Pattern formation driven by cross--diffusion in a 2D domain

In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that cross-diffusion, through Turing bifurcation, is the key mechanism for the formation of spatial patterns. We show that the bifurcation can be regular, degenerate non-resonant and resonant. We use multiple scales expansions to derive the amplitude equations appropriate for each case and show that the system supports patterns like rolls, squares, mixed-mode patterns, supersquares, hexagonal patterns

Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion

In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; %favors the mechanism of pattern formation with respect to the classical linear diffusion case; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal modulation of the phase and amplitude of the homogeneous oscillatory solution.Comment: Accepted for publication in Acta Applicandae Mathematica

Turing pattern formation in the Brusselator system with nonlinear diffusion

In this work we investigate the effect of density dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in 1D and 2D spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover we consider traveling patterning waves: when the domain size is large, the pattern forms sequentially and traveling wavefronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and through a matching procedure we construct the outer amplitude equation and the inner core solution.Comment: Physical Review E, 201

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

Route to chaos in the weakly stratified Kolmogorov flow

We consider a two-dimensional fluid exposed to Kolmogorov’s forcing cos(ny) and heated from above. The stabilizing effects of temperature are taken into account using the Boussinesq approximation. The fluid with no temperature stratification has been widely studied and, although relying on strong simplifications, it is considered an important tool for the theoretical and experimental study of transition to turbulence. In this paper, we are interested in the set of transitions leading the temperature stratified fluid from the laminar solution [U∝cos(ny),0, T ∝ y] to more complex states until the onset of chaotic states. We will consider Reynolds numbers 0 < Re ≤ 30, while the Richardson numbers shall be kept in the regime of weak stratifications (Ri ≤ 5 × 10 −3 ). We shall first review the non-stratified Kolmogorov flow and find a new period-tripling bifurcation as the precursor of chaotic states. Introducing the stabilizing temperature gradient, we shall observe that higher Re are required to trigger instabilities. More importantly, we shall see new states and phenomena: the newly discovered period-tripling bifurcation is supercritical or subcritical according to Ri; more period-tripling and doubling bifurcations may depart from this new state; strong enough stratifications trigger new regions of chaotic solutions and, on the drifting solution branch, non-chaotic bursting solutions

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