Solution of a quadratic quaternion equation with mixed coefficients

A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion variable and its conjugate with right and left quaternion coefficients, while the quadratic term has a quaternion coefficient placed between the variable and its conjugate. It is proved that, for generic coefficients, the equation has two, one, or no solutions, but in certain special instances the solution set may comprise a circle or a 3-sphere in the quaternion space $\mathbb{H}$. The analysis yields solutions for each case, and intuitive interpretations of them in terms of the four-dimensional geometry of the quaternion space $\mathbb{H}$.Comment: 19 pages, to appear in the Journal of Symbolic Computatio

Bambini e ragazzi negli ospedali psichiatrici tra Otto e Novecento: un\u2019indagine tra le carte dell\u2019Istituzione Gian Franco Minguzzi di Bologna

A partire da una ricostruzione storica sulla presenza dei minori negli ospedali psichiatrici italiani ed europei e sull\u2019evoluzione delle modalit\ue0 di cura e rieducazione dei bambini e dei ragazzi con disabilit\ue0 psichica e intellettiva tra Otto e Novecento, questo articolo propone un\u2019analisi dei documenti conservati presso l\u2019archivio dell\u2019Istituzione Gian Franco Minguzzi, con particolare riferimento a quelli che certificano la presenza dei bambini e degli adolescenti, fino ai 15 anni, ricoverati nel manicomio bolognese in un arco temporale molto ampio, che va dal 1811 al 1950. Sono prese in esame le caratteristiche peculiari e innovative dell\u2019istituzione bolognese, le diagnosi l\uec redatte e i destini dei minori coinvolt

A comprehensive characterization of the set of polynomial curves with rational rotation-minimizing frames

A rotation-minimizing frame $({\bf f}_1,{\bf f}_2,{\bf f}_3)$ on a space curve ${\bf r}(\xi)$ defines an orthonormal basis for $\mathbb{R}^3$ in which ${\bf f}_1={\bf r}'/|{\bf r}'|$ is the curve tangent, and the normal-plane vectors ${\bf f}_2$, ${\bf f}_3$ exhibit no instantaneous rotation about ${\bf f}_1$. Polynomial curves that admit rational rotation-minimizing frames (or RRMF curves) form a subset of the Pythagorean-hodograph (PH) curves, specified by integrating the form ${\bf r}'(\xi)={\cal A}(\xi)\,{\bf i}\,{\cal A}^*(\xi)$ for some quaternion polynomial ${\cal A}(\xi)$. By introducing the notion of rotation indicatrix and of core of the quaternion polynomial ${\cal A}(\xi)$, a comprehensive characterization of the complete space of RRMF curves is developed, that subsumes all previously known special cases. This novel characterization helps clarify the structure of the complete space of RRMF curves, distinguishes the spatial RRMF curves from trivial (planar) cases, and paves the way toward new construction algorithms.Comment: 30 pages, 1 figur

SARS-CoV-2 infection as a model to study the effect of cinnamaldehyde as adjuvant therapy for viral pneumonia

Abstract Background The recent pandemic outbursts, due to SARS-CoV-2, have highlighted once more the central role of the inflammatory process in the propagation of viral infection. The main consequence of COVID-19 is the induction of a diffuse pro-inflammatory state, also defined as a cytokine storm, which affects different organs, but mostly the lungs. We aimed to prove the efficacy of cinnamaldehyde, the active compound of cinnamon, as an anti-inflammatory compound, able to reduce SARS-CoV-2 induced cytokine storm. Results We enrolled 53 COVID-19 patients hospitalized for respiratory failure. The cohort was composed by 39 males and 13 females, aged 65.0 ± 9.8 years. We reported that COVID-19 patients have significantly higher IL-1β and IL-6 plasma levels compared to non-COVID-19 pneumonia patients. In addition, human mononuclear cells (PBMCs) isolated from SARS-CoV-2 infected patients are significantly more prone to release pro-inflammatory cytokines upon stimuli. We demonstrated, using in vitro cell models, that macrophages are responsible for mediating the pro-inflammatory cytokine storm while lung cells support SARS-CoV-2 replication upon viral infection. In this context, cinnamaldehyde administration significantly reduces SARS-CoV-2-related inflammation by inhibiting NLRP3 mediated IL-1β release in both PBMCs and THP-1 macrophages, as well as viral replication in CaLu-3 epithelial cells. Lastly, aerosol-administered cinnamaldehyde was able to significantly reduce IL-1β release in an in vivo lung-inflammatory model. Conclusion The obtained results suggest the possible use of cinnamaldehyde as a co-adjuvant preventive treatment for COVID-19 disease together with vaccination, but also as a promising dietary supplement to reduce, more broadly, viral induced inflammation

Imaging side effects and complications of chemotherapy and radiation therapy: a pictorial review from head to toe

Abstract Newer biologic drugs and immunomodulatory agents, as well as more tolerated and effective radiation therapy schemes, have reduced treatment toxicity in oncology patients. However, although imaging assessment of tumor response is adapting to atypical responses like tumor flare, expected changes and complications of chemo/radiotherapy are still routinely encountered in post-treatment imaging examinations. Radiologists must be aware of old and newer therapeutic options and related side effects or complications to avoid a misinterpretation of imaging findings. Further, advancements in oncology research have increased life expectancy of patients as well as the frequency of long-term therapy-related side effects that once could not be observed. This pictorial will help radiologists tasked to detect therapy-related complications and to differentiate expected changes of normal tissues from tumor relapse

Health services utilization in patients with eating disorders: evidence from a cohort study in Emilia-Romagna

Purpose: To estimate the treated prevalence of eating disorders (ED) in Emilia-Romagna, Italy, and to compare health services utilization among age groups and geographical areas. Methods: The study cohort consists of patients aged 12\u201364 years with a primary or secondary ED diagnosis, treated in regional healthcare facilities in 2012. Patients were followed up for 1\ua0year from the first contact. Data were extracted from regional administrative databases. Results: The study cohort included 1550 cases, 36.8\ua0% with anorexia nervosa, 21.9\ua0% with bulimia nervosa and 41.3\ua0% with ED not otherwise specified. Adolescents\ua0(12\u201317 years) were 18.6\ua0%, young adults\ua0(18\u201330) 32.7\ua0% and older adults\ua0(31\u201364) 48.7\ua0%. The annual treated prevalence rate was 5.2/10,000 (13.3 for adolescents, 9.3 for young adults and 3.4 for older adults) and was highest among adolescent (24.6/10,000) and young adult females (17.1/10,000). Cases without a record for ED in the previous year were 46.8\ua0%. Older adults displayed higher comorbidity and used more services including hospital-based care. Outpatient care greatly exceeded inpatient care across age groups. Variations in care patterns across regional areas were found. Conclusions: Our results indicate that the care pathway for ED varies among age groups and geographical areas, but is consistent with the regional care model that favors the use of outpatient services. Future perspectives include evaluating the integration among mental health services, specialty outpatient units and primary care