## Summer School - July 10-16, 2022 - Torgnon

This event is intended for post-docs, PhD or master students, studying mathematics, biology, computer science, engineering, physics and more. Some background knowledge in probability theory is required.

The event will take place at a different venue than the workshop organized the week before by the Politecnico di Torino (more info on the workshop are available at the link above).

## Lecturers

Lea Popovic, Concordia University

## Topic

Stochastic Reaction Networks (SRNs) are mathematical models typically used in system biology, epidemiology, population dynamics, telecommunications, chemistry. In such models, individuals are identical units (e.g. molecules), classified into different groups (e.g. chemical species) and interact through the so-called reactions. The number of available individuals of different groups changes with the occurrence of a reaction. Depending on the applications, reactions could be biochemical transformations (such as protein binding and gene regulation), interactions between animals (such as one predator eating a prey), infection spreading (a susceptible individual can become infected upon contact with another infected individual), etc.
The number of individual of different groups over time is modelled as a stochastic process, specifically as a continuous time Markov chain. A key object in the description and study of the model is the finite graph created by the allowed reactions. Several challenging mathematical issues need to be addressed in applications, such as finding expressions for the stationary behaviour of the system, approximation of complex models (such as metabolic systems), keeping track of spatial diffusion of the individuals.
During the school, a formal and complete introduction to SRNs will be given. Moreover, the following significant contributions to the theory of SRNs will be addressed:
• inference of some qualitative behaviour of the system (like the existence of stable equilibria, or the form of the stationary distribution) from the structural properties of the reaction graph;
• model simulation and approximation of the model trajectories with less computationally expensive ones;
• definition, properties, and simulation of novel models of SRNs that incorporate spatial diffusion and do not assume spatial heterogeneity for the rate of reaction occurrences.

## Program

 Sunday 10 Monday 11 Tuesday 12 Wednesday 13 Thursday 14 Friday 15 Saturday 16 Breakfast Breakfast Breakfast Breakfast Breakfast Breakfast 08:30 10:30 Lecture 08:30 10:30 Lecture 08:30 10:30 Lecture 08:30 10:30 Lecture 08:30 10:30 Lecture 08:30 ShuttleTorgnon > PoliTO 10:30 11:00 Coffee break 10:30 11:00 Coffee break 10:30 11:00 Coffee break 10:30 11:00 Coffee break 10:30 11:00 Coffee break 11:00 13:00 Lecture 11:00 13:00 Lecture 11:00 13:00 Lecture 11:00 13:00 Lecture 11:00 13:00 Lecture 13:00 14:30 Lunch 13:00 14:30 Lunch 13:00 14:30 Lunch 13:00 14:30 Lunch 13:00 14:30 Lunch 14:30 16:30 Group activities 14:30 16:30 Group activities 14:30 19:45 Social event 14:30 16:30 Group activities 14:30 16:30 Group activities 16:00 Shuttle PoliTO > Torgnon 16:30 19:45 Social spare time 16:30 19:45 Social spare time 16:30 19:45 Social spare time 16:30 19:45 Social spare time 19:45 Dinner 19:45 Dinner 19:45 Dinner 19:45 Dinner 19:45 Dinner 19:45 Dinner

## Venue

The school will take place at the Hotel Panoramique Torgnon. Torgnon is a town in the Aosta Valley region of north-western Italy. Facing onto the Valley of the Matterhorn, it offers a unique view onto the most striking mountains of the entire Alpine region. Sitting on the right side of the Valley, Torgnon is sunny for most of the day, earning it the name of “pays du soleil” (sun-kissed town). The town is famous for downhill slopes of variable difficulty, cross-country paths which are among the most panoramic of the Aosta Valley, and trekking routes for all kinds of excursions. If you like hiking (or running), bring appropriate shoes!

## Booking

Every attendee is responsible for booking a room at the Hotel Panoramique Torgnon, by May 8th. Discounted prices for room and full board are available for the event, so do not forget to mention you are attending the school. Limited funds to cover the expenses of very few participants are available. Strongly motivated students that are unable to participate because of lack of funding are welcome to write an email to the organizers.

Piazza Frutaz
11020 Torgnon AO
ITALY

## Venue

The school will take place at the Hotel Panoramique Torgnon. Torgnon is a town in the Aosta Valley region of north-western Italy. Facing onto the Valley of the Matterhorn, it offers a unique view onto the most striking mountains of the entire Alpine region. Sitting on the right side of the Valley, Torgnon is sunny for most of the day, earning it the name of “pays du soleil” (sun-kissed town). The town is famous for downhill slopes of variable difficulty, cross-country paths which are among the most panoramic of the Aosta Valley, and trekking routes for all kinds of excursions. If you like hiking (or running), bring appropriate shoes!

## Booking

Every attendee is responsible for booking a room at the Hotel Panoramique Torgnon, by May 8th. Discounted prices for room and full board are available for the event, so do not forget to mention you are attending the school. Limited funds to cover the expenses of very few participants are available. Strongly motivated students that are unable to participate because of lack of funding are welcome to write an email to the organizers.

Piazza Frutaz
11020 Torgnon AO
ITALY

## How to get to Politecnico di Torino

• From Milano Malpensa (MXP) airport:
there is a shuttle service, see a possible route.
• From Torino Caselle (TRN) airport:
there is a shuttle service, once any 30 minutes, see the complete timetable.
Both shuttle services stops at the Torino Porta Susa train station.

• From Porta Susa (PS) train and bus station:
you can take a walk (map) or get tram n. 10.
• From Porta Nuova (PN) train and bus station:
you can take a walk (map) or get bus n. 33, 58 or 58/.

Please note that public transport tickets must be purchased in advance at kiosks, tobacconist or subway stations.

A shuttle service will be provided from Politecnico to Torgnon on Sunday, July 10th.

## How to get to Politecnico di Torino

• From Milano Malpensa (MXP) airport:
there is a shuttle service, see a possible route.
• From Torino Caselle (TRN) airport:
there is a shuttle service, once any 30 minutes, see the complete timetable.
Both shuttle services stops at the Torino Porta Susa train station.

• From Porta Susa (PS) train and bus station:
you can take a walk (map) or get tram n. 10.
• From Porta Nuova (PN) train and bus station:
you can take a walk (map) or get bus n. 33, 58 or 58/.
Please note that public transport tickets must be purchased in advance at kiosks, tobacconist or subway stations.
A shuttle service will be provided from Politecnico to Torgnon on Sunday, July 10th.

## Registration

In order to facilitate the school attendance, no fee is requested for the registration. To register for the school, please fill in this form by May 8th.

The attendees should autonomously book a room at the Hotel Panoramique Torgnon with full board, and pay for it. The school organization team will not work as intermediary between the school attendees and the hotel. Discounted prices for room and full board are available for the event, so do not forget to mention you are attending the school when booking. Single and double rooms are available, with different prices. Please let the hotel know about any dietary restriction.

Limited funds to cover the expenses of very few participants are available. Strongly motivated students that are unable to participate because of lack of funding are welcome to write an email to the organizers.