Introduction The prognosis for cervical cancer (CC) patients with lymph node metastasis (LNM) is extremely poor. Lipid droplets (LDs) have a pivotal role in promoting tumor metastasis. The crosstalk mechanism between LDs and LNM modulated in CC remains largely unknown. Objectives This study aimed to construct a miRNA-dependent progonostic model for CC patients and investigate whether miR-532-5p has

Introduction The Gross-Pitaevskii equation is a class of the nonlinear Schrödinger equation, whose exact solution, especially soliton solution, is proposed for understanding and studying Bose-Einstein condensate and some nonlinear phenomena occurring in the intersection field of Bose-Einstein condensate with some other fields. It is an important subject to investigate their exact solutions. Objectives

Response to Letter to the Editor: Zhang, J. (2021). The American Statistician. Accepted .

Background Recent research on the implications of gut microbiota on brain functions has helped to gather important information on the relationship between them. Pathogenesis of neurological disorders is found to be associated with dysregulation of gut-brain axis. Some gut bacteria metabolites are found to be directly associated with the increase in reactive oxygen species levels, one of the most important

Introduction Fusarium graminearum is a most destructive fungal pathogen that causes Fusarium head blight (FHB) disease in cereal crops, resulting severe yield loss and mycotoxin contamination in food and feed. Silver nanoparticles (AgNPs) are extensively applied in multiple fields due to their strong antimicrobial activity and are considered alternatives to fungicides. However, the antifungal mechanisms

We derive a continuous-time lace expansion for a broad class of self-interacting continuous-time random walks. Our expansion applies when the self-interaction is a sufficiently nice function of the local time of a continuous-time random walk. As a special case we obtain a continuous-time lace expansion for a class of spin systems that admit continuous-time random walk representations.

Introduction Refractive stromal lenticules from Small Incision Lenticule Extraction (SMILE), though usually discarded, hold a potential for various ophthalmic applications, including refractive correction, stromal volume expansion, and biomechanical strengthening of the cornea. Purpose To investigate the effect of lenticule customization on lenticule neurite length profile and the excitatory response

Abstract We improve students’ understanding of the F-test for linear hypotheses in a linear model by explaining elements that affect the power of the test. Including true restrictions in a joint null hypothesis affects test power in a way that is not generally known. Asking a student whether including the true restrictions from the null hypothesis will increase or decrease power, the student is likely

Introduction Cocaine use disorder (CUD) is a significant public health issue without a current specific approved treatment. Among different approaches to this malady, it is possible to highlight a promising immunologic strategy in which an immunogenic agents may reduce the reinforcing effects of the drug if they are able to yield sufficient specific antibodies capable to bind cocaine and/or its psychoactive

Letter to the Editor: Zhang, J. (2021), “The Mean Relative Entropy: An Invariant Measure of Estimation Error,” The American Statistician, 75, 117-123:comment by Vos and Wu. The American Statistician. Accepted 29 August 2021.

Introduction Alzheimer’s disease (AD) is a progressive brain disorder, and one of the most common causes of dementia and amnesia. Due to the complex pathogenesis of AD, the underlying mechanisms remain unclear. Although scientists have made increasing efforts to develop drugs for AD, no effective therapeutic agents have been found. Objectives Natural products and their constituents have shown promise

In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity k should display a power spectrum along an inertial range contained in the viscous-convective range of the fluid model. This prediction has been extensively tested, both experimentally and numerically, and is a core prediction of passive scalar turbulence.

Introduction The transplantation of mesenchymal stem cells (MSCs) in patients with premature ovarian failure (POF) could lead to clinical improvement. The transplantation to the ovaries among other transplantation methods have been reported in various animal models, however, there is little evidence regarding the optimal method, including the clinical safety and the efficiency for the treatment of

Abstract Rank-based methods are frequently used in the life sciences, and in the empirical sciences in general. Among the best-known examples of nonparametric rank-based tests are the Wilcoxon-Mann-Whitney test and the Kruskal-Wallis test. However, recently, potential pitfalls and paradoxical results pertaining to the use of traditional rank-based procedures for more than two samples have been highlighted

Abstract In an observational study, to investigate the treatment effect, one common strategy is to match the control subjects to the treated subjects. The outcomes between the two groups are then compared after the treatment-control match. However, when the outcome is rare, detection of an outcome difference can be challenging. An alternative approach is to compare the treatment or exposure discrepancy

Abstract We propose a single loop diagram and use it to devise a single loop matrix method to computationally solve the Penney-Ante game. This method avoids the nuances of repeated use of conditional probability and Markov chain representations. We remove the limitations of Conway’s trick as applied to a fair coin and generalize the method where the coin is allowed to be biased. A uniform random number

Soap films at equilibrium are modeled, rather than as surfaces, as regions of small total volume through the introduction of a capillarity problem with a homotopic spanning condition. This point of view introduces a length scale in the classical Plateau's problem, which is in turn recovered in the vanishing volume limit. This approximation of area minimizing hypersurfaces leads to an energy based selection

We study the semiclassical limit of the sine-Gordon (sG) equation with below threshold pure impulse initial data of Klaus-Shaw type. The Whitham averaged approximation of this system exhibits a gradient catastrophe in finite time. In accordance with a conjecture of Dubrovin, Grava, and Klein, we found that in a neighborhood near the gradient catastrophe point, the asymptotics of the sG solution are

Neurons compute by integrating spatiotemporal excitatory (E) and inhibitory (I) synaptic inputs received from the dendrites. The investigation of dendritic integration is crucial for understanding neuronal information processing. Yet quantitative rules of dendritic integration and their mathematical modeling remain to be fully elucidated. Here neuronal dendritic integration is investigated by using

Background Increasing crop production to feed a growing population has driven the use of mineral fertilizers to ensure nutrients availability and fertility of agricultural soils. After nitrogen, phosphorus (P) is the second most important nutrient for plant growth and productivity. However, P availability in most agricultural soils is often limited because P strongly binds to soil particles and divalent

Our first main result is that correlations between monomers in the dimer model in do not decay to 0 when . This is the first rigorous result about correlations in the dimer model in dimensions greater than 2 and shows that the model behaves drastically differently than in two dimensions, in which case it is integrable and correlations are known to decay to zero polynomially. Such a result is implied

Background Although the synthetic vitamin D analogue, Paricalcitol, and omega-3 Fatty acids (ω-3) alleviated diabetic nephropathy (DN), their combination was not previously explored. Objectives This study measured the potential ameliorative effects of single and dual therapies of Paricalcitol and/or ω-3 against DN. Methods Forty rats were assigned as follow: negative (NC) and positive (PC) controls

A matrix is diagonalizable if it has a basis of linearly independent eigenvectors. Since the set of nondiagonalizable matrices has measure zero, every is the limit of diagonalizable matrices. We prove a quantitative version of this fact conjectured by E. B. Davies: for each , every matrix is at least -close to one whose eigenvectors have condition number at worst , for some depending only on n. We

Background Organophosphorus pesticides (OPs), as insecticides or acaricides, are widely used in agricultural products to ensure agricultural production. However, widespread use of OPs leads to environmental contamination and significant negative consequences on biodiversity, food security, and water resources. Therefore, developing a sensitive and rapid method to determine OPs residues in different

For solar-driven water splitting, a molybdenum oxysulphide-cobalt phosphate (MoOxSy-CoPi) photocatalyst is produced from ammonium heptamolybdate, thiourea, and metallic cobalt. The most conspicuous feature is the conformal growth of MoOxSy-CoPi nanoflowers, as observed under FE-SEM and HR-TEM. The surface analysis exposed nanoflowers like encrusted structures, with single-layer thickness up to ∼10

Abstract Motivated by the goal of evaluating real-time forecasts of home team win probabilities in the National Basketball Association, we develop new tools for measuring the quality of continuously updated probabilistic forecasts. This includes introducing calibration surface plots, and simple graphical summaries of them, to evaluate at a glance whether a given continuously updated probability forecasting

(2021). Reviewof Books and Teaching Materials. The American Statistician: Vol. 75, No. 3, pp. 354-354.

Abstract The spread of COVID-19 in the US prompted non-pharmaceutical interventions which caused a reduction in mobility everywhere, although with large disparities between different counties. Using a Bayesian spatial modeling framework, we investigated the association of county-level demographic and socioeconomic factors with changes in workplace mobility at two points in time: during the early stages

SIAM Review, Volume 63, Issue 3, Page 641-650, January 2021. The majority of books in this issue are devoted to modeling in one form or another. The featured review by Thomas Wick discusses a new book by an internationally renowned expert in the field of numerical modeling. It is the book A Primer on Mathematical Modelling, by Alfio Quarteroni and Paola Gervasio. Wick talks enthusiastically about the

SIAM Review, Volume 63, Issue 3, Page 625-637, January 2021. For students in applied mathematics courses, the phenomenon of delay-induced stability and instability offers exciting educational opportunities. Exploration of the onset of instability in delay differential equations (DDEs) invites a blend of analysis (real, complex, and functional), algebra, and computational methods. Moreover, stabilization

SIAM Review, Volume 63, Issue 3, Page 585-624, January 2021. The high speed of $x_{k}\rightarrow x^\ast\in{\mathbb R}$ is usually measured using the $C$-, $Q$-, or $R$-orders: \[ łim \tfrac |x^\ast - x_k+1||x^\ast - x_k|^p_0\in(0,+\infty), łim \tfrac łn |x^\ast - x_k+1|łn |x^\ast - x_k| =q_0, or łim \bigěrtłn |x^\ast - x_k| \big ěrt ^\frac1k =r_0. \] By connecting them to the natural, term-by-term

SIAM Review, Volume 63, Issue 3, Page 583-583, January 2021. The Education section in this issue contains two papers. The first paper, “How Many Steps Still Left to ${x}^*$?,” is written by Emil Cătinaş. This is an important question for everyone who works with numerical methods. One could compare two convergent sequences and analyze which one would get closer to its limit in a given number of steps

SIAM Review, Volume 63, Issue 3, Page 559-582, January 2021. We present a randomized method for computing the min-plus product (a.k.a. tropical product) of two $n \times n$ matrices, yielding a faster algorithm for solving the all-pairs shortest path problem (APSP) in dense $n$-node directed graphs with arbitrary edge weights. In the real random-access machine model, where additions and comparisons

SIAM Review, Volume 63, Issue 3, Page 557-557, January 2021. The SIGEST article in this issue is “From Circuit Complexity to Faster All-Pairs Shortest Paths,” by R. Ryan Williams. The original paper appeared in SIAM Journal on Computing (SICOMP) in 2018 and, as indicated by the high citation count, ideas from this work have inspired a broad range of future activity. For a given $n$-node graph, the

SIAM Review, Volume 63, Issue 3, Page 525-555, January 2021. The determination of the mean first passage time (MFPT) for a Brownian particle in a bounded 2-D domain containing small absorbing traps is a fundamental problem with biophysical applications. The average MFPT is the expected capture time assuming a uniform distribution of starting points for the random walk. We develop a hybrid asymptotic-numerical

SIAM Review, Volume 63, Issue 3, Page 489-524, January 2021. Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. The algorithm can achieve arbitrarily high orders of convergence in terms of a smoothing parameter for computing spectral measures of general differential, integral, and lattice operators

SIAM Review, Volume 63, Issue 3, Page 487-487, January 2021. The first of our two Research Spotlights articles in this issue gives a general framework and corresponding algorithm for computing accurate approximations to the spectral measures of self-adjoint operators, the key to which is the resolvent of the operator. As authors Matthew Colbrook, Andrew Horning, and Alex Townsend detail, the spectral

SIAM Review, Volume 63, Issue 3, Page 435-485, January 2021. Complex systems, composed at the most basic level of units and their interactions, describe phenomena in a wide variety of domains, from neuroscience to computer science and economics. The wide variety of applications has resulted in two key challenges: the generation of many domain-specific strategies for complex systems analyses that are

SIAM Review, Volume 63, Issue 3, Page 433-433, January 2021. Our Survey and Review paper, “The Why, How, and When of Representations for Complex Systems,” by Leo Torres, Ann S. Blevins, Danielle Bassett, and Tina Eliassi-Rad, lists 233 references. Some of them were published in applied mathematics journals, like SIAM Review or SIAM Journal on Applied Algebra and Geometry. Others appeared in well-known

Introduction Biochar utilization for adsorption seems to be the most cost-effective, easy/ fast approach for pollutants removal from water and wastewater. Due to the high adsorption properties, magnetic biochar proved to be efficient in the sorption of heavy metals and nutrients. Although there are several studies on development of magnetic biochars, there is a lack of research on development of high-performance

Numerical homogenization is a methodology for the computational solution of multiscale partial differential equations. It aims at reducing complex large-scale problems to simplified numerical models valid on some target scale of interest, thereby accounting for the impact of features on smaller scales that are otherwise not resolved. While constructive approaches in the mathematical theory of homogenization

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture

In the past decade the mathematical theory of machine learning has lagged far behind the triumphs of deep neural networks on practical challenges. However, the gap between theory and practice is gradually starting to close. In this paper I will attempt to assemble some pieces of the remarkable and still incomplete mathematical mosaic emerging from the efforts to understand the foundations of deep learning

We present an overviewof the basic theory, modern optimal transportation extensions and recent algorithmic advances. Selected modelling and numerical applications illustrate the impact of optimal transportation in numerical analysis.

Neural networks (NNs) are the method of choice for building learning algorithms. They are now being investigated for other numerical tasks such as solving high-dimensional partial differential equations. Their popularity stems from their empirical success on several challenging learning problems (computer chess/Go, autonomous navigation, face recognition). However, most scholars agree that a convincing

This article addresses the inference of physics models from data, from the perspectives of inverse problems and model reduction. These fields develop formulations that integrate data into physics-based models while exploiting the fact that many mathematical models of natural and engineered systems exhibit an intrinsically low-dimensional solution manifold. In inverse problems, we seek to infer uncertain

The notion of a tensor captures three great ideas: equivariance, multilinearity, separability. But trying to be three things at once makes the notion difficult to understand. We will explain tensors in an accessible and elementary way through the lens of linear algebra and numerical linear algebra, elucidated with examples from computational and applied mathematics.

Liquid crystals are a type of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the past four decades, which is of great importance for fundamental scientific research and has widespread applications in industry. In this paper we review the mathematical models and their connections to liquid crystals, and

In the presence of vacuum, the physical entropy for polytropic gases behave singularly, and it is thus a challenge to study its dynamics. It is shown in this paper that the boundedness of the entropy can be propagated up to any finite time provided that the initial vacuum presents only at far fields with sufficiently slow decay of the initial density. More precisely, for the Cauchy problem of the one-dimensional