Fixed Boundary Flows

We consider the fixed boundary flow with canonical interpretability as principal components extended on the non-linear Riemannian manifolds. We aim to find a flow with fixed starting and ending point for multivariate datasets lying on an embedded non-linear Riemannian manifold, differing from the principal flow that starts from the center of the data cloud. Both points are given in advance, using the intrinsic metric on the manifolds. From the perspective of geometry, the fixed boundary flow is defined as an optimal curve that moves in the data cloud. At any point on the flow, it maximizes the inner product of the vector field, which is calculated locally, and the tangent vector of the flow. We call the new flow the fixed boundary flow. The rigorous definition is given by means of an Euler-Lagrange problem, and its solution is reduced to that of a Differential Algebraic Equation (DAE). A high level algorithm is created to numerically compute the fixed boundary. We show that the fixed boundary flow yields a concatenate of three segments, one of which coincides with the usual principal flow when the manifold is reduced to the Euclidean space. We illustrate how the fixed boundary flow can be used and interpreted, and its application in real data

Manifold Fitting under Unbounded Noise

There has been an emerging trend in non-Euclidean dimension reduction of aiming to recover a low dimensional structure, namely a manifold, underlying the high dimensional data. Recovering the manifold requires the noise to be of certain concentration. Existing methods address this problem by constructing an output manifold based on the tangent space estimation at each sample point. Although theoretical convergence for these methods is guaranteed, either the samples are noiseless or the noise is bounded. However, if the noise is unbounded, which is a common scenario, the tangent space estimation of the noisy samples will be blurred, thereby breaking the manifold fitting. In this paper, we introduce a new manifold-fitting method, by which the output manifold is constructed by directly estimating the tangent spaces at the projected points on the underlying manifold, rather than at the sample points, to decrease the error caused by the noise. Our new method provides theoretical convergence, in terms of the upper bound on the Hausdorff distance between the output and underlying manifold and the lower bound on the reach of the output manifold, when the noise is unbounded. Numerical simulations are provided to validate our theoretical findings and demonstrate the advantages of our method over other relevant methods. Finally, our method is applied to real data examples

Plasmonic nano-resonator enhanced one-photon luminescence from single gold nanorods

Strong Stokes and anti-Stokes one-photon luminescence from single gold nanorods is measured in experiments. It is found that the intensity and polarization of the Stokes and anti-Stokes emissions are in strong correlation. Our experimental observation discovered a coherent process in light emission from single gold nanorods. We present a theoretical mode, based on the concept of cavity resonance, for consistently understanding both Stokes and anti-Stokes photoluminescence. Our theory is in good agreement of all our measurements.Comment: 14 pages, 7 figures, 2 table

An activity-based spatial-temporal community electricity vulnerability assessment framework

The power system is among the most important critical infrastructures in urban cities and is getting increasingly essential in supporting people s daily activities. However, it is also susceptible to most natural disasters such as tsunamis, floods, or earthquakes. Electricity vulnerability, therefore, forms a crucial basis for community resilience. This paper aims to present an assessment framework of spatial-temporal electricity vulnerability to support the building of community resilience against power outages. The framework includes vulnerability indexes in terms of occupant demographics, occupant activity patterns, and urban building characteristics. To integrate factors in these aspects, we also proposed a process as activity simulation-mapping-evaluation-visualization to apply the framework and visualize results. This framework can help planners make an effective first-time response by identifying the most vulnerable areas when a massive power outage happens during natural disasters. It can also be integrated into community resilience analysis models and potentially contributes to effective disaster risk managementComment: to be published in Proceedings of the 5th International Conference on Building Energy and Environmen

Community Time-Activity Trajectory Modelling based on Markov Chain Simulation and Dirichlet Regression

Accurate modeling of human time-activity trajectory is essential to support community resilience and emergency response strategies such as daily energy planning and urban seismic vulnerability assessment. However, existing modeling of time-activity trajectory is only driven by socio-demographic information with identical activity trajectories shared among the same group of people and neglects the influence of the environment. To further improve human time-activity trajectory modeling, this paper constructs community time-activity trajectory and analyzes how social-demographic and built environment influence people s activity trajectory based on Markov Chains and Dirichlet Regression. We use the New York area as a case study and gather data from American Time Use Survey, Policy Map, and the New York City Energy & Water Performance Map to evaluate the proposed method. To validate the regression model, Box s M Test and T-test are performed with 80% data training the model and the left 20% as the test sample. The modeling results align well with the actual human behavior trajectories, demonstrating the effectiveness of the proposed method. It also shows that both social-demographic and built environment factors will significantly impact a community's time-activity trajectory. Specifically, 1) Diversity and median age both have a significant influence on the proportion of time people assign to education activity. 2) Transportation condition affects people s activity trajectory in the way that longer commute time decreases the proportion of biological activity (eg. sleeping and eating) and increases people s working time. 3) Residential density affects almost all activities with a significant p-value for all biological needs, household management, working, education, and personal preference.Comment: to be published in Computers, Environment and Urban Syste

Discrete element method to study biofilm deformation in fluid flow

Ph. D. Thesis.Biofilms are the assemblage of one or more types of microorganisms, which are usually found attached and grew on surfaces, embedded in their extracellular polymeric substances (EPS). They could form diverse morphologies to adapt to different environments, especially in a flow system such as water filtration. Hydrodynamic conditions have a significant impact on the deformation and detachment of biofilm, which has been primarily investigated by the experiments. However, relevant modelling research is lacking. Therefore, the individual based model (IbM) is adopted to study the biofilm-fluid interaction in present work. In the first part of this work, the discrete element method was utilized to simulate the biofilm growth, deformation and detachment, where the fluid was mimicked by applying a simple shear force. Due to the fact that the biofilms would also affect the flow pattern in return, the simply one-way approach was then extended to a two-way coupled computational fluid dynamic – discrete element method (CFD-DEM) model. Biofilm deformation and detachment was investigated at varied inlet flow velocity. We have also studied the effect of the EPS content on the deformation and detachment of biofilms. Furthermore, the strain-stress curves during biofilm deformation have been captured by loading and unloading the fluid shear stress. Biofilm streamer (filamentous structure of biofilm) motion under different flow conditions is important for a wide range of industries as well. The flow-induced oscillations and cohesive failure of single and multiple biofilm streamers have been investigated based on the CFD-DEM model. In this section, we have studied the effect of streamer length on the oscillation at varied flow rates. The predicted single biofilm streamer oscillations in various flow rates agreed well with experimental measurements. We have also investigated the effect of the spatial arrangement of streamers on interactions between two oscillating streamers in parallel and tandem arrangements. Besides, cohesive failure of streamers was studied in an accelerating fluid flow, which is important for slowing down biofilm induced cloggingEPSRC, BBSR

Study on the Mechanical Cumulative Damage Model of Slope Fault Fracture Zone under the Cumulative Effect of Blasting Vibration

As for the slope with fault fracture zone, the fault fracture zone is the main sliding surface, whose shear strength parameter is the main calculation parameter of landslide occurrence. In this paper, shaking table model tests and damage theory were used to study the change of shear strength and mechanical cumulative damage model of fault fracture zone under the blasting vibration cyclic load. At first, the slope of Daye Iron Mine is selected as a case to study the shear strength weakening law of fault fracture zone by the similarity theory and the principle of the orthogonal test, in which the influence of the characteristics of vibration loading on the shear strength parameters of fault fracture zone with different thicknesses was studied. Secondly, by the assumption of Lemaitre strain equivalence and according to the extreme value characteristics of the normal stress-shear stress curve, the damage theory model of the fault fracture zone was reconstructed, and the microelement of fault was selected for analysis and divided into two parts, including damaged and undamaged materials. Finally, the results of the shaking table model tests were compared with the results of the shear cumulative damage model to verify the rationality of the theoretical model. Moreover, the predicted results of the theoretical model can better reflect the degradation trend of the fault fracture zone with the loading amplitude, normal stress, and loading times. It can be used as a reference for slope stability prediction under the action of cumulative static and dynamic loads

Evaluation of the differences of myocardial fibers between acute and chronic myocardial infarction: Application of diffusion tensor magnetic resonance imaging in a rhesus monkey model

Objective: To understand microstructural changes after myocardial infarction (MI), we evaluated myocardial fibers of rhesus monkeys during acute or chronic MI, and identified the differences of myocardial fibers between acute and chronic MI. Materials and Methods: Six fixed hearts of rhesus monkeys with left anterior descending coronary artery ligation for 1 hour or 84 days were scanned by diffusion tensor magnetic resonance imaging (MRI) to measure apparent diffusion coefficient (ADC), fractional anisotropy (FA) and helix angle (HA). Results: Comparing with acute MI monkeys (FA: 0.59 +/- 0.02; ADC: 5.0 +/- 0.6 x 10(-4) mm(2)/s; HA: 94.5 +/- 4.4 degrees), chronic MI monkeys showed remarkably decreased FA value (0.26 +/- 0.03), increased ADC value (7.8 +/- 0.8 x 10(-4)mm(2)/s), decreased HA transmural range (49.5 +/- 4.6 degrees) and serious defects on endocardium in infarcted regions. The HA in infarcted regions shifted to more components of negative left-handed helix in chronic MI monkeys (-38.3 +/- 5.0 degrees-11.2 +/- 4.3 degrees) than in acute MI monkeys (-41.4 +/- 5.1 degrees-53.1 +/- 3.7 degrees), but the HA in remote regions shifted to more components of positive right-handed helix in chronic MI monkeys (-43.8 +/- 2.7 degrees-66.5 +/- 4.9 degrees) than in acute MI monkeys (-59.5 +/- 3.4 degrees-64.9 +/- 4.3 degrees). Conclusion: Diffusion tensor MRI method helps to quantify differences of mechanical microstructure and water diffusion of myocardial fibers between acute and chronic MI monkey's models.National Natural Science Foundation of China [81130027, 81301196]SCI(E)[email protected]

Advanced Volleyball Stats for All Levels: Automatic Setting Tactic Detection and Classification with a Single Camera

This paper presents PathFinder and PathFinderPlus, two novel end-to-end computer vision frameworks designed specifically for advanced setting strategy classification in volleyball matches from a single camera view. Our frameworks combine setting ball trajectory recognition with a novel set trajectory classifier to generate comprehensive and advanced statistical data. This approach offers a fresh perspective for in-game analysis and surpasses the current level of granularity in volleyball statistics. In comparison to existing methods used in our baseline PathFinder framework, our proposed ball trajectory detection methodology in PathFinderPlus exhibits superior performance for classifying setting tactics under various game conditions. This robustness is particularly advantageous in handling complex game situations and accommodating different camera angles. Additionally, our study introduces an innovative algorithm for automatic identification of the opposing team's right-side (opposite) hitter's current row (front or back) during gameplay, providing critical insights for tactical analysis. The successful demonstration of our single-camera system's feasibility and benefits makes high-level technical analysis accessible to volleyball enthusiasts of all skill levels and resource availability. Furthermore, the computational efficiency of our system allows for real-time deployment, enabling in-game strategy analysis and on-the-spot gameplan adjustments.Comment: ICDM workshop 202