text large_stringlengths 7 3.02k |
|---|
This note is concerned with Strichartz estimates for the wave equation and orthonormal families of initial data. We provide a survey of the known results and present what seems to be a reasonable conjecture regarding the cases which have been left open. |
We prove stability results in hypercontractivity estimates for the Hopf--Lax semigroup in $\mathbb R^n$ and apply them to deduce stability results for the Euclidean $L^p$-logarithmic Sobolev inequality for any $p>1$. As a main tool, we use recent stability results for the Prékopa--Leindler inequality, due to Böröcz... |
In this work, we employ the $\bar{\partial}$ steepest descent method in order to study the Cauchy problem of the cgNLS equations with initial conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})=\{f\in L^{2}(\mathbb{R}): f',xf\in L^{2}(\mathbb{R})\}$. The large time asymptotic behavior of the solution $u(x,t)... |
We prove a general multiplier theorem for symmetric left-invariant sub-Laplacians with drift on non-compact Lie groups. This considerably improves and extends a result by Hebisch, Mauceri, and Meda. |
This is the first of two papers devoted to the study of the properties of the blow-up surface for the $N$ dimensional semilinear wave equation with subconformal power nonlinearity. In a series of papers, we have clarified the situation in one space dimension. |
We prove that standing-waves solutions to the non-linear Schrödinger equation in dimension one whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and non-degenerate, provided the non-linear term $ G $ satisfies a Euler differential inequality. When the non-linear term $ G $ is a... |
The dynamics of waves in periodic media is determined by the band structure of the underlying periodic Hamiltonian. Symmetries of the Hamiltonian can give rise to novel properties of the band structure. |
In the present work, we adopt the idea of velocity averaging lemma to establish regularity for stationary linearized Boltzmann equations in a bounded convex domain. Considering the incoming data, with three iterations, we establish regularity in fractional Sobolev space in space variable up to order $1^-$. |
We introduce an abstract setting that allows to discuss wave equations with time-dependent boundary conditions by means of operator matrices. We show that such problems are well-posed if and only if certain perturbations of the same problems with homogeneous, time-independent boundary conditions are well-posed. |
In this paper we investigate the existence of positive solutions to the following Schrödinger-Poisson-Slater system [c]{ll} - \Delta u+ u + \lambda\phi u=|u|^{p-2}u & \text{in} \Omega -\Delta\phi= u^{2} & \text{in} \Omega u=\phi=0 & \text{on} \partial\Omega. where $\Omega$ is a bounded domain in $\mathbf{R... |
The Degasperis-Procesi equation is the integrable Camassa-Holm-type model which is an asymptotic approximation for the unidirectional propagation of shallow water waves. This work establishes the orbital stability of localized smooth solitary waves to the Desgasperis-Procesi (DP) equation on the real line. |
The $L^{p}$ theory for non-isentropic Navier-Stokes equations governing compressible viscous and heat-conductive gases is not yet proved completely so far, because the critical regularity cannot control all non linear coupling terms. In this paper, we pose an additional regularity assumption of low frequencies in $\ma... |
Liouville theorems for scaling invariant nonlinear elliptic systems (saying that the system does not possess nontrivial entire solutions) guarantee a priori estimates of solutions of related, more general systems. Assume that $p=2q+3>1$ is Sobolev subritical, $n\le3$ and $\beta\in{\mathbb R}$. |
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lemaître-Robertson-Walker spacetimes. For the case of accelerated expansion, we show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of th... |
We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the power of the nonlinearity, and the decay rate of the initial data at the spati... |
This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are mis-cible, the mixture is subjected to a non-symmetric constraint on the volume. |
We study partial Hölder regularity for nonlinear elliptic systems in divergence form with double-phase growth, modeling double-phase non-Newtonian fluids in the stationary case. |
We revisit the properties of Bessel-Riesz operators and refine the proof of the boundedness of these operators on generalized Morrey spaces using Young's inequality. We also obtain an estimate for the norm of these operators on generalized Morrey spaces. |
We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the velocity field. |
Given a nonnegative, smooth potential $V: \mathbb{R}^k \to \mathbb{R}$ ($k \geq 2$) with multiple zeros, we say that a curve $\mathfrak{q}: \mathbb{R} \to \mathbb{R}^k$ is a connecting orbit if it solves the autonomous system of ordinary differential equations \begin{equation} \mathfrak{q}''= \nabla_{\mathbf{u}... |
In this paper, we study the nonexistence of positive solutions for the following two mixed boundary value problems. The first problem is the mixed nonlinear-Neumann boundary value problem $$ \left\{ <br>\begin{array}{ll} <br>\displaystyle -\Delta u=f(u) &{\rm in}\quad \R, \\ \displaystyle \\ \frac{\partial u}{\par... |
Parabolic partial differential equations with state-dependent delays (SDDs) are investigated. The delay term presented by Stieltjes integral simultaneously includes discrete and distributed SDDs. |
In this paper we study localization properties of the Riesz $s$-fractional gradient $D^s u$ of a vectorial function $u$ as $s \nearrow 1$. The natural space to work with $s$-fractional gradients is the Bessel space $H^{s,p}$ for $0 < s < 1$ and $1 < p < \infty$. |
We study the class of nonlinear Klein-Gordon-Maxwell systems describing a standing wave (charged matter field) in equilibrium with a purely electrostatic field. We improve some previous existence results in the case of an homogeneous nonlinearity. |
In this paper, we are concerned with the local exact relationship for third-order structure functions in the temperature equation, the inviscid MHD equations and the Euler equations in the sense of Duchon-Robert type and Eyink type. It is shown that the local version of Yaglom's $4/3$ law is valid for the dissipat... |
Given $p\in[1,\infty)$ and a bounded open set $\Omega\subset\mathbb R^d$ with Lipschitz boundary, we study the $\Gamma$-convergence of the weighted fractional seminorm \[ [u]_{s,p,f}^p = \int_{\mathbb R^d} \int_{\mathbb R^d} \frac{|\tilde{u} (x)- \tilde{u} |
We consider the problem of determining a polyhedral conductivity inclusion embedded in a homogeneous isotropic medium from boundary measurements. We prove global Lipschitz stability for the polyhedral inclusion from the local Dirichlet-to-Neumann map extending in a highly nontrivial way the results obtained in [18] an... |
Motivated by a study on deception and counter-deception, this paper addresses the problem of identifying an agent's target as it seeks to reach one of two targets in a given environment. In practice, an agent may initially follow a strategy to aim at one target but decide to switch to another midway. |
Background and Objective. With minor differences, most national colorectal cancer (CRC) screening programs in Europe consist of one-size-fits-all aged-based strategies. |
We develop a sparse autologistic model for investigating the impact of diversification and disintermediation strategies in the evolution of financial trading networks. In order to induce sparsity in the model estimates and address substantive questions about the underlying processes the model includes an $L^1$ regular... |
There is increasing evidence that global warming manifests itself in more frequent warm days and that heat waves will become more frequent. Presently, a formal definition of a heat wave is not agreed upon in the literature. |
Introduction: The Oncotype DX (ODX) test is a commercially available molecular test for breast cancer assay that provides prognostic and predictive breast cancer recurrence information for hormone positive, HER2-negative patients. The aim of this study is to propose a novel methodology to assist physicians in their de... |
In this work, we propose a new Bayesian spatial homogeneity pursuit method for survival data under the proportional hazards model to detect spatially clustered patterns in baseline hazard and regression coefficients. Specially, regression coefficients and baseline hazard are assumed to have spatial homogeneity pattern... |
The correct evaluation of the reproductive number $R$ for COVID-19 -- which characterizes the average number of secondary cases generated by each typical primary case -- is central in the quantification of the potential scope of the pandemic and the selection of an appropriate course of action. In most models, $R$ is ... |
The capability of R to do symbolic mathematics is enhanced by the caracas package. This package uses the Python computer algebra library SymPy as a back-end but caracas is tightly integrated in the R environment. |
Changing institution is a scientist's key career decision, which plays an important role in education, scientific productivity, and the generation of scientific knowledge. Yet, our understanding of the factors influencing a relocation decision is very limited. |
Rear-end crashes are one of the most common crash types. Passenger cars involved in rear-end crashes frequently produce severe outcomes. |
Arrivals in queueing systems are typically assumed to be independent and exponentially distributed. Our analysis of an online bookshop, however, shows that there is an autocorrelation structure present. |
A group sequential clinical trial design can be an attractive option when planning a pivotal trial as this approach has the ability to stop the trial early for success, whilst also being well accepted from a regulatory review perspective. Compared to a single stage design there are more moving parts to consider and op... |
Recently learned image compression (LIC) has achieved great progress and even outperformed the traditional approach using DCT or discrete wavelet transform (DWT). However, LIC mainly reduces spatial redundancy in the autoencoder networks and entropy coding, but has not fully removed the frequency-domain correlation ex... |
In this paper, we use a newly constructed dataset to study the geographic distribution of fuel price across the US at a very high resolution. We study the influence of socio-economic variables through different and complementary statistical methods. |
In this paper, we propose a theoretical framework for evaluating psychiatric research strategies. The strategies to be evaluated include a conventional diagnostic category-based approach and dimensional approach that have been encouraged by the National Institute for Mental Health (NIMH), outlined as Research Domain C... |
From the climate system to the effect of the internet on society, chaotic systems appear to have a significant role in our future. Here a method of statistical learning for a class of chaotic systems is described along with underlying theory that can be used not only for predicting those systems a short time ahead, bu... |
Matching and pickup processes are core features of ride-sourcing services. Previous studies have adopted abundant analytical models to depict the two processes and obtain operational insights; while the goodness of fit between models and data was dismissed. |
We consider basket trials in which a biomarker-targeting drug may be efficacious for patients across different disease indications. Patients are enrolled if their cells exhibit some levels of biomarker expression. |
Urban Building Energy Models (UBEM) are vital for enhancing energy efficiency and sustainability in urban planning. However, data scarcity often challenges their validation, particularly the lack of hourly measured data and the variety of building samples. |
Interpretable insights from predictive models remain critical in bio-statistics, particularly when assessing causality, where classical statistical and machine learning methods often provide inherent clarity. While Neural Networks (NNs) offer powerful capabilities for modeling complex biological data, their traditiona... |
Classical time series models have serious difficulties in modeling and forecasting the enormous fluctuations of electricity spot prices. Markov regime switch models belong to the most often used models in the electricity literature. |
Neuroimaging-driven prediction of brain age, defined as the predicted biological age of a subject using only brain imaging data, is an exciting avenue of research. In this work we seek to build models of brain age based on functional connectivity while prioritizing model interpretability and understanding. |
Sparse Bayesian learning (SBL) has emerged as a fast and competitive method to perform sparse processing. The SBL algorithm, which is developed using a Bayesian framework, approximately solves a non-convex optimization problem using fixed point updates. |
Sample size determination for cluster randomised trials (CRTs) is challenging as it requires robust estimation of the intra-cluster correlation coefficient (ICC). Typically, the sample size is chosen to provide a certain level of power to reject the null hypothesis in a hypothesis test. |
The utilization of multi-layer network structures now enables the explanation of complex systems in nature from multiple perspectives. Multi-layer academic networks capture diverse relationships among academic entities, facilitating the study of academic development and the prediction of future directions. |
Genito-Pelvic Pain/Penetration-Disorder (GPPPD) is a common disorder but rarely treated in routine care. Previous research documents that GPPPD symptoms can be treated effectively using internet-based psychological interventions. |
Interferometric phase linking (IPL) has become a prominent technique for processing images of areas containing distributed scaterrers in SAR interferometry. Traditionally, IPL consists in estimating consistent phase differences between all pairs of SAR images in a time series from the sample covariance matrix of pixel... |
We augment linear Support Vector Machine (SVM) classifiers by adding three important features: (i) we introduce a regularization constraint to induce a sparse classifier; |
Waterfall plots are a key tool in early phase oncology clinical studies for visualizing individual patients' tumor size changes and provide efficacy assessment. However, comparing waterfall plots from ongoing studies with limited follow-up to those from completed studies with long follow-up is challenging due to u... |
The interest in "Physically Unclonable Function"-devices has increased rapidly over the last few years, as they have several interesting properties for system security related applications like, for example, the management of cryptographic keys. Unfortunately, the output provided by these devices is noisy and ... |
Recent technological advances have made it possible to simultaneously measure multiple protein activities at the single cell level. With such data collected under different stimulatory or inhibitory conditions, it is possible to infer the causal relationships among proteins from single cell interventional data. |
In a world of utility-driven marketing, each company acts as an adversary to other contenders, with all having competing interests. A major challenge for companies launching a new product is that, despite testing, flaws in their product can remain, potentially risking a loss in market share. |
Random Field Theory has been used in the fMRI literature to address the multiple comparisons problem. The method provides an analytical solution for the computation of precise p-values when its assumptions are met. |
Existing studies show that regulation is a major barrier to global economic integration. Nonetheless, identifying and measuring regulatory barriers remains a challenging task for scholars. |
We investigate the effect that the choice of measurement scale has upon inference and extrapolation in extreme value analysis. Separate analyses of variables from a single process on scales which are linked by a nonlinear transformation may lead to discrepant conclusions concerning the tail behavior of the process. |
Jump stochastic volatility models are central to financial econometrics for volatility forecasting, portfolio risk management, and derivatives pricing. Markov Chain Monte Carlo (MCMC) algorithms are computationally unfeasible for the sequential learning of volatility state variables and parameters, whereby the investo... |
Early detection of person-to-person transmission of emerging infectious diseases such as avian influenza is crucial for containing pandemics. We developed a simple permutation test and its refined version for this purpose. |
Prior to adjustment, accounting conditions between national accounts data sets are frequently violated. Benchmarking is the procedure used by economic agencies to make such data sets consistent. |
Discussion on "Brownian distance covariance" by Gábor J. Székely and Maria L. Rizzo [<a href="https://arxiv.org/abs/1010.0297" data-arxiv-id="1010.0297" class="link-https">arXiv:1010.0297</a>] |
Causal and attribution studies are essential for earth scientific discoveries and critical for informing climate, ecology, and water policies. However, the current generation of methods needs to keep pace with the complexity of scientific and stakeholder challenges and data availability combined with the adequacy of d... |
Aiming at the dilemma that most laboratory data-driven diagnostic and prognostic methods cannot be applied to field batteries in passenger cars and energy storage systems, this paper proposes a method to bridge field data and laboratory data using machine learning. Only two field real impedances corresponding to a med... |
Motivated by the increasing use of and rapid changes in array technologies, we consider the prediction problem of fitting a linear regression relating a continuous outcome $Y$ to a large number of covariates $\mathbf {X}$, for example, measurements from current, state-of-the-art technology. For most of the samples, on... |
One of the challenges in the design of confirmatory trials is to deal with uncertainties regarding the optimal target population for a novel drug. Adaptive enrichment designs (AED) which allow for a data-driven selection of one or more pre-specified biomarker subpopulations at an interim analysis have been proposed in... |
The significance and influence of US Supreme Court majority opinions derive in large part from opinions' roles as precedents for future opinions. A growing body of literature seeks to understand what drives the use of opinions as precedents through the study of Supreme Court case citation patterns. |
Machine learning provides a broad framework for addressing high-dimensional prediction problems in classification and regression. While machine learning is often applied for imaging problems in medical physics, there are many efforts to apply these principles to biological data towards questions of radiation biology. |
Neuroimaging meta-analysis is an important tool for finding consistent effects over studies that each usually have 20 or fewer subjects. Interest in meta-analysis in brain mapping is also driven by a recent focus on so-called "reverse inference": where as traditional "forward inference" identifies the ... |
Whilst evidence-based medicine is the cornerstone of modern practice, it is likely that clinicians are influenced by cultural biases. This work set out to look for evidence of number preference in invasive mechanical ventilatory therapy as a concrete example of subconscious treatment bias. |
Windstorms are a primary natural hazard affecting Europe that are commonly linked to substantial property and infrastructural damage and are responsible for the largest spatially aggregated financial losses. Such extreme winds are typically generated by extratropical cyclone systems originating in the North Atlantic a... |
During the period 1962--1964, I had a tenure track Assistant Professorship in Mathematics at Cornell University in Ithaca, New York, where I did research in probability theory, especially on linear diffusion processes. Being somewhat lonely there and not liking the cold winter weather, I decided around the beginning o... |
Accurately predicting water table dynamics is vital for sustaining groundwater resources that support ecological functions and anthropogenic activities. This study evaluates a statistical model (BigVAR) that handles three major flexibilities: |
Official freely available data about the number of infected at the finest possible level of spatial areal aggregation (Italian provinces) are used to model the spatio-temporal distribution of COVID-19 infections at local level. Data time horizon ranges from 26 February 20020, which is the date when the first case not ... |
The problem of evaluating an individual's risk of drug consumption and misuse is highly important. An online survey methodology was employed to collect data including Big Five personality traits (NEO-FFI-R), impulsivity (BIS-11), sensation seeking (ImpSS), and demographic information. |
A particular focus of water-quality monitoring is the concentrations of sediments and nutrients in rivers, constituents that can smother biota and cause eutrophication. However, the physical and economic constraints of manual sampling prohibit data collection at the frequency required to capture adequately the variati... |
A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly-used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many other approaches, all manner of censored survival times are simultaneously acc... |
Extreme value data with a high clump-at-zero occur in many domains. Moreover, it might happen that the observed data are either truncated below a given threshold and/or might not be reliable enough below that threshold because of the recording devices. |
Background. Several studies have used phylogenetics to investigate Human Immunodeficiency Virus (HIV) transmission among Men who have Sex with Men (MSMs) in Montreal, Quebec, Canada, revealing many transmission clusters. |
In observational studies the assignment of units to treatments is not under control. Consequently, the estimation and comparison of treatment effects based on the empirical distribution of the responses can be biased since the units exposed to the various treatments could differ in important unknown pretreatment chara... |
In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has th... |
Two natural ways of modelling Formula 1 race outcomes are a probabilistic approach, based on the exponential distribution, and econometric modelling of the ranks. Both approaches lead to exactly soluble race-winning probabilities. |
The estimation of missing input vector elements in real time processing applications requires a system that possesses the knowledge of certain characteristics such as correlations between variables, which are inherent in the input space. Computational intelligence techniques and maximum likelihood techniques do posses... |
Forecasts of prospective criminal behavior have long been an important feature of many criminal justice decisions. There is now substantial evidence that machine learning procedures will classify and forecast at least as well, and typically better, than logistic regression, which has to date dominated conventional pra... |
This brief comment reflects on the historical and current uses of the term "snowball sampling. " |
Crime prevention strategies based on early intervention depend on accurate risk assessment instruments for identifying high risk youth. It is important in this context that the instruments be convenient to administer, which means, in particular, that they should also be reasonably brief; adaptive screening tests are u... |
In the domain of Sport Analytics, Global Positioning Systems devices are intensively used as they permit to retrieve players' movements. Team sports' managers and coaches are interested on the relation between players' patterns of movements and team performance, in order to better manage their team. |
Age-specific mortality improvements are non-uniform, neither across ages nor across time. We propose a two-step procedure to estimate the rates of mortality improvement (RMI) in age-specific death rates (ASDR) at ages 85 and above for ten European countries from 1950 to 2019. |
Given the challenges in data acquisition and modeling at the stage of detailed exploration, it is difficult to develop a prospectivity model, particularly for disseminated ore deposits. Recently, the weights of evidence (WofE) method has demonstrated a high efficiency for modeling such deposits. |
The ETS has recently released new estimates of validities of the GRE for predicting cumulative graduate GPA. They average in the middle thirties - twice as high as those previously reported by a number of independent investigators. |
Motivated by the construction of the Itô stochastic integral, we consider a step function method to discretize and simulate volatility modulated Lévy semistationary processes. Moreover, we assess the accuracy of the method with a particular focus on integrating kernels with a singularity at the origin. |
The UK Biobank dataset follows over 500,000 volunteers and contains a diverse set of information related to societal outcomes. Among this vast collection, a large quantity of telemetry collected from wrist-worn accelerometers provides a snapshot of participant activity. |
Large scale disease screening is a complicated process in which high costs must be balanced against pressing public health needs. When the goal is screening for infectious disease, one approach is group testing in which samples are initially tested in pools and individual samples are retested only if the initial poole... |
Which of your team's possible lineups has the best chances against each of your opponents possible lineups? In order to answer this question we develop LinNet. |
Multi-species distribution modeling, which relates the occurrence of multiple species to environmental variables, is an important tool used by ecologists for both predicting the distribution of species in a community and identifying the important variables driving species co-occurrences. Recently, Dunstan, Foster and ... |
Forecasting demand is one of the fundamental components of a successful revenue management system in hospitality. The industry requires understandable models that contribute to adaptability by a revenue management department to make data-driven decisions. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.