On the linear independence of p-adic L-functions modulo p

Inspired by Warren Sinnott 's method we prove a linear independence result modulo p for the Iwasawa power series associated to Kubota-Leopoldt p-adic L-functions

Employment subsidies and substitutable skills : An equilibrium matching approach

This search-matching model is well suited for an equilibrium evaluation of labor market policies. When those policies are targeted on some groups, the usual juxtaposition of labor markets is however a shortcoming. There is a need for a setting where workers’ productivity depends on employment levels in all markets. This paper provides such a theoretical setting. We first develop a streamlined model and then show that it can be extended to deal with interactions among various labor market and fiscal policies. Simulation results focus on the effects of employment subsidies and in-work benefits and on their interactions with the profile of unemployment benefits and with active labor market programs.Unemployment; search-matching equilibrium; wage bargaining; reductions of social security contributions; unemployment insurance; labor market programs

Flexibility of Electric Power Systems by Network Planning and Service Provision: Challenges for Energy Transition

In recent years, the electric power system is meeting a radical evolution due to the increasing penetration of Renewable Energy Sources (RESs). These have a relevant impact on most of the applications concerning the electrical network, such as the electricity markets, regulation services provision and the grid management and protection. However, the deep RESs deployment is the answer that countries all over the world are pursuing to fight climate change according to the Sustainable Development Goals (SDGs) adopted by the United Nations (UN). This evolution requires a great development of the network, that has to host a large quantity of new RESs, and the establishment of new strategies to deal with new challenges. More and more reserves for regulation services are pursued by units that couldn’t provide dispatching services until now, namely small-sized plants and RESs, but also load and storage systems. The demand has become increasingly more active since it has made possible a contribution to instability issues by varying their power profile for a certain amount of time without compromising the final user’s comfort, which means being flexible. As a result, a huge amount of new generation units and load units have started to provide dispatching services by participating to the electricity markets. This condition has led to the need of the improvement of the communication systems among all the actors in the process of power transmission alongside grid balancing, including the Transmission System Operator (TSO), the Distribution System Operators (DSOs), generation, load units and other data aggregators. The observability of the system is essential to forecast load and generation profiles in order to provide a suitable balancing service and to guarantee the reliability, safety and power quality of the electrical network through state estimation methods which are going to be widely used in modern systems. Observability is also important in making decisions for the planning of the network development by giving access to information about the grid operating conditions. Therefore it suggests how to focus the efforts to improve the electric power system performance according to the objectives established to reduce the impact of fossil fuels in the climate change. In sight of this, it can be concluded that the key to deal with climate change is a suitable coordination of such factors: the development of the network, the arrangement of flexibility resources and the communication systems improvement. During the Doctorate (Ph.D.), the author has worked on several research projects related to the topic of the evolution of the electric system. The project are listed in the Appendices. This thesis gathers the work done by underlining the importance of the three factors mentioned before in the context of the power system evolution. The developed applications will be presented as particular approaches that can be applied to a general power system and take place in one or more aspects of the ecological transition. In Chapter 1, the UN strategies to deal with climate change are introduced as well as the main consequences they led to and the new needs of the electric system are described. An introduction to regulation services and their purpose is given. In Chapter 2 the Italian context, as part of the European and Global plan to reduce emissions, is described. The main tools used by the Italian TSO to plan the network development are introduced and the study case of the network of Sicily is explained in the contest of the project ”Assessments of Battery Energy Storage Systems Potential in Improving the Working Condition of the Grid of Sicily”. As a continuation of this work, the method developed in the project ”Optimal Storage Allocation for Transmission Network Development Planning” is applied to the Sicilian network model and its possible contribution to network infrastructure planning is described. In Chapter 3 the impact that the installation of several RESs have on the grid stability is described. The consequent evolution process of the electricity market in order to cope with the increased need of regulation services is explained. In such context, pilot projects have been established by the TSO to encourage research of flexibility resources with reference to the projects concerning regulation service provision from loads and RESs. In Chapter 4, in project ”Flexibility Evaluation of an Aggregate of Thermal Load Units”, a definition of flexibility resources is given and a flexibility analysis of aggregates of thermal loads intended for domestic hot water heating, such as domestic electric water heaters or heat pumps, has been carried out during the research activity. A Monte Carlo approach is adopted for the methodology applied to the study case of Italy and Sicily. Chapter 5 describes and presents the results of the project ”Model Predictive Control for frequency regulation services provision” where the fast frequency reserve service is explored according to the related pilot project by using Model Predictive Control (MPC) based techniques applied on systems with RESs and Battery Energy Storage Systems (BESSs). Such service is meant to replace the beneficial effect of inertia from the traditional generating units which is progressively decreasing because of the implementation of RESs units in the power system. The decrease of inertia leads to more significant frequency variations after fault events that must be solved within extremely high speed actions, even faster than primary frequency regulation service. To complete the thesis, the Conclusions are presented together with some last comments. Finally, the publications produced during the Ph.D. and the projects to which contribution was given, collaborations and attended courses are listed, while references cited in this thesis end the dissertation

Food availability and competition do not modulate the costs of Plasmodium infection in dominant male canaries

Understanding the different factors that may influence parasite virulence is of fundamental interest to ecologists and evolutionary biologists. It has recently been demonstrated that parasite virulence may occur partly through manipulation of host competitive ability. Differences in competitive ability associated with the social status (dominant or subordinate) of a host may determine the extent of this competition-mediated parasite virulence. We proposed that differences between subordinate and dominant birds in the physiological costs of infection may change depending on the level of competition in social groups. We observed flocks of domestic canaries to determine dominant or subordinate birds, and modified competition by providing restricted (high competition) or ad libitum food (low competition). Entire flocks were then infected with either the avian malaria parasite, Plasmodium relictum or a control. Contrary to our predictions we found that the level of competition had no effect on the outcome of infection for dominant or subordinate birds. We found that dominant birds appeared to suffer greater infection mediated morbidity in both dietary treatments, with a higher and more sustained reduction in haematocrit, and higher parasitaemia, than subordinates. Our results show that dominance status in birds can certainly alter parasite virulence, though the links between food availability, competition, nutrition and virulence are likely to be complex and multifaceted

Holographic duals of 6d RG flows

A notable class of superconformal theories (SCFTs) in six dimensions is parameterized by an integer $N$, an ADE group $G$, and two nilpotent elements $\mu_\mathrm{L,R}$ in $G$. Nilpotent elements have a natural partial ordering, which has been conjectured to coincide with the hierarchy of renormalization-group flows among the SCFTs. In this paper we test this conjecture for $G=\mathrm{SU}(k)$, where AdS$_7$ duals exist in IIA. We work with a seven-dimensional gauged supergravity, consisting of the gravity multiplet and two $\mathrm{SU}(k)$ non-Abelian vector multiplets. We show that this theory has many supersymmetric AdS$_7$ vacua, determined by two nilpotent elements, which are naturally interpreted as IIA AdS$_7$ solutions. The BPS equations for domain walls connecting two such vacua can be solved analytically, up to a Nahm equation with certain boundary conditions. The latter admit a solution connecting two vacua if and only if the corresponding nilpotent elements are related by the natural partial ordering, in agreement with the field theory conjecture.Comment: 33 pages, 2 figure

Social interactions modulate the virulence of avian malaria infection

There is an increasing understanding of the context-dependent nature of parasite virulence. Variation in parasite virulence can occur when infected individuals compete with conspecifics that vary in infection status; virulence may be higher when competing with uninfected competitors. In vertebrates with social hierarchies, we propose that these competition-mediated costs of infection may also vary with social status. Dominant individuals have greater competitive ability than competing subordinates, and consequently may pay a lower prevalence-mediated cost of infection. In this study we investigated whether costs of malarial infection were affected by the occurrence of the parasite in competitors and social status in domestic canaries (Serinus canaria). We predicted that infected subordinates competing with non-infected dominants would pay higher costs than infected subordinates competing with infected dominants. We also predicted that these occurrence-mediated costs of infection would be ameliorated in infected dominant birds. We found that social status and the occurrence of parasites in competitors significantly interacted to change haematocrit in infected birds. Namely, subordinate and dominant infected birds differed in haematocrit depending on the infection status of their competitors. However, in contrast to our prediction, dominants fared better with infected subordinates, whereas subordinates fared better with uninfected dominants. Moreover, we found additional effects of parasite occurrence on mortality in canaries. Ultimately, we provide evidence for costs of parasitism mediated by social rank and the occurrence of parasites in competitors in a vertebrate species. This has important implications for our understanding of the evolutionary processes that shape parasite virulence and group living

High-dimensional robust regression under heavy-tailed data: Asymptotics and Universality

We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In particular, we provide a sharp asymptotic characterisation of M-estimators trained on a family of elliptical covariate and noise data distributions including cases where second and higher moments do not exist. We show that, despite being consistent, the Huber loss with optimally tuned location parameter $\delta$ is suboptimal in the high-dimensional regime in the presence of heavy-tailed noise, highlighting the necessity of further regularisation to achieve optimal performance. This result also uncovers the existence of a curious transition in $\delta$ as a function of the sample complexity and contamination. Moreover, we derive the decay rates for the excess risk of ridge regression. We show that, while it is both optimal and universal for noise distributions with finite second moment, its decay rate can be considerably faster when the covariates' second moment does not exist. Finally, we show that our formulas readily generalise to a richer family of models and data distributions, such as generalised linear estimation with arbitrary convex regularisation trained on mixture models.Comment: 9 pages + Supplementary informatio

Universal scattering laws for bouncing cosmology

Bouncing cosmologies can arise from various gravity theories. We model them through a singularity scattering map, as we call it, relating large scale geometries before and after the bounce. By classifying all suitably local maps we uncover universal laws (scaling of Kasner exponents, canonical transformation of matter). We study the singularity scattering map for Bianchi I bounces in string theory, loop quantum cosmology and modified matter models: our classification then determines how general spatial inhomogeneities and anisotropies (without BKL oscillations) are transmitted through bounces.Comment: 5 page

Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces

For spacetimes containing singularity hypersurfaces we propose a general notion of junction conditions based on a prescribed singularity scattering map, as we call it, and we introduce the notion of a cyclic spacetime (also called a multiverse) consisting of spacetime domains bounded by spacelike or timelike singularity hypersurfaces, across which our scattering map is applied. A local existence theory is established here while, in a companion paper, we construct plane-symmetric cyclic spacetimes. We study the singularity data space consisting of the suitably rescaled metric, extrinsic curvature, and matter fields which can be prescribed on each side of the singularity, and for the class of so-called quiescent singularities we establish restrictions that a singularity scattering map must satisfy. We obtain a full characterization of all scattering maps that are covariant and ultralocal, in a sense we define and, in particular, we distinguish between, on the one hand, three laws of bouncing cosmology of universal nature and, on the other hand, model-dependent junction conditions. The theory proposed in this paper applies to spacelike and timelike hypersurfaces and without symmetry restriction, and encompasses bouncing-cosmology scenarios, both in string theory and in loop quantum cosmology, and puts strong restrictions on their possible explicit realizations.Comment: 56 pages. Construction of plane symmetric cyclic spacetimes moved to a separate pape