Primes and prime ideals in short intervals

We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on the inertia property of the counting functions of primes and prime ideals.Comment: minor change to Proposition

Enforcing equilibria in multi-agent systems

We introduce and investigate Normative Synthesis: a new class of problems for the equilibrium verification that counters the absence of equilibria by purposely constraining multi-agent systems. We show that norms are powerful enough to ensure a positive answer to every instance of the equilibrium verification problem. Subsequently, we focus on two optimization versions, that aim at providing a solution in compliance with implementation costs. We show that the complexities of our procedures range between 2exptime and 3exptime, thus that the problems are no harder than the corresponding equilibrium verification ones

Checking Interval Properties of Computations

Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by checking the formula against the model. Classically, system behaviour is expressed by a formula of a temporal logic, such as LTL and the like. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those constraining the temporal relations between pairs of temporally extended events or involving temporal aggregations, which are inherently "interval-based", and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham's interval temporal logic HS over finite Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against finite Kripke structures is decidable by a suitable small model theorem, and we provide a lower bound to its computational complexity.Comment: In Journal: Acta Informatica, Springer Berlin Heidelber, 201

Multi-player games with LDL goals over finite traces

Linear Dynamic Logic on finite traces (LDLF) is a powerful logic for reasoning about the behaviour of concurrent and multi-agent systems. In this paper, we investigate techniques for both the characterisation and verification of equilibria in multi-player games with goals/objectives expressed using logics based on LDLF. This study builds upon a generalisation of Boolean games, a logic-based game model of multi-agent systems where players have goals succinctly represented in a logical way. Because LDLF goals are considered, in the settings we study—Reactive Modules games and iterated Boolean games with goals over finite traces—players' goals can be defined to be regular properties while achieved in a finite, but arbitrarily large, trace. In particular, using alternating automata, the paper investigates automata-theoretic approaches to the characterisation and verification of (pure strategy Nash) equilibria, shows that the set of Nash equilibria in multi-player games with LDLF objectives is regular, and provides complexity results for the associated automata constructions

Synthesis with rational environments

Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. The environment often consists of agents that have objectives of their own. Thus, it makes sense to soften the universal quantification on the behavior of the environment and take the objectives of its underlying agents into an account. Fisman et al. introduced rational synthesis: the problem of synthesis in the context of rational agents. The input to the problem consists of temporal logic formulas specifying the objectives of the system and the agents that constitute the environment, and a solution concept (e.g., Nash equilibrium). The output is a profile of strategies, for the system and the agents, such that the objective of the system is satisfied in the computation that is the outcome of the strategies, and the profile is stable according to the solution concept; that is, the agents that constitute the environment have no incentive to deviate from the strategies suggested to them. In this paper we continue to study rational synthesis. First, we suggest an alternative definition to rational synthesis, in which the agents are rational but not cooperative. We call such problem strong rational synthesis. In the strong rational synthesis setting, one cannot assume that the agents that constitute the environment take into account the strategies suggested to them. Accordingly, the output is a strategy for the system only, and the objective of the system has to be satisfied in all the compositions that are the outcome of a stable profile in which the system follows this strategy. We show that strong rational synthesis is 2ExpTime-complete, thus it is not more complex than traditional synthesis or rational synthesis. Second, we study a richer specification formalism, where the objectives of the system and the agents are not Boolean but quantitative. In this setting, the objective of the system and the agents is to maximize their outcome. The quantitative setting significantly extends the scope of rational synthesis, making the game-theoretic approach much more relevant. Finally, we enrich the setting to one that allows coalitions of agents that constitute the system or the environment

Nash equilibrium and bisimulation invariance

Game theory provides a well-established framework for the analysis of concurrent and multi-agent systems. The basic idea is that concurrent processes (agents) can be understood as corresponding to players in a game; plays represent the possible computation runs of the system; and strategies define the behaviour of agents. Typically, strategies are modelled as functions from sequences of system states to player actions. Analysing a system in such a setting involves computing the set of (Nash) equilibria in the concurrent game. However, we show that, with respect to the above model of strategies (arguably, the "standard" model in the computer science literature), bisimilarity does not preserve the existence of Nash equilibria. Thus, two concurrent games which are behaviourally equivalent from a semantic perspective, and which from a logical perspective satisfy the same temporal logic formulae, may nevertheless have fundamentally different properties (solutions) from a game theoretic perspective. Our aim in this paper is to explore the issues raised by this discovery. After illustrating the issue by way of a motivating example, we present three models of strategies with respect to which the existence of Nash equilibria is preserved under bisimilarity. We use some of these models of strategies to provide new semantic foundations for logics for strategic reasoning, and investigate restricted scenarios where bisimilarity can be shown to preserve the existence of Nash equilibria with respect to the conventional model of strategies in the computer science literature

Empirical vulnerability curves for Italian mansory buildings: evolution of vulnerability model from the DPM to curves as a function of accelertion

In the framework of the emergency management in the case of seismic events, the evaluation of the expected damage represents a basic requirement for risk informed planning. Seismic risk is defined by the probability to reach a level of damage on given exposed elements caused by seismic events occurring in a fixed period and in a fixed area. To this purpose, the expected seismic input, the exposed elements and their vulnerability have to be correctly evaluated. The aim of the research is to define a correct model of vulnerability curves, in PGA, for masonry structures in Italy, by heuristic approach starting from damage probability matrices (DPMs). To this purpose, the PLINIVS database, containing data on major Italian seismic events, has been used and supported by “critical” assumption on missing data. To support the reliability of this assumption, two vulnerability models, considering or not the hypothesis on the missing data, have been estimated and used to calculate the seismic scenario of the L’Aquila 2009 earthquake through the IRMA (Italian Risk MAp) platform. Finally, a comparison between the outcomes elaborated by IRMA platform and the observed damage collected in the AEDES forms, has been done. © 2020, The Author(s)

Caesar II: An Italian decision support tool for the seismic risk. The case study of Torre Pellice, Villar Pellice and Pinerolo municipalities

Italy is a country with high seismic risk; however, a broad seismic classification of the national territory has been introduced only in the last twenty years. Therefore, most of the existing buildings stock do not comply with the current anti-seismic codes. In recent years, the seismic events that occurred in Italy have highlighted the complexity of emergency management and the great challenge for public authorities called to answer to the post-event reconstruction and the planning of effective risk prevention and mitigation measures implemented in "peacetime". In this perspective, the CAESAR II project (Controlling, Mitigating and Managing Earthquake Emergency: Cost-Benefit and Multi-criteria Analysis of Impact Scenarios for Risk Reduction and Increased Resilience) has been developed as a decision support system for public authorities engaged in the development of seismic disaster risk reduction plans. CAESAR II includes a module for the simulation of retrofitting measures applied at the municipal scale, integrating different categories of anti-seismic and energy improvement measures based on the vulnerability analysis of the existing buildings stock. The CAESAR II tool's core is the module for evaluating "seismic impact scenarios" based on the end-users' hazard. The output of the model includes information on expected damage levels for buildings (from D0-no damage to D5- total collapse) and population (dead, injured and homeless). Impact scenarios can be customised according to the minimum unit of analysis assumed (municipality or 250x250m square mesh grid) and the availability of exposure data (from national census data or survey on the spot building by building according to the PLINIVS form). Scenarios include geo-referenced data managed by geo-servers to exchange data in a format compliant with OGC (Open Gis Consortium) standards and the European INSPIRE Directive. Simulation results can be further processed through the Multi-Criteria and Cost-Benefit Analysis modules to support the comparative assessment of alternative seismic and energy measurements. In this work, the procedures included in CAESAR II are described and a case study is reported. It concerns the analysis of the expected damage assessment on buildings and population for three municipalities in northern Italy, Torre Pellice, Villar Pellice and Pinerolo (Piedmont Region)

‘Clearing the air’: Common drivers of climate-smart smallholder food production in Eastern and Southern Africa

African smallholders should adopt climate-smart agriculture to make a sustainable transition towards cleaner, circular and more productive food systems. Farmers must play a key role in that process. However, the adoption and diffusion of climate-smart technologies have been slow. Here, a cross-sectional econometric analysis using primary data on sustainable farming practices in the cereal-legume farming systems of Ethiopia, Malawi, South Africa and Tanzania is applied to analyse the drivers and intensity of innovation adoption. Socio-economic barriers reduce adoption intensity among marginalised farmers, and proper incentives are needed to overcome them. Business links between technology-ready smallholders and small-to-medium enterprises must be created to enable the uptake and scaling-up of innovations and the development of industrial application models. Such results can support the design of evidence-based strategies for the sustainable transformation of production systems. While national climate policies already include climate-smart agriculture as an adaptation blueprint, policy makers need empirical evidence to support large-scale adoption. This research is an innovative contribution to that effort. It uses a unique household dataset where data is scarce; it considers the impact of smallholders’ conditioning factors on technology climate-smartness level; and it estimates the correlations among a wide range of practices, agro-ecologies and geographical contexts

Sinus Floor Elevation with Modified Crestal Approach and Single Loaded Short Implants: A Case Report with 4 Years of Follow-Up

Tooth extraction is usually followed by bone reduction. In the maxillary posterior region, this remodelling combined with sinus pneumatisation and periodontal defects may lead to a reduced basal bone height available for implant placement. Sinus floor elevation can be performed with different surgical techniques. Crestal approach has demonstrated to be effective, less invasive, and associated with a reduced morbidity. This article reports a modified sinus floor elevation by means of rotary, noncutting instruments, addition of xenograft, and 2 short-threaded implant placements. The aim of the study was to evaluate the implant’s success and intrasinus radiographical bone gain after 4 years of functional loading. The premolar implant site presented a starting basal bone height of 6 mm, while the molar site was of 2 mm. In the first surgical step, sinus floor elevation was performed mesially and the implant was inserted, and distally only sinus floor elevation was performed. After 6 months, the mesial implant was uncovered and the second implant was inserted; 4 months later, the second fixture was uncovered, and both fixtures were loaded with single provisional screw-retained crowns and later with single screw-retained porcelain fused to metal crowns. Implants integrated successfully, and crestal bone remodelling did not exceed the smooth collar. Bone gain was 3 mm for the mesial implant and more than 5 mm for the distal one