Article
Automation & Control Systems
Hamed Taghavian, Ross Drummond, Mikael Johansson
Summary: This paper examines the category of logarithmically completely monotonic (LCM) functions and their importance in characterizing externally positive linear systems. It proposes conditions for ensuring a rational function is LCM, which expands the space of linear continuous-time externally positive systems and allows for the development of an efficient and optimal pole-placement procedure for the monotonic tracking controller synthesis problem. These conditions are less conservative than existing approaches and computationally tractable.
Article
Mathematics, Applied
Khaled Mehrez, Sourav Das
Summary: The main goal of this paper is to introduce new classes of logarithmically completely monotonic functions involving q-gamma function. Applications of these classes are made in establishing new classes of Bernstein functions related to the q-gamma function and dilogarithm, as well as deriving various new sharp bounds for the q-digamma and q-trigamma functions. The results obtained in this work are new and the limiting case q -> 1 leads to new results for a class of Bernstein functions and logarithmically completely monotonic function involving Euler's gamma function and dilogarithm, which are also new in the literature.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Multidisciplinary Sciences
Francesco Mainardi, Enrico Masina, Juan Luis Gonzalez-Santander
Summary: This note proposes an application of the Lambert W function in linear viscoelasticity, specifically in a peculiar creep model with two spectral functions. The conjugate symmetry property of the Lambert W function is found to be essential in calculating these spectral functions. The corresponding relaxation function is computed and the plots of all computed functions are provided.
Article
Mathematics, Applied
Christian Berg, Asena Cetinkaya, Dmitrii Karp
Summary: This paper investigates the conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions, provides necessary and sufficient conditions, and gives new examples of logarithmically completely monotonic gamma ratios. The results are then applied to study monotonicity of some gamma ratios and rational functions.
AEQUATIONES MATHEMATICAE
(2021)
Article
Mathematics
Chin-Yuan Hu, Gwo Dong Lin, Jordan M. Stoyanov
Summary: This study explores power-mixture type functional equations in terms of Laplace-Stieltjes transforms of probability distributions on the right half-line [0,infinity). Necessary and sufficient conditions for unique solutions are provided, with an emphasis on the characterization property of a probability distribution that signifies uniqueness. Results in the realm of compound-exponential and compound-Poisson functional equations are presented, addressing both new findings and improvements of existing knowledge.
Article
Mathematics, Applied
Xifeng Wang, Senlin Guo
Summary: In this article, we establish necessary conditions for sequences to be minimal completely monotonic and present some properties for completely monotonic sequences.
Article
Mathematics
Christian Berg, Henrik L. Pedersen
Summary: This article revisits a family of recently investigated Bernstein functions and identifies those functions with logarithmically completely monotonic derivatives. As a result, a class of Bernstein functions, named Horn-Bernstein functions after Roger A. Horn's findings, is introduced.
EXPERIMENTAL MATHEMATICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Emilia Bazhlekova, Sergey Pshenichnov
Summary: This article considers a class of generalized fractional Zener-type viscoelastic models with general fractional derivatives, and derives two integral representations for the corresponding relaxation modulus. The first representation is established by applying the Laplace transform and using the Bernstein functions technique. The second integral representation is obtained by applying the subordination principle for the relaxation equation with generalized fractional derivatives. Two particular examples of the considered class of models are discussed in more detail, and numerical examples are presented to illustrate the analytical results.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics
Zhong-Xuan Mao, Jing-Feng Tian
Summary: The theory of time scale is proposed to combine continuous and discrete statements. This paper introduces the concepts of complete monotonicity, logarithmic complete monotonicity, and absolute monotonicity of multivariate functions on time scales using the delta derivative. The properties of delta complete monotonicity on time scales are investigated and some judgment rules are presented. The concept of completely monotonic degree of univariate and multivariate functions on time scales is presented to quantitatively measure two delta completely monotonic functions on time scales, and some properties of them are explored.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics, Applied
Emilia Bazhlekova
Summary: This work establishes basic properties of the Prabhakar type generalization of the multinomial Mittag-Leffler function, focusing on complete monotonicity. As particular examples, relaxation functions for equations with multiple time-derivatives in natural and modified forms are studied in detail, and useful estimates are derived. The obtained results extend known properties of the classical Mittag-Leffler function, with Laplace transform and Bernstein functions' technique being the main tools used in this work.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
Article
Mathematics, Applied
Vittoria Bruni, Silvia Marconi, Giuseppina Monteverde, Domenico Vitulano
Summary: This paper investigates the properties of the PRNU pattern noise and aims to define distinctive features for identification of acquisition sensors. The discrimination power of the decreasing rearrangement of a function combined with the Radon transform is studied. Preliminary tests show that the Radon Transform of rearranged Flat Field images alone can accurately characterize each device with high accuracy, showing robustness to standard image modifications and independence of image size.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Li-Chun Liang, Li-Fei Zheng, Aying Wan
Summary: In this article, we investigate the monotonicity of a class of functions and provide inequalities involving polygamma functions and the ratio of gamma functions.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Xiaozhuo Zhang, Zhidong Bai, Jiang Hu
Summary: This paper investigates the limiting spectral distribution and analytic behavior of high-dimensional noncentral Fisher matrices and presents the determination criterion for the support of the limiting spectral distribution.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Feng Qi
Summary: This paper investigates the complete monotonicity of a difference defined by four derivatives of a function containing trigamma function, and presents the necessary and sufficient conditions as well as the proof of logarithmic convexity by applying various techniques.
APPLIED AND COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics
Mansour Mahmoud, Feng Qi
Summary: Motivated by conjectures in a previous paper, the authors bound several completely monotonic degrees of the remainders in the asymptotic expansions of the logarithm of the gamma function and the logarithm of the digamma function.
MATHEMATICAL INEQUALITIES & APPLICATIONS
(2022)
Article
Statistics & Probability
Giulia Carella, Javier Perez Trufero, Miguel Alvarez, Jorge Mateu
Summary: The study found that during the COVID-19 pandemic, counties with wealthier families, lower population density, higher proportion of elderly residents, and lower proportion of Hispanic population experienced larger drops in workplace mobility. In the early stages of the pandemic, socioeconomic and demographic factors explained a significant portion of the variance in mobility changes, but this explanation decreased in the recovery phase.
AMERICAN STATISTICIAN
(2022)
Article
Engineering, Environmental
Julia Calatayud, Marc Jornet, Jorge Mateu
Summary: This study presents a stochastic modeling framework for the incidence of COVID-19 in Castilla-Leon (Spain), taking into account the variability in daily reported cases. The framework utilizes generalized logistic growth curves to model the four waves of the pandemic and infers the probability distributions of the input parameters using a Bayesian bootstrap procedure. Results show that this framework provides a more accurate estimation of COVID-19 cases compared to deterministic formulation.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2022)
Article
Statistics & Probability
Abdollah Jalilian, Jorge Mateu
Summary: This paper introduces a method using deep convolutional neural networks and a Siamese framework to distinguish structural differences between spatial point patterns. The adequacy and generality of this method is demonstrated through simulation study and data analysis.
ADVANCES IN DATA ANALYSIS AND CLASSIFICATION
(2023)
Article
Statistics & Probability
Jiri Dvorak, Tomas Mrkvicka, Jorge Mateu, Jonatan A. Gonzalez
Summary: We investigate a testing method for the hypothesis of independence between a covariate and the marks in a marked point process. We propose to study the complete dependence structure in the triangle points-marks-covariates together and use a new variance correction approach for the tests. Simulation studies and real applications are conducted to demonstrate the performance of the methods.
INTERNATIONAL STATISTICAL REVIEW
(2022)
Article
Social Sciences, Mathematical Methods
Andrea Gilardi, Jorge Mateu, Riccardo Borgoni, Robin Lovelace
Summary: This paper demonstrates a network lattice approach for identifying road segments of particular concern and proposes a novel procedure to investigate the presence of MAUP on a network lattice. The results highlight roads that are more prone to collisions in the north-west and south of the city center.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY
(2022)
Article
Ecology
Carles Mila, Jorge Mateu, Edzer Pebesma, Hanna Meyer
Summary: This study proposes a new cross-validation strategy that takes into account the geographical prediction space and compares it with other established methods. The new method, called NNDM LOO CV, provides reliable estimates in all scenarios considered. The existing methods, LOO and bLOO CV, have limitations and only provide accurate estimates in certain situations. Therefore, considering the geographical prediction space is essential when designing map validation methods.
METHODS IN ECOLOGY AND EVOLUTION
(2022)
Article
Statistics & Probability
Somnath Chaudhuri, Pablo Juan, Jorge Mateu
Summary: Using accident records in an urban environment, this study develops a spatio-temporal model to predict the number of traffic collisions and generate risk maps for the entire road network. The use of SPDE network triangulation to estimate spatial autocorrelation on a linear network is a novel approach. The resulting risk maps offer valuable information for accident prevention and interdisciplinary road safety measures.
JOURNAL OF APPLIED STATISTICS
(2023)
Article
Mathematics
Christian Berg, Ryszard Szwarc
Summary: This paper investigates the closable Hankel forms associated with the moments of a positive measure with infinite support on the real line. It provides a new proof for the closure description based on moment considerations. The main focus is on describing the self-adjoint Hankel operators associated with closed Hankel forms in the Hilbert space of square summable sequences, considering different cases of the moment sequence.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Engineering, Environmental
Julia Calatayud, Marc Jornet, Jorge Mateu
Summary: In this study, we developed and calibrated stochastic continuous models to capture crime dynamics in the city of Valencia, Spain. By decomposing the monthly time series into trend and seasonal components, we modeled the former using geometric Brownian motions and the latter using randomly perturbed sine-cosine waves. The models, although simple, demonstrated high ability to simulate real data and showed promising potential for identifying crimes-interaction and short-term predictive policing.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2023)
Article
Mathematics, Applied
Julia Calatayud, Marc Jornet, Jorge Mateu
Summary: We study the dynamics of abstract models for crime evolution, taking into account participation in crime and incarceration. Individuals transition between three segments, and crime is viewed as a social epidemic. The models incorporate spatial variability using discrete and continuous forms of space, and the effect of the basic reproduction number on the long-term dynamics of crime is examined.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Environmental
Julia Calatayud, Marc Jornet, Jorge Mateu
Summary: We propose a methodology for quantitatively fitting and forecasting real spatio-temporal crime data using stochastic differential equations. The study focuses on Valencia, Spain, using 90247 robbery and theft incidents recorded from the 112-emergency phone over eleven years (2010-2020). The incidents are categorized into 26 zip codes, and monthly crime time series are created for each zip code. By modeling the annual trend components using Ito diffusion with correlated noises, this study can simulate spatio-temporal situations and identify risky areas and periods based on present and past data.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2023)
Article
Engineering, Environmental
Asael Fabian Martinez, Somnath Chaudhuri, Carlos Diaz-Avalos, Pablo Juan, Jorge Mateu, Ramses H. Mena
Summary: An unsupervised classification method is proposed for point events occurring on a geometric network. It utilizes the flexibility and practicality of random partition models to discover clustering structures of observations from a specific phenomenon on a given set of edges. By incorporating spatial effects through a random partition distribution induced by a Dirichlet process, the method offers an appealing clustering approach. A Gibbs sampler algorithm is proposed and evaluated with sensitivity analysis. The analysis of crime and violence patterns in Mexico City serves as the motivation and illustration for this proposal.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2023)
Article
Computer Science, Interdisciplinary Applications
I. Fuentes-Santos, W. Gonzalez-Manteiga, J. Mateu
Summary: This work focuses on kernel estimation of the pair correlation function (PCF) for inhomogeneous spatial point processes. We propose a bootstrap bandwidth selector based on minimizing the mean integrated squared error (MISE). The variance term is estimated by nonparametric bootstrap, and the bias by a plug-in approach using a pilot estimator of the PCF. Kernel estimators of the PCF also require a pilot estimator of the first-order intensity. We test the performance of the bandwidth selector and the role of the pilot intensity estimator in a simulation study. The bootstrap bandwidth selector is competitive with cross-validation procedures, but the contribution of the bandwidth parameter to the goodness-of-fit of the kernel PCF estimator is minor in comparison with that of the pilot intensity function. The data-based kernel intensity estimator leads to biased kernel PCF estimators, while both kernel and parametric covariate-based intensities provide accurate estimators of the PCF.
JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION
(2023)
Article
Social Sciences, Mathematical Methods
Andrea Gilardi, Riccardo Borgoni, Luca Presicce, Jorge Mateu
Summary: In recent years, there have been sophisticated approaches proposed by authors to address road casualties and assist authorities in implementing new policies. These models usually consider socio-economic variables while ignoring the impact of measurement error on statistical inference. This paper presents a Bayesian model that analyzes car crash occurrences at the network-lattice level, accounting for measurement error in spatial covariates. The methodology is demonstrated using collision data from the road network in Leeds (UK) between 2011 and 2019, with traffic volumes approximated from extensive counts collected through mobile devices and adjusted using spatial measurement error correction.
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES A-STATISTICS IN SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Julia Calatayud, Marc Jornet, Jorge Mateu, Carla M. A. Pinto
Summary: This study investigates the infestation of rats and cockroaches in Madrid, Spain using differential equation models. Analyzing incidence and seasonal and weather factors is crucial for intervention strategies. The models can be used to predict future infestation dynamics, guiding health policy measures.
CHAOS SOLITONS & FRACTALS
(2023)
