A primer on quasi-convex functions in nonlinear potential theories

We present a self-contained treatment of the fundamental role that quasi-convex functions play in general (nonlinear second order) potential theories, which concerns the study of generalized subharmonics associated to a suitable closed subset (subequations) of the space of 2-jets. Quasi-convex functions build a bridge between classical and viscosity notions of solutions of the natural Dirichlet problem in any potential theory. Moreover, following a program initiated by Harvey and Lawson in [arXiv:0710.3991], a potential-theoretic approach is widely being applied for treating nonlinear partial differential equations (PDEs). This viewpoint revisits the conventional viscosity approach to nonlinear PDEs [arXiv:math/9207212] under a more geometric prospective inspired by Krylov (1995) and takes much insight from classical pluripotential theory. The possibility of a symbiotic and productive relationship between general potential theories and nonlinear PDEs relies heavily on the class of quasi-convex functions, which are themselves the generalized subharmonics of a pure second order constant coefficient potential theory.Comment: 105 pages, 2 figures. Introduction extended, guide to the reader added, exposition refine

I veterani delle milizie urbane in Italia e nelle province di lingua latina. Indagine storico-epigrafica

2013/2014Le coorti pretorie, le coorti urbane e gli equites singulares Augusti costituivano i corpi d'élite dell'esercito romano per via di un reclutamento selezionato e di un trattamento privilegiato rispetto alle altre unità. Lo studio si propone di indagare il fenomeno del veteranato di queste tre formazioni in un arco di tempo che va da Augusto all'ascesa di Diocleziano e in uno spazio che copre l'Italia, con l'esclusione di Roma e del suo suburbio fino al X miglio, e le province di lingua latina. L'indagine si basa sull'esame della documentazione epigrafica nella quale lo status di veterano di uno o più personaggi menzionati nel testo è sicuro e l'appartenenza ad uno dei tre corpi analizzati è certa o molto probabile. Il lavoro si divide in due parti: nella prima vi è un commento ad ogni singola testimonianza, nella seconda vengono svolte considerazioni di carattere generale sui veterani delle milizie urbane. Tali considerazioni scaturiscono da una visione complessiva della documentazione. Si vuole tentare in questo modo di rispondere a interrogativi riguardanti i rapporti sociali e l'integrazione di questi veterani nelle comunità scelte come residenza dopo il congedo, la loro partecipazione alla vita civica e le attività economiche cui si dedicavano. Una particolare attenzione è rivolta a riconoscere quanti veterani decidevano di rientrare in patria o di stabilirsi in località diverse da quelle natie e le motivazioni che guidavano tale scelta, la loro provenienza e la loro estrazione sociale.Due to a preferential treatment and special recruitment among the military units, praetorian guard, urban cohorts and equites singulares Augusti were the élite troops of ancient roman army. This research aims to investigate the social and material life of the veterans of this élite troops, in a period of time included between Augustan age and Diocletian rise. It also considers a territory including Italy, except Rome and its suburbs until the tenth mile, and latin speaking provinces. This work is based on an epigraphic documentation in wich the veteran status of one or more subjects is proven and the belonging to one of the three élite corps is certain or probable. The research is divided into two parts. In the first part an analysis and a description is made for each documentary source. In the second part, general considerations are expressed about the veterans of urban militias. These considerations stem from an accurate documentation overview. The purpose is to answer questions regarding the integration and social relations between veterans and the community chosen to live with after the disbandment or, for example, the activities and the role of a veteran in civic and economical life. Specific attention is also paid to the territorial origin, social background and about the choice, made by a veteran, to return home or settle elsewhere after the service.XXVII Ciclo198

Presenze alloctone nell’ultima fase dell’Impero Romano d’Occidente in Italia settentrionale: l’elemento barbarico

Il contributo si propone di esaminare la presenza di elementi barbarici nell’Italia settentrionale in un lasso di tempo compreso tra l’inizio del V secolo e la morte di Valentiniano III (455). Per prima cosa si vuole offrire un bilancio degli studi sul problema dell’identità di questi elementi barbarici, delineando il controverso dibattito riguardo la nascita e lo sviluppo di popoli barbari con una propria specifica identità (l’etnogenesi). Le popolazioni barbariche erano formate da gruppi eterogenei e gli etnonimi con cui i Romani li definivano non indicavano popoli con un’identità etnica ben definita. Anche la differenza tra ‘Romani’ e ‘barbari’ non era sempre netta ed era spesso definita soprattutto dal diritto. Si vogliono poi analizzare nuovamente le diverse tipologie di fonti documentarie che consentono di individuare dove e come gli elementi barbarici fossero presenti nell’Italia settentrionale e le loro differenti condizioni giuridiche. Le più recenti interpretazioni delle fonti possono offrire nuove prospettive nel chiarire alcune problematiche di ordine storico: la presenza di barbari nelle truppe regolari dell’esercito romano; i compiti dei praefecti gentilium Sarmatarum; la presenza dei laeti nel nord Italia e cosa differenziasse la loro condizione da quella molto simile dei gentiles; la negazione del tradizionale paradigma storiografico che descrive i laeti e i gentiles come soldati-contadini

Comparison principles for nonlinear potential theories and PDEs with fiberegularity and sufficient monotonicity

We present some recent advances in the productive and symbiotic interplay between general potential theories (subharmonic functions associated to closed subsets $\mathcal{F} \subset \mathcal{J}^2(X)$ of the 2-jets on $X \subset \mathbb{R}^n$ open) and subsolutions of degenerate elliptic and parabolic PDEs of the form $F(x,u,Du,D^2u) = 0$. We will implement the monotonicity-duality method begun by Harvey and Lawson in 2009 (in the pure second order constant coefficient case) for proving comparison principles for potential theories where $\mathcal{F}$ has sufficient monotonicity and fiberegularity (in variable coefficient settings) and which carry over to all differential operators $F$ which are compatible with $\mathcal{F}$ in a precise sense for which the correspondence principle holds. We will consider both elliptic and parabolic versions of the comparison principle in which the effect of boundary data is seen on the entire boundary or merely on a proper subset of the boundary. Particular attention will be given to gradient dependent examples with the requisite sufficient monotonicity of proper ellipticity and directionality in the gradient. Example operators we will discuss include the degenerate elliptic operators of optimal transport in which the target density is strictly increasing in some directions as well as operators which are weakly parabolic in the sense of Krylov. Further examples, modeled on hyperbolic polynomials in the sense of G\r{a}rding give a rich class of examples with directionality in the gradient. Moreover we present a model example in which the comparison principle holds, but standard viscosity structural conditions fail to hold.Comment: 52 page

Technical Note: Year, season, and parity effect on weaning performance of the Carmagnola Grey Rabbit breed

To evaluate the main environmental factors in the productivity of Carmagnola Grey rabbits, an endangered breed indigenous to northern Italy, data collected over 8 years were analysed. Production data on the pure closed nucleus herd of the University of Turin were used. Effects of parity, season and age of weaning on the number of rabbits born alive and weaned, litter weight and individual average weight at weaning were studied. The following average performance rates over the 8 years period were determined: 8.1 live born and 7.2 weaned kits per litter and a litter weight at weaning of 7287 g or 1024 g individual weaning weight. Year and season both had a significant effect (P < 0.001) on all the traits studied as well as weaning age (P < 0.001).Lazzaroni, C.; Biagini, D.; Redaelli, V.; Luzi, F. (2012). Technical Note: Year, season, and parity effect on weaning performance of the Carmagnola Grey Rabbit breed. World Rabbit Science. 20(1):57-60. doi:10.4995/wrs.2012.1031SWORD576020

A systematic measurement analyzer for LHC operational data

The CERN Accelerator Logging Service stores data from hundreds of thousands of parameters and measurements, mostly from the Large Hadron Collider (LHC). The systematic measurement analyzer is a Java-based tool that is used to visualize and analyze various beam measurement data over multiple fills and time intervals during the operational cycle, such as ramp or squeeze. Statistical analysis and various manipulations of data are possible, including correlation with several machine parameters such as β^{*} and energy. Examples of analyses performed include checks of collimator positions, beam losses throughout the cycle and tune stability during the squeeze which is then used for feed-forward purposes.peer-reviewe

Smell and taste alterations in Covid-19: a cross-sectional analysis of different cohorts

Olfactory (OD) and gustatory (GD) dysfunction have been proven to be a typical symptom of SARS-CoV-2 infection. However, their prevalence in different patient populations still needs to be clarified

Advancing Focused Ultrasound surgery through Robotics, Simulation, and Augmented Reality: the FUtuRo project

This study introduces a comprehensive system designed to elevate both the planning and evaluation phases of Focused Ultrasound Surgery (FUS) interventions. Through the seamless integration of mechanical, acoustic, and thermal simulations alongside robotic assistance, our approach empowers precise treatment planning and parameter optimization. Leveraging advanced imaging modalities enhances the accuracy of target delineation, while computational modeling provides invaluable insights into therapeutic efficacy. Specifically, this paper will assess the acoustic pressure field and the dimensions of ablated tissue in a custom-made phantom resembling human tissue layers using an appropriate library for acoustic wave simulation

A new tool for touch-free patient registration for robot-assisted intracranial surgery: Application accuracy from a phantom study and a retrospective surgical series

OBJECTIVE The purpose of this study was to compare the accuracy of Neurolocate frameless registration system and frame-based registration for robotic stereoelectroencephalography (SEEG). METHODS The authors performed a 40-trajectory phantom laboratory study and a 127-trajectory retrospective analysis of a surgical series. The laboratory study was aimed at testing the noninferiority of the Neurolocate system. The analysis of the surgical series compared Neurolocate-based SEEG implantations with a frame-based historical control group. RESULTS The mean localization errors (LE) ± standard deviations (SD) for Neurolocate-based and frame-based trajectories were 0.67 ± 0.29 mm and 0.76 ± 0.34 mm, respectively, in the phantom study (p = 0.35). The median entry point LE was 0.59 mm (interquartile range [IQR] 0.25-0.88 mm) for Neurolocate-registration-based trajectories and 0.78 mm (IQR 0.49-1.08 mm) for frame-registration-based trajectories (p = 0.00002) in the clinical study. The median target point LE was 1.49 mm (IQR 1.06-2.4 mm) for Neurolocate-registration-based trajectories and 1.77 mm (IQR 1.25-2.5 mm) for frameregistration- based trajectories in the clinical study. All the surgical procedures were successful and uneventful. CONCLUSIONS The results of the phantom study demonstrate the noninferiority of Neurolocate frameless registration. The results of the retrospective surgical series analysis suggest that Neurolocate-based procedures can be more accurate than the frame-based ones. The safety profile of Neurolocate-based registration should be similar to that of frame-based registration. The Neurolocate system is comfortable, noninvasive, easy to use, and potentially faster than other registration devices

Clinical Study A Noninvasive Neuroprosthesis Augments Hand Grasp Force in Individuals with Cervical Spinal Cord Injury: The Functional and Therapeutic Effects

Objectives. The primary purpose of this study was to evaluate myoelectrically controlled functional electrical stimulation (MeCFES) for enhancing the tenodesis grip in people with tetraplegia. The second aim was to estimate the potential number of candidates for the MeCFES device. The application of MeCFES provides the user with direct control of the grasp force as opposed to triggered FES systems. Methods. Screening 253 medical records of C5 to C7 spinal cord injury resulted in 27 participants who trained activities of daily living for 12 × 2 hours, using the MeCFES. Hand function was evaluated by the Action Research Arm Test (ARAT). Primary outcome was the ARAT change score with/without the device, before/after the intervention period. Secondary outcome was the number of positive or clinically relevant change scores with respect to the cohort. Results. The MeCFES improved hand test score in 63% of the subjects at first application. Training resulted in a significant therapeutic effect, which resulted in an overall increase of hand function in 89% of the participants and 30% experienced a clinically relevant change (6 points or more). Conclusions. Clinical relevance was found both as an assistive aid and as a therapeutic tool in rehabilitation. The therapeutic effect deserves further investigation in clinical studies