The diffusion maps together with the geometric harmonics provide a method for describing the geometry of high dimensional data and for extending these descriptions to new data points and to functions, which are defined on the data. This method suffers from two limitations. First, even though real-life data is often heterogeneous , the assumption in diffusion maps is that the attributes of the processed dataset are comparable. Second, application of the geometric harmonics requires careful setting for the correct extension scale and condition number. In this paper, we propose a method for representing and learning heterogeneous datasets by using diffusion maps for unifying and embedding heterogeneous dataset and by replacing the geometric harmonics with the Laplacian pyramid extension. Experimental results on three benchmark datasets demonstrate how the learning process becomes straightforward when the constructed representation smoothly parameterizes the task-related function.
The adoption of detailed mechanisms for chemical kinetics often poses two 1 types of severe challenges: First, the number of degrees of freedom is large; and second, 2 the dynamics is characterized by widely disparate time scales. As a result, reactive flow 3 solvers with detailed chemistry often become intractable even for large clusters of CPUs, 4 especially when dealing with direct numerical simulation (DNS) of turbulent combustion 5 problems. This has motivated the development of several techniques for reducing the 6 complexity of such kinetics models, where eventually only a few variables are considered 7 in the development of the simplified model. Unfortunately, no generally applicable a priori 8 recipe for selecting suitable parameterizations of the reduced model is available, and the 9 choice of slow variables often relies upon intuition and experience. We present an automated 10 approach to this task, consisting of three main steps. First, the low dimensional manifold 11 of slow motions is (approximately) sampled by brief simulations of the detailed model, 12 starting from a rich enough ensemble of admissible initial conditions. Second, a global 13 parametrization of the manifold is obtained through the Diffusion Map (DMAP) approach, 14 which has recently emerged as a powerful tool in data analysis/machine learning. Finally, a 15 simplified model is constructed and solved on the fly in terms of the above reduced (slow) 16 variables. Clearly, closing this latter model requires nontrivial interpolation calculations, 17 enabling restriction (mapping from the full ambient space to the reduced one) and lifting 18 (mapping from the reduced space to the ambient one). This is a key step in our approach, 19 and a variety of interpolation schemes are reported and compared. The scope of the proposed 20 procedure is presented and discussed by means of an illustrative combustion example. 21 arXiv:1307.6849v1 [math.DS] 22 29the development of a plethora of approaches aiming at reducing the computational complexity of such 30 detailed combustion models, ideally by recasting them in terms of only a few new reduced variables. 31(see e.g.[1] and references therein). The implementation of many of these techniques typically involves 32 three successive steps. First, a large set of stiff ordinary differential equations (ODEs) is considered 33 for modeling the temporal evolution of a spatially homogenous mixture of chemical species under 34 specified stoichiometric and thermodynamic conditions (usually fixed total enthalpy and pressure for 35 combustion in the low Mach regime). It is well known that, due to the presence of fast and slow 36 dynamics, the above systems are characterized by low dimensional manifolds in the concentration 37 space (or phase-space), where a typical solution trajectory is initially rapidly attracted towards the 38 manifold, while afterwards it proceeds to the thermodynamic equilibrium point always remaining in 39 close proximity to the manifold. Clearly, the presence of a manifold for...
We propose a robust algorithm to detect the arrival of a vehicle of arbitrary type when other noises are present. It is done via analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. To achieve it with minimum number of false alarms, we combine a construction of a training database of acoustic signatures signals emitted by vehicles using the distribution of the energies among blocks of wavelet packet coefficients with a procedure of random search for a near-optimal footprint (RSNOFP). The number of false alarms in the detection is minimized even under severe conditions such as: the signals emitted by vehicles of different types differ from each other, whereas the set of non-vehicle recordings (the training database) contains signals emitted by planes, helicopters, wind, speech, steps, etc. The proposed algorithm is robust even when the tested conditions are completely different from the conditions where the training signals were recorded. The proposed technique has many algorithmic variations. For example, it can be used to distinguish among different types of vehicles. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real time detection.
Conclusions: We demonstrated that PBM induces arteriolar vasodilatation that results in both immediate and long-lasting increased capillary flow and tissue perfusion in healthy individuals. This response was wavelengthdependent and modified by skin temperature. These findings regarding physiological parameters associated with sensitivity or resistance to PBM provide information of direct relevance for patient-specific therapy. Lasers Surg. Med.
Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical phenomena, and can also dramatically assist in accelerating the simulations themselves. In this paper, we discuss and illustrate the use of nonlinear intrinsic variables (NIV) in the mining of high-dimensional multiscale simulation data. In particular, we focus on the way NIV allows us to functionally merge different simulation ensembles, and different partial observations of these ensembles, as well as to infer variables not explicitly measured.The approach relies on certain simple features of the underlying process variability to filter out measurement noise and systematically recover a unique reference coordinate frame. We illustrate the approach through two distinct sets of atomistic simulations: a stochastic simulation of an enzyme reaction network exhibiting both fast and slow time scales, and a molecular dynamics simulation of alanine dipeptide in explicit water.
Rapid and sensitive screening tools for SARS-CoV-2 infection are essential to limit the spread of COVID-19 and to properly allocate national resources. Here, we developed a new point-of-care, non-contact thermal imaging tool to detect COVID-19, based on advanced image processing algorithms. We captured thermal images of the backs of individuals with and without COVID-19 using a portable thermal camera that connects directly to smartphones. Our novel image processing algorithms automatically extracted multiple texture and shape features of the thermal images and achieved an area under the curve (AUC) of 0.85 in COVID-19 detection with up to 92% sensitivity. Thermal imaging scores were inversely correlated with clinical variables associated with COVID-19 disease progression. In summary, we show, for the first time, that a hand-held thermal imaging device can be used to detect COVID-19. Non-invasive thermal imaging could be used to screen for COVID-19 in out-of-hospital settings, especially in low-income regions with limited imaging resources.
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