Geometry of Gaussian quantum states

We study the Hilbert-Schmidt measure on the manifold of mixed Gaussian states in multi mode continuous variable quantum systems. An analytical expression for the Hilbert-Schmidt volume element is derived. Its corresponding probability measure can be used to study typical properties of Gaussian states. It turns out that although the manifold of Gaussian states is unbounded, an ensemble of Gaussian states distributed according to this measure still has a normalizable distribution of symplectic eigenvalues, from which unitarily invariant properties can be obtained. By contrast, we find that for an ensemble of one-mode Gaussian states based on the Bures measure the corresponding distribution cannot be normalized. As important applications, we determine the distribution and the mean value of von Neumann entropy and purity for the Hilbert-Schmidt measure

The role of demand response in mitigating market power - A quantitative analysis using a stochastic market equilibrium model. ESRI WP635, August 2019

Market power is a dominant feature of many modern electricity markets with an oligopolistic structure, resulting in increased consumer cost. This work investigates how consumers, through demand response (DR), can mitigate against market power. Within DR, our analysis particularly focusses on the impacts of load shifting and self-generation. A stochastic mixed complementarity problem is presented to model an electricity market characterised by oligopoly with a competitive fringe. It incorporates both energy and capacity markets, multiple generating firms and different consumer types. The model is applied to a case study based on data for the Irish power system in 2025. The results demonstrate how DR can help consumers mitigate against the negative effects of market power and that load shifting and self-generation are competing technologies, whose effectivity against market power is similar for most consumers. We also find that DR does not necessarily reduce emissions in the presence of market power

Configuration of Stable Evolutionary Strategy of Homo Sapiens and Evolutionary Risks of Technological Civilization (the Conceptual Model Essay)

Stable evolutionary strategy of Homo sapiens (SESH) is built in accordance with the modular and hierarchical principle and consists of the same type of self-replicating elements, i.e. is a system of systems. On the top level of the organization of SESH is the superposition of genetic, social, cultural and techno-rationalistic complexes. The components of this triad differ in the mechanism of cycles of generation - replication - transmission - fixing/elimination of adoptively relevant information. This mechanism is implemented either in accordance with the Darwin-Weismann modus, or according to the Lamarck modus, the difference between them is clear from the title. The integral attribute of the system of systems including ESSH is the production of evolutionary risks. The sources of evolutionary risk for stable adaptive strategy of Homo sapiens are the imbalance of (1) the intra-genomic co-evolution (intragenomic conflicts); (2) the gene-cultural coevolution; (3) the inter-cultural co-evolution; (4) techno-humanitarian balance; (5) intertechnological conflicts (technological traps). At least phenomenologically the components of the evolutionary risk are reversible, but in the aggregate they are in potentio irreversible destructive ones for bio-social, and cultural self-identity of Homo sapiens. When the actual evolution is the subject of a rationalist control and/or manipulation, the magnitude of the 4th and 5th components of the evolutionary risk reaches the level of existential significance

Analysing long-term interactions between demand response and different electricity markets using a stochastic market equilibrium model. ESRI WP585, February 2018

Power systems based on renewable energy sources (RES) are characterised by increasingly distributed, volatile and uncertain supply leading to growing requirements for flexibility. In this paper, we explore the role of demand response (DR) as a source of flexibility that is considered to become increasingly important in future. The majority of research in this context has focussed on the operation of power systems in energy only markets, mostly using deterministic optimisation models. In contrast, we explore the impact of DR on generator investments and profits from different markets, on costs for different consumers from different markets, and on CO2 emissions under consideration of the uncertainties associated with the RES generation. We also analyse the effect of the presence of a feed-in premium (FIP) for RES generation on these impacts. We therefore develop a novel stochastic mixed complementarity model in this paper that considers both operational and investment decisions, that considers interactions between an energy market, a capacity market and a feed-in premium and that takes into account the stochasticity of electricity generation by RES. We use a Benders decomposition algorithm to reduce the computational expenses of the model and apply the model to a case study based on the future Irish power system. We find that DR particularly increases renewable generator profits. While DR may reduce consumer costs from the energy market, these savings may be (over)compensated by increasing costs from the capacity market and the feed-in premium. This result highlights the importance of considering such interactions between different markets