Interval Temporal Random Forests with an Application to COVID-19 Diagnosis

Symbolic learning is the logic-based approach to machine learning. The mission of symbolic learning is to provide algorithms and methodologies to extract logical information from data and express it in an interpretable way. In the context of temporal data, interval temporal logic has been recently proposed as a suitable tool for symbolic learning, specifically via the design of an interval temporal logic decision tree extraction algorithm. Building on it, we study here its natural generalization to interval temporal random forests, mimicking the corresponding schema at the propositional level. Interval temporal random forests turn out to be a very performing multivariate time series classification method, which, despite the introduction of a functional component, are still logically interpretable to some extent. We apply this method to the problem of diagnosing COVID-19 based on the time series that emerge from cough and breath recording of positive versus negative subjects. Our experiment show that our models achieve very high accuracies and sensitivities, often superior to those achieved by classical methods on the same data. Although other recent approaches to the same problem (based on different and more numerous data) show even better statistical results, our solution is the first logic-based, interpretable, and explainable one

Neural-Symbolic Temporal Decision Trees for Multivariate Time Series Classification

Multivariate time series classification is a widely known problem, and its applications are ubiquitous. Due to their strong generalization capability, neural networks have been proven to be very powerful for the task, but their applicability is often limited by their intrinsic black-box nature. Recently, temporal decision trees have been shown to be a serious alternative to neural networks for the same task in terms of classification performances, while attaining higher levels of transparency and interpretability. In this work, we propose an initial approach to neural-symbolic temporal decision trees, that is, an hybrid method that leverages on both the ability of neural networks of capturing temporal patterns and the flexibility of temporal decision trees of taking decisions on intervals based on (possibly, externally computed) temporal features. While based on a proof-of-concept implementation, in our experiments on public datasets, neural-symbolic temporal decision trees show promising results

Fitting’s Style Many-Valued Interval Temporal Logic Tableau System: Theory and Implementation

Many-valued logics, often referred to as fuzzy logics, are a fundamental tool for reasoning about uncertainty, and are based on truth value algebras that generalize the Boolean one; the same logic can be interpreted on algebras from different varieties, for different purposes and pose different challenges. Although temporal many-valued logics, that is, the many-valued counterpart of popular temporal logics, have received little attention in the literature, the many-valued generalization of Halpern and Shoham’s interval temporal logic has been recently introduced and studied, and a sound and complete tableau system for it has been presented for the case in which it is interpreted on some finite Heyting algebra. In this paper, we take a step further in this inquiry by exploring a tableau system for Halpern and Shoham’s interval temporal logic interpreted on some finite FLew-algebra, therefore generalizing the Heyting case, and by providing its open-source implementation

On Coarser Interval Temporal Logics

The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir's coarser interval algebras, which generalize the classical Allen's Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham's logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely HS3, not only is decidable, but PSpace-complete in the finite/discrete case, and PSpace-hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen's relations are a guarantee of decidability, as we prove that the second variant, namely , remains undecidable in all interesting cases.TIN15-70266-C2-P-1, founded by the Spanish Ministry of Science. FPU15/05883, founded by Spanish Ministry of Education. Project Formal Methods for Verification and Synthesis of Discrete and Hybrid Systems, founded by the Italian INDAM GNCS

UV-VIS AND FLUORESCENCE INVESTIGATION OF SOME POLY(ACRYLIC) GELS

Poly(acrylic) gels, (PAA), with polymeric concentrations 0.5, 1 and 1.5%, in aqueous state and neutralized with triethanolamine, (TEA), were investigated by UV-VIS and fluorescence methods. Such gels are suitable to obtain biocompatible matrices for some medical drugs. The aqueous gel with 1% PAA concentration shows an important absorption at 214 nm. At 1.5% PAA concentration the absorption increases and the peak shifts slowly to 212 nm. The absorption increases after neutralization and the maximum of absorbance shifts to 200 nm. Excitation of aqueous gels at 250, 270 and 290 nm is followed by two important fluorescence transition centered at 320 and 405 nm. The position of the fluorescence peaks is influenced by the polymeric concentration and by the neutralization. The UV-VIS and fluorescence investigations indicate some conformational changes determined by the neutralization

UV-VIS AND FLUORESCENCE INVESTIGATION OF SOME POLY(ACRYLIC) GELS

Poly(acrylic) gels, (PAA), with polymeric concentrations 0.5, 1 and 1.5%, in aqueous state and neutralized with triethanolamine, (TEA), were investigated by UV-VIS and fluorescence methods. Such gels are suitable to obtain biocompatible matrices for some medical drugs. The aqueous gel with 1% PAA concentration shows an important absorption at 214 nm. At 1.5% PAA concentration the absorption increases and the peak shifts slowly to 212 nm. The absorption increases after neutralization and the maximum of absorbance shifts to 200 nm. Excitation of aqueous gels at 250, 270 and 290 nm is followed by two important fluorescence transition centered at 320 and 405 nm. The position of the fluorescence peaks is influenced by the polymeric concentration and by the neutralization. The UV-VIS and fluorescence investigations indicate some conformational changes determined by the neutralization

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio