechanisms of water attack of the zeolite in vapor or liquid phase are highlighted and explained, as well as the effect of hydrophobic/hydrophilic properties of the zeolite walls. In parallel, the various roles of water as modifier of reactivity are reviewed and discussed, both for plain zeolites as well as rare-earth or phosphorous-modified materials.