Giulia Terenzi
(Univ. Tor Vergata)

We present an algorithm for the pricing of European and American options in the Heston model and in other stochastic volatility models which generalize it. Our procedure is based on a backward induction that works following a finite difference PDE method in the direction of the share process and a tree approximation in the direction of the volatility. Numerical results show that the algorithm turns out to be reliable and efficient. We study the stability of the algorithm by means of a Von Neumann analysis, but only limited convergence results have been proved.

Laurent Gosse
(IAC-CNR)

Starting from the elementary example of the Kolmogorov equation, $\partial_t f + v \partial_x f = \partial^2_vv f$, a general strategy for building numerical schemes which really incorporate 2D features is outlined. For kinetic equations, it relies on Pagani's elementary solutions. For both diffusion and drift-diffusion ones, numerical fluxes are derived by applying Steklov-Poincaré (aka Dirichlet-to-Neumann, or voltage-to-current) operator to a restricted amount of grid values. Surprisingly, it is found that such a strategy, when applied to the heat equation, recovers the usual 5-points cross-scheme, suggesting that there are no real 2D effects in such a model.

Angelo Vulpiani
(Univ. Sapienza)

Il caos deterministico nasce dal lavoro di Poincare' sul problema dei tre corpi e venne riscoperto negli anni 60 del 20-mo secolo. Ora e` ben chiaro che non siamo di fronte ad una patologia matematica bensi' ad un comportamento generico presente in molti ambiti (astronomia, chimica, ottica, geofisica etc). L'essenza del caos deterministico puo' essere riassunta nella sua sensibile dipendenza dalle condizioni iniziali, passata al grande pubblico come "effetto farfalla". Il fatto che due traiettorie molto vicine si allontanino velocemente (in modo esponenziale) ha interessanti conseguenze sia pratiche che concettuali. In particolare verra' discusso la rilevanza del caos nel problema delle previsioni; e la possibilita` dell'utilizzo di un approccio probabilistico anche in sistemi deterministici caotici.
Bibiografia:
D. Ruelle "Caso e caos" (Bollati-Boringhieri, 2013)
A. Vulpiani "Determinismo e Caos" (Nuova Italia Scientifica, 1994; Carocci, 2004)

Filippo Geraci
(IIT-CNR)

The advent of sequencing technologies and the consequent computational analysis of genomes has confirmed the evidence that DNA sequences contain a relevant amount of repetitions. A particularly represented category of these is that of tandem repeats (TRs) that have been observed since the first sequencing data became available in the early 90s. TRs are short, almost identical sequences that lie adjacent to each other. Although not elucidated yet, the abundance of TRs in Eukaryotic genomes suggests that they play a role in many cellular processes and, indeed, are also involved in the onset and progress of several genetic disorders. The growth of the number of genetic disorders associated to the expansion of TRs (to date more than 45 associations between TRs and diseases have been confirmed) has kindled the hope of finding in the tandem repeat polymorphism a first interpretation of those genetic diseases that are still unexplained. As a result, a consistent number of research projects aimed at a genome-scale analysis of repetitions have been set up in recent years. Within the RepeatALS project, we performed a comprehensive genome-wide research of tandem repeats in all gene regions using several algorithms. Then, we performed a comparative analysis to assess the polymorphism of the retrieved TRs. As a result, we obtained a catalogue of more than 370k polymorphic tandem repeats. Subsequently, we produced the sequencing data for a cohort of 70 ALS patients and developed a bioinformatics pipeline for TRPs genotyping from NGS data. This new procedure was applied to our patients so as we could screen the population for rare variants. Although a PCR-based analysis of a larger cohort of patients and controls is still ongoing, we have already identified a short list of few polymorphic tandem repeats that seems to be statistically correlated with ALS. Nevertheless, further research is still necessary to draw conclusions.

Mario Santoro
(IAC-CNR)

The Structural Topic Model is a general framework for topic modeling with document-level covariate information. The covariates can improve inference and qualitative interpretability and are allowed to affect topical prevalence, topical content or both. The software package fo R implements the estimation algorithms for the model and also includes tools for every stage of a standard workflow from reading in and processing raw text through making publication quality figures and interactive web representations.

Francesco Mattioli
(IFN-CNR)

The superconducting nanowire single photon detector (SNSPD) has received considerable attention because of its intrinsic high speed, low dark count rate, and single photon sensitivity in the near infrared spectral region with high detection efficiencies. In order to achieve high quantum efficiency, current realizations of SNSPDs use nanowires of ultrathin 3–5 nm NbN about 100 nm wide. To achieve a large area coverage, SNSPDs are typically made of a very long nanowire patterned into a meander shape. SNSPD can also be integrated with quantum photonic components and circuits on a chip in order to scale implementations of optical quantum information processing to meaningful numbers of qubits. Moreover, fields such as deep space optical communication, linear optics quantum computing, source characterization, laser radar and fluorescence measurement techniques would benefit from an ideal photon detector, combining single-photon sensitivity with a linear response over a large dynamic range.

In this talk, the absorption mechanism of photons and the output pulse generation in ultrathin and narrow superconducting nanowires will be described from the microscopic behaviour to the macroscopic geometries that enables single and multi-photon detection. Electrical, cryogenic and optical setups will also be described with particular care to optical coupling from a standard single mode optical fibre to the detector.

Andrea d'Andrea
(CNR-Istituto dei Sistemi Complessi)

In fisica dello stato solido i modelli di eccitazione, introdotti da Frenkel e Wannier all’inizio del ventesimo secolo, servivano per spiegare alcune anomalie riscontrate nel trasporto di energia in materiali organici ed inorganici non metallici. In quel periodo, in cui il calcolo a “molti-corpi” ed in particolare il calcolo delle bande nei solidi era nella sua infanzia, poter disporre di modelli semplici, ma capaci di spiegare complicati fenomeni legati alla dinamica indotta dall’interazione radiazione- materia nel “mare di Fermi” delle cariche, strutturato dalla simmetria del cristallo, costituiva un notevole progresso nell’interpretazione delle proprietà ottiche dei solidi non metallici. Si noti che solo all’inizio del 21 secolo, con l’avvento del metodo di calcolo GW, basato sul formalismo della “density function”, si è potuto calcolare “ab initio” e con soluzioni self-consistent” le proprietà ottiche a bordo banda valenza-conduzione in semiconduttori a gap diretta (eccitone di Wannier). Il seminario consiste in un breve inquadramento storico della tematica divisa in tre periodi, che corrispondono ad altrettanti sviluppi tecnologici nella risposta ottica della materia condensata. Il primo periodo va dagli articoli di Frenkel e Wannier fino alle soglie degli anni 50, prima della realizzazione delle sorgenti di luce coerente (lasers), il secondo periodo va dall’utilizzo delle sorgenti laser alle strutture a confinamento quantistico degli anni 80, in concomitanza con i nuovi metodi di deposizione in ultra alto vuoto con la tecnica dei fasci molecolari (MBE, MOCVD,...). Infine il terzo periodo va dagli anni 80 ai nostri giorni con lo studio della risposta ottica nei così detti meta-materiali (in particolare crystalli fotonici risonanti).

Dopo l’introduzione storica verranno discussi i differenti “frameworks” teorici con cui è possibile calcolare la risposta ottica in questi sistemi e verrà presentato, con un certo dettaglio, il metodo così detto: delle “ABC free theory” (K.Cho) implementato dal metodo dei “Shiva diagrams” (M.Combescot) per il calcolo auto-consistente della risposta ottica..

Infine, come validazione del metodo impiegato, presenterò alcuni risultati notevoli ottenuti dal gruppo teorico del CNR di Montelibretti nella sua ormai trentennale attività di ricerca.

Giovanni Ciccotti
(IAC - Univ. Sapienza di Roma - UCD Dublin)

The talk intend to explain at fundamental level (i) why Molecular Simulations (MS: Molecular Dynamics, MD, and, generally , Metropolis Monte Carlo, MC, although the talk will concentrate on MD simulations, the only containing dynamical information) are a rigorous scientific tool and (ii) how they have been able to produce applicative and practical impact. In particular, in the second part, it will address the question of how it can help the progress of modern flow engineering by constructing direct, atomistic, simulation of non-equilibrium hydro-dynamical flows.

In more details, as for the first question, it will explain: (i) where Molecular Dynamics (MD) is from; (ii) what is it and which complexity it can cope with; (iii) how MD has extended its predictive power toward predicting the thermodynamic and structural properties of materials and coping with chemical questions such as chemical reactivity, nucleation, etc (in short, activated processes). As for the second, the applicative success will be illustrated discussing: (i) how to cope with nucleation phenomena; (ii) how to avoid the need of constitutive relations in “ab-initio”, atomistic, hydrodynamical calculations.

Luca Businaro
(IFN-CNR)

The quest to realize reliable experimental model to measure phenomena occurring in complex biological system has become one of the frontiers of microfluidics. The idea to reconstitute the interaction among different cell population, or subset of organs functionalities, on small, microscopy compliant, low cost, plastic devices is today a reality with concrete industrial applications and is known as the organs-on-chip approach. These models allow the direct simultaneous observation of hundreds of different cells, moving, interacting and responding to signals coming from the microenvironment nearby, that give access to a number of parameters describing the system that must be properly measured and elaborated.

During the talk I'll present our approach to perform and analyze immune system–cancer cross talk through microfluidic based reconstitution of complex biological system. Flanking in-vivo and in-vitro experiments with on chip co-cultures of primary human PBMC, immune cell subpopulations or murine spleen cells with melanoma, breast and colorectal cancer cells allowed us to test the on-chip model and to extract meaningful kinetics and behavioral data in the microfluidic controlled environments. The experimental setup allowed us to describe the effects of drugs or genetic modifications on the cell population crosstalk, highlighting or confirming important mechanisms in boosting the immune response against cancer. Our vision is that modern microscopy and on chip immune system reconstitution represent the needed bridge to link biology to advanced mathematical methods developed in complex system physics and to numerical simulation, allowing the development of integrated “cybernetic” models able to explore fundamental biology, and to tackle critical issues of drug testing with impact on clinical trials.

Christine Nardini
(Personalgenomics S.r.l., University of Bologna)

With the tachnological revolution brought in by high-throughput biology, exact sciences have fiercely entered the realm of live sciences, with approaches supporting applications ranging from molecular biology to medicine, with the recent and particular focus on evidence-based medicine.
Over the time of this talk I will present the tools we developed with bases rooted in engineering and exact sciences (network construction, reconstruction and simulations) to approach a specific theme in medicine: degenerative diseases, a class of systemic, often autoimmune and chronic maladies, with no cure, consequent high societal costs and spreading at very fast pace wordlwide.
In particular, with the design of a clinical pilot study in animals  (Nardini et al. 2016) and a pilot clinical study in humans (ClinicalTrials.gov ID: NCT01619176) we explored the systemic effects of mechanical stimulations delivered in the subcutanous tissue, thanks to the collection of heterogeneous omic data (mRNA-, 16S-rRNA-, miRNA-seq), at different histological (blood, gut-intestinal microbiome, synovial tissue, subcutanoues tissue) and temporal point (before therapy, early genes activation, after therapy).
This lead to the realization that the molecular events triggered locally have a systemic resonance, a very well understandable fact in the frame of non-linear equation and chaos theory, whose translation in medicinen is however far from trivial, leading to potential extremely innovative applications in medicine, here discussed with the model disease of rheumatoid arthritis.
I will close this talk with the presentation of the future steps we have taken to continue this exploration in a computational, biological and technological integrated perspective with the presentation of the recently submitted Sinergia Proposal.

Michele Di Pierro
(Center for Theoretical Biological Physics, Rice University, Houston, Texas)

Chromatin consists of DNA and hundreds of proteins that interact with the genetic material. In vivo, chromatin folds into nonrandom structures. The physical mechanism leading to these characteristic conformations, however, remains poorly understood. We recently introduced MiChroM [1], a model that generates chromosome conformations by using the idea that chromatin can be subdivided into types based on its biochemical interactions. Here we extend and complete our previous finding by showing that structural chromatin types can be inferred from ChIP-Seq data. Chromatin types, which are distinct from DNA sequence, are partially epigenetically controlled and change during cell differentiation, thus constituting a link between epigenetics, chromosomal organization, and cell development. We show that, for GM12878 lymphoblastoid cells we are able to predict accurate chromosome structures with the only input of genomic data. The degree of accuracy achieved by our prediction supports the viability of the proposed physical mechanism of chromatin folding and makes the computational model a powerful tool for future investigations.

References:
[1] M. Di Pierro, et al. ; Transferable model for chromosome architecture; PNAS 2016 113 (43) 12168-12173
[2] Commentary by G. Gürsoy and J. Liang; PNAS 2016 113 (43) 11991-11993

Alessandro Celestini
(IAC-CNR)

Tor is an anonymity network, composed by volunteer-operated routers. It allows users to access the Internet anonymously, evading traditional network surveillance and traffic analysis mechanisms. Tor can also provide receiver privacy for Internet services through a feature called “hidden services”. Tor’s hidden services let users publish web sites and other services without revealing the location of the site.

Donato Bini
(IAC-CNR)

Verranno richiamate brevemente: 1) La definizione di GW (esatta) in Relatività Generale, 2) alcuni aspetti matematici collegati alle soluzioni note, 3) l'interazione nonlineare tra onde gravitazionali. Si introdurrà poi il formalismo effective-one-body per la trattazione analitica di effetti di perturbazioni gravitazionali associati a sistemi binari.

Davide Poggiali
(Università di Padova)

In Neuroscience study, imaging systems as Magnetic Resonance Imaging (MRI) and Positron Emission Tomography (PET) has assumed a crucial role in the last years. To extract quantitative information from MRI and PET images, many mathematical algorithms has been gathered into widely used software suites as Freesurfer, SPM, FLS or the most recent ANTs.
A good knowledge about such algorithm is useful in order to correctly choose optional parameters and to avoid misuse.
In this talk some important algorithm of image will be presented, explained in detail and showed in action with some examples. In particular we will focus on MRI segmentation, registration, cortical thickness evaluation, and PET compartment models.

Nicola Apollonio
(IAC-CNR)

Una matrice su {0,1} è bilanciata se la somma degli elementi di ogni sua sottomatrice con esattamente due "1" per riga e per colonna è un multiplo di 4. La "bilanciatezza" è una proprietà combinatoria molto interessante giacché le matrici che la godono inducono poliedri con vertici interi. Un grafo è "bilanciato" se tale è la matrice di incidenza delle clique massimali di ogni suo sottografo indotto. Una caratterizzazione di tali grafi appare ancora difficile e non vi sono congetture a riguardo. In questa comunicazione presenterò la prima caratterizzazione per sottografi proibiti per la classe dei grafi "diamond-free" e discuterò alcuni risultati ottenuti nel caso generale. Curiosamente, "quozientando opportunamente" i sottografi che appaiono nella caratterizzazione, si ritrovano le parole di Dyck (enumerate dal numero di Catalan in combinatoria enumerativa). Tutti i risultati sono stati ottenuti insieme ad Anna Galluccio.

Mario Santoro
(IAC-CNR)

The Structural Topic Model is a general framework for topic modeling with document-level covariate information. The covariates can improve inference and qualitative interpretability and are allowed to affect topical prevalence, topical content or both. The software package fo R implements the estimation algorithms for the model and also includes tools for every stage of a standard workflow from reading in and processing raw text through making publication quality figures and interactive web representations .

Abdul Barakat
(Ecole Polytechnique, France)

The pathological complications of atherosclerosis, namely heart attacks and strokes, are the leading cause of mortality in the world. We are interested in understanding the development of atherosclerosis and in devising novel treatments for the disease. To this end, we are studying the role of mechanics in two central events in the development of atherosclerosis: dysfunction of the endothelial cells that line blood vessels and the increased movement of leukocytes from the bloodstream into the arterial wall. We are also investigating ways by which today's treatments for atherosclerosis, most notably stent performance, can be improved to minimize patient complications. Finally, we are exploring novel therapeutic and diagnostic pathways including nanoparticle-based targeted drug delivery and smart implantable devices. In this talk, I will provide an overview of our work on: 1) endothelial cell mechanotransduction, 2) leukocyte-endothelial interactions, 3) nanoparticle-based drug delivery, and 4) optimization of today's stents and development of tomorrow's smart and communicating stents.

Monika Twarogowska
(Università dell'Aquila)

We investigate numerically a one-dimensional linear kinetic equation derived from a velocity jump process modeling bacterial chemotaxis in presence of a chemical signal, produced by cells, and nutrient present in the environment. The model was used to describe accurately lab experiments, in which bands of bacteria are moving across a micro-channel at constant speed. The problem is very different from classical reaction-diffusion traveling waves, as biased transport is the dominant effect here. Calvez et al. obtained analytic results on the existence of traveling waves in the diffusive limit of the velocity-jump process with temporal sensing. The kinetic part of the system is approximated by the well-balanced scheme with the time-space dependent scattering matrix containing coupling with the parabolic system for the concentrations of the chemoattractants. The method gives an accurate resolution in the velocity field and we compare it with the classical time-splitting approach. Then we study numerically the formation and stability of the traveling waves emerging in the kinetic model. Finally, we consider a discrete velocity field and show some sets of parameters for which there exists a numerical cont-example to the existence and stability of traveling waves.

Daniele Peri
(IAC-CNR)

Il problema della minimizzazione del tempo di evacuazione di una stanza da parte di un gruppo di persone rappresenta un problema di grande interesse pratico. La disponibilità di un modello matematico adeguato rende possibile l'analisi delle criticità presenti, consentendo di suggerire soluzioni ed accorgimenti. L'uso di un algoritmo di ottimizzazione consente una investigazione ampia ed imparziale di un largo numero di soluzioni alternative, identificando le caratteristiche salienti delle soluzioni più interessanti, consentendo anche di considerare gli effetti legati a specifiche ipotesi progettuali.

Paula De Oliveira
(Center of Mathematics of the University of Coimbra, Portugal)

The transport of drug molecules in body tissues depends on their properties but also on the physiological properties of the target tissues. A compromised elasticity, a larger stiffness, an increased porosity and a chronic inflammation are common characteristics that can be found in aging tissues. The aim of this talk is to show how these properties influence the pharmacokinetics of drugs. Mathematical models that represent the coupling between drug delivery devices and body tissues are presented. Numerical simulations show how these models can pave the way for a personalized medicine.

Robert Smits
(New Mexico State University)

A recent probabilistic interpretation of p-harmonic functions involving a 2 person, zero sum game has led to a major increase in the investigations of the p-Laplacian, motion by mean curvature, AMLE and related problems. I will discuss the 2 player game, tug-of-war, it's relationship to the p-Laplacian and some of the difficulties involved with the numerics of non-variational, highly degenerate elliptic problems. I will discuss a novel scheme for solving the Poisson problem associated to the game p-Laplacian which doesn't involve interpolation with the infinity Laplacian and show numerical examples from implementing the scheme.

Tiziana Giorgi
(New Mexico State University)

Liquid crystals are mostly known to the general public for their use in Liquid Crystal Display (LCD) technology, which by and large is currently based on nematic phases and operates very close to physical limits.
The LCD industry has an open interest in the development of technology that employs tilted chiral smectic mesophases since, due to ferroelectric or antiferroelectric properties, devices based on these phases harbor the potential for superior operational speed and resolution. My presentation will deal with the mathematical analysis of soft matter systems that show liquid crystalline phases with some degree of layered orientational order. I will start by giving some background on the modeling of smectic phases in liquid crystals via phenomenological Landau-de Gennes type functionals, then proceed to presenting an overview of recent analytical and numerical results for bent-core molecule columnar and Smectic A phases. This is joint work with Sookyung Joo (Old Dominion University), Carlos Garcia-Cervera (University of California Santa Barbara) and Feras Yousef (New Mexico State University).

Daniela De Canditiis
(IAC - Roma)

Motivati dall'analisi di dati astronomici di dipo conteggio si presenterà un metodo per la stima della f.d.p. (funzione densità di probabiltà) della intensità di dati di tipo Poisson. La necessità di dare all'intensità un carattere stocastico nasce dall'esigenza di modellizzare una extra-variabilità contenuta nei dati. Le difficoltà della stima della f.d.p. sono assimilabili a quelle della soluzione (numerica) di un problema lineare mal-posto. La soluzione, intesa come uno stimatore della f.d.p, ha ottime proprietà di convergenza. La metodologia verrà presentata in termini generali e dunque può essere presa come spunto per la risoluzione di altri problemi di analisi dati di tipo conteggio. Verranno infine presentati alcuni risultati ottenuti in simulazione ed i risultati ottenuti nel caso reale considerato.

Monika Twarogowska
(IAC - Roma)

Emiliano Cristiani
(IAC - Roma)

Vincenzo Bonifaci
(IASI - Roma)

Natural processes are often capable of exhibiting remarkable information processing abilities. Physarum polycephalum -- the 'many headed' slime mold -- is a single-cell, multiple nuclei organism that is apparently able to solve rather complex tasks, such as finding the shortest path between two points in a maze while foraging food. Mathematical models have been proposed by biomathematicians to describe the feedback mechanism used by Physarum to adapt its tubular channels while foraging two food sources s0 and s1. We prove that, under one such model, the mass of the mold will eventually converge to the shortest s0-s1 path of the network that the mold lies on, independently of the structure of the network or of the initial mass distribution. This matches the experimental observations by the biologists and can be seen as an example of a "natural algorithm", that is, an algorithm developed by evolution over millions of years.
Natural algorithms provide an information processing perspective on biological processes, as well as inspiration for innovative solutions in computer science. We discuss how to turn the Physarum dynamics into a discrete algorithm that is suitable for implementation on modern computers. We also illustrate some of the many open questions concerning Physarum's computational capabilities.

Sean McGinty
(Univ. Strathclyde - UK)

The study of drug/device combinations for controlled drug release has gained significant momentum in recent years and is responsible for considerable global research budgets across academia and Industry. In this talk, I will discuss my group’s research in this area which includes modelling drug release from polymer-coated and nanoporous drug delivery devices, coupling drug release with tissue absorption, and parameter estimation methods. The mechanisms of drug release typically include diffusion, dissolution and in some cases a combination of both. Within the tissue, convection, diffusion and reaction typically occur simultaneously. We adopt a three-pronged approach to tackle these problems, making use of analytical, numerical and experimental techniques.

Alessandro Degregorio
(Univ. Sapienza)

The motion of a particle whose velocity undergoes jumps of random size at random times constitutes the prototype of a transport process (also called random flight or random evolution). In this talk the probabilistic construction of the isotropic transport processes is outlined. In particular, we assume that the joint probability distribution of the lengths of the displacements is a Dirichlet law. Several results in this context are discussed. We also introduce reflecting transport processes by means of a geometric approach. These processes are often applied in statistical physics and biology.

Fabio Pellacini
(Univ. Sapienza Roma)

Matteo Rucco
(Univ. Camerino)

Federico Toschi
(IAC - Roma
Eindhoven University of Technology)

Gabriella Bretti
(IAC - Roma)

Nicolas Vauchelet
Universite' Pierre et Marie Curie, Paris VI

Chemotaxis is the phenomenon in which cells direct their motion according to a chemical present in their environment. Since experimental observations have shown that the motion of bacteria (e.g. Escherichia Coli) is due to the alternation of 'runs and tumbles', mathematical modelling thanks to a kinetic description has been proposed. The starting point of the study is the so-called Othmer-Dunbar-Alt model governing the dynamics of the distribution function of cells. From this system, macroscopic model can be derived after rescaling. When the taxis is small compared to the unbiased movement of cells, the scaling must be of diff usive type. The limiting model allows to recover the travelling pulse observed in experiments. When taxis dominates the unbiased movements, a hyperbolic limit can be derived, leading to aggregation equations. For such system, blow up in finite time of solutions is observed. Then a study of solutions in the sense of measures for the aggregation equation has been carried out. The numerical simulation of such solutions is then very challenging.

Fabio Priuli
(IAC - Roma)

Emiliano Cristiani
(IAC - Roma)

Giacomo Albi
(TUM - Monaco)