The role of biological processes in affecting the dynamics and fate of microplastics in coastal marine systems

Microplastics (MP) are omnipresent contaminants in the marine environment. Ingestion of MP has been reported for a wide range of marine biota, but to what extent the uptake by organisms affects the dynamics and fate of MP in the marine system has received little attention. My thesis explored this topic by integrating laboratory tests and experiments, field quantitative surveys of MP distribution and dynamics, and the use of specialised analytical techniques such as Attenuated-Total-Reflectance- (ATR) and imaging- Fourier Transformed Infrared Spectroscopy (FTIR). I compared different methodologies to extract MP from wild invertebrate specimens, and selected the use of potassium hydroxide (KOH) as the most cost-effective approach. I used this approach to analyse the MP contamination in various invertebrate species with different ecological traits from European salt marshes. I found that 96% of the analysed specimens (330) did not contain any MP. As preliminary environmental analyses showed high levels of environmental MP contamination, I hypothesised that most MP do not accumulate into organisms but are rather fast egested. I subsequently used laboratory multi-trophic experiments and a long-term field experiment using the filter-feeding mussel Mytilus galloprovincialis and the detritus feeding polychaete Hediste diversicolor to test the aforementioned hypothesis. Overall, results showed that MP are ingested but rapidly egested by marine invertebrates, which may limit MP transfer via predator-prey interactions but at the same time enhance their transfer via detrital pathways in the sediments. These processes seem to be extremely variable over time, with potential unexplored environmental consequences. This rapid dynamics also limits the conclusions that can be derived from static observations of MP contents in marine organisms, not fully capturing the real levels of potential contaminations by marine species. This emphasises the need to consider such dynamics in future work to measure the uptake rates by organisms in natural systems.

On the Wick product and Wong-Zakai approximations.

This thesis is a compilation of 6 papers that the author has written together with Alberto Lanconelli (chapters 3, 5 and 8) and Hyun-Jung Kim (ch 7). The logic thread that link all these chapters together is the interest to analyze and approximate the solutions of certain stochastic differential equations using the so called Wick product as the basic tool. In the first chapter we present arguably the most important achievement of this thesis; namely the generalization to multiple dimensions of a Wick-Wong-Zakai approximation theorem proposed by Hu and Oksendal. By exploiting the relationship between the Wick product and the Malliavin derivative we propose an original reduction method which allows us to approximate semi-linear systems of stochastic differential equations of the Itô type. Furthermore in chapter 4 we present a non-trivial extension of the aforementioned results to the case in which the system of stochastic differential equations are driven by a multi-dimensional fraction Brownian motion with Hurst parameter bigger than 1/2. In chapter 5 we employ our approach and present a “short time” approximation for the solution of the Zakai equation from non-linear filtering theory and provide an estimation of the speed of convergence. In chapters 6 and 7 we study some properties of the unique mild solution for the Stochastic Heat Equation driven by spatial white noise of the Wick-Skorohod type. In particular by means of our reduction method we obtain an alternative derivation of the Feynman-Kac representation for the solution, we find its optimal Hölder regularity in time and space and present a Feynman-Kac-type closed form for its spatial derivative. Chapter 8 treats a somewhat different topic; in particular we investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of semi-linear stochastic differential equations describing a predator-prey model perturbed by Gaussian noise.

Congenital Nystagmus eye movements analysis and oculomotor system models evaluation

The term Congenital Nystagmus (Early Onset Nystagmus or Infantile Nystagmus Syndrome) refers to a pathology characterised by an involuntary movement of the eyes, which often seriously reduces a subject’s vision. Congenital Nystagmus (CN) is a specific kind of nystagmus within the wider classification of infantile nystagmus, which can be best recognized and classified by means of a combination of clinical investigations and motility analysis; in some cases, eye movement recording and analysis are indispensable for diagnosis. However, interpretation of eye movement recordings still lacks of complete reliability; hence new analysis techniques and precise identification of concise parameters directly related to visual acuity are necessary to further support physicians’ decisions. To this aim, an index computed from eye movement recordings and related to the visual acuity of a subject is proposed in this thesis. This estimator is based on two parameters: the time spent by a subject effectively viewing a target (foveation time - Tf) and the standard deviation of eye position (SDp). Moreover, since previous studies have shown that visual acuity largely depends on SDp, a data collection pilot study was also conducted with the purpose of specifically identifying eventual slow rhythmic component in the eye position and to characterise in more detail the SDp. The results are presented in this thesis. In addition, some oculomotor system models are reviewed and a new approach to those models, i.e. the recovery of periodic orbits of the oculomotor system in patients with CN, is tested on real patients data. In conclusion, the results obtained within this research consent to completely and reliably characterise the slow rhythmic component sometimes present in eye position recordings of CN subjects and to better classify the different kinds of CN waveforms. Those findings can successfully support the clinicians in therapy planning and treatment outcome evaluation.

Constraint based methods for allocation and scheduling of periodic applications

This work presents exact algorithms for the Resource Allocation and Cyclic Scheduling Problems (RA&CSPs). Cyclic Scheduling Problems arise in a number of application areas, such as in hoist scheduling, mass production, compiler design (implementing scheduling loops on parallel architectures), software pipelining, and in embedded system design. The RA&CS problem concerns time and resource assignment to a set of activities, to be indefinitely repeated, subject to precedence and resource capacity constraints. In this work we present two constraint programming frameworks facing two different types of cyclic problems. In first instance, we consider the disjunctive RA&CSP, where the allocation problem considers unary resources. Instances are described through the Synchronous Data-flow (SDF) Model of Computation. The key problem of finding a maximum-throughput allocation and scheduling of Synchronous Data-Flow graphs onto a multi-core architecture is NP-hard and has been traditionally solved by means of heuristic (incomplete) algorithms. We propose an exact (complete) algorithm for the computation of a maximum-throughput mapping of applications specified as SDFG onto multi-core architectures. Results show that the approach can handle realistic instances in terms of size and complexity. Next, we tackle the Cyclic Resource-Constrained Scheduling Problem (i.e. CRCSP). We propose a Constraint Programming approach based on modular arithmetic: in particular, we introduce a modular precedence constraint and a global cumulative constraint along with their filtering algorithms. Many traditional approaches to cyclic scheduling operate by fixing the period value and then solving a linear problem in a generate-and-test fashion. Conversely, our technique is based on a non-linear model and tackles the problem as a whole: the period value is inferred from the scheduling decisions. The proposed approaches have been tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances achieving good results on practical size problem.