Some Notes about Inference for the Lognormal Diffusion Process with Exogenous Factors

Different versions of the lognormal diffusion process with exogenous factors have been used in recent years to model and study the behavior of phenomena following a given growth curve. In each case considered, the estimation of the model has been addressed, generally by maximum likelihood (ML), as has been the study of several characteristics associated with the type of curve considered. For this process, a unified version of the ML estimation problem is presented, including how to obtain estimation errors and asymptotic confidence intervals for parametric functions when no explicit expression is available for the estimators of the parameters of the model. The Gompertz-type diffusion process is used here to illustrate the application of the methodology.This work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain, under Grants MTM2014-58061-P and MTM2017-85568-P

A hyperbolastic type-I diffusion process: Parameter estimation by means of the firefly algorithm

A stochastic diffusion process, whose mean function is a hyperbolastic curve of type I, is presented. The main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered. To this end, the firefly metaheuristic optimization algorithm is applied after bounding the parametric space by a stagewise procedure. Some examples based on simulated sample paths and real data illustrate this development

Statistical analysis and first-passage-time applications of a lognormal diffusion process with multi-sigmoidal logistic mean

We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary.Universita degli Studi di Salerno within the CRUI-CARE Agreemen

Hyperbolastic type-III diffusion process: Obtaining from the generalized Weibull diffusion process

The modeling of growth phenomena has become a matter of great interest in many different fields of application and research. New stochastic models have been developed, and others have been updated to this end. The present paper introduces a diffusion process whose main characteristic is that its mean function belongs to a wide family of curves derived from the classic Weibull curve. The main characteristics of the process are described and, as a particular case, a di usion process is considered whose mean function is the hyperbolastic curve of type III, which has proven useful in the study of cell growth phenomena. By studying its estimation we are able to describe the behavior of such growth patterns. This work considers the problem of the maximum likelihood estimation of the parameters of the process, including strategies to obtain initial solutions for the system of equations that must be solved. Some examples are provided based on simulated sample paths and real data to illustrate the development carried out.This work was supported in part by the Ministerio de Economía, Industria y Competitividad, Spain, under Grant MTM2017-85568-P

Bootstrap Resampling in Gompertz Growth Model with Levenberg–Marquardt Iteration

Soybean plants have limited growth with a planting period of 12 weeks, which causes the observed sample to be very small. A small sample of soybean plant growth observations can be bias causes in the conclusion of prediction results on soybean plant growth. The  purpose this study is to apply  the bootstrap resampling technique in Gompertz growth model which overcomes residual distribution with small samples, the research data was taken from soybean plant growth in four varieties with four spacing treatments, five replications and twelve weeks (long planting period).   Gompertz growth model uses nonlinear least squares method in estimating parameters with Levenberg–Marquardt iteration. The value of the Gompertz model after resampling bootstrap has no significant difference. The adjusted R2 value of 0.96 is close to 1. This means that the total diversity of plant heights can be explained by the Gompertz model of 96 percent. Judging from the graph of predictions of soybean plant growth before resampling and after resampling coincide with each other it can also be seen in the initial growth values before resampling 14, 05 and 14.18, the maximum growth values are 55.13 and 55.60. Bootsrap resampling technique can overcome residual normality in the Gompertz growth model, but does not change the information in the initial data

Study of a general growth model

We discuss a general growth curve including several parameters, whose choice leads to a variety of models including the classical cases of Malthusian, Richards, Gompertz, Logistic and some their generalizations. The advantage is to obtain a single mathematically tractable equation from which the main characteristics of the considered curves can be deduced. We focus on the effects of the involved parameters through both analytical results and computational evaluations

Modeling Tumor Clonal Evolution for Drug Combinations Design

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure toward drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review we discuss the promising opportunities that these interdisciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.David H. Koch Cancer Research Fund (Grant P30-CA14051)National Cancer Institute (U.S.). Integrative Cancer Biology Program (Grant U54-CA112967)National Institute of General Medical Sciences (U.S.). Interdepartmental Biotechnology Training Program (5T32GM008334

The Amarna South Tombs Cemetery: Biocultural Dynamics of a Disembedded Capital City in New Kingdom Egypt

abstract: The Egyptian New Kingdom city of Akhetaten (modern: Tell el-Amarna, el-Amarna, or simply Amarna) provides a unique opportunity to study ancient biocultural dynamics. It was a disembedded capital removed from the major power bases of Memphis and Thebes that was built, occupied, and abandoned within approximately 20 years (c. 1352–1336 BCE). This dissertation used the recently excavated Amarna South Tombs cemetery to test competing models for the development of disembedded capitals, such as the geographic origin of its migrants and its demographic structure in comparison to contrastive models for the establishment of settlements. The degree to which biological relatedness organized the South Tombs cemetery was also explored. The results suggest that the Nile Valley into the New Kingdom (1539–1186 BCE) was very diverse in dental cervical phenotype and thus highly mobile in respects to gene flow, failing to reject that the Amarna city was populated by individuals and families throughout the Nile Valley. In comparison, the Amarna South Tombs cemetery contained the least amount of dental phenotypic diversity, supporting a founder effect due to migration from larger, more diverse gene pools to the city or the very fact that the city and sample only reflect a 20-year interval with little time to accumulate phenotypic variation. Parts of the South Tombs cemetery also appear to be organized by biological affinity, showing consistent and significant spatial autocorrelation with biological distances generated from dental cervical measurements in male, female, and subadult (10–19 years of age) burials closest to the South Tombs. This arrangement mimics the same orderliness in the residential areas of the Amarna city itself with officials surrounded by families that supported their administration. Throughout the cemetery, adult female grave shaft distances predict their biological distances, signaling a nuclear family dynamic that included many females including mothers, widows, and unwed aunts, nieces, and daughters. A sophisticated paleodemographic model using simulated annealing optimization projected the living population of the South Tombs cemetery, which overall conformed to a transplanted community similar to 19th century mill villages of the United States and United Kingdom.Dissertation/ThesisDoctoral Dissertation Anthropology 201

Toward an Ising Model of Cancer and Beyond

Theoretical and computational tools that can be used in the clinic to predict neoplastic progression and propose individualized optimal treatment strategies to control cancer growth is desired. To develop such a predictive model, one must account for the complex mechanisms involved in tumor growth. Here we review resarch work that we have done toward the development of an "Ising model" of cancer. The review begins with a description of a minimalist four-dimensional (three in space and one in time) cellular automaton (CA) model of cancer in which healthy cells transition between states (proliferative, hypoxic, and necrotic) according to simple local rules and their present states, which can viewed as a stripped-down Ising model of cancer. This model is applied to model the growth of glioblastoma multiforme, the most malignant of brain cancers. This is followed by a discussion of the extension of the model to study the effect on the tumor dynamics and geometry of a mutated subpopulation. A discussion of how tumor growth is affected by chemotherapeutic treatment is then described. How angiogenesis as well as the heterogeneous and confined environment in which a tumor grows is incorporated in the CA model is discussed. The characterization of the level of organization of the invasive network around a solid tumor using spanning trees is subsequently described. Then, we describe open problems and future promising avenues for future research, including the need to develop better molecular-based models that incorporate the true heterogeneous environment over wide range of length and time scales (via imaging data), cell motility, oncogenes, tumor suppressor genes and cell-cell communication. The need to bring to bear the powerful machinery of the theory of heterogeneous media to better understand the behavior of cancer in its microenvironment is presented.Comment: 55 pages, 21 figures and 3 tables. To appear in Physical Biology. Added reference

Catalysts and Processes for H2S Conversion to Sulfur

Today, more stringent regulations on SOx emissions and growing environmental concerns have led to considerable attention on sulfur recovery from hydrogen sulfide (H2S). Hydrogen sulfide is commonly found in raw natural gas and biogas, even if a great amount is obtained through sweetening of sour natural gas and hydrodesulphurization of light hydrocarbons. It is highly toxic, extremely corrosive and flammable, and for these reasons, its elimination is necessary prior to emission in atmosphere. There are different technologies for the removal of H2S, the drawbacks of which are the high costs and limited H2S conversion efficiency. The main focus of this Special Issue will be on catalytic oxidation processes, but the issue is devoted to the development of catalysts able to maximize H2S conversion to sulfur minimizing SO2 formation, pursuing the goal of “zero SO2 emission”.This Special Issue is particularly devoted to the preparation of novel powdered/structured supported catalysts and their physical–chemical characterization, the study of the aspects concerning stability and reusability, as well as the phenomena that could underlie the deactivation of the catalyst.This Special Issue comprises seven articles, one communication, and one review regarding the desulfurization of sour gases and fuel oil, as well as the synthesis of novel adsorbents and catalysts for H2S abatement. In the following, a brief description of the papers included in this issue is provided to serve as an outline to encourage further reading