Bimodules and branes in deformation quantization

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space $X$. The result implies in particular that the Kontsevich deformation quantizations of $\mathrm{S}(X^*)$ and $\wedge(X)$ associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantization.Comment: 40 pages, 15 figures; a small change of notations in the definition of the 4-colored propagators; an Addendum about the appearance of loops in the $L_\infty$-quasi-isomorphism and a corresponding change in the proof of Theorem 7.2; several changes regarding completions, when dealing with general $A_\infty$-structure

Beam loading assisted matching scheme for high quality plasma acceleration in linear regime

We propose and we numerically design a working point for beam driven plasma wakefield acceleration that allows us to preserve the witness quality. This working point is a new scheme where a low density driver generates a wakefield in linear regime and the witness transverse evolution is dominated by the beam loading effect. We derived optimal matching conditions to prevent the phase space degradation by means of a transverse envelope equation

Computational Study of Neuronal Oscillations In Motor Control Circuits

In this thesis we used mathematical and computational models to study neuronal net- works that control motor behaviours. Specifically, we modelled two neuronal circuits from two opposite ends of the brain complexity spectrum: the swimming circuit of the hatchling Xenopus tadpole and the human basal ganglia. Due to its relative simplicity, tadpole is a unique animal for studying locomotion us- ing both experiments and models. This allowed us to define three biologically-realistic spiking models to clarify the interplay between the architecture of synaptic connections (structure) and the network’s ability to generate activities that correspond to its swim- ming behaviour (function). First, we investigated how the structural variability of individual circuits produces similar behaviours. To answer this question, we defined a probabilistic model of connectivity and dynamics for the neurons in the spinal cord. Simulations of the model showed that the swimming behaviours generated by different connectivities are remarkably similar. We used graph theory measures to characterise structural properties of networks un- derlying swimming. For example, we applied them to (1) predict the swimming period and (2) detect key neurons and connections that promote the swimming rhythm. Second, we built a minimal model of the central pattern generator (CPG) which repro- duces all the experimentally recorded oscillatory regimes: swimming and synchrony - anti-phase and in-phase oscillations between two body sides, respectively. Using bifurcation theory, we defined stabilities for these regimes and demonstrated the exis- tence of bi-stablity for a physiological range of parameters. Considering a vicinity of the critical parameter values of a saddle-node bifurcation, we explained how long-lasting synchrony transitions can appear both in model and experiment. Third, we expanded our CPG model by adding three sensory pathways. Our modelling is based on available anatomical and physiological data and on our new probabilistic ap- proach for modelling connections. The expanded model contains approximately 1700 neurons and about 100,000 connections. The model reproduces the experimentally recorded neuronal activities during the initiation, acceleration, continuation, modula- tion and termination of locomotion. Therefore, it can describe the complete swimming behaviour of the tadpole in response to sensory inputs. Inspired by our study of oscillations and synchronisation in the tadpole nervous sys- tem, we proposed a theoretical model of action selection in the basal ganglia. We use a mathematical formalism known as Arnold tongues to explain how modulatory inputs from the cortex can partially synchronise subsets of neurons in the basal ganglia and generate a rhythmic action. This mechanism can explain how the transitions between multiple oscillatory states might work, thus effectively resolving the switching between competing actions. Although theoretical, the model could serve as a qualitative tool to understand the basic working principles of action selection. For example, model simula- tions match experimental recordings in rodents showing that the cortex can synchronise neurons in the basal ganglia and generate Arnold tongues synchronisation.University of Plymout

Ethics of the algorithmic prediction of goal of care preferences: from theory to practice

Artificial intelligence (AI) systems are quickly gaining ground in healthcare and clinical decision-making. However, it is still unclear in what way AI can or should support decision-making that is based on incapacitated patients’ values and goals of care, which often requires input from clinicians and loved ones. Although the use of algorithms to predict patients’ most likely preferred treatment has been discussed in the medical ethics literature, no example has been realised in clinical practice. This is due, arguably, to the lack of a structured approach to the epistemological, ethical and pragmatic challenges arising from the design and use of such algorithms. The present paper offers a new perspective on the problem by suggesting that preference predicting AIs be viewed as sociotechnical systems with distinctive life-cycles. We explore how both known and novel challenges map onto the different stages of development, highlighting interdisciplinary strategies for their resolution

An Ethical Framework for Incorporating Digital Technology into Advance Directives: Promoting Informed Advance Decision Making in Healthcare

Despite the presumed value of advance directives, research to demonstrate impact has shown mixed results. For advance directives to serve their role promoting patient autonomy, it is important that patients be informed decision makers. The capacity to make decisions depends upon understanding, appreciation, reasoning, and communication. Advance directives are in part faulty because these elements are often limited. The present paper explores how the application of digital technology could be organized around a framework promoting these four elements. Given the state of digital advancements, there is great potential for advance directives to be meaningfully enhanced. The beneficial effects of incorporating digital technology would be maximized if they were organized around the aim of making advance directives not only documents for declaring preferences but also ethics-driven tools with decision aid functionality. Such advance directives would aid users in making decisions that involve complex factors with potentially far-reaching impact and would also elucidate the users' thought processes to aid those tasked with interpreting and implementing decisions based on an advance directive. Such advance directives might have embedded interactive features for learning; access to content that furthers one's ability to project oneself into possible, future scenarios; review of the logical consistency of stated preferences; and modes for effective electronic sharing. Important considerations include mitigating the introduction of bias depending on the presentation of information; optimizing interfacing with surrogate decision makers and treating clinicians; and prioritizing essential components to respect time constraints. Keywords: Advance Care Planning; Advance Directives; Autonomy; Decision Support Techniques; Digital Technology; Patient Rights

Bimodules and branes in deformation quantization

We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich deformation quantizations of S(X*) and (X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantizatio

A case for preference-sensitive decision timelines to aid shared decision-making in intensive care: need and possible application

In the intensive care unit, it can be challenging to determine which interventions align with the patients' preferences since patients are often incapacitated and other sources, such as advance directives and surrogate input, are integral. Managing treatment decisions in this context requires a process of shared decision-making and a keen awareness of the preference-sensitive instances over the course of treatment. The present paper examines the need for the development of preference-sensitive decision timelines, and, taking aneurysmal subarachnoid hemorrhage as a use case, proposes a model of one such timeline to illustrate their potential form and value. First, the paper draws on an overview of relevant literature to demonstrate the need for better guidance to (a) aid clinicians in determining when to elicit patient preference, (b) support the drafting of advance directives, and (c) prepare surrogates for their role representing the will of an incapacitated patient in clinical decision-making. This first section emphasizes that highlighting when patient (or surrogate) input is necessary can contribute valuably to shared decision-making, especially in the context of intensive care, and can support advance care planning. As an illustration, the paper offers a model preference-sensitive decision timeline—whose generation was informed by existing guidelines and a series of interviews with patients, surrogates, and neuro-intensive care clinicians—for a use case of aneurysmal subarachnoid hemorrhage. In the last section, the paper offers reflections on how such timelines could be integrated into digital tools to aid shared decision-making