A general stochastic model for sporophytic self-incompatibility

Disentangling the processes leading populations to extinction is a major topic in ecology and conservation biology. The difficulty to find a mate in many species is one of these processes. Here, we investigate the impact of self-incompatibility in flowering plants, where several inter-compatible classes of individuals exist but individuals of the same class cannot mate. We model pollen limitation through different relationships between mate availability and fertilization success. After deriving a general stochastic model, we focus on the simple case of distylous plant species where only two classes of individuals exist. We first study the dynamics of such a species in a large population limit and then, we look for an approximation of the extinction probability in small populations. This leads us to consider inhomogeneous random walks on the positive quadrant. We compare the dynamics of distylous species to self-fertile species with and without inbreeding depression, to obtain the conditions under which self-incompatible species could be less sensitive to extinction while they can suffer more pollen limitation

Branching Feller diffusion for cell division with parasite infection

We describe the evolution of the quantity of parasites in a population of cells which divide in continuous-time. The quantity of parasites in a cell follows a Feller diffusion, which is splitted randomly between the two daughter cells when a division occurs. The cell division rate may depend on the quantity of parasites inside the cell and we are interested in the cases of constant or monotone division rate. We first determine the asymptotic behavior of the quantity of parasites in a cell line, which follows a Feller diffusion with multiplicative jumps. We then consider the evolution of the infection of the cell population and give criteria to determine whether the proportion of infected cells goes to zero (recovery) or if a positive proportion of cells becomes largely infected (proliferation of parasites inside the cells)

3 CAPD Awards Helped Generate 2 National Presentations and 5 Publications.

There were 3 CAPD awards that have resulted in 2 presentations at national meetings and they also helped in the publication of 5 articles in peer-reviewed professional dental journals. There were 15 faculty, 4 pre-doctoral and 2 postdoctoral students who were involved: CAPD.(2020) Presentation at American Dental Education Association Meeting, award to Booth, Tran Presentation-Greene RS, Greene SS, Tran CD. Graphic rapid extrusion: evolutionary novel electronic orthodontic management guide. Accepted for presentation American Dental Education Association. March 12, 2021 Boston, MA (Virtual) Publication- Greene RS, Greene SS, Tran CD. Graphic rapid extrusion: evolutionary novel electronic orthodontic management guide. Journal of Dental Education. Volume 85, Number2, page 275–277, Feb 2021 CAPD (2020): “Advanced Biomedical Camera: Dental Education Focus,” award to Brady, Booth, Tran Presentation- Tran C, Kosturos M, Booth M, Gallagher D, Brady M, Greene S, Ellerhorst T, Buchanan P, Gupta S, Savage R. Early implementation, electronic instruction occlusal milled guard, pre-doctoral clinic Accepted for presentation American Dental Education Association. March 2020 Washington DC Publication- Brady M, Tran C, Booth M, Radke R. Esthetic clasp design for removable partial dentures on anterior teeth: Decisions in Dentistry. Volume 6 Number 4: page 22-25 April2020. Tran C, Kosturos M, Booth M, Gallagher D, Brady M, Greene S, Ellerhorst T, Buchanan P, Gupta S, Savage R. Early implementation, electronic instruction occlusal milled guard, predoctoral clinic. Journal of Dental Education. Volume 84, Number 2, page 268, Feb 2020Schulze K, Smutko O, Tang T, Kenyon BJ, Peterson E, Tran C, Buchanan P. 10 year follow upon resin modified glass ionomer restorations. Decisions in Dentistry; Volume 6 Number 10:page 22-25 October 2020 CAPD (2021). “Overlay Model Graphic Augmented Reality Technique: Enhanced Implant Evaluation Instruction Outcome, award to Gonzalez, Tran Publication- Trivedi H, Gonzalez Espinoza E, Gupta S, Tran C, Yadav S. .Fixed treatment options for single incisor replacement. Decisions in Dentistry; Volume 7 Number 4: page 8-12, April 202

Regression with respect to sensing actions and partial states

In this paper, we present a state-based regression function for planning domains where an agent does not have complete information and may have sensing actions. We consider binary domains and employ the 0-approximation [Son & Baral 2001] to define the regression function. In binary domains, the use of 0-approximation means using 3-valued states. Although planning using this approach is incomplete with respect to the full semantics, we adopt it to have a lower complexity. We prove the soundness and completeness of our regression formulation with respect to the definition of progression. More specifically, we show that (i) a plan obtained through regression for a planning problem is indeed a progression solution of that planning problem, and that (ii) for each plan found through progression, using regression one obtains that plan or an equivalent one. We then develop a conditional planner that utilizes our regression function. We prove the soundness and completeness of our planning algorithm and present experimental results with respect to several well known planning problems in the literature.Comment: 38 page

Stochastic dynamics of adaptive trait and neutral marker driven by eco-evolutionary feedbacks

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effects of the trait are also expected to influence the generation and maintenance of neutral variation. We consider a large population limit with rare mutation, under the assumption that the neutral marker mutates faster than the trait under selection. We prove the convergence of the stochastic individual-based process to a new measure-valued diffusive process with jumps that we call Substitution Fleming-Viot Process (SFVP). When restricted to the trait space this process is the Trait Substitution Sequence first introduced by Metz et al. (1996). During the invasion of a favorable mutation, a genetical bottleneck occurs and the marker associated with this favorable mutant is hitchhiked. By rigorously analysing the hitchhiking effect and how the neutral diversity is restored afterwards, we obtain the condition for a time-scale separation; under this condition, we show that the marker distribution is approximated by a Fleming-Viot distribution between two trait substitutions. We discuss the implications of the SFVP for our understanding of the dynamics of neutral variation under eco-evolutionary feedbacks and illustrate the main phenomena with simulations. Our results highlight the joint importance of mutations, ecological parameters, and trait values in the restoration of neutral diversity after a selective sweep.Comment: 29 page

The 2d-directed spanning forest converges to the Brownian web

The two-dimensional directed spanning forest (DSF) introduced by Baccelli and Bordenave is a planar directed forest whose vertex set is given by a homogeneous Poisson point process $\mathcal{N}$ on $\mathbb{R}^2$. If the DSF has direction $-e_y$, the ancestor $h(u)$ of a vertex $u \in \mathcal{N}$ is the nearest Poisson point (in the $L_2$ distance) having strictly larger $y$-coordinate. This construction induces complex geometrical dependencies. In this paper we show that the collection of DSF paths, properly scaled, converges in distribution to the Brownian web (BW). This verifies a conjecture made by Baccelli and Bordenave in 2007

Tissue engineering cartilage for focal defects

Articular cartilage provides a near frictionless surface for the articulating ends of bones. Cartilage functions to lubricate and transmit compressive forces resulting from joint loading and impact. If damaged, whether by traumatic injury or disease, cartilage lacks the ability for self-repair. This study explores the production of scaffoldree cartilage and investigates the effect of Tissue Growth Technologies’ CartiGen Bioreactor on the cartilage. Chondrocyte and bone marrow-derived stem cell (BMSC) attachment to chitosan is also investigated in hopes of producing a bilayered construct for osteochondral repair. Results demonstrate that culturing of scaffoldree cartilage in the CartiGen bioreactor resulted in an enhancement of the scaffoldree cartilage’s biomechanical and biochemical properties and that the chitosan microspheres were able to successfully support porcine chondrocyte and BMSC attachment. Results from both studies are encouraging for future work involving tissue engineered cartilage

Transanal irrigation is more beneficial in symptomatic management of neurogenic bowel disease than conservative bowel management

A clinical decision report appraising Christensen P, Bazzocchi G, Coggrave M, et al. A Randomized, Controlled Trial of Transanal Irrigation Versus Conservative Bowel Management in Spinal Cord–Injured Patients. Gastroenterology. 2006;131(3):738-747. https://doi.org/10.1053/j.gastro.2006.06.00