This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Examensarbetet som beskrivs i denna rapport handlar om en ny teknik för att förbättra säkerheten för flygplan i luften och i närheten av flygplatser. Denna teknik benämns ADS-B (Automatic Dependent Surveillance Broadcast), och är tänkt att göra det möjligt för piloter att själva få information om trafik i närområdet. Nuvarande system baserar sig i huvudsak på visuella observationer från flygledare i kontrolltorn samt radarspaning omkring flygplatserna. Med det nuvarande systemet kommer det att bli både dyrt och svårt att upprätthålla en acceptabel nivå på flygsäkerheten när trafiken ökar. Arbetet har bedrivits i AerotechTelubs regi i Linköping samt med hjälp ifrån företaget Sectra Wireless Technologies AB. Huvuddelen av arbetet inriktar sig på implementerandet av C-funktioner för att hantera kommunikationen och sammankopplandet av ett tidigare skapat system, för grafikvisning, med en transponder som hanterar ADS-B (tillverkad av Sectra). Målet med detta var att göra förberedande arbete åt AerotechTelub som de förhoppningsvis kommer att kunna använda i ett eventuellt kommande projekt. Rapporten tar upp några standarder som hör till konceptet GP&C (Global Positioning & Communication), samt beskriver de delar som ligger till grund för programmets funktion. Examensarbetet har resulterat i ett demonstrationsprogram för att visa hur en lösning av problemet kan se ut. Det har tyvärr inte gått att säkerställa om programmet fungerar till fullo, men genom simuleringar och andra tester har huvuddelen av programmets funktioner gått att verifiera.

Since mid to late 2010 image synthesizing using neural networks has become a trending research topic. And the framework mostly used for solving these tasks is the Generative adversarial network (GAN). GAN works by using two networks, a generator and a discriminator that trains and competes alongside each other. In today’s research regarding image synthesis, it is mostly about generating or altering images in any way which could be used in many fields, for example creating virtual environments. The topic is however still in quite an early stage of its development and there are fields where image synthesizing using Generative adversarial networks fails. In this work, we will answer one thesis question regarding the limitations and discuss for example the limitation causing GAN networks to get stuck during training. In addition to some limitations with existing GAN models, the research also lacks more experimental GAN variants. It exists today a lot of different variants, where GAN has been further developed and modified. But when it comes to GAN models where the discriminator has been changed to a different network, the number of existing works reduces drastically. In this work, we will experiment and compare an existing deep convolutional generative adversarial network (DCGAN), which is a GAN variant, with one that we have modified using a deep neuro-fuzzy system. We have created the first DCGAN model that uses a deep neuro-fuzzy system as a discriminator. When comparing these models, we concluded that the performance differences are not big. But we strongly believe that with some further improvements our model can outperform the DCGAN model. This work will therefore contribute to the research with the result and knowledge of a possible improvement to DCGAN models which in the future might cause similar research to be conducted on other GANmodels.

The urban climate of the city of Trento, adopted as a representative case study of urban weather and climate phenomena in a mid-sized city lying in a mountain valley, is investigated using different methods and on different spatial scales. First the intensity of the Urban Heat Island (UHI) is analyzed evaluating the differences between air temperatures measured at an urban automated weather station on a tower, over mean rooftop level, and at five suburban/rural weather stations, located few kilometers around the city boundaries. It is found that the extra-urban weather stations, being affected by different local-scale climatic conditions, display different temperature contrasts compared to the urban site. However the diurnal cycle of the UHI is characterized by similar behaviors at all the extra-urban weather stations: the UHI intensity is stronger at night, while during the central hours of the day an “urban cool island†is likely to occur. The diurnal maximum UHI intensity turns out to be typically of order 3°C, but under particularly favorable conditions it may be higher than 6°C. Wind speed and cloud cover are the weather factors which most affect UHI intensity, making it weaker with stronger winds and cloudier skies. The investigation of the urban climate of Trento focuses then on a smaller spatial scale, analyzing in detail the thermal field inside an urban canyon located in the city center, by means of two experimental campaigns and the use of a simple model. This simple model simulates the energy balance of the different surfaces composing the urban canyon, calculating both surface and air temperatures inside the canopy. During the two field measurements, carried out in the summer 2007 and in the winter 2008- 2009, temperature sensors were placed at various levels near the walls flanking the canyon and on a traffic light in the center of the street. It is found that the air temperature near the walls, both in summer and in winter, is strongly influenced by direct solar radiation, thus inducing a quite strong imbalance within the canyon: during sunny days an overheating of the east-facing sensors is found in the morning, while in the afternoon west-facing sensors are the warmest. On the other hand, when solar radiation is weak or absent, the temperature field inside the canyon is homogeneous. Moreover air temperature inside the canyon is generally higher than above roof level, the differences being larger during summertime, when solar radiation is stronger and can penetrate for longer inside the street. The measurements performed during the field campaigns, along with observations of wall surface temperatures taken from the literature, allow to validate the results of the urban canyon model. A good agreement between experimental measurements and numerical results is found for both surface and air temperatures, in different seasons and under different weather conditions. The urban area of Trento, being located in the Alpine Adige Valley, interacts with the atmospheric phenomena typical of these contexts, in particular thermally driven local circulation systems. Moreover the city is located at a point where various narrow tributary valleys or gullies join the Adige Valley, and, as a consequence, complex interactions of local circulation systems are present in the area of Trento. In order to study these phenomena, first the main features of local circulation systems developing in the Adige, Sarca and Lakes valleys, which directly influence the climate of the city, are investigated by means of the analysis of a dataset from surface weather stations covering the period 2004-2011. After that, high-resolution (500 m) numerical simulations with the mesoscale meteorological WRF model, coupled with the multilayer Building Environment Parameterization (BEP) scheme, are utilized to study the urban climate of Trento in the Adige Valley context. Suitable datasets of land use, urban morphology and anthropogenic heat flux have been specifically prepared for these numerical simulations. Both methods highlight the substantial differences occurring between the local circulation system developing in the Adige Valley, and that blowing in the Sarca and Lakes valleys. The former is a typical valley wind, while the latter is a combination of a lake breeze and a valley wind. The along-valley wind developing in the Adige Valley is mainly determined by the local geometry of the valley, which controls the penetration of solar radiation and the heating of the valley slopes. The lake breeze, the so-called Ora del Garda, starts to blow from the shores of Lake Garda in the morning and then propagates with its cooler air towards north in the Sarca and Lakes valleys, outbreaking into the Adige Valley north of Trento in the first part of the afternoon. In some days the lake breeze is even able to reach the central part of the urban area of Trento, thus lowering the temperature in the city in hot summer afternoons. Focusing on the urban effects, the model is able to simulate correctly the daily cycle of the UHI, with high intensities during the night and negligible values in the central part of the day. Numerical results suggest that at night the temperature sharply increases at the city boundaries, while the thermal field is quite homogeneous inside the urban area, with only slightly higher temperatures where the urban morphology is more compact. Finally it is found that the presence of the city influences considerably also the wind field, due to the high roughness of the urban area.

Among the many possible applications of laser ablation one of the more recent taken is related to nanosatellites propulsion. The study of Laser Ablation Propulsion (LAP) requires research activity on different fields like high power pulsed lasers, laser ablation itself, because it is still a problem to relate the well known mechanisms to impulse generation, and finally materials that represent the fuel in LAP. This thesis presents a research activity on LAP from its very beginning, with the development of an experimental apparatus to measure laser generated impulse and the first results on metals and polymers that paves the way to the development of future LAP materials. Chapter 1 presents an overview of the actual situation of space economy and its recent fast evolution that led in the last years to the exploitation of space for many different applications, also by private companies. The so called New Space Economy is the background on which LAP develops, as an attractive propulsion technique for nano satellites, nowadays extremely diffused in all kind of space missions, and as a possible solution for the space debris problem. In this Chapter typical results obtained in LAP are also reviewed and compared with other solutions both for space debris and propulsion, in order to obtain a better image of its applicability range. Chapter 2 deals with laser ablation. Initially the parameters that play a role in laser ablation are discussed, in particular those related to the laser source like wavelength, pulse duration and repetition rate, to give an overview of the experimental conditions involved. Then general phenomenological observations on laser ablation are presented and related to the physical mechanisms involved, both in the case of metals and polymers, highlighting the main differences between these two classes of materials. The experimental part of this thesis starts in Chapter 3, with the description of the experimental apparatus developed to measure the laser generated mechanical impulses in the order of uN s. The different strategies to perform this kind of measurements are reviewed and compared to the one adopted in this work, based on a ballistic pendulum, and main advantages and problems are discussed. A technical description of the apparatus is given, focusing in particular on all the precautions that have been taken in order to let the pendulum operate in as ideal as possible conditions. The measurement procedure developed during this work is then described in detail, by discussing data analysis and showing some examples. Chapter 4 also deals with the development of the apparatus, in particular for what concerns the estimation of the laser energy density that reaches the target material (fluence), a fundamental parameter for LAP measurements. Some measurements on metals are also presented here in order to discuss some features related to the measurements of some common LAP parameters. Chapter 5 and 6 deal with LAP using polymers, and in particular with experiments devoted to the understanding of material properties that mainly affect LAP performances. The starting material chosen for these experiments is poly(vinyl chloride)(PVC), a benchmark in LAP experiments. Chapter 5 compares localized or uniform laser absorption by PVC, that can be obtained respectively by including carbon nanoparticles in the polymer matrix or by mixing PVC with an absorbing polymer (poly(styrene sulfonate)). The comparison is carried out from the optical an thermodynamical point of view, along with impulse generation. Specific ablation mechanisms are also discussed, showing that a localized absorption of laser radiation is more energetically efficient for impulse generation. Chapter 6 then continues the work on PVC containing nanoparticles, investigating the role of their size, morphology and concentration in laser ablation and in impulse generation. Both commercial and green produced carbon nanoparticles are used for these experiments showing that, at least in the considered size range, the only parameter that affects laser ablation is the number density of absorption centers in the polymer matrix, and not size or morphology. This points the direction to follow in the development of a polymeric material for LAP applications. Some open problems and future works are presented in Chapter 7. Effects on impulse generated by irradiating multiple times the same region are discussed, showing opposite behaviours between metals and polymers, for which still there is not a clear explanation. Then experimental issues and some results on specific impulse measurements are presented, and difficulties related to this measurement in metals briefly discussed. Finally laser ablation in a confined geometry is considered as an attracting technique to enhance impulse generation. And some results on PVC are shown. As a conclusion, main results obtained in this thesis are highlighted, and possible future research activities, developments and perspectives are discussed.

Bose-Einstein condensates (BECs) of ultra-cold atoms have been subjects of a large research effort, that started a century ago as a purely theoretical subject and is now, since the invention of evaporative cooling thirty years ago, a rich research topic with many experimental apparatuses around the world. A deep knowledge of its underlying physics has been now acquired, for example on the thermodynamics of the gas, superfluidity, topological excitations and many-body physics. However, many topics are still open for investigation, thanks to the flexibility and the high degree of control of these systems. During the course of my PhD, I developed and realized a new experimental apparatus for the realization of coherently-coupled mixtures of sodium BECs. The highly stable and low-noise magnetic environment of this apparatus enables the experimental investigation of a previously inaccessible regime, where the energy of the coupling becomes comparable to the energy of spin excitations of the mixture. With this apparatus, I concluded two experimental investigations: I produced and investigated non-dispersive spin-waves in an two-component BEC and I experimentally observed the quantum spin-torque effect on a elongated bosonic Josephson junction.The research activity in multi-component BECs of alkali atoms begun shortly after the first realization of a condensate, thanks to the low energy splitting between the internal sub-states of the electronic ground state. These internal states can be coherently coupled with an external electromagnetic field and can interact via mutual mean-field interaction, generating interestinc effects such as ground states with different magnetic ordering depending on their interaction constants, density as well as spin dynamics and internal Josephson effects. The research interest on mixtures of sodium atoms sparks from the peculiar characteristic of the system: in the $ket{F = 1, m_F = pm 1}$ states, the interaction constants are such that the ground state has anti-ferromagnetic ordering and the system is perfectly symmetric for exchanges of the two species. In these peculiar system, density- and spin-excitations have very different energetic cost, with the latter being much less energetic, and can be completely decoupled. Moreover, spin-excitations, that are connected to excitations in the relative-phase between the components, change drastically in nature when a coupling of comparable energy is added between the states. The presence of the coupling effectively locks the relative-phase in the bulk and spin excitations become localized. While extensive theoretical predictions on the spin dynamics of this system has been already performed, experimental confirmation was still lacking because of the high sensitivity to external forces (due to the very low energy of the spin excitations) and the impossibility of realizing a low-energy coupling between these states in the presence of environmental magnetic noise. During my PhD, I realized an experimental apparatus where magnetic noises are suppressed by five orders of magnitude using a multi-layer magnetic shield made of an high-permeability metal alloy (μ-metal), that encases the science chamber. In this apparatus, I developed a protocol, compatible with the technical limitations of the magnetic shield, to produce BECs in a spin-insensitive optical trapping potential. I then characterized the residual magnetic noise and found it compatible with the requirements for observing spin-dynamics effects. Finally, I realized a system and a set of protocols for the manipulation of the internal state of the sample allowing arbitrary preparation of the sample while maintaining the long coherence times necessary to observe the spin dynamics, that have been used in the subsequent experimental observations. The first experimental result discussed in this thesis, is the production of magnetic solitons and the observation of their dynamic in a trapped sample. Waves in general spread during their propagation in a medium, however this tendency can be counterbalanced by a self-focusing effect if dispersion of the wave is non-linear, generating non-dispersive and long-lived wavepackets commonly named solitons. These have been found in many fields of physics, such as fluid dynamics, plasma physics, non-linear optics and cold-atoms BECs, attracting interest because of their ability to transport information or energy unaltered over long distances, as they are robust against the interaction with in-homogeneities in the medium. Of these systems, cold-atoms can be widely manipulated to generated different kinds of solitons, both in single and in multi-components systems. A new kind of them, named magnetic solitons, has been predicted in a balanced mixture of BECs of sodium in $ket{F = 1, m_F = pm 1}$, however experimental observation was still lacking. I deterministically produced magnetic solitons via phase engineering of the condensate using a spin-sensitive optical potential. I then developed a tomographic imaging technique to semi-concurrently measure the densities of both components and the discontinuities in their relative phase, allowing for the reconstruction of all the relevant quantities of the spinor wavefunction. This allowed to observe the dispersionless dynamics of the solitons as they perform multiple oscillation in the trapped sample in a timescale of the order of the second. Moreover, I engineered collisions between different kinds of magnetic solitons and observed their robustness to mutual interaction. The second experimental results presented in this thesis is the observation of the breaking of magnetic hetero-structures in BECs due to the quantum spin torque effect, an effect with strong analogies with electronic spins traveling through magnetic devices. Spins in magnetic material precess around the axis of the effective magnetic field, and their dynamics must take into account the external field as well as non-linear magnetization and the inhomogeneity of the material. These effects are commonly described by the Landau-Lifshitz equation and have been mainly studied for electronic spins in magnetic hetero-structures, where the inhomogeneity in the material at the interfaces enhances the exchange effects between spins. For homogeneous materials, this description reduces to the Josephson system, a closely related effect that is more known in cold-atoms systems. The Josephson effect arises when a macroscopic number of interacting bosonic particles are distributed in two possible states, weakly tunnel-coupled together, with the average energy of particles occupying each of the states depending on the occupation number itself. In these conditions, the dynamics of the system depends on the difference in occupation numbers, the relative phase between the states and the self-interaction to tunneling ratio, giving raise to macroscopic quantum effects such as oscillating AC and DC Josephson currents and self-trapping. While these phenomena has been historically studied in junctions between superconducting systems, they can be also realized with cold-atoms systems, allowing the study of Josephson junctions with finite dimensions and in regimes that are hard to reach for superconducting systems. In this thesis, I realized a magnetic hetero-structure in a two-component elongated BECs thanks to the simultaneous presence of self-trapped (ferromagnetic) and oscillating (paramagnetic) regions in the sample. While the dynamics at short times is correctly described by the Josephson effects, at the interface between the regions the particle nature of the gas creates a strong exchange effect, named the quantum spin torque, that produces magnetic excitations that spread trough the sample and break the local Josephson behaviour. I experimentally studied the spread and nature of these magnetic excitations, while numerical simulations confirmed the dominant role played by the quantum spin torque effect. The structure of this thesis is the following: in the first chapter is given a review of theoretical concepts and existing literature. In the second chapter is described the experimental apparatus and the protocols developed to prepare the ultra-cold atoms sample. In the third chapter is presented the experimental observation of magnetic solitons. In the fourth chapter is presented the experimental investigation of the quantum spin torque effect in magnetic heterostructures. The last chapter is devoted to conclusions and outlook of this work.

The first detection of a gravitational wave (GW) enabled our observation of the Universe through a revolutionary messenger and unveiled phenomena that are occurring in a range of very strong gravitational fields and relativistic velocities. These physical regimes, previously inaccessible to humankind, can now be studied. In particular, the discoveries of an unexpected population of stellar-mass binary black holes (BBH), and unexpected masses for binary neutron star (BNS) components have both pointed to new astrophysics, and to unprecedented tests of the general relativity theory. This thesis focuses on the development of a new method of gravitational wave data analysis, aiming to investigate weak features in the proximity to well-identified BBH merger signals. The method is based on a dedicated version of coherentWaveBurst (cWB), an unmodelled gravitational waves transient search algorithm, developed in the LIGO Scientific Collaboration (LSC) and Virgo Collaboration and widely used on LIGO-Virgo-KAGRA (LVK) data. CoherentWaveBurst relies on the coherent detection of an excess of energy inside the combined data of all the gravitational waves detectors inside the detectors network. Such excess of energy must pass several internal thresholds of the pipeline to be accepted as a possible gravitational wave candidate and these thresholds evaluate not only the strength of the signal with respect to the background noise but also how balanced is the energy distribution among the detectors of the network, its coherence, as well as other quantities whose purpose is to rule out possible outliers due to the presence of non-stationary noise. To develop such a method, it was decided to adopt as science case the search for echoes. In literature, it has been proposed that the gravitational radiation generated from a binary compact objects (CBCs) coalescence might display exotic characteristics if compared to the predicted one generated by black hole-black hole (BH-BH), neutron star-neutron star (NS-NS), or neutron star-black hole (NS-BH) binaries which are, for now, the only detected emitters of gravitational waves. Such differences arise from the proposal that the involved compact objects (COs) of the binary are not standard black holes but instead black hole mimickers called exotic compact objects (ECOs). If this is the case the gravitational wave signal generated from such a binary would display repeated gravitational wave pulses, of widely uncertain morphology, after the merger-ringdown phase of the gravitational signal. These repeated gravitational wave pulses are called echoes, one class of low energetic signals whose presence inside gravitational wave data, this new algorithm is searching for. The proposed data analysis methodology searching for echoes is agnostic over the properties of the predicted gravitational wave pulses emitted by an ECO binary. Indeed, the variety of theoretical alternatives to black holes is not converging over a well-defined post-merger-ringdown signal, each model has its own properties and characteristic features. Therefore, the possibility to investigate the morphological features of possible outliers in the post-merger phase of detected GW signals is fundamental in the process of inferring their nature. Having their morphology recovered without priors makes the proposed search more general than the variety of theoretical models of echoes. This procedure is tested over real data from past LIGO-Virgo observing runs (O1, O2, and O3), and the capability of the search in estimating the main morphological parameters of echoes, such as their arrival time, mean frequency, as well as the amplitude attenuation between subsequent pulses, is investigated. This work concludes that the current state-of-the-art methods and detectors find no evidence for echoes of any morphologies. Such a study extended to lower signal-to-noise ratio (SNR) the detectability of echoes associated with the public gravitational-wave transient catalog of BBH mergers released by the LIGO and Virgo Collaboration. It also sets best quantitative upper limits on the amplitude of low energy signals occurring after the merger-ringdown. To achieve these results, new post-processing tools are developed and optimised to detect and characterize possible energy excess inside a user-defined time window. This required the development of the code and to adapt the cWB infrastructure to the new working requirements which also involves a re-tuning of cWB itself. The optimization of the performances is based on off-source simulations for assessing the detection efficiency and false alarm probability of signal candidates.

This thesis is concerned with effects of spin polarization in neutron stars. In particular, we focus on static and dynamic properties of dense neutron matter. We use two different kind of potential to perform our studies: the phenomenological two-body Argonne V$8$' potential plus the three-body Urbana IX force and a modern local version of chiral effective potential up to next-to-next-to-leading order (N$2$LO). Estimates are calculated for the neutrino mean free path in partially spin-polarized neutron matter starting from Quantum Monte Carlo (QMC) simulations and using mean-field approaches to compute the response function in the longitudinal and transverse channel. We also compute magnetic susceptibility of dense neutron matter from accurate QMC calculations of partially spin-polarized systems. Twist-averaged boundary conditions (TABC) have been implemented to reduce finite-size effects. In the results, we also account for the theoretical uncertainty coming from the chiral expansion scheme. These results may play a role in studying high-energy phenomena such as neutron star mergers and supernova explosions, although they have been computed only at T$=0$ K.

Low-resolution, coarse-grained models are powerful computational tools to investigate the behavior of biological systems over time and length scales that are not accessible to all-atom Molecular Dynamics simulations. While several algorithms exist that aim at constructing accurate coarse-grained potentials, few works focus on the choice of the reduced representation, or mapping, to be employed to describe the high-resolution system with a lower number of degrees of freedom. This thesis proposes a series of approaches to investigate and characterise the representation problem in coarse-grained modelling of proteins. This is achieved by employing a collection of diverse methods, including statistical mechanics, machine learning algorithms and information-theoretical tools. The central mathematical object of this work is the mapping entropy, a Kullback-Leibler divergence that measures the intrinsic quality of a given reduced representation. When this quantity is minimised, we obtain the maximally informative coarse-grained mappings of a biomolecule, which cover the structure with an uneven level of detail. Tests conducted over a set of well-known proteins show that regions preserved with high probability are often related to important functional mechanisms of the molecule. Applications of the mapping entropy outside of the field of structural biology show promising results, leading to the identification of those combinations of features that retain the maximum amount of information about the high-resolution system. Additionally, a purely structural notion of scalar product and distance between coarse-grained mappings is introduced, which allow to analyse the metric and topological properties of the mapping space. The thorough exploration of such space leads to the discovery of qualitatively different reduced representations of the biomolecule of interest.

Proteins are one of the most studied biological molecules of the last decades. A great amount of experimental techniques provide to researchers direct or indirect informations on proteins structure and function. In silico simulations can be used as a “computational microscope” giving the possibility to observe protein dynamic properties at atomistic resolution. In this work, various applications of computational methods to biological systems are presented. In particular, all-atom Molecular Dynamics (MD) simulations were employed to investigate the behaviour of proteins at atomstic resolution. The term “Molecular Dynamics” is usually referred to computational methods used for the simulation of classical many-body systems. These techniques are applied to microscopic systems and they represent a powerful approach for the study of physical processes, providing a tool for their interpretation. They have been widely used in the past decades to elucidate a large variety of molecular processes in different fields such as solid state physics, material science, chemistry, biochemistry and biophysics. Here, all-atom MD simulations were employed to observe equilibrium properties of several biologically relevant proteins. This allowed us to direct perform a comparison of molecular mechanisms occurring at the atomistic level as obtained from in silico studies with experimental data, which usually describe processes at larger length and time scales. These MD simulations were also meant as a starting point for the construction of simplified models, as they were processed through coarse-graining procedures to extrapolate crucial systems features, such as informative protein sites, on the basis of information theory approaches. Specifically we studied the dynamics of pembrolizumab, a humanized immunoglobulin of type G4 (IgG4) used as a therapeutic antibody. It is employed for the treatment of lung cancer, melanoma, stomach and head cancer and Hodgkin’s lymphoma. This antibody interacts with the programmed cell death protein 1 (PD-1) receptor, blocking the suppression of the immune response during cancer development. The studied systems are three: the apo state of pembrolizumab, the holo state (i.e. pembrolizumab bound to PD-1) and the glycosylated apo configuration. Each configuration was simulated for 2μs, for a total of 6μs. The analysis of the trajectories was carried out by combining standard structural analysis techniques and information theory-based measures of correlation. From MD trajectories we could extract valuable informations on the connectivity that exists among the structural domains that compose the antibody structure. Moreover, it was possible to infer which regions are involved in the structural rearrangement in the case of the antigen binding. We could observe that the presence of the antigen reduces the conformational variability of the molecule giving a greater stability to it. The second studied system is the P53 protein complex. In this case we focused on the tetramerization domain (TD) region that is composed by 2 identical dimers and has the function of bringing together the four monomers of the p53 complex. Starting from the observation that in case of the mutation of residue R337 several pathologies are developed in humans, we constructed computational models to reproduce the dynamics of the mutants and investigate their behaviour in silico. We performed simulations for a total of 16 μs divided in 8 different cases. In the first part of the study the wild type (WT) protein was compared to the R337C and the R337H mutant in three different protonation states: delta protonated Histidine, epsilon protonated Histidine ad double protonated Histidine. In the second part of the study we highlighted the differences between the WT configuration and three rationally designed mutants: R337D-352D, 337R-D352R, R337D-D352R. In this part of the investigation, the importance of the electrostatic interaction between residues R337 and D352 in the stability of the tetramerization do- main was discussed. Furthermore, we matched the obtained computational results of p53 tetramerization domain with functional experiments in yeasts (performed in collaboration with the CIBIO department) of all the simulated forms. The third simulated protein is the zinc sensing transcriptional repressor (CzrA), an homodimeric protein that binds DNA in Staphylococcus aureus. All-atom MD simulations of two different configurations were performed for a total of 4μs, the first one is the WT apo protein while the second is the WT holo system, where the protein is complexed with two Zn ions. In this case, in addition to standard analysis techniques, we applied the mapping entropy minimization protocol to highlight the most informative protein regions, from the perspective of information theory. Finally, our in silico results were compared to available NMR data of the protein itself.