Cristina Parigini

This paper introduces a versatile approach for computing the risk of collision specifically tailored for scenarios featuring low relative encounter velocities, but with potential applicability across a wide range of situations. The technique employs Differential Algebra (DA) to express the non-linear dynamical flow of the initial distribution in the primary-secondary objects relative motion through high-order Taylor polynomials. The entire initial uncertainty set is subdivided into subsets through Automatic Domain Splitting (ADS) techniques to control the accuracy of the Taylor expansions. The methodology samples the initial conditions of the relative state and evaluates the polynomial expansions for each sample while retaining their temporal dependency. The classical numerical integration of the initial statistics over the set of conditions for which a collision occurs is thus reduced to an evaluation of mono-dimensional time polynomials. Specifically, samples reaching a relative distance below a critical value are identified along with the time at which this occurs. The approach is tested against a Monte Carlo (MC) simulation for various literature test cases, yielding accurate results and a consistent gain in computational time.

We present the solution approach developed by the team “TheAntipodes” during the 12th edition of the Global Trajectory Optimization Competition (GTOC12). An overview of the approach is as follows: (1) generate asteroid subsets, (2) chain building with beam search, (3) convex low-thrust trajectory optimization, (4) manual refinement of rendezvous times, and (5) optimal solution set selection. The generation of asteroid subsets involves a heuristic process to find sets of asteroids that are likely to permit high-scoring asteroid chains. Asteroid sequences “chains” are built within each subset through a beam search based on Lambert transfers. Low-thrust trajectory optimization involves the use of sequential convex programming (SCP), where a specialized formulation finds the mass-optimal control for each ship’s trajectory within seconds. Once a feasible trajectory has been found, the rendezvous times are manually refined with the aid of the control profile from the optimal solution. Each ship’s individual solution is then placed into a pool where the feasible set that maximizes the final score is extracted using a genetic algorithm. Our final submitted solution placed fifth with a score of 15,489.

We propose a method for a fast and accurate estimation of the collision probability in a short window following the generation of a debris cloud. A multirevolution Lambert targeting problem is employed to determine all the locations where the collision probability is nonnegligible. Then, the Lambert problem and state transition matrix are used to obtain the image of the target body in the spread velocity space, where the collision probability computation is performed. To perform and control the accuracy of the integration of the collision rate needed to obtain collision probabilities, we apply high-order Taylor expansion and automatic domain splitting techniques. The method is validated using a Monte Carlo simulation and a literature-based test case. Test cases demonstrate the validity of the approach for Keplerian and perturbed dynamics.

To maintain renewing epithelial tissues in a healthy, homeostatic state, cell divisions and differentiation need to be tightly regulated. Mechanisms of homeostatic regulation often rely on crowding feedback control: cells are able to sense the cell density in their environment, via various molecular and mechanosensing pathways, and respond by adjusting division, differentiation, and cell state transitions appropriately. Here, we determine, via a mathematically rigorous framework, which general conditions for the crowding feedback regulation (i) must be minimally met, and (ii) are sufficient, to allow the maintenance of homeostasis in renewing tissues. We show that those conditions naturally allow for a degree of robustness toward disruption of regulation. Furthermore, intrinsic to this feedback regulation is that stem cell identity is established collectively by the cell population, not by individual cells, which implies the possibility of ‘quasi-dedifferentiation’, in which cells committed to differentiation may reacquire stem cell properties upon depletion of the stem cell pool. These findings can guide future experimental campaigns to identify specific crowding feedback mechanisms.

The paper presents a possible approach to define - within the same global optimization the guidance history and the configuration of each different flight regime an atmospheric Entry-Descent-Landing (EDL) vehicle has to deal with. Precision landing constraints as well as inertial and thermal loads containment are considered. The optimization is focused on detecting a set of possible preliminary solutions to be further investigated by a local finer optimizer. A partially revisited Particle Swarm Optimization technique has been here successfully applied to deal with both a multiobjective and distributed optimization architecture specifically thought to cope with the complexity of the proposed problem. The proposed approach turned out to be powerful in identifying, quite rapidly, a set of feasible good solutions both from the guidance and the configuration point of view for each of the aerodynamics phases the probe goes through