Path-wise control of stochastic systems: overcoming the curse of causality

In this thesis we address the topic of path-wise control of stochastic systems defined by stochastic differential equations. By path-wise control we mean that the controller's decisions are not intended to regulate the moments of the state or the output (or a function of them), as customary in stochastic control. Instead, we aim at designing a controller that achieves a desired, specific, trajectory of the state (or the output) itself, for all possible realisations of the noise affecting the system. We show that path-wise control is cursed by insuperable causality issues, because in order to perfectly attain a predefined trajectory for each realisation of the noise, the controller needs to access measurements of the noise itself, which is not possible in practice. Therefore, we approach path-wise control in two steps. Firstly, we design idealistic controllers, which achieve exact regulation by employing a feedback of the noise. Although unrealistic, these designs are preliminary to the second step, i.e. the construction of practical controllers, which estimate the noise from measurements of available quantities (state or output) and use such estimates to perform approximate path-wise control in a hybrid way. We show that the performance of the practical controllers can retrieve the idealistic ones in a limit behaviour. In this framework we address two classical control problems. Firstly, we consider output regulation of linear stochastic systems. We show that the idealistic controllers achieve a zero steady-state tracking error, while the practical controllers allow for a nonzero steady-state error, which, however, can be made arbitrarily small by tuning a design parameter. Secondly, we consider the control of stochastic systems defined by nonlinear, control-affine, stochastic differential equations. In this case, we show that the idealistic controllers achieve exact feedback linearisation and output tracking, while the practical controllers achieve state (and output) trajectories which can be made close to the idealistic ones by tuning a design parameter, thus obtaining approximate feedback linearisation and tracking.Open Acces

Investigating the role of histones in fission yeast centromere function

The centromere is the chromosomal region which is responsible for the accurate segregation of chromosomes during mitosis and meiosis. Failure to properly segregate replicated chromosomes causes aneuploidy and contributes to cancer progression. Fission Yeast centromeres display several features in common with the centromeres of higher eukaryotes. They are assembled in a specialised silent heterochromatin composed of underacetylated histones and methylated histone H3. To investigate the role of histone H3 and H4 N-tails in centromere structure and function, conserved lysines of histone N-termini were mutated to mimic hyperacetylated or non-methylated states. Since the fission yeast haploid genome contains three copies of both histones H3 and H4, initially a strain harbouring a single H3 and H4 gene was generated and analysed. This phenotypically wild type strain provided a genetic background in which to perform site-directed mutagenesis of the histone tails. These mutants showed that the H4 tail is not critical for silencing, while the H3 tail plays an essential role and is required for centromere function. Centromeric nucleosomes contain an essential histone H3-like protein, CENP-A. Antibodies were raised against the fission yeast CENP-A homologue Cnpl and were used to map Cnp1 association with the central domain of the centromere. Cnp1 appears to replace histone H3 in this domain and can coat a large fragment of non-centromeric DMA artificially inserted within this centromeric domain. Futhermore, strains expressing more histone H3 than H4 showed delocalisation of Cnp1, alleviation of centromeric silencing and missegregation of chromosomes in mitosis indicating that a fine balance between histone H3 and H4 is important for centromere function and that histone H3 can compete with Cnp1 in nucleosome assembly

Prototype: A Community Center for the Slums of Sao Paulo, Brazil

Poverty can be viewed through 5 different perspectives: urbanism, economy, sociology, politics, and legislation. Architecture can refer to all of them, but my decision is to deal with primarily urbanistic problems

Baby Bay And The Big, LOUD Ocean

This is a children\u27s book that depicts some of the serious effects of noise pollution on marine organisms, especially larger mammals such as Baleen Whales. Through this little story about a baby whale and his mom, trying to find the rest of their pod amidst an ocean filled with noise pollution, we hope to spread awareness about this problem and provide hope to younger generations that if we work hard enough at protecting our oceans, we can provide a much nicer and safer life for the creatures that live within it.https://dune.une.edu/env_studproj/1000/thumbnail.jp

Birds on the move: Special column on bird movement

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Normal form and exact feedback linearisation of nonlinear stochastic systems: the ideal case

This paper introduces the concepts of stochastic relative degree, normal form and exact feedback linearisation for single-input single-output nonlinear stochastic systems. The systems are defined by stochastic differential equations in which both the drift and the diffusion terms are nonlinear functions of the states and the control input. First, we define new differential operators and the concept of stochastic relative degree. Then we introduce a suitable coordinate change and we show that the dynamics of the transformed state has a simplified structure, which we name normal form. Finally, we show that a condition on the stochastic relative degree of the system is sufficient for it to be rendered linear via a coordinate change and a nonlinear feedback. We provide an analytical example to illustrate the theory

The time is out of joint. Teacher subjectivity during COVID-19

In this study, we address the issue of mathematics teachers’ personal and professional responsiveness to changing circumstances, such as the shift in external demands made on teacher practice due to the COVID-19 pandemic. For investigating a such delicate issue, we take a theoretical approach, which is quite novel in the feld of mathematics education: Lacan’s psychoanalytical lens. Specifcally, we will use this psychoanalytical lens to analyze a case study focusing on a primary school teacher during the frst lockdown in Italy, during which school was organized exclusively in the form of distance education. The analysis of the teacher’s crisis and the strategies she adopted to overcome this crisis give some suggestions about possible directions and issues to consider for future mathematics teacher training proposals