VDPC: Variational Density Peak Clustering Algorithm

<div>Clustering is an important unsupervised knowledge acquisition method, which divides the unlabeled data into different groups \cite{atilgan2021efficient,d2021automatic}. Different clustering algorithms make different assumptions on the cluster formation, thus, most clustering algorithms are able to well handle at least one particular type of data distribution but may not well handle the other types of distributions. For example, K-means identifies convex clusters well \cite{bai2017fast}, and DBSCAN is able to find clusters with similar densities \cite{DBSCAN}. </div><div>Therefore, most clustering methods may not work well on data distribution patterns that are different from the assumptions being made and on a mixture of different distribution patterns. Taking DBSCAN as an example, it is sensitive to the loosely connected points between dense natural clusters as illustrated in Figure~\ref{figconnect}. The density of the connected points shown in Figure~\ref{figconnect} is different from the natural clusters on both ends, however, DBSCAN with fixed global parameter values may wrongly assign these connected points and consider all the data points in Figure~\ref{figconnect} as one big cluster.</div>

VDPC: Variational Density Peak Clustering Algorithm

<div>Clustering is an important unsupervised knowledge acquisition method, which divides the unlabeled data into different groups \cite{atilgan2021efficient,d2021automatic}. Different clustering algorithms make different assumptions on the cluster formation, thus, most clustering algorithms are able to well handle at least one particular type of data distribution but may not well handle the other types of distributions. For example, K-means identifies convex clusters well \cite{bai2017fast}, and DBSCAN is able to find clusters with similar densities \cite{DBSCAN}. </div><div>Therefore, most clustering methods may not work well on data distribution patterns that are different from the assumptions being made and on a mixture of different distribution patterns. Taking DBSCAN as an example, it is sensitive to the loosely connected points between dense natural clusters as illustrated in Figure~\ref{figconnect}. The density of the connected points shown in Figure~\ref{figconnect} is different from the natural clusters on both ends, however, DBSCAN with fixed global parameter values may wrongly assign these connected points and consider all the data points in Figure~\ref{figconnect} as one big cluster.</div>

A model based on a high-resolution flux matrix explains the spread of diseases in a spatial network and the effect of mitigation strategies

Propagation of an epidemic across a spatial network of communities is described by a variant of the SIR model accompanied by an intercommunity infectivity matrix. This matrix is estimated from fluxes between communities, obtained from cell-phone tracking data recorded in the USA between March 2020 and February 2021. We have applied this model to the 2020 dynamics of the SARS-CoV-2 pandemic. We find that the numbers of susceptible and infected individuals predicted by the model agree with the reported cases in each community by fitting just one global parameter representing the frequency of interaction between individuals. The effect of "shelter-in-place" policies introduced across the USA at the onset of the pandemic is clearly seen in our results. We then consider the effect that alternative policies would have had, namely restricting long-range travel. We find that this policy is successful in decreasing the epidemic size and slowing down the spread, at the expense of a substantial restriction on mobility as a function of distance. When long-distance mobility is suppressed, this policy results in a traveling wave of infections, which we characterize analytically. In particular, we show the dependence of the wave velocity and profile on the transmission parameters. Finally, we discuss a policy of selectively constraining travel based on an edge-betweenness criterion.

Which Global Sagittal Parameter Could Most Effectively Predict the Surgical Outcome for Patients With Adult Degenerative Scoliosis?

Study design Retrospective study. Objective To evaluate the predictive effect of the 3 global sagittal parameters (Sagittal Vertical Axis [SVA], T1 Pelvic Angle [TPA], and relative TPA [rTPA]) in the surgical outcome of patients with adult degenerative scoliosis (ADS), then to define the optimum corrective goal based on the best of them. Methods 117 ADS patients were included in this study and followed-up for an average of 3 years. Functional evaluation and radiographs were assessed preoperatively and postoperatively. The predictive accuracy of SVA, TPA, and relative TPA was analyzed through receiver operating characteristic (ROC) curve. The cutoff value of TPA was obtained at the maximal Youden index from ROC curve. Results TPA most highly correlated with postoperative oswestry disability index (ODI). The best cutoff value of TPA was set at 19.3° (area under curve =0.701). TPA >19.3° was the highest risk factor in multivariate logistic regression analysis (OR = 7.124, P = 0.022). Patients with TPA <19.3° at 3 months after operation showed a better ODI than those with TPA >19.3°. Correcting TPA less than 19.3° for patients with preoperative TPA >19.3° attributed to a better health related quality of life (HRQOL) and sagittal balance at last follow-up. The formula “Postoperative TPA = 0.923 × PI - 0.241 × postoperative LL - 0.593 × postoperative SS - 2.471 ( r = 0.914, r2 = 0.836, P < .001)” described the relation between SS, LL, PI, and TPA. Conclusion TPA was a useful global parameter for the prediction of postoperative HRQOL for patients with ADS. Keeping TPA <19.3° could improve the postoperative HRQOL for ADS patients with preoperative TPA >19.3°, and TPA <19.3° could be an optimum correction target for patients with ADS.

Retrieving the leaked signals from noise using a fast dictionary learning method

Most traditional seismic denoising algorithms will cause damages to useful signals, which are visible from the removed noise profiles and are known as signal leakage. The local signal-and-noise orthogonalization method is an effective method for retrieving the leaked signals from the removed noise. Retrieving leaked signals while rejecting the noise is compromised by the smoothing radius parameter in the local orthogonalization method. It is not convenient to adjust the smoothing radius because it is a global parameter while the seismic data is highly variable locally. To retrieve the leaked signals adaptively, we propose a new dictionary learning method. Because of the patch-based nature of the dictionary learning method, it can adapt to the local feature of seismic data. We train a dictionary of atoms that represent the features of the useful signals from the initially denoised data. Based on the learned features, we retrieve the weak leaked signals from the noise via a sparse co ding step. Considering the large computational cost when training a dictionary from high-dimensional seismic data, we leverage a fast dictionary up dating algorithm, where the singular value decomposition (SVD) is replaced via the algebraic mean to update the dictionary atom. We test the performance of the proposed method on several synthetic and field data examples, and compare it with that from the state-of-the-art local orthogonalization method.

A SOLUTION TO STEFAN PROBLEM USING EULERIAN TWO FLUID VOF MODEL

A novel approach for the solution of Stefan problem within the framework of the multi fluid model supplemented with Volume of Fluid (VOF) method, i.e. two-fluid VOF, is presented in this paper. The governing equation set is comprised of mass, momentum and energy conservation equations, written on a per phase basis and supplemented with closure models via the source terms. In our method, the heat and mass transfer is calculated from the heat transfer coefficient, which has a fictitious function and depends on the local cell size and the thermal conductivity, and the implementation is straightforward because of the usage of the local value instead of a global parameter. The interface sharpness is ensured by the application of the geometrical reconstruction scheme implemented in VOF. The model is verified for three types of computational meshes including triangular cells, and good agreement was obtained for the interface position and the temperature field. Although the developed method was validated only for Stefan problem, the application of the method to engineering problems is considered to be straightforward since it is implemented to a commercial CFD code only using a local value; especially in the field of naval hydrodynamics wherein the reduction of ship resistance using boiling flow can be computed efficiently since the method handles phase change processes using low resolution meshes.

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Background It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events. Methods Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence. Results We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age. Conclusions This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

Hybrid Process Models in Electrochemical Syntheses under Deep Uncertainty

Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities.

Effects of Cornell-type scalar potential on a generalized KG-oscillator field in Kaluza–Klein theory

We study a generalized KG-oscillator in the five-dimensional cosmic string geometry background with a magnetic field and quantum flux using Kaluza–Klein theory under the effects of a Cornell-type scalar potential, and observe the gravitational analogue of the Aharonov–Bohm effect. We see that the scalar potential allows the formation of bound states solution, and the energy eigenvalue depends on the global parameter characterizing the space–time. We also see that the magnetic field depends on quantum numbers of the relativistic system which shows a quantum effect.