On the estimation of persistence intensity functions and linear representations of persistence diagrams

The prevailing statistical approach to analyzing persistence diagrams is concerned with filtering out topological noise. In this paper, we adopt a different viewpoint and aim at estimating the actual distribution of a random persistence diagram, which captures both topological signal and noise. To that effect, Chazel and Divol (2019) proved that, under general conditions, the expected value of a random persistence diagram is a measure admitting a Lebesgue density, called the persistence intensity function. In this paper, we are concerned with estimating the persistence intensity function and a novel, normalized version of it -- called the persistence density function. We present a class of kernel-based estimators based on an i.i.d. sample of persistence diagrams and derive estimation rates in the supremum norm. As a direct corollary, we obtain uniform consistency rates for estimating linear representations of persistence diagrams, including Betti numbers and persistence surfaces. Interestingly, the persistence density function delivers stronger statistical guarantees

Displacement and Deformation of the First Tunnel Lining During the Second Tunnel Construction

A three-dimensional twin tunnels scale model was established utilizing the discrete element method (DEM) with PFC3D. This model aims to investigate the displacement (in horizontal and vertical directions) and deformation of the first tunnel lining in four different cases which the clear distance of twin tunnels are 5, 10, 15 and 20 m during the second tunnel construction process. The numerical results indicate that the clear distance between twin tunnels and the distance between the measurement points of the first tunnel and the excavation area of the second tunnel are two most critical factors that influence the displacement and deformation of the first tunnel lining. Meanwhile, the soil arching effect, gravity, water pressure and lateral pressure also have an impact on the behavior of the first tunnel. The maximum disturbance of horizontal and vertical displacements occurred in the time points of finishing of the second tunnel. However, the horizontal displacement of the first tunnel is much more sensitive to the vertical displacement. The first tunnel turns to the right and down in direction while having an anticlockwise rotation (φ) during the process of construction of the second tunnel. In addition, the displacement and deformation of the lining of the first tunnel are critical to monitor, and the necessary precautions should be taken to decrease the risk of craze. In conclusion, the influence of the second tunnel excavation on the first tunnel lining could be neglected when their distance is more than 15 m

Sharp high-probability sample complexities for policy evaluation with linear function approximation

This paper is concerned with the problem of policy evaluation with linear function approximation in discounted infinite horizon Markov decision processes. We investigate the sample complexities required to guarantee a predefined estimation error of the best linear coefficients for two widely-used policy evaluation algorithms: the temporal difference (TD) learning algorithm and the two-timescale linear TD with gradient correction (TDC) algorithm. In both the on-policy setting, where observations are generated from the target policy, and the off-policy setting, where samples are drawn from a behavior policy potentially different from the target policy, we establish the first sample complexity bound with high-probability convergence guarantee that attains the optimal dependence on the tolerance level. We also exhihit an explicit dependence on problem-related quantities, and show in the on-policy setting that our upper bound matches the minimax lower bound on crucial problem parameters, including the choice of the feature maps and the problem dimension.Comment: The first two authors contributed equall

Discrete element modeling of vibration compaction effect of the vibratory roller in roundtrips on gravels

This paper aims to study the vibration compaction mechanism of the vibratory roller on gravels using a two-dimensional discrete element method. The roadbed model was established by gravel particles with irregular shapes, which was closer to reality. The performance parameters of the vibratory roller, such as operating frequency and rolling velocity, were investigated to explore their influences on the operating efficiency of the vibratory roller in roundtrips. The frequencies of 15 Hz and 17 Hz were proved to be the optimal frequency and resonance frequency in the current simulations, respectively. The vibratory roller could achieve a better vibration compaction effect with less power consumption at the optimal frequency. In addition, the number of roundtrips and power consumption should be considered in the selection of the optimal rolling velocity. The movement direction and the contact force distribution of gravels were illustrated by the displacement field, velocity field, as well as the contact force chains. Our results provide a better understanding of the mechanical behavior of gravel particles and their interactions with the vibratory roller

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6′-O-galloylpaeoniflorin (GPF), a galloylated derivative of paeoniflorin isolated from peony root, has been proven to possess antioxidant potential. In this present study, we revealed that GPF treatment exerted significant neuroprotection of PC12 cells following OGD, as evidenced by a reduction of oxidative stress, inflammatory response, cellular injury, and apoptosis in vitro. Furthermore, treatment with GPF increased the levels of phosphorylated Akt (p-Akt) and nuclear factor-erythroid 2-related factor 2 (Nrf2), as well as promoted Nrf2 translocation in PC12 cells, which could be inhibited by Ly294002, an inhibitor of phosphoinositide 3-kinase (PI3K). In addition, Nrf2 knockdown or Ly294002 treatment significantly attenuated the antioxidant, anti-inflammatory, and antiapoptotic activities of GPF in vitro. In vivo studies indicated that GPF treatment significantly reduced infarct volume and improved neurological deficits in rats subjected to CIRI, as well as decreased oxidative stress, inflammation, and apoptosis, which could be inhibited by administration of Ly294002. In conclusion, these results revealed that GPF possesses neuroprotective effects against oxidative stress, inflammation, and apoptosis after ischemia-reperfusion insult via activation of the PI3K/Akt/Nrf2 pathway

Predictive model for inflammation grades of chronic hepatitis B: Large‐scale analysis of clinical parameters and gene expressions

BackgroundLiver biopsy is the gold standard to assess pathological features (eg inflammation grades) for hepatitis B virus‐infected patients although it is invasive and traumatic; meanwhile, several gene profiles of chronic hepatitis B (CHB) have been separately described in relatively small hepatitis B virus (HBV)‐infected samples. We aimed to analyse correlations among inflammation grades, gene expressions and clinical parameters (serum alanine amino transaminase, aspartate amino transaminase and HBV‐DNA) in large‐scale CHB samples and to predict inflammation grades by using clinical parameters and/or gene expressions.MethodsWe analysed gene expressions with three clinical parameters in 122 CHB samples by an improved regression model. Principal component analysis and machine‐learning methods including Random Forest, K‐nearest neighbour and support vector machine were used for analysis and further diagnosis models. Six normal samples were conducted to validate the predictive model.ResultsSignificant genes related to clinical parameters were found enriching in the immune system, interferon‐stimulated, regulation of cytokine production, anti‐apoptosis, and etc. A panel of these genes with clinical parameters can effectively predict binary classifications of inflammation grade (area under the ROC curve [AUC]: 0.88, 95% confidence interval [CI]: 0.77‐0.93), validated by normal samples. A panel with only clinical parameters was also valuable (AUC: 0.78, 95% CI: 0.65‐0.86), indicating that liquid biopsy method for detecting the pathology of CHB is possible.ConclusionsThis is the first study to systematically elucidate the relationships among gene expressions, clinical parameters and pathological inflammation grades in CHB, and to build models predicting inflammation grades by gene expressions and/or clinical parameters as well.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139116/1/liv13427.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139116/2/liv13427_am.pd

DEM study of the shear behavior and formation of shear band in biaxial test

International audienc

Influence of Temperature Effects on CPT in Granular Soils by Discrete Element Modeling in 3D

This study employs a 3D discrete element method (DEM) to simulate cone penetration tests (CPTs) in granular soils, taking into account the effect of temperature. A coupled thermal mechanical model is developed to allow for heat transfer and storage in the granular materials. The CPT simulations are conducted on granular samples prepared at various temperatures, with the specific heat and velocity of thermal conductivity being identified as two critical factors that influence sample heating time. Additionally, the thermal expansion coefficient is a crucial parameter that is closely related to the porosity of the sample. As the sample temperature increases, the particles expand, resulting in an increase in cone resistance