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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.

We report a measurement of two energy-weighted gamma cascade angular distributions from polarized slow neutron capture on the ${}^{35}$Cl nucleus, one parity-odd correlation proportional to $\vec{s_{n}} \cdot \vec{k_{\gamma}}$ and one parity-even correlation proportional to $\vec{s_{n}} \cdot \vec{k_{n}} \times \vec{k_{\gamma}}$. A parity violating asymmetry can appear in this reaction due to the weak nucleon-nucleon (NN) interaction which mixes opposite parity S and P-wave levels in the excited compound $^{36}$Cl nucleus formed upon slow neutron capture. If parity-violating (PV) and parity-conserving (PC) terms both exist, the measured differential cross section can be related to them via $\frac{d\sigma}{d\Omega}\propto1+A_{\gamma, PV}\cos\theta+A_{\gamma,PC}\sin\theta$. The PV and PC asymmetries for energy-weighted gamma cascade angular distributions for polarized slow neutron capture on $^{35}$Cl averaged over the neutron energies from 2.27~meV to 9.53~meV were measured to be $A_{\gamma,PV}=(-23.9\pm0.7)\times 10^{-6}$ and $A_{\gamma,PC}=(0.1\pm0.7)\times 10^{-6}$. These results are consistent with previous experimental results. Systematic errors were quantified and shown to be small compared to the statistical error. These asymmetries in the angular distributions of the gamma rays emitted from the capture of polarized neutrons in $^{35}$Cl were used to verify the operation and data analysis procedures for the NPDGamma experiment which measured the parity-odd asymmetry in the angular distribution of gammas from polarized slow neutron capture on protons.

In this paper we deal with the restricted Block Relocation Problem. We present a new lower bound and a heuristic approach for the problem. The proposed lower bound can be computed in polynomial time and it is provably better than some previously known lower bounds. We use it within a bounded beam search algorithm to solve the Block Relocation Problem and show that the considered heuristic approach outperforms the other existing algorithms on most of the instances in the literature. In order to test the approaches on real-size dimensions, new large instances of the Block Relocation Problem are also introduced.

Particle acceleration in microstructures driven by ultrafast solid state lasers is a rapidly evolving area of advanced accelerator research, leading to a variety of concepts based on planar-symmetric dielectric gratings, hollow core fibers, photonic crystals, and plasmonic meta-surfaces. This approach leverages well-established industrial fabrication capabilities and the commercial availability of tabletop lasers to reduce cost, with demonstrated axial accelerating fields in the GV/m range. Wide-ranging international efforts have significantly improved understanding of gradient limits, structure design, particle focusing and transport, staging, and development of compatible low-emittance electron sources. With a near-term focus on low-current MeV-scale applications for compact scientific and medical instruments, as well as novel diagnostics capabilities, structure-based laser-driven accelerators have several key benefits that warrant consideration for future high-energy physics machines, including low beamstrahlung energy loss, modest power requirements, stability, and readiness of supporting technologies., Comment: arXiv admin note: substantial text overlap with arXiv:2203.03811, arXiv:1901.10370

Deep reinforcement learning is an increasingly popular technique for synthesising policies to control an agent's interaction with its environment. There is also growing interest in formally verifying that such policies are correct and execute safely. Progress has been made in this area by building on existing work for verification of deep neural networks and of continuous-state dynamical systems. In this paper, we tackle the problem of verifying probabilistic policies for deep reinforcement learning, which are used to, for example, tackle adversarial environments, break symmetries and manage trade-offs. We propose an abstraction approach, based on interval Markov decision processes, that yields probabilistic guarantees on a policy's execution, and present techniques to build and solve these models using abstract interpretation, mixed-integer linear programming, entropy-based refinement and probabilistic model checking. We implement our approach and illustrate its effectiveness on a selection of reinforcement learning benchmarks., Comment: NFM 2022

We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of differential equations; (b) it can be enhanced by up-to techniques; and (c) it allows the specification of pairs which ought not to be included in the output. Using a prototype, these advantages are demonstrated on case studies from systems biology for applications to model reduction and comparison. Notably, we report four orders of magnitude smaller runtimes than partition-refinement approaches when disproving equivalences between Markov chains.