Meta-heuristic algorithms play an important role in the optimization field thanks to their robustness and programming simplicity. Many meta-heuristic methods have been devised in recent years. ...Inspired by nature, they usually simulate natural or human-specific phenomena in a better way. A large amount of them are based on complicated behaviors requiring several implementation steps and algorithm-specific control parameters, which impedes users and limits solutions to different types of optimization problems. Hence, designing effective simple and parameter-free optimization methods attracts much attention. In this paper, we propose a novel population-based optimization algorithm based on balancing composite motions (BCMO). The core idea is balancing composite motion properties of individuals in solution space. Equalizing global and local searches via a probabilistic selection model creates a movement mechanism of each individual. Four test suites selected in the literature, which vary from numerical benchmarks to practical problems, to demonstrate the performance of BCMO include: (1) 23 classical benchmark functions, (2) CEC 2005 benchmark functions, (3) CEC 2014 benchmark functions, and (4) 3 real engineering design problems. The statistical results reveal the promising performance and application of BCMO in a variety of optimization and practical problems with constrained and unknown search spaces.
This paper is devoted to the study of solutions with critical regularity for the two-dimensional Muskat equation. We prove that the Cauchy problem is well-posed on the endpoint Sobolev space of
L
2
...functions with three-half derivative in
L
2
. This result is optimal with respect to the scaling of the equation. One well-known difficulty is that one cannot define a flow map such that the lifespan is bounded from below on bounded subsets of this critical Sobolev space. To overcome this, we estimate the solutions for a norm which depends on the initial data themselves, using the weighted fractional Laplacians introduced in our previous works. Our proof is the first in which a null-type structure is identified for the Muskat equation, allowing to compensate for the degeneracy of the parabolic behavior for large slopes.
Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a highly pathogenic virus that has caused the global COVID-19 pandemic. Tracing the evolution and transmission of the virus is crucial ...to respond to and control the pandemic through appropriate intervention strategies. This paper reports and analyses genomic mutations in the coding regions of SARS-CoV-2 and their probable protein secondary structure and solvent accessibility changes, which are predicted using deep learning models. Prediction results suggest that mutation D614G in the virus spike protein, which has attracted much attention from researchers, is unlikely to make changes in protein secondary structure and relative solvent accessibility. Based on 6324 viral genome sequences, we create a spreadsheet dataset of point mutations that can facilitate the investigation of SARS-CoV-2 in many perspectives, especially in tracing the evolution and worldwide spread of the virus. Our analysis results also show that coding genes E, M, ORF6, ORF7a, ORF7b and ORF10 are most stable, potentially suitable to be targeted for vaccine and drug development.
In this note we study advection-diffusion equations associated to incompressible
W
1
,
p
velocity fields with
p
>
2
. We present new estimates on the energy dissipation rate and we discuss ...applications to the study of upper bounds on the enhanced dissipation rate, lower bounds on the
L
2
norm of the density, and quantitative vanishing viscosity estimates. The key tools employed in our argument are a propagation of regularity result, coming from the study of transport equations, and a new result connecting the energy dissipation rate to regularity estimates for transport equations. Eventually we provide examples which underline the sharpness of our estimates.
Local and global pointwise gradient estimates are obtained for solutions to the quasilinear elliptic equation with measure data −div(A(x,∇u))=μ in a bounded and possibly nonsmooth domain Ω in Rn. ...Here div(A(x,∇u)) is modeled after the p-Laplacian. Our results extend earlier known results to the singular case in which 3n−22n−1<p≤2−1n.
Weighted good-
λ
type inequalities and Muckenhoupt–Wheeden type bounds are obtained for gradients of solutions to a class of quasilinear elliptic equations with measure data. Such results are ...obtained globally over sufficiently flat domains in
R
n
in the sense of Reifenberg. The principal operator here is modeled after the
p
-Laplacian, where for the first time singular case
3
n
-
2
2
n
-
1
<
p
≤
2
-
1
n
is considered. Those bounds lead to useful compactness criteria for solution sets of quasilinear elliptic equations with measure data. As an application, sharp existence results and sharp bounds on the size of removable singular sets are deduced for a quasilinear Riccati type equation having a gradient source term with linear or super-linear power growth.
Comparison estimates are an important technical device in the study of regularity problems for quasilinear possibly degenerate elliptic and parabolic equations. Such tools have been employed ...indispensably in the papers of Mingione, Duzaar–Mingione, and Kuusi–Mingione, etc. on certain measure datum problems to obtain pointwise bounds for solutions and their full or fractional derivatives in terms of appropriate linear or nonlinear potentials. However, a comparison estimate for
p
-Laplace type elliptic equations with measure data is still unavailable in the strongly singular case
1
<
p
≦
3
n
-
2
2
n
-
1
, where
n
≧
2
is the dimension of the ambient space. This issue will be completely resolved in this work by proving a comparison estimate in a slightly larger range
1
<
p
<
3
/
2
. Applications include a ‘sublinear’ Poincaré type inequality, pointwise bounds for solutions and their derivatives by Wolff’s and Riesz’s potentials, respectively. Some global pointwise and weighted estimates are also obtained for bounded domains, which enable us to treat a quasilinear Riccati type equation with possibly sublinear growth in the gradient.
This article is devoted to the study of the Cauchy problem for the Muskat equation. We consider initial data belonging to the critical Sobolev space of functions with three-half derivative in L
2
, ...up to a fractional logarithmic correction. As a corollary, we obtain the first local and global well-posedness results for initial free surfaces which are not Lipschitz.
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