The task is to develop international research collaborations among different teams, using different approaches and combining state-of-the-art tools. The research is focused on the study of mathematical models subject to the following main fields: Neuroscience, Oncology, Biochemistry ( with specific emphasize to Metabolic processes), Physiology, Clinical Psychopathology. The network has a multidisciplinary character, integrating different approaches. Typically, the research projects are in early stage, most of the projects seem attractive starting points for PhD students, ESR as well as they give possibilities to develop successfully different project phases: research, design, implementation preparation as well as planning for evaluation and impact measurement.

The fields of the research interests of researchers and the researchers involved in supervising PhD students at CIM are presented in

http://www.math.uu.se/cim/Research/

Possible topics that can be proposed to ESR:

• Simulation of the human respiratory system. When patients in intensive care undergo mechanical ventilation, the muscles that drive natural breathing, in particular the diaphragm, are damaged. This is called Ventilator Induced Diaphragmatic Dysfunction (VIDD). By building a numerical model of the respiratory system, we can perform simulations in silico of different interventive measures that can prevent or mitigate the damage caused by ventilation. The mathematical models for the diaphragm are non-linear, involve large displacements, anisotropic materials, and hysteresis effects, and are therefore mathematically and numerically challenging to work with. People involved: Elisabeth Larsson, external collaborators.
• Simulation of viral infections. Organs and other components of the human body typically have irregular geometries that need to be modelled accurately. In this project we propose to use highly accurate meshless methods to simplify accurate modelling of processes in the human body as for example chronic hepatitis infections in the liver, for which there are indications that the geometry plays an important role. Elisabeth Larsson, external and internal collaborators.

Different research projects can be found in the page

https://www.maths.nottingham.ac.uk/postgraduate/projects/

Possible topics that can be proposed to ESR:

• Estimate of HLA distribution and possibility of finding appropriate donor in population.

We propose to develop a model for the population HLA haplotype frequency distribution that incorporates the distribution of the population into sub-populations. We then plan to generate a st ochastic model for the effect of sampling on such populations and the estimate of the probability to find an appropriate match with a full (10/10) HLA compatibility. This model will be validated using extensive data on the outcome of transplantations, and over 18,000,000 sampled HLA haplotypes. The work requires statistical analysis, and stochastic processes.

• Combined epidemiological and genetic model for the spread of viruses.

We will develop in parallel a stochastic spatial and genetic model to study the parallel spread of the viruses in sequences and physical space, to study the emerging combined dynamics. We plan in parallel to sequence viruses from disease spreading in animal and human diseases, and combine this information with spatio-temporal patterns to produce combined genetic-epidemiological model of disease spread. The models and observations will be combined to a Maximum Lilkelihood framework to estimate disease spread parameters.

• Estimate of Time to most recent common ancestor in viral populations.

Genetic diversity grows with the population size in most neutral evolution models. The empirical evidence of large viral populations with limited diversity has been proposed to be either the result of genetic bottlenecks occurring in periods of a smaller population or of selection. Recent estimates of the distribution of the offspring number of each individual virus highlight the possibility that genetic diversity may actually decrease as the population size increases, in both constant and growing population neutral models. We study the possible collapses of the genetic diversity can even under neutral evolution assumptions in large populations. This completely new phenomenon may explain the observed rapid fixation of many viral strains within and between hosts.

1)Modeling the interplay between human behaviour and epidemics

2)Models and algortihms for imaging for Diabetes

3)Methodological issues in epidemiology of diabetes and obesity

The main topics involve: •  C ellular Neural Networks (C NN ) immune response inspired models.

•  Modeling the operation of the inner part of the mammalian retina which is still unknown for neuroscientists. The essence of these models is the representation of the receptive field, or more precisely, the local interaction properties of the neurons. This local interconnectedness is the key element of many sensory organs. A schematic in Figure below shows the general structure with its outputs at the ganglion layer.

• Many organs or parts of the brain, especially the sensing related ones and many cortical areas, have a CNN like architecture. This means that there are a few sheets of two-dimensional strata of neurons, locally connected and/or bus-like connected, as well as mainly locally connected between the strata (e.g. pyramidal cells). This architecture allow us to construct neuromorphic CNN models of different organs .
• Dissipative wave equations with applications in biology. Klein Gordon models in DNA and protein molecules.
• New methods for integration in gene expression (mRNA), variations of DNA (copy number) and next generation NGS with application in cancer imunoteraphy and searching for biomarkers.

Possible topics that can be proposed to ESR:

• Mathematical models of processes in human brain, Mathematical processing of EEG and MEG signals. People involved: Vesela Pasheva, Ivatz Dakov, George Venkov;
• Statistical data processing for tracking the impact of drug treatment. People involved: Krasimira Prodanova;
• Mathematical methods for investigation the air, water and soil pollution and presenting such kind of processes in GIS (geographic information system). People involved: Mosko Aladjem ;
• DNA computing and cryptography. People involved: Ivan Trendafilov, Mariana Durcheva;
• Scattering Theory and Biomedical Engineering. People involved: Iani Arnaudov, George Venkov;

Possible topics that can be proposed to ESR:

• Study of mathematical methods for metabolomic data in patients with diabetes People involved: Ele Ferrannini, Maria Laura Manca.
• Development of multi-objective optimization algorithms for diabetes. People involved. Maria Laura Manca, Ele Ferrannini.

Possible topics that can be proposed to ESR:

• Study of Kuramoto type equations and their implementation in REM NREM cycles in sleep models. Of special importance is the development of models and the collaboration with the Center of Sleep medicine, Pisa. . People involved: Maria Laura Manca, Paolo Acquistapace, Vladimir Georgiev, Annalina Canderolo.
• Mass transportation problems with and without congestion; optimal location problems and detection of targets; ramified structures and their growth. People involved: Giuseppe Buttazzo, Serena Guarino.
• Microscopic stochastic models and the corresponding macroscopic limits, in Mathematical Oncology; specifically, interacting particle systems described by stochastic differential equations, modelling cell dynamic, proliferation, contact and long range interactions, both for tumor in situ and invasive tumors with angiogenic cascade; and the corresponding systems of reaction-diffusion equations, with Fisher-KPP terms and the case of porus media terms for contact interactions. People involved: Franco Flandoli
• Prediction of conformational movements of proteins on the basis ov novel models originating from the optimal mass transportation problems. Prediction of movements of a protein molecule between stable conformation is one of the fundamental tasks of computational proteomics. By now by now many methods are developed which adequately predict such movements on short (e.g. nanoseconds) timescales in absense of external forcing or when the latter may be considered known (in view of the shortness of the timescale), but usually give inadequate results over large timescales (microseconds) when the external forcing field is unpredictable. The idea is to produce a new set of coarse-grain models for conformational movements over large timescale which involve the known chemical and physical constraints on the movement and are based on minimization of special cost functionals resembling those used in Monge-Kantorovich optimal mass transportation theory.People involved: E.Stepanov
• Study of dynamics of protein production in a living cell. The dynamics of protein production is usually described as a system of ordinary differential equations with nonlinear feedbacks determined by gene regulatory networks, and with a small parameter. The asymptotical dynamics of this system seems to be highly nonlocal, and may involve complicated behaviour, like sliding modes (similar to the classical Filippov theory) and also memory effects, and is quite s(List of Publications of Stepanov) imilar to that of hybrid control systems with feedback governed by finite state machines. People involved: E.Stepanov
• Modelling of Drug Resistance in Cancer Therapies. Drug resistance is one of the most problematic complications that can arise during the administration of cancer therapies. A therapy is effective if it significantly reduces the tumour mass. Resistance is usually diagnosed by observing the size of the tumour: when the tumour mass restarts growing it means that a relevant fraction of the tumour cells have become resistant to the therapy, and hence the therapy has to be changed. Early diagnosis of drug resistance is essential. As soon as a few cells become resistant to the administered drug the fate of the therapy is determined. Moreover, continuing with a therapy for which some resistant cells have been originated gives a selective advantage to the drug resistant sub-population thus favouring its growth. Mathematical and computational modelling can have a significant role in early diagnosis and prediction of development of drug resistance. Models of tumour growth, pharmacokinetics and pharmacodynamics can predict the emergence of resistance before tumour re-growth. Moreover, the use of computational modelling and analysis means can allow therapy changes to be evaluated in silico on the basis of patient-specific parameters in order to choose the combination of drugs and the administration schedule that offers the greatest chances of success. The aim of this research is the development of specific modelling methodologies with applications, in particular, to colon and lung cancers. People involved: R. Barbuti and P. Milazzo, in collaboration with Pharmacologists of UNIPI.
• Branching processes and cell division. The cell division phenomenon is typically modelled as a branching process. A branching process starts with one individual in generation 0. This individual produces a random number of individuals for generation 1, the number distributed according to a probability law G. Each individual in generation 1 and all subsequent generations produces offspring independently according to the law G. We shall develop some features of such processes that seem not yet considered in the literature. The expected results will yield the possibility of numerical approximations. We also will explore more complicated situations in which some of the assumptions in the basic model must be relaxed, e.g. age-dependent branching process (in which generation times are assumed to be variable). People involved Rita Giuliano. Relevant literature: (a) Rita Giuliano,Tien-Chung Hu,Andrei Volodin, On a branching model for cell division, preprint (b) Cowan, R. Branching process results in terms of moments of the generation time distribution. Biometrics 41 681-689 (1985).
• Beta densities and bounded noises. Typical bounded noises used in the existing literature on Pharmakokinetics have a stationary beta distribution which is symmetric. Nevertheless, for other kind of problems (not of biological nature) also non-symmetric beta distributions are used. We shall investigate the consequences of using non-symmetric beta distributions in Pharmakokinetics modelling. People involved Rita Giuliano. Relevant literature: (a) A. d'Onofrio, Bounded Noises in Physics, Biology and Engineering (b) MICHAEL R. FLYNN, A Stochastic Differential Equation for Exposure Yields a Beta Distribution, Ann. occup. Hyg., Vol. 48, No. 5, pp. 491??“497, 2004 doi:10.1093/annhyg/meh032 (c) Domingo, D. Bounded Noises: new theoretical developments and applications in Pharmakokinetics, Master's Thesis, University of Pisa.
• Analysis of probabilistic and statistical models for HIV infection. We plan to analyze the mathematical and statistical techniques underlying the models used to understand the population dynamics of not only HIV but also other infectious diseases. People involved Rita Giuliano. Relevant literature: (a) S. Giampiccolo, "ANALISI STATISTICA DI UN MODELLO GAUSSIANO PER LO STUDIO DELL??™INFEZIONE DA HIV" Master's Thesis, University of Pisa. (b) Charles J Mode , Candace K Sleeman Stochastic Processes in Epidemiology HIV/AIDS, Other Infectious Diseases and Computers, World Scientific (2000) (c) A. Sania, D.P. Kroesea, P.K. Polletta, Stochastic models for the spread of HIV in a mobile heterosexual population.
• Study of some delay or memory type dissipative phenomena on the global behaviour of dispersive type problems used in simulation of cancer evolution. People involved: Vladimir Georgiev, Luca Guidi.
• Existence of steady states and their stability for different models in Oncology, Neuroscience. Of special importance is the study (both theoretical and numerical) of steady states associated with Gompertz type nonlinearities having compact support. This phenomena is quite different from the classical notion of stable traveling waves or solitary waves having rapid decay at infinity, but always noncompact support. Therefore, our goal is to study the strong localization effect for the models in oncology and associated free boundary problems in order to obtain stability of the steady states. People involved: Vladimir Georgiev, Marco Ferrigo.