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Background Literature has paid little attention in describing the specific contribution of each modifiable and non-modifiable characteristics on health-related quality of life (HRQoL) in physician-managed anticoagulated patients using vitamin K antagonists (VKAs). To describe how patients’ treatment-specific knowledge, health literacy, treatment beliefs, clinical, and socio-demographic characteristics influence HRQoL in Italian physician-managed anticoagulated patients using VKAs. Methods Cross-sectional multicentre study with a consecutive sampling strategy, enrolling 164 long-term anticoagulated patients. Clinical and socio-demographic characteristics were collected from electronic medical records. Valid and reliable questionnaires were used to collect patients’ treatment-specific knowledge, health literacy, beliefs about VKAs, physical and health perceptions. Results Obtaining and understanding health information (i.e., communicative health literacy) positively predicts both adequate mental (OR adjusted  = 10.9; 95%CI = 1.99–19.10) and physical (OR adjusted  = 11.54; 95%CI = 1.99–34.45) health perceptions. Conversely, the ability to perform proper health decision making (i.e., critical health literacy) was associated with lower rates of adequate mental health perception (OR adjusted  = 0.13; 95%CI = 0.03–0.63). Further, age negatively predicted physical health perception (OR adjusted  = 0.87; 95%CI = 0.81–0.93). Conclusions Health literacy plays an interesting role in predicting HRQoL. The relationship between critical health literacy and mental health perception could be influenced by some psychological variables, such as distress and frustration, which could be present in patients with higher levels of critical health literacy, as they could be more inclined for self-monitoring. For this reason, future research are needed to identify the most suitable patients’ profile for each OAC-management model, by longitudinally describing the predictive performance of each modifiable and non-modifiable determinant of HRQoL.

The technological advancements of recent decades, coupled with the ever-existing interest in expanding the boundaries of our knowledge of the universe, are enabling new types of space missions, each presenting its own unique challenges. Deep space missions increasingly demand autonomous navigation capabilities, and Optical Navigation (OPNAV) has proven to be a promising response to this need. Developing new navigation solutions, and refining existing ones, is a thriving area of research.When developing algorithms for OPNAV, a convenient mathematical framework is provided by algebraic geometry. Algebraic geometry studies polynomial equations, and its connection with navigation becomes evident when realizing how many features and physical phenomena in the world of spacecraft navigation can be described in polynomial form. Keplerian orbits, elliptical crater rims, ellipsoidal celestial bodies, atmospheric bands, planetary rings, and the path traced by any object bound to the surface of a spinning body are all curves and surfaces that can be described in terms of polynomials of degree two. Furthermore, the Doppler effect, stellar aberration, image distortion, the line-of-sight observation of an orbiting body are only some examples of phenomena or constraints which are either represented or well-modeled in terms of polynomials.This dissertation explores the application of some techniques from algebraic and projective geometry to address multiple navigation-related challenges. The first part of this work explores how analytical tools can be leveraged to obtain the closed form expression of the projection of a crater rim imaged with a pushbroom camera. Crater rims are often visible in the images captured by such sensors, and the knowledge of their analytical shape enables interesting capabilities, such as crater reconstruction and spacecraft state estimation.After that, projective geometry will be used to develop an analytical framework for the representation of Keplerian orbits. This framework led to a novel velocity propagation technique, and to a solution to the problem of fitting a conic with constrained focus location to three points. Additionally, tools from numerical algebraic geometry will be used to initialize the state of an orbiting transmitter.Finally, algebraic geometry will be used to address two image analysis tasks. First, a new technique for partially calibrating a camera from a single celestial body is presented. Then, the conic intersection problem, encountered when identifying craters in a digital image, is revisited and an algorithmic framework providing a simpler solution compared with current techniques is developed.

Initial Orbit Determination (IOD) is a classical problem in astrodynamics. The space around Earth is crowded by a great many objects whose orbits are unknown, and the number of space debris is constantly increasing because of break-up events and collisions. Reconstructing the orbit of a body from observations allows us to create catalogs that are used to avoid collisions and program missions for debris removal. Also, comparing the observations of celestial bodies with predictions of their positions made based on our knowledge of the universe has been in the past, and is still today, one of the most effective means to make improvements in our cosmological model. In this work, a purely geometric solution to the angles-only IOD problem is analyzed, and its performance under various scenarios of observations is tested. The problem formulation is based on a re-parameterization of the orbit as a disk quadric, and relating the observations to the unknowns leads to a polynomial system that can be solved using tools from numerical algebraic geometry. This method is time-free and does not require any type of initialization. This makes it unaffected by the problems related to the estimate of the time-of-flight, that usually affects the accuracy of the solution. A similar approach may be used to analyze the performance of the solver when streaks are used, together with lines of sight, as inputs to the problem. Streaks on digital images form, together with the camera location, planes that are tangent to the orbit. This produces two different types of constraints, that can be written as polynomial equations. The accuracy and the robustness of the solver are decreased by the presence of streaks, but they remain a valid input when diversity in the observed directions guarantees the departure from the singular configuration of almost coplanar observations.

Chronic rhinosinusitis (CRS) includes two main phenotypes: without sal polyps (CRSsNP) and with sal polyps (CRSwNP). CRSwNP may be associated with comorbidity, mainly concerning asthma, aspirin intolerance, and allergy. CRSwNP patients may also be evaluated by clinical-cytological grading (CCG). The current study investigated the prevalence and characteristics of the different CCG and phenotypes in CRSwNP outpatients examined in clinical practice. This retrospective cross-sectiol study enrolled 791 consecutive CRSwNP outpatients (424 males, mean age 48.8 years). In the total population, asthma was a common comorbidity (30.8%) as well as aspirin intolerance (24.8%), and allergy (50.8%). As concerns CCG-grading, 210 (26.5%) outpatients had low-grade, 366 (46.3%) medium, and 215 (27.2%) high. As regards cytological phenotypes, 87 (11%) had neutrophilic type, 371 (46.3%) eosinophilic, 112 (14.2%) mast cell, and 221 (27.9%) mixed. High-grade CCG was significantly associated with more frequent asthma, aspirin intolerance, allergy, recurrent surgery, and mixed cytological phenotype. Low-grade CCG was characterized by fewer comorbidities and operations, and neutrophilic phenotype. Therefore, the present study confirmed that CCG is a useful tool in the magement of outpatients with CRSwNP. CRSwNP is frequently associated with asthma, aspirin intolerance, and allergy comorbidity. High-grade CCG is frequently characterized by a mixed cytological phenotype, thus, by more severe progress. These real-world outcomes underline that CRSwNP deserves adequate attention for careful magement and optimal identification of the best-tailored therapy; CCG and cytological phenotyping could be fruitful tools in clinical practice. Asthma and aspirin intolerance should be adequately investigated in all CRS patients.

Background. Enterobacter cloacae complex producing extended-spectrum beta-lactamase - ESBL (ECCOE) is a group of gram-negative pathogens responsible for nosocomial outbreaks in vulnerable patients, among whom neonatal patients represent one of the highest risk groups. Methods. We present data from an ECCOE outbreak identified at the Cremona hospital in January 2024, when a case of ECCOE bacteremia was diagnosed in patient admitted to the Neonatology ward. Following the identification of the index case, an infection prevention and control (IPC) program was implemented, based on: isolation of all positive patients with contact precautions, weekly screening of all hospitalized patients, environmental sampling, a program to improve adherence to hand hygiene, enhanced disinfection procedures, and regular data feedback to the ward staff. Results. The retrospective analysis identified a second infection in January 2024. In 2023, no clinical cases were identified and only one positivity for ECCOE emerged from 301 microbiological screening swabs (0.3%). The prospective analysis did not reveal other infections in the following 11 months. Patient surveillance through swabs showed a baseline prevalence of ECCOE of 15.4% in January, which rose to 30.8% in February, significantly decreased in March, then increased again to 38.5% in June and finally dropped to zero in August. The environmental sampling highlighted only one positivity out of 79 samples (1.3% of the samples). The consumption of alcohol hand rub solution, very low at the start of the outbreak (26 L/1,000 patient days - PD), increased to 113 L/1,000 PD, and then decreased by 70% after the outbreak ended. Conclusions. A rapid and complex IPC intervention focusing on improving hand hygiene can help control an ECCOE outbreak in neonatology. However, maintaining adequate adherence to hand hygiene over time remains very challenging.

Finding the intersection of two conics is a commonly occurring problem. For example, it occurs when identifying patterns of craters on the lunar surface, detecting the orientation of a face from a single image, or estimating the attitude of a camera from 2D-to-3D point correspondences. Regardless of the application, the study of this classical problem presents a number of delightful geometric results. In most of the cases, the intersection points are computed by finding the degenerate conic consisting of two lines passing through the common points. Once a linear combination of the two conic matrices has been constructed, the solution of an eigenvalue problem provides four possible degenerate conics, of which only one coincides with the sought pair of lines. Then, the method proceeds by finding the intersection between one of the conics and the two lines. Other approaches make use of different methods, such as Gr\"obner bases or geometric algebra. Conic intersection, however, may be solved more intuitively with a convenient change of coordinates. In this work, we will consider two such coordinate changes. In the first approach, one of the conics is transformed into a parabola, which reduces the intersection problem to finding the solution of a quartic. In the second approach, we instead use the concept of self-polar triangles - which, amazingly, reduces the conic intersection problem to the solution of a simple quadratic equation.

Orbit determination (OD) from three position vectors is one of the classical problems in astrodynamics. Early contributions to this problem were made by J. Willard Gibbs in the late 1800s and OD of this type is known today as ``Gibbs Problem''. There are a variety of popular solutions to the Gibbs problem. While some authors solve for the orbital elements directly, most contemporary discussions are based on a vector analysis approach inspired by Gibbs himself. This work presents a completely different solution to those just described. Although there is nothing wrong with the vector analysis approach, some interesting insights may be gained by considering the problem from the perspective of algebraic projective geometry. Such an algebraic solution is presented here. The OD procedure is based upon a novel and geometrically meaningful solution to the algebraic fitting of an ellipse with a focus at the origin using only three points. Although the final OD result is identical to the classical vector analysis approach pioneered by Gibbs, this new algebraic solution is interesting in its own right.

Initial Orbit Determination (IOD) is the classical problem of estimating the orbit of a body in space without any presumed information about the orbit. The geometric formulation of the ''angles-only'' IOD in three-dimensional space: find a conic curve with a given focal point meeting the given lines of sight (LOS). We provide an algebraic reformulation of this problem and confirm that five is the minimal number of lines necessary to have a finite number of solutions in a non-special case, and the number of complex solutions is 66. We construct a subdivision method to search for the normal direction to the orbital plane as a point on the real projective plane. The resulting algorithm is fast as it discovers only a handful of the solutions that are real and physically meaningful.

The task of position and velocity estimation of a moving transmitter (with either a known or unknown frequency) is a common problem arising in many different application domains. Based on the Doppler effect, this work presents a direct solution using only the frequency measured by a multitude of receivers with a known state. A natural rewriting of the problem as a system of polynomial equations allows for the use of homotopy continuation to find the global solution without any a priori information about the frequency source. We show that the data from six or seven receivers is sufficient in case of known or unknown frequency, respectively. After a brief development of the mathematics, two simple examples are provided: (1) position and velocity estimation of a vocalizing dolphin emitting an acoustic signal and (2) initial orbit determination of a satellite emitting an electromagnetic signal.

Scientific imaging of the Moon, Mars, and other celestial bodies is often accomplished with pushbroom cameras. Craters with elliptical rims are common objects of interest within the images produced by such sensors. This work provides a framework to analyze the appearance of crater rims in pushbroom images. With knowledge of only common ellipse parameters describing the crater rim, explicit formulations are developed and shown to be convenient for drawing the apparent crater in pushbroom images. Implicit forms are also developed and indicate the orbital conditions under which craters form conics in images. Several numerical examples are provided which demonstrate how different forms of crater rim projections can be interpreted and used in practice.