This event is the second part of the “Giornata Indam Unità di ricerca di Bari 2021” held in Bari on May 28, 2021.

The one-day workshop “Mathematics and Industry: from basic research to applications” mainly focuses on young researchers in mathematics working either in Academia or in Research & Development departments of local industries.

The event will physically take place in Bari at the “Aula Magna” of DICAR, Polytechnic of Bari. In order to attend the event in presence, a valid green pass is requested.

To remotely attend the event via Microsoft Teams: link To enroll for free and to receive additional info about the event: link

L'evento si pone come continuazione della Giornata Indam Unità di ricerca di Bari 2021 tenutasi a Bari il 28 Maggio scorso.

La giornata “Matematica e Industria: dalle ricerche di base alle applicazioni” prevede in particolare il coinvolgimento di giovani ricercatori di discipline matematiche dell'Università e dei centri di ricerca e sviluppo di alcune aziende locali.

Si svolgerà in presenza presso l'Aula Magna del Dipartimento di Scienze dell'Ingegneria Civile e dell'Architettura (DICAR), Politecnico di Bari, per partecipare in presenza è richiesto il green pass.

Per accedere all'evento su Microsoft Teams: link Per registrarsi gratuitamente e avere ulteriori informazioni sull'evento: link

# PROGRAM AND ABSTRACTS

**9:30 Institutional greetings **

** 9:40 Salvatore Di Stefano, POLIBA**

*A variational approach assessing some mechanical aspects of cell-matrix decohesion*

We present a mathematical model assessing the way in which decohesion affects the mechanical interactions exchanged between cells and the extra-cellular environment, by focusing our attention on focal adhesions. Specifically, we consider a one-dimensional scheme in which both the focal adhesion and the substratum are modelled as linear elastic fibres and we propose a variational procedure by taking inspiration from the Griffith’s theory of fracture. Our model let us deduce macroscopic mechanical quantities (decohesion force, elongation thresholds) and the decohesion front advancement, based on the constitutive properties of the adhering layers and cohesion energy. Finally, the model is able to capture the transition from a ductile to fragile regime of fracture. The results are in excellent agreement with those available in literature both theoretically and experimentally.

**10:00 Vincenzo Fazio, POLIBA**

*A mathematical model for the mechanical behaviour of spider silks: the roles of humidity and temperature*

The spider silk is studied for a long time as natural material with the highest mechanical properties, also in the spirit of biomimetics. We propose a model that relates the nano and micro-structure quantities characterizing the silk with its macroscopic behavior. The model is inspired to the experimentally known micro-structure composition of the silk thread. Since the mechanical response of the material is significantly influenced by humidity and temperature conditions, the key relationship of the model account for the macromolecular modification induced by hydration water and high temperature. The effectiveness of the model is demonstrated by reproducing quantitatively different experimentally observed phenomena such as temperature and humidity softening, variation of limit stretches and supercontraction.

**10:20 Gabriele Mancini, UNIBA**

*On a class of elliptic problems involving exponential-type non-linearities*

In this talk, I will give a brief overview on some existence and classification results for solutions to a family of Liouville-type equations arising from classical problems in differential geometry and fluid mechanics. I will focus on a specific class of local and non-local elliptic equations related to the existence of Riemannian metrics with constant Q-curvature and prescribed volume on the Euclidean space. I will describe the distinction between normal and non-normal metrics and I will present some results obtained in collaboration with A. Hyder and L. Martinazzi concerning the existence of normal and non-normal metrics with a prescribed singularity at the origin under suitable volume constraints.

**10:40 Alessandro Coclite, POLIBA**

*A dynamic method for computing the vascular journey of Micrometric carriers in narrow capillaries*

In vascular targeted therapies, blood-borne carriers should realize sustained drug release from the luminal side towards the diseased tissue. In this context, such carriers are required to firmly adhere vascular walls for a sufficient period of time while resisting hydrodynamics perturbations induced by the blood flow. Here, a hybrid computational model, combining a Lattice Boltzmann (LBM) and Immersed Boundary Methods (IBM), is proposed for predicting the dynamics of rigid and deformable adhesive micro-carriers navigating a capillary with physiological hematocrit. Red cells and particles are modeled as a collection of mass-spring elements responding to a bending resistance, an elastic potential and total enclosed volume conservation constraint. Furthermore, particle surfaces are uniformly decorated with adhesive molecules (ligands) interacting with receptors disposed on the walls. Particle adhesion is modeled as a short-range ligand-receptor interaction and in term of formation and destruction probability functions that discriminate whether a chemical bond can be formed or destroyed. If a bond is established an attractive elastic force is activated.

**11:00 Federico Pintore, UNIBA**

* Privacy-preserving signatures from isogenies between elliptic curves*

Privacy-preserving signatures – which have recently found application in cryptocurrencies – allow a signer to create a signature on behalf of an ad hoc group of users, while hiding his/her true identity. In this talk, I will present the first practical privacy-preserving signatures based on isogenies between elliptic curves defined over finite fields. The security of these signatures relies on mathematical problems that are believed to remain hard even in the presence of quantum computers

**11:20 Coffee Break**

**12:00 Antonella Falini, UNIBA**

*A Hermite spline Quasi-Interpolation application to Univariate Time-Series *

In this talk we present an application of an Hermite spline Quasi-Interpolant (QI) operator to the study of univariate time-series. In particular, time-series is a collection of ordered data at specific time instants that need to be pre-processed in terms of cleaning, imputation of missing values, smoothing, and so on. With the adopted QI we can efficiently construct a local smooth approximant with two valid strategies: by fixing the degree of the QI basis to d, we can construct either a C^{d-1} smooth spline or a C^{d} smooth spline model via an integral representation. Both techniques are validated through the imputation, smoothing, forecasting and anomaly detection tasks on artificial datasets and real datasets provided by Planetek Italia s.r.l. and Yahoo!. More in details, regarding the anomaly detection, we also combine the used QI with the DBSCAN clustering method and a dynamic version of the T-student copula in order to increase the achieved accuracy of standard non supervised algorithms.

**12:20 ****Gianluca Orlando, POLIBA**

*Frustration in a spin model: chirality transitions via a discrete-to-continuum variational analysis*

Spin models are lattice models that describe magnetic properties of materials. In this talk, we will examine a frustrated a 2-dimensional planar spin model, namely, a model where conflicting interatomic forces prevent the energy of every pair of interacting spins to be simultaneously minimized. The frustration mechanism, due to the competition of ferromagnetic and antiferromagnetic interactions, entails some complex geometric patterns in the material, that we study by carrying out a discrete-to-continuum variational analysis as the lattice spacing tends to zero. In particular, we will show that the description of chirality transitions is captured by a continuum energy that selects solutions to the eikonal equation.

**12:40 Yaroslav D. Sergeyev, Università della Calabria**

*Computations with numerical infinities and infinitesimals*

In this lecture, a recent computational methodology is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework. It is based on the principle ‘The part is less than the whole’ applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The new methodology evolves ideas of Cantor and Levi-Civita in a more applied way and, among other things, introduces new infinite integers that possess both cardinal and ordinal properties as usual finite numbers. The methodology uses as a computational device the Infinity Computer (patented in USA and EU) working numerically with infinite and infinitesimal numbers that can be written in a positional system with an infinite radix. On a number of examples (numerical differentiation and optimization, divergent series, ordinary differential equations, fractals, set theory, etc.) it is shown that the new approach can be useful from both theoretical and computational points of view. The accuracy of the obtained results is continuously compared with results obtained by traditional tools used to work with mathematical objects involving infinity. The Infinity Calculator working with infinities and infinitesimals numerically is shown during the lecture.

**13:30 Lunch Buffet**

**15:00 Rosalina Mastronardi, IVIS Technologies s.r.l**

*Mathematics applications in ophthalmology*

Specific algorithms based on numerical methods were designed and implemented to solve the problems in the diagnosis and treatment of the eye disorders which are studied in the iVis Technologies S.r.l. company, a manufacturer of medical devices for the refractive corneal surgery. Here are some examples:

- Calculation of the least squares spline best fitting a set of scattered points to represent the surfaces of the cornea, which is the most external part of the eye, by continuous functions.
- Application of the Partial Differential Equations (PDEs) inpainting techniques to calculate the lacking data of the corneal surfaces within the detected domain.
- In the refractive corneal surgery treatment planning, calculation of a surface which links the ideal corneal surface, designed by the surgeon in the central corneal domain to correct a refractive error, and the preoperative corneal surface so that the new surface is smooth everywhere.

**15:20 Agnese Dedonno, Planetek Italia**

* Math's role in space challenges*

* From earth observation to planetary exploration missions*

The challenges in the space segment are growing and continue to lead mankind higher and higher towards ever more ambitious goals. In this compelling context, Planetek has an important role and its mission has something in common with mathematics, namely to simplify the complexity of space. In fact, mathematics has always been fundamental because it provides tools to simplify complex problems through clear and flexible models that allow a better understanding of phenomena and their relative evolutions. In particular, the recent development of techniques based on neural networks has made it possible to find new solutions in the monitoring of the space segment and in the analysis of time series telemetry to quickly detect failures and various problems aboard the satellite. Even in the field of planetary exploration, thanks to neural networks, it has been possible to develop novelty detection techniques based on onboard data processing to automate the decisions that a rover must make to explore the new planetary surface.

**15:40 Antonio De Carlo, MER MEC S.p.A.**

*A MATLAB geometric model of a moving target for laser-camera system calibration*

MERMEC Track Geometry Measurement System (TGMS) is an opto-inertial system which measures the geometry of rails. Laboratory tests on a custom designed test bench are done to calculate the metrological characteristics, such as uncertainty and reproducibility. To simulate the relative movement of rails and TGMS, the test is performed using a target which moves through the field of view of the laser – camera system measuring its position in a certain number of precisely known points and comparing the measured position with the expected one. The choice of the target is a crucial point of this process, as it is important to avoid every error which can be introduced by a particular shape or material. This work is the implementation of a MATLAB 3D – geometric model of the moving target with different shapes (cylindric, hexagonal, squared), together with the algorithms used to estimate its position starting from a set of points of its profile acquired by the TGMS. The aim of this work was to provide the better choice of the target, based on the results of the simulations.

**16:00 Amedeo Altavilla, UNIBA**

* The math of quaternions*

In this seminar, I will describe some research topics related to the algebra of quaternions and other relevant hypercomplex algebras with special regard to their expression in analysis, geometry, and some other concrete application. The seminar will have a divulgation character and the applications will concern, mainly, harmonic analysis and the theory of

PH curves, i.e. spatial polynomial curves which have tangent vector with polynomial norm.

**16:20 Federica Caforio, University of Graz, Austria**

*A novel 3D-1D model of cardiac electromechanics and arterial circulation to study the effects of pulse wave propagation on cardiac function*

Image-based computational models of cardiac electromechanics (EM) are a powerful tool to understand the mechanisms underlying physiological and pathological conditions in cardiac function and to improve diagnosis and therapy planning. However, in order to enable the clinical translation of such models, it is crucial to develop efficient multiphysics, personalised models that are able to reproduce the physiological reality of a given patient. In this talk I will report on recent advances in EM cardiac model development and personalisation. In particular, I will present a novel coupled model based on a 3D EM model of the heart function together with a 1D model of blood flow in the arterial system. 1D arterial models of the circulation can efficiently capture the effects of distributed vascular properties and geometric aspects and allow to correctly capture phenomena related to physiological and disrupted pulse wave propagation, comprising aortic stiffening, aortic stenosis and bifurcations. Thus, the use of our coupled 3D-1D model shows great promise for the investigation of a broad spectrum of clinical applications where wave transmission effects are under study. A variance-based sensitivity analysis is also performed to characterise the relative importance of model input parameters on the coupled model, in the perspective of model personalisation.

**17:00 Round Table**