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Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and processes. We construct an affine calculus for 1-bounded complete metric spaces and the monad for probability measures equipped with the Kantorovic distance. The calculus includes a form of guarded recursion interpreted via Banach's fixed point theorem, useful, e.g., for recursive programming with processes. We then define an affine higher-order quantitative logic for reasoning about terms of our calculus. The logic includes novel principles for guarded recursion, and induction over probability measures and natural numbers. Examples of reasoning in the logic include proofs of upper bounds on distances of processes. We also show how our logic can express coupling proofs - a powerful technique for comparing probabilistic processes.

The physical and orbital parameters of Trans-Neptunian Objects (TNOs) provide valuable information about the Solar System's formation and evolution. In particular, the characterization of binaries provides insights into the formation mechanisms that may be playing a role at such large distances from the Sun. Studies show two distinct populations, and (38628) Huya occupies an intermediate position between the unequal-size binaries and those with components of roughly equal sizes. In this work, we predicted and observed three stellar occultation events by Huya. Huya and its satellite - S/2012 (38628) 1 - were detected during occultations in March 2021 and again in June 2023. Additionally, an attempt to detect Huya in February 2023 resulted in an additional single-chord detection of the secondary. A spherical body with a minimum diameter of D = 165 km can explain the three single-chord observations and provide a lower limit for the satellite size. The astrometry of Huya's system, as derived from the occultations and supplemented by observations from the Hubble Space Telescope and Keck Observatory, provided constraints on the satellite orbit and the mass of the system. Therefore, assuming the secondary is in an equatorial orbit around the primary, the limb fitting was constrained by the satellite orbit position angle. The system density, calculated by summing the most precise measurement of Huya's volume to the spherical satellite average volume, is $\rho_{1}$ = 1073 $\pm$ 66 kg m$^{-3}$. The density that the object would have assuming a Maclaurin equilibrium shape with a rotational period of 6.725 $\pm$ 0.01 hours is $\rho_{2}$ = 768 $\pm$ 42 kg m$^{-3}$. This difference rules out the Maclaurin equilibrium assumption for the main body shape., Comment: Manuscript accepted by Planetary Science Journal (PSJ)

We present a novel experimental approach to detect dark matter by probing Yukawa interactions, commonly referred to as a fifth force, between dark matter and baryonic matter. Our method involves optically levitating nanoparticles within a Bessel-Gaussian beam to detect minute forces exerted by potential dark matter interaction with test masses. The non-diffracting properties of Bessel-Gaussian beams, combined with feedback cooling techniques, provide exceptional sensitivity to small perturbations in the motion of the nanoparticles. This setup allows for precise control over trapping conditions and enhances the detection sensitivity to forces on the order of \(10^{-18}\) N. We explore the parameter space of the Yukawa interaction, focusing on the coupling strength (\(\alpha\)) and interaction range (\(\lambda\)), and discuss the potential of this experiment to place new constraints on dark matter couplings, complementing existing direct detection methods., Comment: 22 pages, 7 figures, 1 table

We propose a low energy model for simulating an analog black hole on an optical lattice using ultracold atoms. Assuming the validity of the holographic principle, we employ the Sachdev-Ye-Kitaev (SYK) model, which describes a system of randomly infinite range interacting fermions, also conjectured to be an exactly solvable UV-complete model for an extremal black hole in a higher dimensional Anti-de Sitter (AdS) dilaton gravity. At low energies, the SYK model exhibits an emergent conformal symmetry and is dual to the extremal black hole solution in near AdS2 spacetime. Furthermore, we show how the SYK maximally chaotic behaviour at large N limit, found to be dual to a gauge theory in higher dimensions, can also be employed as a non-trivial investigation tool for the holographic principle. The proposed setup is a theoretical platform to realize the SYK model with relevant exotic effects and behaviour at low energies as a highly non-trivial example of the AdS/CFT duality and a framework for studying black holes., Comment: 15 pages, 3 figures

Large-scale MIMO systems with a massive number N of individually controlled antennas pose significant challenges for minimum mean square error (MMSE) channel estimation, based on uplink pilots. The major ones arise from the computational complexity, which scales with $N^3$, and from the need for accurate knowledge of the channel statistics. This paper aims to address both challenges by introducing reduced-complexity channel estimation methods that achieve the performance of MMSE in terms of estimation accuracy and uplink spectral efficiency while demonstrating improved robustness in practical scenarios where channel statistics must be estimated. This is achieved by exploiting the inherent structure of the spatial correlation matrix induced by the array geometry. Specifically, we use a Kronecker decomposition for uniform planar arrays and a well-suited circulant approximation for uniform linear arrays. By doing so, a significantly lower computational complexity is achieved, scaling as $N\sqrt{N}$ and $N\log N$ for squared planar arrays and linear arrays, respectively., Comment: To appear on IEEE Transactions on Wireless Communications, 11 figures, 3 tables

We study Polynomial Lawvere logic PL, a logic defined over the Lawvere quantale of extended positive reals with sum as tensor, to which we add multiplication, thereby obtaining a semiring structure. PL is designed for complex quantitative reasoning, allowing judgements that express inequalities between polynomials on the extended positive reals. We introduce a deduction system and demonstrate its expressiveness by deriving a classical result from probability theory relating the Kantorovich and the total variation distances. Although the deductive system is not complete in general, we achieve completeness for finitely axiomatizable theories. The proof of completeness relies on the Krivine-Stengle Positivstellensatz (a variant of Hilbert's Nullstellensatz). Additionally, we provide new complexity results, both for PL and its affine fragment AL, regarding two decision problems: satisfiability of a set of judgements and semantical consequence from a set of judgements. The former is NP-complete in AL and in PSPACE for PL; the latter is co-NP complete in PL and in PSPACE for PL.

This work aims at constraining the size, shape, and geometric albedo of the dwarf planet candidate 2002 MS4 through the analysis of nine stellar occultation events. Using multichord detection, we also studied the object's topography by analyzing the obtained limb and the residuals between observed chords and the best-fitted ellipse. We predicted and organized the observational campaigns of nine stellar occultations by 2002 MS4 between 2019 and 2022, resulting in two single-chord events, four double-chord detections, and three events with three to up to sixty-one positive chords. Using 13 selected chords from the 8 August 2020 event, we determined the global elliptical limb of 2002 MS4. The best-fitted ellipse, combined with the object's rotational information from the literature, constrains the object's size, shape, and albedo. Additionally, we developed a new method to characterize topography features on the object's limb. The global limb has a semi-major axis of 412 $\pm$ 10 km, a semi-minor axis of 385 $\pm$ 17 km, and the position angle of the minor axis is 121 $^\circ$ $\pm$ 16$^\circ$. From this instantaneous limb, we obtained 2002 MS4's geometric albedo and the projected area-equivalent diameter. Significant deviations from the fitted ellipse in the northernmost limb are detected from multiple sites highlighting three distinct topographic features: one 11 km depth depression followed by a 25$^{+4}_{-5}$ km height elevation next to a crater-like depression with an extension of 322 $\pm$ 39 km and 45.1 $\pm$ 1.5 km deep. Our results present an object that is $\approx$138 km smaller in diameter than derived from thermal data, possibly indicating the presence of a so-far unknown satellite. However, within the error bars, the geometric albedo in the V-band agrees with the results published in the literature, even with the radiometric-derived albedo.

Holographic MIMO (hMIMO) systems with a massive number of individually controlled antennas N make minimum mean square error (MMSE) channel estimation particularly challenging, due to its computational complexity that scales as $N^3$ . This paper investigates uniform linear arrays and proposes a low-complexity method based on the discrete Fourier transform (DFT) approximation, which follows from replacing the covariance matrix by a suitable circulant matrix. Numerical results show that, already for arrays with moderate size (in the order of tens of wavelengths), it achieves the same performance of the optimal MMSE, but with a significant lower computational load that scales as $N \log N$. Interestingly, the proposed method provides also increased robustness in case of imperfect knowledge of the covariance matrix., Comment: 5 pages,4 figures, Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, USA, Nov. 2023

This paper explores the transition between Compton Scattering and Inverse Compton Scattering (ICS), which is characterized by an equal exchange of energy and momentum between the colliding particles (electrons and photons). This regime has been called Symmetric Compton Scattering (SCS) and has the unique property of cancelling the energy-angle correlation of scattered photons, and, when the electron recoil is large, transferring mono-chromaticity from one colliding beam to the other, resulting in back-scattered photon beams that are intrinsically monochromatic. The paper suggests that large-recoil SCS or quasi-SCS can be used to design compact intrinsic monochromatic gamma-ray sources based on compact linacs, thus avoiding the use of GeV-class electron beams together with powerful laser/optical systems as those typically required for ICS sources.

Rainfall precipitation maps are usually derived based on the measurements collected by classical weather devices, such as rain gauges and weather stations. This article aims to show the benefits obtained by opportunistic rainfall measurements based on signal strength measurements provided by commercial-grade satellite terminals (e.g., used in TV broadcasting). To assess not only the feasibility of this approach, with significant advantages in terms of capital and operational expenditure, but also improvements in terms of accuracy, we focus on a case study for agricultural applications using a Gaussian-modeled synthetic rain over a specific, real-world test area., Comment: 5 pages, 7 figures

Effective integration of terrestrial and non-terrestrial segments is one of the key research avenues in the design of current and future wireless communication networks. To this aim, modern communication-satellite constellations intend to attain sufficiently high throughput in terms of bit rate per unit area on the ground by rather aggressive patterns of spatial frequency reuse. This goal calls for on-board narrow-beam antennas, whose size turns out to be in many cases incompatible with the size/mass and accommodation constraints of the hosting satellite. This paper investigates the attainable performance of large distributed arrays of antennas implemented as the ensemble of a few to many simpler sub-antennas of smaller sizes, carried by one (small) satellite each. The sub-antennas can in their turn be implemented like (regular) 2D arrays of simple radiating elements, realizing an overall (distributed) antenna architecture that we call "Formation of Arrays" (FoA). The satellites that implement this radiating architecture need to be relatively close to each other and constitute a formation of flying objects, to be coordinated and controlled as a whole. In this paper, we develop a theoretical analysis of an FoA antenna, and we show how to take advantage of this new technology to improve network throughput in a multi-beam S-band mobile communication network with low-earth or geostationary orbiting satellites directly providing 5G-like communication services to hand-held user terminals., Comment: to appear on IEEE Trans. Aerospace and Electronic Systems

Modern MIMO communication systems are almost exclusively designed under the assumption of locally plane wavefronts over antenna arrays. This is known as the far-field approximation and is soundly justified at sub-6-GHz frequencies at most relevant transmission ranges. However, when higher frequencies and shorter transmission ranges are used, the wave curvature over the array is no longer negligible, and arrays operate in the so-called radiative near-field region. This letter aims to show that the classical far-field approximation may significantly underestimate the achievable spectral efficiency of multi-user MIMO communications operating in the 30-GHz bands and above, even at ranges beyond the Fraunhofer distance. For planar arrays with typical sizes, we show that computing combining schemes based on the far-field model significantly reduces the channel gain and spatial multiplexing capability. When the radiative near-field model is used, interference rejection schemes, such as the optimal minimum mean-square-error combiner, appear to be very promising, when combined with electrically large arrays, to meet the stringent requirements of next-generation networks., Comment: submitted to IEEE Wireless Communications Letters

Continuous-time Markov chains (CTMCs) are popular modeling formalism that constitutes the underlying semantics for real-time probabilistic systems such as queuing networks, stochastic process algebras, and calculi for systems biology. Prism and Storm are popular model checking tools that provide a number of powerful analysis techniques for CTMCs. These tools accept models expressed as the parallel composition of a number of modules interacting with each other. The outcome of the analysis is strongly dependent on the parameter values used in the model which govern the timing and probability of events of the resulting CTMC. However, for some applications, parameter values have to be empirically estimated from partially-observable executions. In this work, we address the problem of estimating parameter values of CTMCs expressed as Prism models from a number of partially-observable executions. We introduce the class parametric CTMCs -- CTMCs where transition rates are polynomial functions over a set of parameters -- as an abstraction of CTMCs covering a large class of Prism models. Then, building on a theory of algorithms known by the initials MM, for minorization-maximization, we present iterative maximum likelihood estimation algorithms for parametric CTMCs covering two learning scenarios: when both state-labels and dwell times are observable, or just state-labels are. We conclude by illustrating the use of our technique in a simple but non-trivial case study: the analysis of the spread of COVID-19 in presence of lockdown countermeasures.

Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for quantitative metric reasoning, we investigate three $[0,\infty]$-valued propositional logics over the Lawvere quantale. The basic logical connectives shared by all three logics are those that can be interpreted in any quantale, viz finite conjunctions and disjunctions, tensor (addition for the Lawvere quantale) and linear implication (here a truncated subtraction); to these we add, in turn, the constant $1$ to express integer values, and scalar multiplication by a non-negative real to express general affine combinations. Quantitative equational logic can be interpreted in the third logic if we allow inference systems instead of axiomatic systems. For each of these logics we develop a natural deduction system which we prove to be decidably complete w.r.t. the quantale-valued semantics. The heart of the completeness proof makes use of the Motzkin transposition theorem. Consistency is also decidable; the proof makes use of Fourier-Motzkin elimination of linear inequalities. Strong completeness does not hold in general, even (as is known) for theories over finitely-many propositional variables; indeed even an approximate form of strong completeness in the sense of Pavelka or Ben Yaacov -- provability up to arbitrary precision -- does not hold. However, we can show it for theories axiomatized by a (not necessarily finite) set of judgements in normal form over a finite set of propositional variables when we restrict to models that do not map variables to $\infty$; the proof uses Hurwicz's general form of the Farkas' Lemma.

Inspired by the seminal work of Hyland, Plotkin, and Power on the combination of algebraic computational effects via sum and tensor, we develop an analogous theory for the combination of quantitative algebraic effects. Quantitative algebraic effects are monadic computational effects on categories of metric spaces, which, moreover, have an algebraic presentation in the form of quantitative equational theories, a logical framework introduced by Mardare, Panangaden, and Plotkin that generalises equational logic to account for a concept of approximate equality. As our main result, we show that the sum and tensor of two quantitative equational theories correspond to the categorical sum (i.e., coproduct) and tensor, respectively, of their effects qua monads. We further give a theory of quantitative effect transformers based on these two operations, essentially providing quantitative analogues to the following monad transformers due to Moggi: exception, resumption, reader, and writer transformers. Finally, as an application, we provide the first quantitative algebraic axiomatizations to the following coalgebraic structures: Markov processes, labelled Markov processes, Mealy machines, and Markov decision processes, each endowed with their respective bisimilarity metrics. Apart from the intrinsic interest in these axiomatizations, it is pleasing they have been obtained as the composition, via sum and tensor, of simpler quantitative equational theories.