arXiv subjects
Publications and source records attributed to Andrea Giusti.
We refine and slightly enlarge the recently proposed first-order thermodynamics of scalar-tensor gravity to include gravitational scalar fields with timelike and past-directed gradients. The implications and subtleties arising in this situation are discussed and an exact cosmological solution of scalar-tensor theory in first-order thermodynamics is revisited in light of these results.
Collaborative AI systems (CAISs) aim at working together with humans in a shared space to achieve a common goal. This critical setting yields hazardous circumstances that could harm human beings. Thus, building such systems with strong assurances of compliance with requirements, domain-specific standards and regulations is of greatest importance. Only few scale impact has been reported so far for such systems since much work remains to manage possible risks. We identify emerging problems in this context and then we report our vision, as well as the progress of our multidisciplinary research team composed of software/systems, and mechatronics engineers to develop a risk-driven assurance process for CAISs.
We revisit the analogy between a minimally coupled scalar field in general relativity and a perfect fluid, correcting previous identifications of effective temperature and chemical potential. This provides a useful complementary picture for the first-order thermodynamics of scalar-tensor gravity, paving the way for the Einstein frame formulation (which eluded previous attempts) and raises interesting questions to further develop the analogy.
Geometric pattern formation is crucial in many tasks involving large-scale multi-agent systems. Examples include mobile agents performing surveillance, swarm of drones or robots, or smart transportation systems. Currently, most control strategies proposed to achieve pattern formation in network systems either show good performance but require expensive sensors and communication devices, or have lesser sensor requirements but behave more poorly. Also, they often require certain prescribed structural interconnections between the agents (e.g., regular lattices, all-to-all networks etc). In this paper, we provide a distributed displacement-based control law that allows large group of agents to achieve triangular and square lattices, with low sensor requirements and without needing communication between the agents. Also, a simple, yet powerful, adaptation law is proposed to automatically tune the control gains in order to reduce the design effort, while improving robustness and flexibility. We show the validity and robustness of our approach via numerical simulations and experiments, comparing it with other approaches from the existing literature.
We generate new spherical and time-dependent solutions of viable Horndeski gravity by disforming a solution of the Einstein equations with scalar field source and positive cosmological constant. They describe dynamical objects embedded in asymptotically FLRW spacetimes and contain apparent horizons and a finite radius singularity that evolve in time in peculiar ways apparently not encountered before in Einstein and "old" scalar-tensor gravity.
In the context of the recently proposed first-order thermodynamics of scalar-tensor gravity, we discuss the possibility of zero-temperature states of equilibrium other than Einstein gravity, including pathological Brans-Dicke theory, Palatini $f(R)$ gravity, and cuscuton gravity, all with non-dynamical scalar fields. The formalism is extended to Nordström gravity, which contains only a scalar degree of freedom and has negative temperature relative to general relativity.
Bootstrapped Newtonian gravity is a non-linear version of Newton's law which can be lifted to a fully geometric theory of gravity starting from a modified potential. Here, we study geodesics in the bootstrapped Newtonian effective metric in vacuum and obtain bounds on a free parameter from Solar System data and S-star orbits near our Galaxy centre. These bounds make vacuum bootstrapped Newtonian gravity experimentally indistinguishable from General Relativity.
A new thermodynamics of scalar-tensor gravity is applied to spatially homogeneous and isotropic cosmologies in this class of theories and tested on analytical solutions. A forever-expanding universe approaches the Einstein "state of equilibrium" with zero effective temperature at late times and departs from it near spacetime singularities. "Cooling" by expansion and "heating" by singularities compete near the Big Rip, where it is found that the effective temperature diverges in the case of a conformally coupled scalar field.
We consider the quantum description of a toy model universe in which the Schwarzschild-de Sitter geometry emerges from the coherent state of a massless scalar field. Although highly idealised, this simple model allows us to find clear hints supporting the conclusion that the reaction of the de Sitter background to the presence of matter sources induces i) a modified Newtonian dynamics at galactic scales and ii) different values measured for the present Hubble parameter. Both effects stem from the conditions required to have a normalisable quantum state.
We discuss and expand a new approach to the thermodynamics of scalar-tensor gravity and its diffusion toward general relativity (seen as an equilibrium state) proposed in a previous Letter [Phys. Rev. D 103, L121501 (2021)], upon which we build. We describe scalar-tensor gravity as an effective dissipative fluid and apply Eckart's first order thermodynamics to it, obtaining explicitly effective quantities such as heat flux, "temperature of gravity", viscosities, entropy density, plus an equation describing the "diffusion" to Einstein gravity. These quantities, still missing in the usual thermodynamics of spacetime, are obtained with minimal assumptions. Furthermore, we examine certain exact solutions of scalar-tensor gravity to test the proposed formalism and gain some physical insight on the "approach to equilibrium" for this class of theories.
We present a novel definition of variable-order fractional Laplacian on Rn based on a natural generalization of the standard Riesz potential. Our definition holds for values of the fractional parameter spanning the entire open set (0, n/2). We then discuss some properties of the fractional Poisson's equation involving this operator and we compute the corresponding Green function, for which we provide some instructive examples for specific problems.
We extend to the Horndeski realm the irreversible thermodynamics description of gravity previously studied in "first generation" scalar-tensor theories. We identify a subclass of Horndeski theories as an out-of--equilibrium state, while general relativity corresponds to an equilibrium state. In this context, we identify an effective heat current, "temperature of gravity", and shear viscosity in the space of theories. The identification is accomplished by recasting the field equations as effective Einstein equations with an effective dissipative fluid, with Einstein gravity as the equilibrium state, following Eckart's first-order thermodynamics.
Several approaches to the formulation of a fractional theory of calculus of "variable order" have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an alternative view on the problem, originally proposed by G. Scarpi in the early seventies, based on a naive modification of the representation in the Laplace domain of standard kernels functions involved in (constant-order) fractional calculus. We frame Scarpi's ideas within recent theory of General Fractional Derivatives and Integrals, that mostly rely on the Sonine condition, and investigate the main properties of the emerging variable-order operators. Then, taking advantage of powerful and easy-to-use numerical methods for the inversion of Laplace transforms of functions defined in the Laplace domain, we discuss some practical applications of the variable-order Scarpi integral and derivative.
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the effective dissipative fluid describing scalar-tensor gravity. Surprisingly, we obtain simple expressions for the effective heat flux, "temperature of gravity", shear and bulk viscosity, and entropy density, plus a generalized Fourier law in a consistent Eckart thermodynamical picture. Well-defined notions of temperature and approach to equilibrium, missing in the current thermodynamics of spacetime scenarios, naturally emerge.
We review spherical and inhomogeneous analytic solutions of the field equations of Einstein and of scalar-tensor gravity, including Brans-Dicke theory, non-minimally (possibly conformally) coupled scalar fields, Horndeski, and beyond Horndeski/DHOST gravity. The zoo includes both static and dynamic solutions, asymptotically flat, and asymptotically Friedmann-Lemaître-Robertson-Walker ones. We minimize overlap with existing books and reviews and we place emphasis on scalar field spacetimes and on geometries that are "general" within certain classes. Relations between various solutions, which have largely emerged during the last decade, are pointed out.
We develop several formal analogies between the logistic equation and the spatially homogeneous and isotropic relativistic cosmology described by the Einstein-Friedmann equations. These analogies produce an effective Lagrangian and Hamiltonian and new symmetries for the logistic equation.
We report a new one-parameter family of spherically symmetric, inhomogeneous, and time-dependent solutions of the vacuum Brans-Dicke field equations which are conformal to the Roberts scalar field geometries of Einstein gravity. The new solution is spherical and time-dependent and contains a naked central singularity. We use it as a seed to generate another two-parameter family of solutions using a known symmetry of vacuum Brans-Dicke gravity.
Collaborative AI systems aim at working together with humans in a shared space to achieve a common goal. This setting imposes potentially hazardous circumstances due to contacts that could harm human beings. Thus, building such systems with strong assurances of compliance with requirements domain specific standards and regulations is of greatest importance. Challenges associated with the achievement of this goal become even more severe when such systems rely on machine learning components rather than such as top-down rule-based AI. In this paper, we introduce a risk modeling approach tailored to Collaborative AI systems. The risk model includes goals, risk events and domain specific indicators that potentially expose humans to hazards. The risk model is then leveraged to drive assurance methods that feed in turn the risk model through insights extracted from run-time evidence. Our envisioned approach is described by means of a running example in the domain of Industry 4.0, where a robotic arm endowed with a visual perception component, implemented with machine learning, collaborates with a human operator for a production-relevant task.