Efficient Algorithms for Collision Avoidance at Intersections

We consider the problem of synthesising the least restrictive controller for collision avoidance of multiple vehicles at an intersection. The largest set of states for which there exists a control that avoids collisions is known as the maximal controlled invariant set. Exploiting results from the scheduling literature we prove that, for a general model of vehicle dynamics at an intersection, the problem of checking membership in the maximal controlled invariant set is NP-hard. We then describe an algorithm that solves this problem approximately and with provable error bounds. The approximate solution is used to design a supervisor for collision avoidance whose complexity scales polynomially with the number of vehicles. The supervisor is based on a hybrid algorithm that employs a dynamic model of the vehicles and periodically solves a scheduling problem

Supervisory control of differentially flat systems based on abstraction

The limiting factor in most implementations of safety enforcing controllers is the model's complexity, and a common work-around includes the abstraction of the physical model, based on differential equations, to a finite symbolic model. We exploit the specific structure of a class of systems (the differentially flat systems) to perform the abstraction. The objective is to construct a supervisor enforcing a set of safety rules, while imposing as little constraints as possible on the system's functionality. An example - a collision avoidance algorithm for a fleet of vehicles converging to an intersection - is presented. Our approach improves on previous results by providing a deterministic symbolic model irrespective of the stability properties of a system, and by addressing explicitly the problem of enforcing safety.National Science Foundation (U.S.) (Award CNS 0930081

Robust multi-agent collision avoidance through scheduling

We propose a class of computationally efficient algorithms for conflict resolution in the presence of modeling and measurement uncertainties. Specifically, we address a scenario where a number of agents, whose dynamics are possibly nonlinear, must cross an intersection avoiding collisions. We obtain an exact solution and an approximate one with quantified error bound whose complexity scales polynomially with the number of agents.National Science Foundation (U.S.) (Award CNS 0930081)Roberto Rocca Foundatio

Laser treatment of 13 benign oral vascular lesions by three different surgical techniques

Objectives: Benign Oral Vascular Lesions (BOVLs) are a group of vascular diseases characterized by congenital, inflammatory or neoplastic vascular dilations clinically evidenced as more or less wide masses of commonly dark bluish color. If traumatized BOVLs are characterized by a great risk of hemorrhage and their treatment usually requires great caution to prevent massive bleeding. In the last decades lasers have dramatically changed the way of treatment of BOVLs permitting the application of even peculiar techniques that gave interesting advantages in their management reducing hemorrhage risks. The aim of this study was to evaluate the capabilities and disadvantages of three laser assisted techniques in the management of BOVLs. Study design: In this study 13 BOVLs were treated by three different laser techniques: the traditional excisional biopsy (EB), and two less invasive techniques, the transmucosal thermocoagulation (TMT) and the intralesional photocoagulation (ILP). Two different laser devices were adopted in the study: a KTP laser (DEKA, Florence, Italy, 532nm) and a GaAlAs laser (Laser Innovation, Castelgandolfo, Italy, 808nm) selected since their great effectiveness on hemoglobin. Results: In each case, lasers permitted safe treatments of BOVLs without hemorrhages, both during the intervention and in the post-operative period. The minimally invasive techniques (TMT and ILP) permitted even the safe resolution of big lesions without tissue loss. Conclusions: Laser devices confirm to be the gold standard in BOVLs treatment, permitting even the introduction of minimal invasive surgery principles and reducing the risks of hemorrhage typical of these neoplasms. As usual in laser surgery, it is necessary a clear knowledge of the devices and of the laser-tissue interaction to optimize the results reducing risks and disadvantages

Evaluation of wound healing and postoperative pain after oral mucosa laser biopsy with the aid of compound with chlorhexidine and sodium hyaluronate: a randomized double blind clinical trial

OBJECTIVES: The aim of this study is to evaluate secondary intention healing process and postoperative pain of oral soft tissues after laser surgery with the use of a compound containing chlorhexidine and sodium hyaluronate. MATERIALS AND METHODS: This double-blind, randomized clinical study included 56 patients affected by benign oral lesions and subjected to excisional biopsy with diode laser and randomly divided into three groups. Study group (SG) received 0.2% chlorhexidine digluconate and 0.2% sodium hyaluronate treatment; control group (CG) received 0.2% chlorhexidine digluconate; and placebo group (PG) followed the same protocol, taking a neutral solution having the same organoleptic characteristics. Wound healing was evaluated using percentage healing index (PHI). Numeric rating scale (NRS) was used to evaluate postoperative pain. RESULTS: PHI (T1 = 7 days) was 67.25% for SG, 58.67% for CG, and 54.55% for PG. PHI (T2 = 14 days) was 94.35% for SG, 77.79% for CG, and 78.98% for PG. A statistically significant difference was between the groups for PHI at T2 p = 0.001. No difference was detectable for pain index. CONCLUSIONS: A solution containing sodium hyaluronate and chlorhexidine is a good support to increase wound healing by secondary intention after laser biopsy, but no differences were in postoperative perception of pain. CLINICAL RELEVANCE: The use of the tested solution can be recommended after laser oral biopsies, to achieve a healing without suture. About the postoperative pain, the compound has not showed the same results and did not have measurable effects

Low energy spectrum of the XXZ model coupled to a magnetic field

It is shown that, for a class of Hamiltonians of XXZ chains in an external magnetic field that are small perturbations of an Ising Hamiltonian, the spectral gap above the ground-state energy remains strictly positive when the perturbation is turned on, uniformly in the length of the chain. The result is proven for both the ferromagnetic and the antiferromagnetic Ising Hamiltonian; in the latter case the external magnetic field is required to be small, and for an even number of sites the two-fold degenerate ground-state energy of the unperturbed Hamiltonian may split into two energy levels whose difference is small. This result is proven by using a new, quite subtle refinement of a method developed in earlier work and used to iteratively block-diagonalize Hamiltonians of ever larger subsystems with the help of local unitary conjugations. One novel ingredient of the method presented in this paper consists of the use of Lieb-Robinson bounds.Comment: 6 figure

Two Results in the Quantum Theory of Measurements

Two theorems with applications to the quantum theory of measurements are stated and proven. The first one clarifies and amends von Neumann's Measurement Postulate used in the Copenhagen interpretation of quantum mechanics. The second one clarifies the relationship between ``events'' and ``measurements'' and the meaning of measurements in the $ETH$-Approach to quantum mechanics.Comment: 14 pages, 0 figures, volume in memory of Giovanni Morchio, to be published by Springer-Nature in 202

Reading and modulating Cortical ß rursts from motor unit spiking activity

β Oscillations (13–30 Hz) are ubiquitous in the human motor nervous system. Yet, their origins and roles are unknown. Traditionally, β activity has been treated as a stationary signal. However, recent studies observed that cortical β occurs in “bursting events,” which are transmitted to muscles. This short-lived nature of β events makes it possible to study the main mechanism of β activity found in the muscles in relation to cortical β. Here, we assessed whether muscle β activity mainly results from cortical projections. We ran two experiments in healthy humans of both sexes (N = 15 and N = 13, respectively) to characterize β activity at the cortical and motor unit (MU) levels during isometric contractions of the tibialis anterior muscle. We found that β rhythms observed at the cortical and MU levels are indeed in bursts. These bursts appeared to be time-locked and had comparable average durations (40–80 ms) and rates (approximately three to four bursts per second). To further confirm that cortical and MU β have the same source, we used a novel operant conditioning framework to allow subjects to volitionally modulate MU β. We showed that volitional modulation of β activity at the MU level was possible with minimal subject learning and was paralleled by similar changes in cortical β activity. These results support the hypothesis that MU β mainly results from cortical projections. Moreover, they demonstrate the possibility to decode cortical β activity from MU recordings, with a potential translation to future neural interfaces that use peripheral information to identify and modulate activity in the central nervous system