Generators and Bases for Monadic Closures

It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To tackle this issue, a number of sub-classes of nondeterministic automata have been identified, all admitting canonical minimal representatives. In previous work, we have shown that such representatives can be recovered categorically in two steps. First, one constructs the minimal bialgebra accepting a given regular language, by closing the minimal coalgebra with additional algebraic structure over a monad. Second, one identifies canonical generators for the algebraic part of the bialgebra, to derive an equivalent coalgebra with side effects in a monad. In this paper, we further develop the general theory underlying these two steps. On the one hand, we show that deriving a minimal bialgebra from a minimal coalgebra can be realized by applying a monad on an appropriate category of subobjects. On the other hand, we explore the abstract theory of generators and bases for algebras over a monad

Optimizing Automata Learning via Monads

Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design, prove correct, and implement a wide class of such optimizations. The former perspective on monads allows us to develop a new algorithm and accompanying correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that our approach allows us to uniformly capture existing algorithms, develop new ones, and add optimizations. The latter perspective allows us to effortlessly translate the theory into practice: we provide a Haskell library implementing our general framework, and we show experimental results for two specific instances: non-deterministic and weighted automata

Learning automata with side-effects

Automata learning has been successfully applied in the verification of hardware and software. The size of the automaton model learned is a bottleneck for scalability, and hence optimizations that enable learning of compact representations are important. This paper exploits monads, both as a mathematical structure and a programming construct, to design and prove correct a wide class of such optimizations. Monads enable the development of a new learning algorithm and correctness proofs, building upon a general framework for automata learning based on category theory. The new algorithm is parametric on a monad, which provides a rich algebraic structure to capture non-determinism and other side-effects. We show that this allows us to uniformly capture existing algorithms, develop new ones, and add optimizations

Thermography as a method to detect dental anxiety in oral surgery

(1) Background: the aim of this study was to evaluate if dental anxiety can be measured objectively using thermal infrared imaging. (2) Methods: Patients referred to the Department of Oral Surgery of the University of Naples Federico II and requiring dental extractions were consecutively enrolled in the study. Face thermal distribution images of the patients were acquired before and during their first clinical examination using infrared thermal cameras. The data were analyzed in relation to five regions of interest (ROI) of the patient’s face (nose, ear, forehead, zygoma, chin). The differences in the temperatures assessed between the two measurements for each ROI were evaluated by using paired T‐test. The Pearson correlation and linear regression were performed to evaluate the association between differences in temperatures and Modified Dental Anxiety Scale (MDAS) questionnaire score, age, and gender; (3) results: sixty participants were enrolled in the study (28 males and 32 females; mean age 57.4 year‐old; age range 18–80 year‐old). Only for nose and ear zone there was a statistically significant difference between measurements at baseline and visit. Correlation between the thermal imaging measurements and the scores of the MDAS questionnaire was found for nose and ear, but not for all of the other regions. (4) Conclusions: the study demonstrated a potential use of thermal infrared imaging to measure dental anxiety

Canonical Automata via Distributive Law Homomorphisms

The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that converts an automaton with side-effects, given by a monad, into a deterministic automaton accepting the same language. The resulting automaton has additional algebraic properties, both in the state space and transition structure, inherited from the monad. In this paper, we study the reverse construction and present a framework in which a deterministic automaton with additional algebraic structure over a given monad can be converted into an equivalent succinct automaton with side-effects. Apart from recovering examples from the literature, such as the canonical residual finite-state automaton and the átomaton, we discover a new canonical automaton for a regular language by relating the free vector space monad over the two element field to the neighbourhood monad. Finally, we show that every regular language satisfying a suitable property parametric in two monads admits a size-minimal succinct acceptor

Spatio-temporal variability of micro-, nano- and pico-phytoplankton in the Mediterranean Sea from satellite ocean colour data of SeaWiFS

Abstract. The seasonal and year-to-year variability of the phytoplankton size class (PSC) spatial distribution has been examined in the Mediterranean Sea by using the entire time series of Sea-viewing Wide Field-of-view Sensor (SeaWiFS) space observations (1998–2010). Daily maps of PSCs have been determined using an empirical model based on a synoptic relationship between surface chlorophyll a and diagnostic pigments referred to different taxonomic groups. The analysis of micro-, nano- and pico-phytoplankton satellite time series (1998–2010) describes, quantitatively, the algal assemblage structure over the basin and reveals that the main contribution to chlorophyll a in most of the Mediterranean Sea comes from the pico-phytoplankton component, especially in nutrient-poor environments. Regions with different and peculiar features are the Northwestern Mediterranean Sea, the Alborán Sea and several coastal areas, such as the North Adriatic Sea. In these areas, local interactions between physical and biological components modulate the composition of the three phytoplankton size classes. It results that, during the spring bloom season, micro-phytoplankton dominates in areas of intense vertical winter mixing and deep/intermediate water formation, while in coastal areas micro-phytoplankton dominates in all seasons because of the nutrient supply from the terrestrial inputs. In the Alborán Sea, where the Atlantic inflow modulates the nutrient availability, any predominance of one class over the other two has been observed. The nano-phytoplankton component instead remains widespread over the entire basin along the year, and its contribution to chlorophyll a is of the order of 30–40 %. The largest inter-annual signal occurs in the Northwestern Mediterranean Sea, driven by the year-to-year variation in intensity and extension of the spring bloom, followed by the Alborán Sea, in which the inter-annual variability is strongly modulated by the Atlantic inflow. In absence of sufficient in situ data of community composition, the satellite-based analysis demonstrated that pico-, nano- and micro-phytoplankton classes often coexist. The predominance of one group over the other ones is strongly dependent on the physical and biological processes occurring at the mesoscale. These processes directly influence the nutrient and light availability, which are the principal forcing for the algae growth

Learning nominal automata

We present an Angluin-style algorithm to learn nominal automata, which are acceptors of languages over infinite (structured) alphabets. The abstract approach we take allows us to seamlessly extend known variations of the algorithm to this new setting. In particular we can learn a subclass of nominal non-deterministic automata. An implementation using a recently developed Haskell library for nominal computation is provided for preliminary experiments

Influence of the Antithrombotic Therapy in the Healing of Simple Post-Extraction Sockets: A Randomized Clinical Trial

Background: An adequate blood supply plays a leading role in the healing process of the post-extractive socket; its coagulation leads to fibrin clot formation, which acts as a physical barrier able to prevent postoperative bleeding and microbial infection. The purpose of this study was to evaluate the effectiveness of antiaggregant drugs in healing post-extraction sockets compared to natural wound healing. Methods: This was a single-center prospective clinical trial. Extraction sockets allocated in healthy patients and in patients assuming antiplatelet drugs were considered. Thirty consecutive patients under (treated with/in treatment with) oral antiplatelet treatment were enrolled in the test group. In order to provide a control group, 30 consecutive patients meeting all the exclusion and inclusion criteria were enrolled. The extraction of the mono-radicular tooth was atraumatically performed without gingivoplasty or osteotomy procedures that could influence the healing process. Photographs were obtained before and immediately after surgery and at 3-, 7-, 14-and 28-days follow-up. Results: All patients assumed the prescribed therapy and their postoperative recovery was uneventful without any kind of post-extractive complications. The results of inter-group comparison show that on the third and seventh days of follow-up, the antiplatelet group expressed a statistically significant higher level of healing compared to the control group (p < 0.05), while no statistically significant differences were recorded at 14-and 28-days follow-up. Conclusions: Patients treated with antiplatelet agents seemed to show that this therapy can positively affect the healing process after tooth extractions

Tree Automata as Algebras: Minimisation and Determinisation

We study a categorical generalisation of tree automata, as algebras for a fixed endofunctor endowed with initial and final states. Under mild assumptions about the base category, we present a general minimisation algorithm for these automata. We then build upon and extend an existing generalisation of the Nerode equivalence to a categorical setting and relate it to the existence of minimal automata. Finally, we show that generalised types of side-effects, such as non-determinism, can be captured by this categorical framework, leading to a general determinisation procedure