Elena De Angelis

GENERALIZED KINETIC (BOLTZMANN) MODELS: MATHEMATICAL STRUCTURES AND APPLICATIONS

This paper deals with the development of suitable general mathematical structures including a large variety of Boltzmann type models. The contents are organized in three parts. The first part is devoted to modeling the above general framework. The second part to the development of specific models of interest in applied sciences. The third part develops a critical analysis towards research perspectives both on modeling and analytic problems.

Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy

This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analyzed. Moreover, this paper deals with the modeling and optimization of therapeutical actions. The aim of the critical analysis and review consists in providing the background framework towards the development of research perspectives in this promising new field of applied mathematics.

FROM THE MODELING OF THE IMMUNE HALLMARKS OF CANCER TO A BLACK SWAN IN BIOLOGY

This paper deals with the modeling of the early stage of cancer phenomena, namely mutations, onset, progression of cancer cells, and their competition with the immune system. The mathematical approach is based on the kinetic theory of active particles developed to describe the dynamics of large systems of interacting cells, called active particles. Their microscopic state is modeled by a scalar variable which expresses the main biological function. The modeling focuses on an interpretation of the immune-hallmarks of cancer.

QUALITATIVE ANALYSIS OF A MEAN FIELD MODEL OF TUMOR-IMMUNE SYSTEM COMPETITION

This paper deals with the qualitative analysis of a model related to the immune response to the evolution of the progression of endothelial cells which have lost their differentiation and start their evolution toward methastatic states. We prove the existence of solutions to the Cauchy problem related to the model. The asymptotic behavior in time of our solutions is also investigated.

Modeling of the immune response: conceptual frameworks and applications

This paper deals with the modelling of the immune response to the evolution of the progression of endothelial cells which have lost their differentiation and start their evolution toward methastatic states. The aim of this paper is to design a general mathematical framework toward modelling the so-called kinetic cellular theory. Some specific models are proposed within the above framework and suitable simulations are developed with special attention to bifurcation analysis.

On the kinetic theory for active particles: A model for tumor-immune system competition

This paper deals with the qualitative analysis of a model describing the competition between tumor and immune cells. Such competition is characterized by proliferation-destruction phenomena and the interacting entities are characterized by a microscopic state which is modified by interactions. The model also includes the description of the natural trend of immune cells to reach a healthy or sentinel level, even when they have been involved in the competition with the tumor cells. The model is developed in the mathematical framework of the kinetic theory for active particles.

On the mathematical theory of post-Darwinian mutations, selection, and evolution

This paper is devoted to the modeling, qualitative analysis and simulation of Darwinian selection phenomena and their evolution. The approach takes advantage of the mathematical tools of the kinetic theory of active particles which are applied to describe the selective dynamics of evolution processes. The first part of the paper focuses on a mathematical theory that has been developed to describe mutations and selection processes. The second part deals with different modeling strategies and looks ahead to research perspectives.

Generalized kinetic models in applied sciences : lecture notes on mathematical problem

From the Boltzmann Equation to the Averaged Boltzmann Equation - On the Cauchy Problem for the Averaged Boltzmann Equation - Asymptotic Theory for the Averaged Boltzmann Equation - Kinetic (Boltzmann) Models: Modeling and Analytic Problems - Critical Analysis and Research Perspectives

Use Case II: Imaging Biomarkers and New Trends for Integrated Glioblastoma Management

Glioblastoma (GB) implies a devastating prognosis with an average survival of 14–16 months using the current standard of care treatment [1]. GB is the most frequent malignant tumour originating from the brain parenchyma, and it is characterised by a marked intratumoural heterogeneity, proneness to infiltrate throughout the brain parenchyma, robust angiogenesis and necrosis as well as intense resistance to apoptosis and genomic instability.

Preface [Special issue on Towards a Mathematical Description of Cancer: Analytical, Numerical and Modelling Aspects]

Optical, infrared, and radio astronomies are the historical pillars of astrophysics. They are continuing to contribute a large part of the astrophysical information and are the prerequisite for observations with highenergy information carrier. The investigation of the astrophysical properties of the targets triggers the building of the large observational facilities and shapes their characteristics. The textbook is organized from the point of view of the science targets, tackling optical, infrared, and radio astronomies as scientific research areas. In place of presenting the observational techniques and showing how they could be used in different domains of the electromagnetic spectrum, the textbook is focused on the science targets and the measurement of their fluxes and spectra, providing a link between observational techniques and astrophysical science. The textbook has grown up out of several years of teaching the courses of astrophysical techniques to graduate students at the University of Pisa who were specializing in astrophysics. The text shows the state of the art and the future evolution of instrumentation and observational methods. The aim of the work is to be a comprehensive guide through the steps needed to acquire and analyze optical, infrared, and radio data: planning the observation, choosing the signal-to-noise ratio, selecting a telescope or radio telescope with the suitable instrumentation to observe the selected object at the proper epoch, performing the observations, securing the calibration data, and extracting the astrophysical information as fluxes or spectra. Thus, for each astronomy research area investigated in the book, the relevant orders of magnitudes are firstly presented. Then, the physical principles of the telescopes, the detectors, and the components needed for flux and spectra measurements are discussed. The signal-to-noise ratio of the observations and the limits of instrumentation are discussed in detail in view of writing proposals for telescope observing time. Finally, the data analysis techniques are presented. The bibliography at the end of each chapter suggests monographs of interest for the reader. Web links are provided for the instrumentation. The first part of the textbook is devoted to the basics of astronomical observations: the electromagnetic radiation and its interactions, the effect of the atmosphere on observations, and the observational windows (Chap. 1). Then, the ingredients