A doubly relaxed minimal-norm Gauss-Newton method for underdetermined nonlinear least-squares problems

When a physical system is modeled by a nonlinear function, the unknown parameters can be estimated by fitting experimental observations by a least-squares approach. Newton's method and its variants are often used to solve problems of this type. In this paper, we are concerned with the computation of the minimal-norm solution of an underdetermined nonlinear least-squares problem. We present a Gauss-Newton type method, which relies on two relaxation parameters to ensure convergence, and which incorporates a procedure to dynamically estimate the two parameters, as well as the rank of the Jacobian matrix, along the iterations. Numerical results are presented

Ascertaining the ideality of photometric stereo datasets under unknown lighting

The standard photometric stereo model makes several assumptions that are rarely verified in experimental datasets. In particular, the observed object should behave as a Lambertian reflector and the light sources should be positioned at an infinite distance from it, along a known direction. Even when Lambert's law is approximately fulfilled, an accurate assessment of the relative position between the light source and the target is often unavailable in real situations. The Hayakawa procedure is a computational method for estimating such information directly from the data images. It occasionally breaks down when some of the available images deviate too much from ideality. Indeed, in narrow shooting scenarios, typical, e.g., of archaeological excavation sites, it may be impossible to position a flashlight at a sufficient distance from the observed surface. It is then necessary to understand if a given dataset is reliable and which images should be selected to better reconstruct the target. In this paper, we propose some algorithms to perform this task and explore their effectiveness

CASSCF response equations revisited: a simple and efficient iterative algorithm

We present an algorithm to solve the CASSCF linear response equations that is both simple and efficient. The algorithm makes use of the well established symmetric and antisymmetric combinations of trial vectors, but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric, block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Preliminary numerical tests show that the algorithm is robust and stable

Advances in the Management of Medullary Thyroid Carcinoma. Focus on Peptide Receptor Radionuclide Therapy

Effective treatment options in advanced/progressive/metastatic medullary thyroid carcinoma (MTC) are currently limited. As in other neuroendocrine neoplasms (NENs), peptide receptor radionuclide therapy (PRRT) has been used as a therapeutic option in MTC. To date, however, there are no published reviews dealing with PRRT approaches. We performed an in-depth narrative review on the studies published in this field and collected information on registered clinical trials related to this topic. We identified 19 published studies, collectively involving more than 200 patients with MTC, and four registered clinical trials. Most cases of MTC were treated with PRRT with somatostatin analogues (SSAs) radiolabelled with 90 yttrium (90Y) and 177 lutetium (177Lu). These radiopharmaceuticals show efficacy in the treatment of patients with MTC, with a favourable radiological response (stable disease, partial response or complete response) in more than 60% of cases, coupled with low toxicity. As MTC specifically also expresses cholecystokinin receptors (CCK2Rs), PRRT with this target has also been tried, and some randomised trials are ongoing. Overall, PRRT seems to have an effective role and might be considered in the therapeutic strategy of advanced/progressive/metastatic MTC

The double-sided of human leukocyte antigen-G molecules in type 1 autoimmune hepatitis

The immunomodulatory effects of HLA-G expression and its role in cancers, human liver infections and liver transplantation are well documented, but so far, there are only a few reports addressing autoimmune liver diseases, particularly autoimmune hepatitis (AIH). Method and materialsWe analyzed the genetic and phenotypic characteristics of HLA-G in 205 type 1 AIH patients (AIH-1) and a population of 210 healthy controls from Sardinia (Italy). ResultsAnalysis of the HLA-G locus showed no substantial differences in allele frequencies between patients and the healthy control population. The HLA-G UTR-1 haplotype was the most prevalent in both AIH-1 patients and controls (40.24% and 34.29%). Strong linkage was found between the HLA-G UTR-1 haplotype and HLA-DRB1*03:01 in AIH-1 patients but not controls (D' = 0.92 vs D' = 0.50 respectively; P = 1.3x10(-8)). Soluble HLA-G (sHLA-G) levels were significantly lower in AIH-1 patients compared to controls [13.9 (11.6 - 17.4) U/mL vs 21.3 (16.5 - 27.8) U/mL; P = 0.011]. Twenty-four patients with mild or moderate inflammatory involvement, as assessed from liver biopsy, showed much higher sHLA-G levels compared to the 28 patients with severe liver inflammation [33.5 (23.6 - 44.8) U/mL vs 8.8 (6.1 - 14.5) U/mL; P = 0.003]. Finally, immunohistochemistry analysis of 52 liver biopsies from AIH-1 patients did not show expression of HLA-G molecules in the liver parenchyma. However, a percentage of 69.2% (36/52) revealed widespread expression of HLA-G both in the cytoplasm and the membrane of plasma cells labeled with anti-HLA-G monoclonal antibodies. ConclusionThis study highlights the positive immunomodulatory effect of HLA-G molecules on the clinical course of AIH-1 and how this improvement closely correlates with plasma levels of sHLA-G. However, our results open the debate on the ambiguous role of HLA-G molecules expressed by plasma cells, which are pathognomonic features of AIH-1

Pathology reporting in neuroendocrine neoplasms of the digestive system: everything you always wanted to know but were too afraid to ask

During the 5th NIKE (Neuroendocrine tumors Innovation in Knowledge and Education) meeting, held in Naples, Italy, in May 2019, discussions centered on the understanding of pathology reports of gastroenetropancreactic neuroendocrine neoplasms. In particular, the main problem concerned the difficulty that clinicians experience in extrapolating relevant information from neuroendocrine tumor pathology reports. During the meeting, participants were asked to identify and rate issues which they have encountered, for which the input of an expert pathologist would have been appreciated. This article is a collection of the most rated questions and relative answers, focusing on three main topics: 1) morphology and classification; 2) Ki67 and grading; 3) immunohistochemistry. Patient management should be based on multidisciplinary decisions, taking into account clinical and pathology-related features with clear comprehension between all health care professionals. Indeed, pathologists require clinical details and laboratory findings when relevant, while clinicians require concise and standardized reports. In keeping with this last statement, the minimum requirements in pathology datasets are provided in this paper and should be a baseline for all neuroendocrine tumor professionals

Natural killer-cell immunoglobulin-like receptors trigger differences in immune response to SARS-CoV-2 infection

Background: The diversity in the clinical course of COVID-19 has been related to differences in innate and adaptative immune response mechanisms. Natural killer (NK) lymphocytes are critical protagonists of human host defense against viral infections. It would seem that reduced circulating levels of these cells have an impact on COVID-19 progression and severity. Their activity is strongly regulated by killer-cell immuno-globulin-like receptors (KIRs) expressed on the NK cell surface. The present study's focus was to investigate the impact of KIRs and their HLA Class I ligands on SARS-CoV-2 infection. Methods: KIR gene frequencies, KIR haplotypes, KIR ligands and combinations of KIRs and their HLA Class I ligands were investigated in 396 Sardinian patients with SARS-CoV-2 infection. Comparisons were made between 2 groups of patients divided according to disease severity: 240 patients were symptomatic or paucisymptomatic (Group A), 156 hospitalized patients had severe disease (Group S). The immunogenetic characteristics of patients were also compared to a population group of 400 individuals from the same geographical areas. Results: Substantial differences were obtained for KIR genes, KIR haplotypes and KIR-HLA ligand combinations when comparing patients of Group S to those of Group A. Patients in Group S had a statistically significant higher frequency of the KIR A/A haplotype compared to patients in Group A [34.6% vs 23.8%, OR = 1.7 (95% CI 1.1-2.6); P = 0.02, Pc = 0.04]. Moreover, the KIR2DS2/HLA C1 combination was poorly represented in the group of patients with severe symptoms compared to those of the asymptomatic-paucisymptomatic group [33.3% vs 50.0%, OR = 0.5 (95% CI 0.3-0.8), P = 0.001, Pc = 0.002]. Multivariate analysis confirmed that, regardless of the sex and age of the patients, the latter genetic variable correlated with a less severe disease course [ORM = 0.4 (95% CI 0.3-0.7), PM = 0.0005, PMC = 0.005]. Conclusions: The KIR2DS2/HLA C1 functional unit resulted to have a strong protective effect against the adverse outcomes of COVID-19. Combined to other well known factors such as advanced age, male sex and concomitant autoimmune diseases, this marker could prove to be highly informative of the disease course and thus enable the timely intervention needed to reduce the mortality associated with the severe forms of SARS-CoV-2 infection. However, larger studies in other populations as well as experimental functional studies will be needed to confirm our findings and further pursue the effect of KIR receptors on NK cell immune-mediated response to SARS-Cov-2 infection

On the computation of the minimal-norm solution of linear and nonlinear problems

The main topic of the thesis is the study of inverse problems and, in particular, it is the study of numerical methods for the computation of the minimal-norm solution of linear inverse problems in the continuous case and nonlinear ones in the discrete case. Inverse problems arise in many areas of science and engineering, from the need to interpret indirect and incomplete measurements. The most usual situation giving rise to an inverse problem is the need to interpret indirect physical measurements of an unknown object of interest, for instance, if one is interested in determining the internal structure of a physical system from the system’s measured behavior, or in determining the unknown input that gives rise to a measured output signal. Inverse problems are a recent topic in mathematics. Their study is motivated by the technological development of the last decades; for example, some of the more sophisticated medical diagnostic machines solve inverse problems, such as X-ray computed tomography, in which the inverse problem is to reconstruct the inner structure of an unknown physical body from the knowledge of X-ray images taken from different directions. An example of inverse problem, which will be treated in some numerical experiments of this thesis, concerns the study of the subsoil in a non-destructive way, through the propagation of electromagnetic waves, in order to know some properties of the subsoil. Another example concerns image processing, where the goal is to find the sharp photograph from a given blurry image. An inverse problem takes the form F(x) = b, where F is a linear or nonlinear operator, x represents the unknown solution, and b is the information available, that is, the measurements dataset. The goal is to reconstruct x starting from b. Inverse problems are closely related to the concept of ill-posed problems. To understand this concept we need to resort to the definition given by Hadamard at the beginning of the last century: such problems may not have a solution, or may have more than one, or that solution is not stable with respect to perturbation in the data. In applications, ill-posed problems are common whenever there is little available measured data compared to the number of unknowns. In this case, it is necessary to reformulate the original ill-posed problem into a well-posed problem. A typical approach is to resort to a least-squares problem, in which the mean squared error between F(x) and b is required to be minimal. In this thesis, we are concerned with problems that have no unique solution. Among the different solutions, we want to determine the minimal-norm solution. The subjects discussed in this thesis can be divided into two themes: nonlinear least-squares problems and systems of linear integral equations of the first kind

“There’s a Lot of Beauty in Ordinary Things, Isn’t That Kind of the Point?”: A Study of the Effect of Exposure to American Sitcoms on Natural Speech Acquisition

openIn our globalized world, English learning has become a central issue for Italian students. Research conducted by the World Economic Forum on European countries shows that less than 30% of the population can fluently speak English, compared to the average 70% of the northern countries. In this context, alternative methods for language acquisition have been studied intensely to appeal to young students and increase their second language skills. However, few studies focused on American sitcoms as tools for learning the colloquial aspects of English, the key to a more effortless expression and comprehension of the language. The present study demonstrates the effectiveness of the 2000s TV show “The Office” in Italian students’ development of spontaneous and colloquial conversation. To identify significant grammar patterns and informal expressions, transcripts from the show have been analyzed and compared to the TV Corpus. Then, such material has been included in B1-level English activities and tested on a group of students aged 14-19 during one hour lesson. After completing a questionnaire on movies and TV series viewing preferences, students have been evaluated through objective exercises based on the phraseology of the scenes seen in class. Results have shown that not only was there a relevant increase in listening comprehension and ability to communicate naturally, but also a shift in the class environment, as the students seemed to lower their affective filter showing higher motivation, critical thinking ability, and will to interact with each other in the second language. The limitation of the study comprised the lack of experimentation regarding activities and exercises related to the audiovisual material; so that further research could focus on the implementation of American sitcoms in secondary school teaching units in more diverse and creative ways

The minimal-norm Gauss-Newton method and some of its regularized variants. ETNA - Electronic Transactions on Numerical Analysis

Nonlinear least-squares problems appear in many real-world applications. When a nonlinear model is used to reproduce the behavior of a physical system, the unknown parameters of the model can be estimated by fitting experimental observations by a least-squares approach. It is common to solve such problems by Newton's method or one of its variants such as the Gauss-Newton algorithm. In this paper, we study the computation of the minimal-norm solution to a nonlinear least-squares problem, as well as the case where the solution minimizes a suitable semi-norm. Since many important applications lead to severely ill-conditioned least-squares problems, we also consider some regularization techniques for their solution. Numerical experiments, both artificial and derived from an application in applied geophysics, illustrate the performance of the different approaches