A gradient bound for free boundary graphs

We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free boundary that is a graph is also smooth. The method we use also leads to a new proof of the classical minimal surface gradient bound

A semigroup characterization of well-posed linear control systems

We study the well-posedness of a linear control system $\Sigma(A,B,C,D)$ with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space $\mathcal{X}^p$ and call it $p$-well-posed if $\mathcal{A}$ generates a strongly continuous semigroup on $\mathcal{X}^p$. Our approach is based on the Laplace transform and Fourier multipliers

Critically separable rational maps in families

Given a number field K, we consider families of critically separable rational maps of degree d over K possessing a certain fixed-point and multiplier structure. With suitable notions of isomorphism and good reduction between rational maps in these families, we prove a finiteness theorem which is analogous to Shafarevich's theorem for elliptic curves. We also define the minimal critical discriminant, a global object which can be viewed as a measure of arithmetic complexity of a rational map. We formulate a conjectural bound on the minimal critical discriminant, which is analogous to Szpiro's conjecture for elliptic curves, and we prove that a special case of our conjecture implies Szpiro's conjecture in the semistable case.Comment: In this version, some notation and terminology has changed. In particular, this results in a slight change in the title of the paper. Many small expository changes have been made, a reference has been added, and a remark/example has been added to the end of section

An estimate for the multiplicity of binary recurrences

In this paper we improve drastically the estimate for the multiplicity of a binary recurrence. The main contribution comes from an effective version of the Faltings' Product Theorem

Automatic extraction of robotic surgery actions from text and kinematic data

The latest generation of robotic systems is becoming increasingly autonomous due to technological advancements and artificial intelligence. The medical field, particularly surgery, is also interested in these technologies because automation would benefit surgeons and patients. While the research community is active in this direction, commercial surgical robots do not currently operate autonomously due to the risks involved in dealing with human patients: it is still considered safer to rely on human surgeons' intelligence for decision-making issues. This means that robots must possess human-like intelligence, including various reasoning capabilities and extensive knowledge, to become more autonomous and credible. As demonstrated by current research in the field, indeed, one of the most critical aspects in developing autonomous systems is the acquisition and management of knowledge. In particular, a surgical robot must base its actions on solid procedural surgical knowledge to operate autonomously, safely, and expertly. This thesis investigates different possibilities for automatically extracting and managing knowledge from text and kinematic data. In the first part, we investigated the possibility of extracting procedural surgical knowledge from real intervention descriptions available in textbooks and academic papers on the robotic-surgical domains, by exploiting Transformer-based pre-trained language models. In particular, we released SurgicBERTa, a RoBERTa-based pre-trained language model for surgical literature understanding. It has been used to detect procedural sentences in books and extract procedural elements from them. Then, with some use cases, we explored the possibilities of translating written instructions into logical rules usable for robotic planning. Since not all the knowledge required for automatizing a procedure is written in texts, we introduce the concept of surgical commonsense, showing how it relates to different autonomy levels. In the second part of the thesis, we analyzed surgical procedures from a lower granularity level, showing how each surgical gesture is associated with a given combination of kinematic data

Determination of nanoscale ferroelectric domain distribution in multilayer piezoelectric actuators

Caratterizzazione in scala nanometrica della distribuzione di domini ferroelettrici in attuatori piezoelettrici multistrato, utilizzati negli iniettori dei motori diesel. Le analisi sono state fatte attraverso la tecnica: Piezoresponse Force Microscopy (PFM). Essa consiste in un microscopio a forza ionica (AFM),in cui viene applicata una differenza di potenziale alla punta che entra in contatto con il materiale.ope

VOIDING DYSFUNCTION AND DETRUSOR INSTABILITY AFTER THE COLPOSUSPENSION OPERATION FOR GENUINE STRESS INCONTINENCE

Colposuspension is an effective treatment for genuine stress incontinence. Continence is restored by positioning the bladder neck in a fixed and elevated retro-pubic position. Despite a high success rate of up to 90%, post-operative complications occur which may have an adverse effect on quality of life. Voiding difficulties develop in 0-43% of patients and detrusor instability in 2- 25%. This considerable variability is due to differences in definition, the timing of assessment, patient selection, and probably also in surgical technique. The natural history of these complications is not clearly known due to the lack of prospective follow-up studies. There is also general uncertainty with regards to their causes. While retrospective studies have attempted to identify pre-operative risk factors, there are no prospective studies which attempt to correlate the anatomical and functional changes caused by surgery with the development of voiding dysfunction and detrusor instability. This study has investigated prospectively 77 women undergoing the operation of colposuspension in relation to the incidence, natural history and causes of post-operative voiding dysfunction and detrusor instability. The complications were identified and followed-up objectively by means of serial urodynamic studies. Patients were also assessed clinically and using quality of life measures. The development of complications were correlated to a number of anatomical and functional changes caused by surgery. Anatomical changes were identified mainly by imaging the bladder neck with Magnetic Resonance Imaging (MRI). Functional changes were identified using urodynamic studies. Voiding dysfunction after colposuspension was common, with 69% of women requiring a catheter for more than seven days, and 28% for longer than 14 days. Improvement occurred gradually in most cases, with only 7. 7% and 2.5% of them needing catheterization at three months and one year respectively. De novo detrusor instability occurred in 21% of women at three months follow-up, and was symptomatic in 66% of these cases. Objective and subjective resolution was seen in 50% of these at one year follow-up. Quality of life after colposuspension improved in most cases despite the development of these complications, probably due to the resolution of their incontinence. Voiding dysfunction and detrusor instability after colposuspension were found to be multifactorial, due to patient related factors (age and detrusor contractility for voiding dysfunction, and age and a past history of bladder neck surgery for detrusor instability), and to operative factors (amount of bladder neck elevation and urethral compression). These findings might lead to the development of preventative measures

Logarithmic moments of characteristic polynomials of random matrices

In a recent article we have discussed the connections between averages of powers of Riemann's $\zeta$-function on the critical line, and averages of characteristic polynomials of random matrices. The result for random matrices was shown to be universal, i.e. independent of the specific probability distribution, and the results were derived for arbitrary moments. This allows one to extend the previous results to logarithmic moments, for which we derive the explicit universal expressions in random matrix theory. We then compare these results to various results and conjectures for $\zeta$-functions, and the correspondence is again striking.Comment: 10 pages, late