Quantum entanglement: insights via graph parameters and conic optimization

In this PhD thesis we study the effects of quantum entanglement, one of quantum mechanics most peculiar features, in nonlocal games and communication problems in zero-error information theory. A nonlocal game is a thought experiment in which two cooperating players, who are forbidden to communicate, want to perform a certain task. Zero-error information theory is the mathematical field that studies communication problems where no error is tolerated. The unifying link among the various scenarios we consider is their combinatorial nature and in particular their reformulations as graph theoretical problems, mainly concerning the chromatic and stability numbers and some quantum generalizations thereof. In this thesis we propose a novel approach to the study of these quantum graph parameters using the paradigm of conic optimization. For that, we introduce and study the completely positive semidefinite cone, a new matrix cone consisting of all symmetric matrices that admit a Gram representation by positive semidefinite matrices. Furthermore, we investigate whether entanglement allows for better-than-classical communication schemes in some well-known problems from zero-error information theory. For example we study the channel coding problem, which asks a sender to transmit data reliably to a receiver in the presence of noise, as well as some of its generalizations

Modeling multi-agent systems with hybrid interacting dynamics

We present a new framework for describing multi-agent systems with hybrid interacting dynamics, where the interaction between agents occurs at both the continuous and discrete levels. We define multi-agent systems as Interconnected Hybrid Systems, recast fundamental hybrid concepts such as hybrid execution and reachability in this new interconnected hybrid systems framework, and prove a necessary and sufficient condition for the existence and uniqueness of the interconnected hybrid executions, extending previous work on hybrid systems. We provide conditions on each agent\u27s hybrid model that guarantee the multi-agent system\u27s existence and uniqueness property. Finally, we provide an example that shows how to apply the existence and uniqueness conditions in the design of the agents\u27 dynamics

Preliminary Results on Interconnected Hybrid Systems

We present a new framework for describing multi-agent systems with hybrid individual dynamics where the interaction between agents occurs at both the continuous and discrete levels. We formally define these multi-agent systems as interconnected hybrid systems and then recast fundamental hybrid concepts such as a hybrid metric, hybrid execution, and reachability in this new interconnected hybrid systems framework. We then prove a necessary condition for the existence of the interconnected hybrid executions

Potential of model predictive control of a polder water system including pumps, weirs and gates

This work presents an assessment of the potential of model predictive control (MPC) of a Dutch polder system. The system drains to the Linge river and includes 13 weirs, 4 hydraulic gates and 4 large pumping stations each equipped with multiple pumps, managed by the Water Board Rivierenland. The management of the system must comply with several goals: keep the water levels within the bounds of safety, pump out the excess water at minimum cost or CO2 emission, but always have enough water for irrigation and shipping. To achieve these goals there are weirs regulating the water level in different pools, pumping stations to pump water in and out and gates to let water in and out by free flow when possible. These pumping stations consume large amounts of energy. We propose multi-objective mixed-integer optimization by using goal programming to prioritize different operational objectives. For the control of the pumps mixed-integer optimization is used, which makes it possible to not only model the energy consumption of the pumps while in operation, but also to model if the pumps are turned on or off. The control system is implemented using RTC-Tools, an open-source software tool to implement MPC. It is demonstrated that the proposed control system implementation can comply with the operational goals of the water board: keeping the water levels within the bounds while reducing the operational costs. The proposed control system has been tested numerically on data from the year 2013, and it is shown that it highly outperforms the current operation.</p

Statistical Learning for Optimal Control of Hybrid Systems

In this paper we explore a randomized alternative for the optimization of hybrid systems\u27 performance. The basic approach is to generate samples from the family of possible solutions, and to test them on the plant\u27s model to evaluate their performance. This result is obtained by first presenting the general hybrid optimal control problem, and then converting it into an optimization problem within a statistical learning framework. The results are applied to examples already existing in the literature, in order to highlight certain operational aspects of the proposed methods

Mediterranean old-growth forests exhibit resistance to climate warming

Old-growth mountain forests represent an ideal setting for studying long-term impacts of climate change. We studied the few remnants of old-growth forests located within the Pollino massif (southern Italy) to evaluate how the growth of conspecific young and old trees responded to climate change. We investigated two conifer species (Abies alba and Pinus leucodermis) and two hardwood species (Fagus sylvatica and Quercus cerris). We sampled one stand per species along an altitudinal gradient, ranging from a drought-limited low-elevation hardwood forest to a cold-limited subalpine pine forest. We used a dendrochronological approach to characterize the long-term growth dynamics of old (age > 120 years) versus young (age < 120 years) trees. Younger trees grew faster than their older conspecifics during their juvenile stage, regardless of species. Linear mixed effect models were used to quantify recent growth trends (1950–2015) and responses to climate for old and young trees. Climate sensitivity, expressed as radial growth responses to climate during the last three decades, partially differed between species because high spring temperatures enhanced conifer growth, whereas F. sylvatica growth was negatively affected by warmer spring conditions. Furthermore, tree growth was negatively impacted by summer drought in all species. Climate sensitivity differed between young and old trees, with younger trees tending to be more sensitive in P. leucodermis and A. alba, whereas older F. sylvatica trees were more sensitive. In low-elevation Q. cerris stands, limitation of growth due to drought was not related to tree age, suggesting symmetric water competition. We found evidence for a fast-growth trend in young individuals compared with that in their older conspecifics. Notably, old trees tended to have relatively stable growth rates, showing remarkable resistance to climate warming. These responses to climate change should be recognized when forecasting the future dynamics of old-growth forests for their sustainable management. © 2021 The Author