Sparse Density Estimation with Measurement Errors

This paper aims to estimate an unknown density of the data with measurement errors as a linear combination of functions from a dictionary. The main novelty is the proposal and investigation of the corrected sparse density estimator (CSDE). Inspired by the penalization approach, we propose the weighted Elastic-net penalized minimal ℓ2-distance method for sparse coefficients estimation, where the adaptive weights come from sharp concentration inequalities. The first-order conditions holding a high probability obtain the optimal weighted tuning parameters. Under local coherence or minimal eigenvalue assumptions, non-asymptotic oracle inequalities are derived. These theoretical results are transposed to obtain the support recovery with a high probability. Some numerical experiments for discrete and continuous distributions confirm the significant improvement obtained by our procedure when compared with other conventional approaches. Finally, the application is performed in a meteorology dataset. It shows that our method has potency and superiority in detecting multi-mode density shapes compared with other conventional approaches.

A computational model of mutual antagonism in the mechano-signaling network of RhoA and nitric oxide

Background RhoA is a master regulator of cytoskeletal contractility, while nitric oxide (NO) is a master regulator of relaxation, e.g., vasodilation. There are multiple forms of cross-talk between the RhoA/ROCK pathway and the eNOS/NO/cGMP pathway, but previous work has not studied their interplay at a systems level. Literature review suggests that the majority of their cross-talk interactions are antagonistic, which motivates us to ask whether the RhoA and NO pathways exhibit mutual antagonism in vitro, and if so, to seek the theoretical implications of their mutual antagonism. Results Experiments found mutual antagonism between RhoA and NO in epithelial cells. Since mutual antagonism is a common motif for bistability, we sought to explore through theoretical simulations whether the RhoA-NO network is capable of bistability. Qualitative modeling showed that there are parameters that can cause bistable switching in the RhoA-NO network, and that the robustness of the bistability would be increased by positive feedback between RhoA and mechanical tension. Conclusions We conclude that the RhoA-NO bistability is robust enough in silico to warrant the investment of further experimental testing. Tension-dependent bistability has the potential to create sharp concentration gradients, which could contribute to the localization and self-organization of signaling domains during cytoskeletal remodeling and cell migration.

FALL3D-8.0: a computational model for atmospheric transport and deposition of particles, aerosols and radionuclides – Part 1: Model physics and numerics

This paper presents FALL3D-8.0, the last version release of an open-source code with 15+ years of track record and a growing number of users in the volcanological and atmospheric communities. The code has been redesigned and rewritten from scratch in the framework of the EU Centre of Excellence for Exascale in Solid Earth (ChEESE) in order to overcome legacy issues and allow for successive optimisations in the preparation of the code towards extreme-scale computing. However, this baseline version already contains substantial improvements in terms of model physics, solving algorithms, and code accuracy and performance. The code, originally conceived for atmospheric dispersal and deposition of tephra particles, has been extended to model other types of particles, aerosols and radionuclides. The solving strategy has also been changed, replacing the former central-difference scheme for a high-resolution central-upwind scheme derived from finite volumes, which minimises numerical diffusion even in the presence of sharp concentration gradients and discontinuities. The parallelisation strategy, input/output (I/O), model pre-process workflows and memory management have also been reconsidered, leading to substantial improvements on code scalability, efficiency and overall capability to handle much larger problems. All these new features and improvements have implications on operational model performance and allow, among others, adding data assimilation and ensemble forecast in future releases. This paper details the FALL3D-8.0 model physics and the numerical implementation of the code.

FALL3D-8.0: a computational model for atmospheric transport and deposition of particles, aerosols and radionuclides. Part I: model physics and numerics

This manuscript presents FALL3D-8.0, the last version release of an open-source code with 15+ years of track record and a growing number of users in the volcanological and atmospheric communities. The code has been redesigned and rewritten from scratch in the framework of the EU Center of Excellence for Exascale in Solid Earth (ChEESE) in order to overcome legacy issues and allow for successive optimisations that are already planned in the preparation of the code towards extreme-scale computing. However, this baseline version already contains substantial improvements in terms of model physics, solving algorithms, and code accuracy and performance. The code, originally conceived for atmospheric dispersal and deposition of tephra particles, has been extended to model other types of particles, aerosols and radionuclides. The solving strategy has also been changed, replacing the former central-differences scheme for a high-resolution central-upwind scheme derived from finite volumes, which minimises numerical diffusion even in presence of sharp concentration gradients and discontinuities. The parallelisation strategy, Input/Output (I/O), model pre-process workflows and memory management have also been reconsidered, leading to substantial improvements on code scalability, efficiency, and overall capability to handle much larger problems. This paper details the FALL3D-8.0 model physics and the numerical implementation of the code.

Laboratory and Computational Fluid Dynamics Investigation of Homogenization in a Tank Stirred by External Pump

The scope of this study was to investigate the homogenization of a two-layer stratified liquid in a tank where liquid stirring was achieved by carrying out external recirculation. Furthermore, the aim of the research was to observe the effect of the height of the outlet during the time of mixing one. The experimental fluid was two-layer, density stratified liquid. From the perspective of homogeneity, the effect of the height of the outlet was investigated in laboratory. Moreover, the experimental device was modeled in CFD. In simulation examination, laminar - and k-ε-model were used, and the influence of the outlet position was observed. The difference was remarkable in the first part of the measurement caused by the presence of sharp concentration variation in the tank. After the operating time, the expected homogeneity was fulfilled at the outlet in all cases. Regarding of CFD research, the results suggest that the laminar model is more effective to describe the concentration changes at the sampling point in the tank investigated.

Sharp concentration of the equitable chromatic number of dense random graphs

An equitable colouring of a graph G is a vertex colouring where no two adjacent vertices are coloured the same and, additionally, the colour class sizes differ by at most 1. The equitable chromatic number χ=(G) is the minimum number of colours required for this. We study the equitable chromatic number of the dense random graph ${\mathcal{G}(n,m)}$ where $m = \left\lfloor {p\left( \matrix{ n \cr 2 \cr} \right)} \right\rfloor $ and 0 < p < 0.86 is constant. It is a well-known question of Bollobás [3] whether for p = 1/2 there is a function f(n) → ∞ such that, for any sequence of intervals of length f(n), the normal chromatic number of ${\mathcal{G}(n,m)}$ lies outside the intervals with probability at least 1/2 if n is large enough. Bollobás proposes that this is likely to hold for f(n) = log n. We show that for the equitable chromatic number, the answer to the analogous question is negative. In fact, there is a subsequence ${({n_j})_j}_{ \in {\mathbb {N}}}$ of the integers where $\chi_=({\mathcal{G}(n_j,m_j)})$ is concentrated on exactly one explicitly known value. This constitutes surprisingly narrow concentration since in this range the equitable chromatic number, like the normal chromatic number, is rather large in absolute value, namely asymptotically equal to n/(2logbn) where b = 1/(1 − p).

Study of Pollutant Transport in Environmental Flows Using Depth-Averaged Random Walk Method

A depth-averaged random walk scheme is applied to investigate the process of solute transport, including advection, diffusions and reaction. Firstly, the model is used to solve an instantaneous release problem in a uniform flow, for which analytical solutions exist. Its performance is examined by comparing numerical predictions with analytical solutions. The advantage of the random walk model includes high accuracy and small numerical diffusion. Extensive parametric studies are carried out to investigate the sensitivity of the predictions to the number of particles. The result reveals that the particle number influences the accuracy of the model significantly. Finally, the model is applied to track a pollutant cloud in the Thames Estuary, where the domain geometry and bed elevation are complex. The present model is free of fictitious oscillations close to sharp concentration gradients and displays encouraging efficiency and accuracy in solving the solute transport problems in a natural aquatic environment.

Sharpened Adams Inequality and Ground State Solutions to the Bi-Laplacian Equation in ℝ4

In this paper, we establish a sharp concentration-compactness principle associated with the singular Adams inequality on the second-order Sobolev spaces in{\mathbb{R}^{4}}. We also give a new Sobolev compact embedding which states{W^{2,2}(\mathbb{R}^{4})}is compactly embedded into{L^{p}(\mathbb{R}^{4},|x|^{-\beta}\,dx)}for{p\geq 2}and{0<\beta<4}. As applications, we establish the existence of ground state solutions to the following bi-Laplacian equation with critical nonlinearity:\displaystyle\Delta^{2}u+V(x)u=\frac{f(x,u)}{|x|^{\beta}}\quad\mbox{in }% \mathbb{R}^{4},where{V(x)}has a positive lower bound and{f(x,t)}behaves like{\exp(\alpha|t|^{2})}as{t\to+\infty}. In the case{\beta=0}, because of the loss of Sobolev compact embedding, we use the principle of symmetric criticality to obtain the existence of ground state solutions by assuming{f(x,t)}and{V(x)}are radial with respect toxand{f(x,t)=o(t)}as{t\rightarrow 0}.