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In Super-resolution, a varying-illumination image stack is required. This enriched the dataset typically necessitates precise mechanical control and micron scale optical alignment and repeatability. Here, we introduce a novel methodology for super-resolution microscopy called Stochastically Structured Illumination Microscopy (S2IM), which bypasses the need for illumination control instead exploiting the random, uncontrolled movement of the target object. We tested our methodology within the clinically relevant ophthalmoscopic setting, harnessing the inherent saccadic motion of the eye to induce stochastic displacement of the illumination pattern on the retina. We opted to avoid human subjects by utilizing a phantom eye model, featuring a retina composed of human induced pluripotent stem cells (iPSC) retinal neurons, and replicating the ocular saccadic movements by custom actuators. Our findings demonstrate that S$^2$IM unlocks scan-less super-resolution with a resolution enhancement of 1.91, with promising prospects also beyond ophthalmoscopy applications such as active matter or atmospheric/astronomical observation.

We present the algebraic classification of the gravitational field in four-dimensional general metric-affine geometries, thus extending the current results of the literature in the particular framework of Weyl-Cartan geometry by the presence of the traceless nonmetricity tensor. This quantity switches on four of the eleven fundamental parts of the irreducible representation of the curvature tensor under the pseudo-orthogonal group, in such a way that three of them present similar algebraic types as the ones obtained in Weyl-Cartan geometry, whereas the remaining one includes thirty independent components and gives rise to a new algebraic classification. The latter is derived by means of its principal null directions and their levels of alignment, obtaining a total number of sixteen main algebraic types, which can be split into many subtypes. As an immediate application, we determine the algebraic types of the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity., Comment: 47 pages, 5 figures, minor changes, references added

Electronic correlations arise from the competition between the electrons' kinetic and Coulomb interaction energy and give rise to a rich phase diagram and many emergent quasiparticles. The binding of doubly-occupied and empty sites into a doublon-holon exciton is an example of this in the Hubbard model. Unlike traditional excitons in semiconductors, in the Hubbard model it is the kinetic energy which provides the binding energy. Upon doping, we find the emergence of exciton complexes, such as a holon-doublon-holon trion. The appearance of these low-lying collective excitations make screening more effective in the doped system. As a result, Hubbard-based modelling of correlated materials should use different values of $U$ for the doped system and the insulating parent compound, which we illustrate using the cuprates as an example., Comment: 8 pages, 9 figures

In this note we study estimates from below of the single radius spherical discrepancy in the setting of compact two-point homogeneous spaces. Namely, given a $d$-dimensional manifold $\mathcal M$ endowed with a distance $\rho$ so that $(\mathcal M, \rho)$ is a two-point homogeneous space and with the Riemannian measure $\mu$, we provide conditions on $r$ such that if $D_r$ denotes the discrepancy of the ball of radius $r$, then, for an absolute constant $C>0$ and for every set of points $\{x_j\}_{j=1}^N$, one has $\int_{\mathcal M} |D_{r}(x)|^2\, d\mu(x)\geqslant C N^{-1-\frac1d}$. The conditions on $r$ that we have depend on the dimension $d$ of the manifold and cannot be achieved when $d \equiv 1 \ ( \operatorname{mod}4)$. Nonetheless, we prove a weaker estimate for such dimensions as well., Comment: 16 pages

First-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification language for the verification of complex infinite-state systems is appealing. However, a missing piece, which has proved to be an invaluable tool in dealing with other temporal logics, is an automaton model capable of capturing the logic. In this paper we address this issue, by defining and studying such a model, which we call first-order automaton. We define this very general class of automata, and the corresponding notion of regular first-order language, showing their closure under most common language-theoretic operations. We show how they can capture any FOLTL formula over any signature and theory, and provide sufficient conditions for the semi-decidability of their non-emptiness problem. Then, to show the usefulness of the formalism, we prove the decidability of monodic FOLTL, a classic result known in the literature, with a simpler and direct proof.

Operator Precedence Languages (OPL) have been recently identified as a suitable formalism for model checking recursive procedural programs, thanks to their ability of modeling the program stack. OPL requirements can be expressed in the Precedence Oriented Temporal Logic (POTL), which features modalities to reason on the natural matching between function calls and returns, exceptions, and other advanced programming constructs that previous approaches, such as Visibly Pushdown Languages, cannot model effectively. Existing approaches for model checking of POTL have been designed following the explicit-state, automata-based approach, a feature that severely limits their scalability. In this paper, we give the first symbolic, SMT-based approach for model checking POTL properties. While previous approaches construct the automaton for both the POTL formula and the model of the program, we encode them into a (sequence of) SMT formulas. The search of a trace of the model witnessing a violation of the formula is then carried out by an SMT-solver, in a Bounded Model Checking fashion. We carried out an experimental evaluation, which shows the effectiveness of the proposed solution., Comment: 30 pages, 6 figures

Recently, there has been growing attention on behalf of both academic and practice communities towards the ability of Artificial Intelligence (AI) systems to operate responsibly and ethically. As a result, a plethora of frameworks and guidelines have appeared to support practitioners in implementing Trustworthy AI applications (TAI). However, little research has been done to investigate whether such frameworks are being used and how. In this work, we study the vision AI practitioners have on TAI principles, how they address them, and what they would like to have - in terms of tools, knowledge, or guidelines - when they attempt to incorporate such principles into the systems they develop. Through a survey and semi-structured interviews, we systematically investigated practitioners' challenges and needs in developing TAI systems. Based on these practical findings, we highlight recommendations to help AI practitioners develop Trustworthy AI applications.

In recent months, the social impact of Artificial Intelligence (AI) has gained considerable public interest, driven by the emergence of Generative AI models, ChatGPT in particular. The rapid development of these models has sparked heated discussions regarding their benefits, limitations, and associated risks. Generative models hold immense promise across multiple domains, such as healthcare, finance, and education, to cite a few, presenting diverse practical applications. Nevertheless, concerns about potential adverse effects have elicited divergent perspectives, ranging from privacy risks to escalating social inequality. This paper adopts a methodology to delve into the societal implications of Generative AI tools, focusing primarily on the case of ChatGPT. It evaluates the potential impact on several social sectors and illustrates the findings of a comprehensive literature review of both positive and negative effects, emerging trends, and areas of opportunity of Generative AI models. This analysis aims to facilitate an in-depth discussion by providing insights that can inspire policy, regulation, and responsible development practices to foster a human-centered AI., Comment: Presented at GoodIT2023 - ACM Conference on Information Technology for Social Good

We analyse the stability of the vector and axial sectors of Poincar\'e gauge theory around general backgrounds in the presence of cubic order invariants defined from the curvature and torsion tensors, showing how the latter can in fact cancel out well-known instabilities arising from the quadratic curvature invariants of the theory and accordingly help in the construction of healthy models with both curvature and torsion. For this task, we introduce the most general parity preserving cubic Lagrangian with mixing terms of the curvature and torsion tensors, and find the relations of its coefficients to avoid a pathological behaviour from the vector and axial modes of torsion. As a result, on top of the gravitational constant of General Relativity and the mass parameters of torsion, our action contains 23 additional coupling constants controlling the dynamics of this field. As in the quadratic Poincar\'e gauge theory, we show that a further restriction on the cubic part of the action allows the existence of Reissner-Nordstr\"om-like black hole solutions with dynamical torsion., Comment: 16 pages, minor changes, references added. It matches the version published in PRD

In the ever-expanding landscape of Artificial Intelligence (AI), where innovation thrives and new products and services are continuously being delivered, ensuring that AI systems are designed and developed responsibly throughout their entire lifecycle is crucial. To this end, several AI ethics principles and guidelines have been issued to which AI systems should conform. Nevertheless, relying solely on high-level AI ethics principles is far from sufficient to ensure the responsible engineering of AI systems. In this field, AI professionals often navigate by sight. Indeed, while recommendations promoting Trustworthy AI (TAI) exist, these are often high-level statements that are difficult to translate into concrete implementation strategies. There is a significant gap between high-level AI ethics principles and low-level concrete practices for AI professionals. To address this challenge, our work presents an experience report where we develop a novel holistic framework for Trustworthy AI - designed to bridge the gap between theory and practice - and report insights from its application in an industrial case study. The framework is built on the result of a systematic review of the state of the practice, a survey, and think-aloud interviews with 34 AI practitioners. The framework, unlike most of those already in the literature, is designed to provide actionable guidelines and tools to support different types of stakeholders throughout the entire Software Development Life Cycle (SDLC). Our goal is to empower AI professionals to confidently navigate the ethical dimensions of TAI through practical insights, ensuring that the vast potential of AI is exploited responsibly for the benefit of society as a whole.

In the present paper we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite family of corners. We also prove two analogous results for the discrepancy on the torus with respect to squares and balls., Comment: 25 pages

We formulate cosmological perturbation theory around the spatially curved FLRW background in the context of metric-affine gauge theory of gravity which includes torsion and nonmetricity. Performing scalar-vector-tensor decomposition of the spatial perturbations, we find that the theory displays a rich perturbation spectrum with helicities 0, 1, 2 and 3, on top of the usual scalar, vector and tensor metric perturbations arising from Riemannian geometry. Accordingly, the theory provides a diverse phenomenology, e.g. the helicity-2 modes of the torsion and/or nonmetricity tensors source helicity-2 metric tensor perturbation at the linear level leading to the production of gravitational waves. As an immediate application, we study linear perturbation of the nonmetricity helicity-3 modes for a general parity-preserving action of metric-affine gravity which includes quadratic terms in curvature, torsion, and nonmetricity. We then find the conditions to avoid possible instabilities in the helicity-3 modes of the spin-3 field., Comment: Matches published version in PRD. 23+20 pages, 5 appendices

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring to different time points can be compared. In general, LTLfMT was shown to be semi-decidable for any decidable first-order theory (e.g., linear arithmetics), with a tableau-based semi-decision procedure. In this paper we present a sound and complete pruning rule for the LTLfMT tableau. We show that for any LTLfMT formula that satisfies an abstract, semantic condition, that we call finite memory, the tableau augmented with the new rule is also guaranteed to terminate. Last but not least, this technique allows us to establish novel decidability results for the satisfiability of several fragments of LTLfMT, as well as to give new decidability proofs for classes that are already known., Comment: Extended version of a conference paper accepted at the 26th European Conference on Artificial Intelligence (ECAI 2023)

In the timeline-based approach to planning, the evolution over time of a set of state variables (the timelines) is governed by a set of temporal constraints. Traditional timeline-based planning systems excel at the integration of planning with execution by handling temporal uncertainty. In order to handle general nondeterminism as well, the concept of timeline-based games has been recently introduced. It has been proved that finding whether a winning strategy exists for such games is 2EXPTIME-complete. However, a concrete approach to synthesize controllers implementing such strategies is missing. This paper fills this gap, by providing an effective and computationally optimal approach to controller synthesis for timeline-based games., Comment: arXiv admin note: text overlap with arXiv:2209.10319

In the last years, the raise of Artificial Intelligence (AI), and its pervasiveness in our lives, has sparked a flourishing debate about the ethical principles that should lead its implementation and use in society. Driven by these concerns, we conduct a rapid review of several frameworks providing principles, guidelines, and/or tools to help practitioners in the development and deployment of Responsible AI (RAI) applications. We map each framework w.r.t. the different Software Development Life Cycle (SDLC) phases discovering that most of these frameworks fall just in the Requirements Elicitation phase, leaving the other phases uncovered. Very few of these frameworks offer supporting tools for practitioners, and they are mainly provided by private companies. Our results reveal that there is not a "catching-all" framework supporting both technical and non-technical stakeholders in the implementation of real-world projects. Our findings highlight the lack of a comprehensive framework encompassing all RAI principles and all (SDLC) phases that could be navigated by users with different skill sets and with different goals.

We present a complete algebraic classification for the curvature tensor in Weyl-Cartan geometry, by applying methods of eigenvalues and principal null directions on its irreducible decomposition under the group of global Lorentz transformations, thus providing a full invariant characterisation of all the possible algebraic types of the torsion and nonmetricity field strength tensors in Weyl-Cartan space-times. As an application, we show that in the framework of Metric-Affine Gravity the field strength tensors of a dynamical torsion field cannot be doubly aligned with the principal null directions of the Riemannian Weyl tensor in scalar-flat, slowly rotating, stationary and axisymmetric space-times., Comment: 22 pages, minor changes, references added. It matches the version published in PRD Mathematica file as supplemental material available at https://community.wolfram.com/groups/-/m/t/2996064

Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason with diverse and potentially conflicting viewpoints by means of indexed modalities. Another multi-modal logic of import is linear temporal logic (LTL) - a formalism used to express temporal properties of systems and processes, having prominence in formal methods and fields related to artificial intelligence. In this paper, we present standpoint linear temporal logic (SLTL), a new logic that combines the temporal features of LTL with the multi-perspective modelling capacity of SL. We define the logic SLTL, its syntax, and its semantics, establish its decidability and complexity, and provide a terminating tableau calculus to automate SLTL reasoning. Conveniently, this offers a clear path to extend existing LTL reasoners with practical reasoning support for temporal reasoning in multi-perspective settings.