On the Smooth Locus in Flat Linear Degenerations of Flag Varieties

We use some moment graph techniques, recently introduced by Lanini and P\"utz, to provide a combinatorial description of the smooth locus in flat linear degenerations of flag varieties, generalizing a result proved by Cerulli Irelli, Feigin and Reineke for the Feigin degeneration. Moreover, we propose a different combinatorial criterion linking the smoothness at a fixed point to transitive tournaments.Comment: 19 pages, 15 figures. Comments are welcome

On Reeder's Conjecture for type B and C Lie algebras

In the paper we propose a proof of Reeder's Conjecture on the graded multiplicities of small representations in the exterior algebra $\Lambda$g for the simple Lie algebras of type B and C.Comment: 22 page

Quantum Integer Programming: an Annealing approach to the Job Shop Scheduling problem

openIn this thesis i developed a complete workflow to get optimal solutions of the JSS problem. During this work i deeply analized many of the steps required in the usage of quantum annealers. In detail i tested 2 different approaches to the minor-embedding procedure and compared them with the current default euristic implemented by Dwave. I also tested an hybrid algorithm wich extract the elements of the Graver basis of the problem and then augment an initial feasible solution to obtain an optimal one. The obtained results shows that the quantum annealers can get to optimal solutions in a competitive time but, due to the limited numer of working qubits and the sparse connectivity among them, only small instances can be efficiently solved with the current hardware.In this thesis i developed a complete workflow to get optimal solutions of the JSS problem. During this work i deeply analized many of the steps required in the usage of quantum annealers. In detail i tested 2 different approaches to the minor-embedding procedure and compared them with the current default euristic implemented by Dwave. I also tested an hybrid algorithm wich extract the elements of the Graver basis of the problem and then augment an initial feasible solution to obtain an optimal one. The obtained results shows that the quantum annealers can get to optimal solutions in a competitive time but, due to the limited numer of working qubits and the sparse connectivity among them, only small instances can be efficiently solved with the current hardware

On the Spectrum of Exterior Algebra, and Generalized Exponents of Small Representations

We present some results about the irreducible representations appearing in the exterior algebra $\Lambda \mathfrak{g}$, where $\mathfrak{g}$ is a simple Lie algebra over $\mathbb{C}$. For Lie algebras of type $B$, $C$ or $D$ we prove that certain irreducible representations, associated to weights characterized in a combinatorial way, appear as irreducible components of $\Lambda \mathfrak{g}$. Moreover, we propose an analogue of a conjecture of Kostant, about irreducibles appearing in the exterior algebra of the little adjoint representation. Finally, we give some closed expressions, in type $B$, $C$ and $D$, for generalized exponents of small representations that are fundamental representations and we propose a generalization of some results of De Concini, M\"oseneder Frajria, Procesi and Papi about the module of special covariants of adjoint and little adjoint type.Comment: 28 pages. Comments are welcome. To appear in Bollettino dell'Unione Matematica Italian

Optimized non-invasive MRI protocols for characterizing tissue microstructures: applications in humans to prostate cancer and fetal brain development

This PhD project was aimed to optimize MRI protocols for pelvis imaging, in particular for the diagnosis of prostate cancer (PCa) and for the fetal brain development. Different non-invasive MRI techniques were employed to investigate biological tissues, with the purpose to obtain information on microstructures and potentially metabolism. Prostate cancer is the second most common malignancy and the fifth leading cause of death in men worldwide. Due to the high incidence of PCa and the limitations of current diagnostic methods, the primary goal of this work was to develop an MRI protocol able to improve the sensitivity of the diagnostic. The investigation of prostate cancer started with ex-vivo experiments conducted on specimens of human prostate gland, obtained after radical prostatectomy, with the 9.4T scanner at the NMR and Medical Physics Laboratory of CNR-ISC (Sapienza). Diffusion Tensor Imaging (DTI) and Diffusion Kurtosis Imaging (DKI) were performed at high-resolution (70x70 micrometers in plane) to evaluate diffusion metrics in the different prostate compartment and directly compare measurements with the histopathology results. This study proceeded with in-vivo experiments with a 3T clinical MR scanner (Philips Achieva at Policlinico Tor Vergata) on subjects with diagnosed PCa. DTI was performed with the purpose to assess its diagnostic ability in individuating and classifying PCa with different ranges of diffusion weightings, i.e. b-values. Our results showing that the diagnostic accuracy of DTI is improved with high diffusion weightings motivated our interest in performing DKI, a technique that captures water diffusion features when high b-values are employed, providing additional information on tissue microstructures, inaccessible to DTI technique. The second part of this PhD project was conducted at the Center for Magnetic Resonance Research (CMRR) in Minneapolis and was funded by the European Union's Horizon 2020 research and innovation program under the Marie Curie grant agreement No 691110 (MICROBRADAM). The study was dedicated to perform prostate cancer imaging with new contrast mechanisms, based on T1rho and T2rho relaxation times. T1rho and T2rho characterize the relaxation of the nuclear magnetization in the rotating frame and they are sensitive to molecular dynamics occurring at frequencies in the range of kHz, characteristic of several in-vivo processes, enabling the access to important information on tissue microenvironment. T1rho and T2rho imaging is limited by the intensive energy deposited by the acquisition sequence, which it is usually overcome by increasing the acquisition time, preventing the possibility of diagnostic applications. Therefore the aim of this work was to develop a new approach to perform imaging in the rotating frame with a three-dimensional acquisition method, recently developed at the CMRR, in order to address the aforementioned shortcomings. Given the incidence of PCa, this research has international interest and potentially contributes to improve not only the sensitivity of PCa diagnostic but also the knowledge of the tissue micro-changing caused by the tumor development. A part of this project was dedicated to Diffusion MRI application in woman pelvis to image fetuses during gestation. The aim of this work was to develop a fast and reliable protocol for fetal imaging to minimize mother-fetal motion artifact and perfusion effects. The protocol designed for acquisition and post-processing was employed to successfully study fetal brain development during the second and third trimester of gestation, in normal cases and in fetuses affected by ventriculomegaly disease. These preliminary data can contribute to delineate a reference standard to assess the normal progress of sulcation and myelination as well as the normative biometry of the fetal brain, improving the knowledge of brain maturation. Globally, the impact of this research lies in having demonstrated that the sensitivity of DMRI for microstructural changes in body tissue caused by cancer, brain disease or normal condition like brain maturation can be fruitfully utilized in combination with artifact correction methods. Moreover, new strategy of image reconstruction, such as 3D gradient echo, can be successfully employed to perform abdominal imaging, enriching the investigation of in-vivo systems with information on tissue microenvironment and metabolism

Comorbid depressive disorders in ADHD. the role of ADHD severity, subtypes and familial psychiatric disorders

ObjectiveaaTo evaluate the presence of Major Depressive Disorder (MDD) and Dysthymic Disorder (DD) in a sample of Italian children with Attention Deficit Hyperactivity Disorder (ADHD) and to explore specific features of comorbid depressive disorders in ADHD. MethodsaaThree hundred and sixty-six consecutive, drug-naïve Caucasian Italian outpatients with ADHD were recruited and comorbid disorders were evaluated using DSM-IV-TR criteria. To evaluate ADHD severity, parents of all children filled out the ADHD Rating Scale. Thirty-seven children with comorbid MDD or DD were compared with 118 children with comorbid conduct disorder and 122 without comorbidity for age, sex, IQ level, family psychiatric history, and ADHD subtypes and severity. Resultsaa42 of the ADHD children displayed comorbid depressive disorders: 16 exhibited MDD, 21 DD, and 5 both MDD and DD. The frequency of hyperactive-impulsive subtypes was significantly lower in ADHD children with depressive disorders, than in those without any comorbidity. ADHD children with depressive disorders showed a higher number of familial psychiatric disorders and higher score in the Inattentive scale of the ADHD Rating Scale, than children without any comorbidity. No differences were found for age, sex and IQ level between the three groups. Conclusions: Consistent with previous studies in other countries, depressive disorders affect a significant proportion of ADHD children in Italy. Patient assessment and subsequent treatment should take into consideration the possible presence of this comorbidity, which could specifically increase the severity of ADHD attention problems

Short communication: Relationships between milk quality and acidification in the production of table Mozzarella without starters.

The effect of some quality parameters of the milk (refrigeration time, pH, protein, and fat/protein ratio) on the extent of acidification in the production technology of table Mozzarella without starters was investigated. A screening phase carried out at the laboratory level demonstrated that variations of the milk characteristics require different levels of acidification to keep constant the quality of the cheese. The elaboration of the data collected throughout the successive experimentation on industrial scale allowed us to find a mathematical model to describe the relationships between the pH of the curd at stretching time and the milk characteristics, of which the protein concentration and the refrigeration time play the main roles

Combinatorial and topological aspects of path posets, and multipath cohomology

Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets and to provide computational tools for multipath cohomology. In particular, we develop acyclicity criteria and provide computations of multipath cohomology groups of oriented linear graphs. We further interpret the path poset as the face poset of a simplicial complex, and we investigate realisability problems