Minimizers of the prescribed curvature functional in a Jordan domain with no necks

We provide a geometric characterization of the minimal and maximal minimizer of the prescribed curvature functional $P(E)-\kappa |E|$ among subsets of a Jordan domain $\Omega$ with no necks of radius $\kappa^{-1}$, for values of $\kappa$ greater than or equal to the Cheeger constant of $\Omega$. As an application, we describe all minimizers of the isoperimetric profile for volumes greater than the volume of the minimal Cheeger set, relative to a Jordan domain $\Omega$ which has no necks of radius $r$, for all $r$. Finally, we show that for such sets and volumes the isoperimetric profile is convex.Comment: 24 pages, 4 figure

The Cheeger constant of a Jordan domain without necks

We show that the maximal Cheeger set of a Jordan domain \u3a9 without necks is the union of all balls of radius r=h(\u3a9)^ 121 contained in \u3a9. Here, h(\u3a9) denotes the Cheeger constant of \u3a9, that is, the infimum of the ratio of perimeter over area among subsets of \u3a9, and a Cheeger set is a set attaining the infimum. The radius r is shown to be the unique number such that the area of the inner parallel set \u3a9r is equal to \u3c0 r^2. The proof of the main theorem requires the combination of several intermediate facts, some of which are of interest in their own right. Examples are given demonstrating the generality of the result as well as the sharpness of our assumptions. In particular, as an application of the main theorem, we illustrate how to effectively approximate the Cheeger constant of the Koch snowflake

A smart financial advisory system exploiting Case-Based Reasoning

In the financial advisory context, knowledge-based recommendations based on Case-Based Reasoning are an emerging trend. They usually exploit knowledge about past experiences and about the characterization of both customers and financial products. In the present paper, we report the experience related to the development of a case-based recommendation module in a project called SmartFasi. We present a solution aimed at personalizing the asset picking phase, by taking into consideration choices made by customers who have a financial and personal data profile "similar" to the current one. We discuss the notion of distance-based similarity adopted in our system and how to actually implement an asset recommendation strategy integrated with the other software modules of SmartFasi. We finally discuss the impact such a strategy may have both from the point of view of private investors and professional users

Structural Positional Encoding for knowledge integration in transformer-based medical process monitoring

Predictive process monitoring is a process mining task aimed at forecasting information about a running process trace, such as the most correct next activity to be executed. In medical domains, predictive process monitoring can provide valuable decision support in atypical and nontrivial situations. Decision support and quality assessment in medicine cannot ignore domain knowledge, in order to be grounded on all the available information (which is not limited to data) and to be really acceptable by end users. In this paper, we propose a predictive process monitoring approach relying on the use of a {\em transformer}, a deep learning architecture based on the attention mechanism. A major contribution of our work lies in the incorporation of ontological domain-specific knowledge, carried out through a graph positional encoding technique. The paper presents and discusses the encouraging experimental result we are collecting in the domain of stroke management

New technologies to improve root canal disinfection

Effective irrigant delivery and agitation are prerequisites to promote root canal disinfection and debris removal and improve successful endodontic treatment. This paper presents an overview of the currently available technologies to improve the cleaning of the endodontic space and their debridement efficacy. A PubMed electronic search was conducted with appropriate key words to identify the relevant literature on this topic. After retrieving the full-text articles, all the articles were reviewed and the most appropriate were included in this review. Several different systems of mechanical activation of irrigants to improve endodontic disinfection were analysed: manual agitation with gutta-percha cones, endodontic instruments or special brushes, vibrating systems activated by low-speed hand-pieces or by sonic or subsonic energy, use of ultrasonic or laser energy to mechanically activate the irrigants and apical negative pressure irrigation systems. Furthermore, this review aims to describe systems designed to improve the intracanal bacterial decontamination by a specific chemical action, such as ozone, direct laser action or light-activated disinfection. The ultrasonic activation of root canal irrigants and of sodium hypochlorite in particular still remains the gold standard to which all other systems of mechanical agitation analyzed in this article were compared. From this overview, it is evident that the use of different irrigation systems can provide several advantages in the clinical endodontic outcome and that integration of new technologies, coupled with enhanced techniques and materials, may help everyday clinical practice

On the relationship between drag and vertical velocity fluctuations in flow over riblets and liquid infused surfaces

Direct numerical simulations (DNS) of flow over triangular and rectangular riblets in a wide range of size and Reynolds number have been carried out. The flow within the grooves is directly resolved by exploiting the immersed-boundary method. It is found that the drag reduction property is primarily associated with the capability of inhibiting vertical velocity fluctuations at the plane of the crests, as in liquid-infused surfaces (LIS) devices. This is mimicked in DNS through artificial suppression of the vertical velocity component, which yields large drag decrease, proportionate to the riblets size. A parametrization of the drag reduction effect in terms of the vertical velocity variance is found to be quite successful in accounting for variation of the controlling parameters. A Moody-like friction diagram is thus introduced which incorporates the effect of slip velocity and a single, geometry-dependent parameter. Reduced drag-reduction efficiency of LIS-like riblets is found as compared to cases with artificially imposed slip velocity. Last, we find that simple wall models of riblets and LIS-like devices are unlikely to provide accurate prediction of the flow phenomenon, and direct resolution of flow within the grooves in necessary

A knowledge-intensive approach to process similarity calculation

Process model comparison and similar processes retrieval are key issues to be addressed in many real world situations, and particularly relevant ones in some applications (e.g., in medicine), where similarity quantification can be exploited in a quality assessment perspective. Most of the process comparison techniques described in the literature suffer from two main limitations: (1) they adopt a purely syntactic (vs. semantic) approach in process activity comparison, and/or (2) they ignore complex control flow information (i.e., other than sequence). These limitations oversimplify the problem, and make the results of similarity-based process retrieval less reliable, especially when domain knowledge is available, and can be adopted to quantify activity or control flow construct differences. In this paper, we aim at overcoming both limitations, by introducing a framework which allows to extract the actual process model from the available process execution traces, through process mining techniques, and then to compare (mined) process models, by relying on a novel distance measure. The novel distance measure, which represents the main contribution of this paper, is able to address issues (1) and (2) above, since: (1) it provides a semantic, knowledge-intensive approach to process activity comparison, by making use of domain knowledge; (2) it explicitly takes into account complex control flow constructs (such as AND and XOR splits/joins), thus fully considering the different semantic meaning of control flow connections in a reliable way. The positive impact of the framework in practice has been tested in stroke management, where our approach has outperformed a state-of-the art literature metric on a real world event log, providing results that were closer to those of a human expert. Experiments in other domains are foreseen in the future