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Separation of the two mirror images of a chiral molecule, the enantiomers, is a historically complicated problem of major relevance for biological systems. Since chiral molecules are optically active, it has been speculated that strong coupling to circularly polarized fields may be used as a general procedure to unlock enantiospecific reactions. In this work, we focus on how chiral cavities can be used to drive asymmetry in the photochemistry of chiral molecular systems. We first show that strong coupling to circularly polarized fields leads to enantiospecific Rabi splittings, an effect that displays a collective behavior in line with other strong coupling phenomena. Additionally, entanglement with circularly polarized light generates an asymmetry in the enantiomer population of the polaritons, leading to a condensation of the excitation on a preferred molecular configuration. These results confirm that chiral cavities represent a tantalizing opportunity to drive asymmetric photochemistry in enantiomeric mixtures., Comment: 45 pages and 16 figures

Coronal dimmings are regions of reduced emission in the lower corona, observed after coronal mass ejections (CMEs) and representing their footprints. In order to investigate the long-term evolution of coronal dimming and its recovery, we propose two approaches that focus on both the global and the local evolution of dimming regions: the fixed mask approach and the pixel boxes approach. We present four case studies (September 6, 2011; March 7, 2012; June 14, 2012; and March 8, 2019) in which a coronal dimming is associated with a flare/CME eruption. We identified the dimming region by image segmentation, then restricted the analysis to a specific portion of the dimming and tracked the time evolution of the dimming brightness and area. In addition, we studied the behavior of small subregions inside the dimming area, of about 3x3 pixels, to compare the recovery in different regions of the dimming. Three out of the four cases show a complete recovery 24 hours after the flare/CME eruption. The recovery of the brightness follows a two-step trend, with a steeper and quicker segment followed by a slower one. In addition, some parts of the dimming, which may be core dimmings, are still present at the end of the analysis time and do not recover within 3 days, whereas the peripheral regions (secondary dimmings) show a full recovery. We demonstrate that the primary mechanism for recovery identified in the observations is the expansion of coronal loops into the dimming region, which gradually increase their intensity. Our developed approaches enable the analysis of dimmings alongside these bright structures, revealing different timescales of recovery for core and secondary/twin dimming regions. Combined with magnetic field modeling, these methods lay the foundation for further systematic analysis of dimming recovery and enhance the knowledge gained from already-analyzed events., Comment: 18 pages, 18 figures, 5 movies, accepted to Astronomy & Astrophysics

It is usually assumed that the memory of any thermo-mechanical protocol applied to a glass can be erased by heating the material in the supercooled liquid. While this is true for thermally treated amorphous solids, we show that hydrostatic compression can irreversibly modify the atomic motion, thermodynamic state and structure of a prototypical metallic glass-former, in a way which depends on the degree of ergodicity reached by the material during compression. While enhanced kinetic and thermodynamic stability can be obtained by quenching the dense liquid, high-pressure annealing in the glass leads to thermal rejuvenation and complex structural rearrangements at the level of the short and medium range order. When heated above their glass transition temperature, these compressed glasses do not convert into the pristine supercooled liquid but rather transform into different systems, challenging the generally accepted idea of an equilibrium recovery controlled solely by the microscopic $\alpha$-relaxation process.

We present a new ab-initio approach to study molecules containing heavy atoms strongly interacting with quantum fields in optical devices. The relativistic quantum electrodynamics (QED) theory has been rewritten with a formalism close to relativistic quantum chemistry. This general framework represents the ideal starting point to extend the main quantum chemistry methods to relativistic polaritonic. The Polaritonic Dirac Hartree Fock (Pol-DHF) approach is the first method we propose based on this theory. Pol-DHF allows for the simulation of field induced effects on the ground and excited state properties of heavy transition metals molecular complexes. The method is able to include not only the effects of the photons but can be easily extended also to include explicit interactions with positrons. Application of Pol-DHF to three metal hydrides revealed the importance of including relativistic effects to the treatment in strong coupling conditions. Due to an accurate description of spin-orbit coupling, the method is able to reproduce polaritonic effects happening at the crossing between singlet and triplet potential energy surfaces., Comment: 18 pages, 8 figures

This work studies offline Reinforcement Learning (RL) in a class of non-Markovian environments called Regular Decision Processes (RDPs). In RDPs, the unknown dependency of future observations and rewards from the past interactions can be captured by some hidden finite-state automaton. For this reason, many RDP algorithms first reconstruct this unknown dependency using automata learning techniques. In this paper, we show that it is possible to overcome two strong limitations of previous offline RL algorithms for RDPs, notably RegORL. This can be accomplished via the introduction of two original techniques: the development of a new pseudometric based on formal languages, which removes a problematic dependency on $L_\infty^\mathsf{p}$-distinguishability parameters, and the adoption of Count-Min-Sketch (CMS), instead of naive counting. The former reduces the number of samples required in environments that are characterized by a low complexity in language-theoretic terms. The latter alleviates the memory requirements for long planning horizons. We derive the PAC sample complexity bounds associated to each of these techniques, and we validate the approach experimentally., Comment: To appear in EWRL 2024

Recurrent Neural Cascades (RNC) are the class of recurrent neural networks with no cyclic dependencies among recurrent neurons. Their subclass RNC+ with positive recurrent weights has been shown to be closely connected to the star-free regular languages, which are the expressivity of many well-established temporal logics. The existing expressivity results show that the regular languages captured by RNC+ are the star-free ones, and they leave open the possibility that RNC+ may capture languages beyond regular. We exclude this possibility for languages that include an identity element, i.e., an input that can occur an arbitrary number of times without affecting the output. Namely, in the presence of an identity element, we show that the languages captured by RNC+ are exactly the star-free regular languages. Identity elements are ubiquitous in temporal patterns, and hence our results apply to a large number of applications. The implications of our results go beyond expressivity. At their core, we establish a close structural correspondence between RNC+ and semiautomata cascades, showing that every neuron can be equivalently captured by a three-state semiautomaton. A notable consequence of this result is that RNC+ are no more succinct than cascades of three-state semiautomata., Comment: Full version with appendix of a paper with the same title that will appear in the proceedings of KR 2024

We analyze the real-time electron-photon dynamics in long-range polariton-mediated energy transfer using a real-time quantum electrodynamics coupled cluster (RT-QED-CC) model, which allows for spatial and temporal visualization of transport processes. We compute the time evolution of photonic and molecular observables, such as the dipole moment and the photon coordinate, following the excitation of the system induced by short laser pulses. Our simulation highlights the different time scales of electrons and photons under light-matter strong coupling, the role of dark states, and the differences with the electronic (F\"orster and Dexter) energy exchange mechanisms. The developed method can simulate multiple high-intensity laser pulses while explicitly retaining electronic and electron-photon correlation and is thus suited for nonlinear optics and transient absorption spectroscopies of molecular polaritons., Comment: 19 pages and 9 figures

In this work, we present ab initio cavity QED methods which include interactions with a static magnetic field and nuclear spin degrees of freedom using different treatments of the quantum electromagnetic field. We derive explicit expressions for QED-HF magnetizability, nuclear shielding, and spin-spin coupling tensors. We apply this theory to explore the influence of the cavity field on the magnetizability of saturated, unsaturated, and aromatic hydrocarbons, showing the effects of different polarization orientations and coupling strengths. We also examine how the cavity affects aromaticity descriptors, such as the nucleus-independent chemical shift and magnetizability exaltation. We employ these descriptors to study the trimerization reaction of acetylene to benzene. We show how the optical cavity induces modifications in the aromatic character of the transition state leading to variations in the activation energy of the reaction. Our findings shed light on the effects induced by the cavity on magnetic properties, especially in the context of aromatic molecules, providing valuable insights into understanding the interplay between the quantum electromagnetic field and molecules., Comment: 62 pages and 10 figures

A new experimental setup combining X-Ray Photon Correlation Spectroscopy (XPCS) in the hard x-ray regime and a high-pressure sample environment is developed to monitor the pressure dependence of the internal motion of complex systems down to the atomic scale in the multi-GPa range, from room temperature to 600K. The high flux of coherent high energy x-rays at 4th generation synchrotron source solves the problems caused by the absorption of the Diamond Anvil Cells used to generate the high pressure, enabling the measurement of the intermediate scattering function over 6 orders of magnitude in time, from $10^{-3}$ s to $10^{3}$s. The constraints posed by the high-pressure generation such as the preservation of the x-ray's coherence, as well as the sample, pressure and temperature stability are discussed, and the feasibility of high pressure XPCS is demonstrated through results obtained on metallic glasses.

Intermolecular interactions are pivotal for aggregation, solvation, and crystallization. We demonstrate that the collective strong coupling of several molecules to a single optical mode results in notable changes in the molecular excitations around an impurity, e.g., in the first aggregation or solvation shell. A competition between short-range Coulombic and long-range photonic correlation inverts the local transition density in a polaritonic state, suggesting notable changes in the polarizability of the solvation shell. Our results provide an alternative perspective on recent work in polaritonic chemistry and pave the way for the rigorous treatment of cooperative effects in aggregation, solvation, and crystallization.

Recurrent Neural Cascades (RNCs) are the recurrent neural networks with no cyclic dependencies among recurrent neurons. This class of recurrent networks has received a lot of attention in practice. Besides training methods for a fixed architecture such as backpropagation, the cascade architecture naturally allows for constructive learning methods, where recurrent nodes are added incrementally one at a time, often yielding smaller networks. Furthermore, acyclicity amounts to a structural prior that even for the same number of neurons yields a more favourable sample complexity compared to a fully-connected architecture. A central question is whether the advantages of the cascade architecture come at the cost of a reduced expressivity. We provide new insights into this question. We show that the regular languages captured by RNCs with sign and tanh activation with positive recurrent weights are the star-free regular languages. In order to establish our results we developed a novel framework where capabilities of RNCs are accessed by analysing which semigroups and groups a single neuron is able to implement. A notable implication of our framework is that RNCs can achieve the expressivity of all regular languages by introducing neurons that can implement groups., Comment: Full version with appendix of a paper with the same title that appears in the proceedings of AAAI 2024

Chemical and photochemical reactivity, as well as supramolecular organization and several other molecular properties, can be modified by strong interactions between light and matter. Theoretical studies of these phenomena require the separation of the Schr\"odinger equation into different degrees of freedom as in the Born-Oppenheimer approximation. In this paper, we analyze the electron-photon Hamiltonian within the cavity Born-Oppenheimer approximation (CBOA), where the electronic problem is solved for fixed nuclear positions and photonic parameters. Specifically, we focus on intermolecular interactions in representative dimer complexes. The CBOA potential energy surfaces are compared with those obtained using a polaritonic approach, where the photonic and electronic degrees of freedom are treated at the same level. This allows us to assess the role of electron-photon correlation and the accuracy of CBOA., Comment: 9 pages, 8 figures

The development of new methodologies for the selective synthesis of individual enantiomers is still one of the major challenges in synthetic chemistry. Many biomolecules, and therefore many pharmaceutical compounds, are indeed chiral. While the use of chiral reactants or catalysts has led to significant progress in the field of asymmetric synthesis, a systematic approach applicable to general reactions has still not been proposed. In this work, we show that strong coupling to circularly polarized fields represents a promising alternative for reaching highly selective asymmetric synthesis in a non-invasive fashion. We demonstrate that the field induces stereoselectivity in the early stages of the chemical reaction, by selecting an energetically preferred direction of approach for the reagents., Comment: 15 pages, 5 figures

Two-dimensional moir\'e materials have emerged as the most versatile platforms for realizing quantum phases of electrons. Here, we explore the stability origins of correlated states in WSe2/WS2 moir\'e superlattices. We find that ultrafast electronic excitation leads to melting of the Mott states on time scales five times longer than predictions from the charge hopping integrals and the melting rates are thermally activated, with activation energies of 18 and 13 meV for the one- and two-hole Mott states, respectively, suggesting significant electron-phonon coupling. DFT calculation of the one-hole Mott state confirms polaron formation and yields a hole-polaron binding energy of 16 meV. These findings reveal a close interplay of electron-electron and electron-phonon interactions in stabilizing the polaronic Mott insulators at transition metal dichalcogenide moir\'e interfaces., Comment: 14 pages, 4 figures, 11 SI figures

Polaritonic chemistry is an interdisciplinary emerging field that presents several challenges and opportunities in chemistry, physics, and engineering. A systematic review of polaritonic response theory is presented, following a chemical perspective based on molecular response theory. We provide the reader with a general strategy for developing response theory for ab initio cavity quantum electrodynamics (QED) methods and critically emphasize details that still need clarification and require cooperation between the physical and chemistry communities. We show that several well-established results can be applied to strong coupling light-matter systems, leading to novel perspectives on the computation of matter and photonic properties. The application of the Pauli-Fierz Hamiltonian to polaritons is discussed, focusing on the effects of describing operators in different mathematical representations. We thoroughly examine the most common approximations employed in ab initio QED, such as the dipole approximation. We introduce the polaritonic response equations for recently developed ab initio QED Hartree-Fock and QED coupled cluster methods. The discussion focuses on the similarities and differences from standard quantum chemistry methods, providing practical equations for computing the polaritonic properties., Comment: 37 pages, 3 figures

We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some of them subsume existing temporal operators, while others are entirely novel. Of particular interest are transformation operators based on semigroups. They enable logics to harness the richness of semigroup theory, and we show them to yield logics capable of creating hierarchies of increasing expressivity and complexity which are non-trivial to characterise in existing logics. The result is a genuinely novel and yet unexplored landscape of temporal logics, each of them with the potential of matching the trade-off between expressivity and complexity required by specific applications., Comment: Extended version with appendix of a paper with the same title that appears in the proceedings of IJCAI 2024

After the discovery of the Higgs boson in 2012 at the CERN Large Hadron Collider (LHC), the study of its properties still leaves room for an extended Higgs sector with more than one Higgs boson. 2-Higgs Doublet Models (2HDMs) are well-motivated extensions of the Standard Model (SM) with five physical Higgs bosons: two CP-even states $h$ and $H$, one CP-odd state $A$, and two charged states $H^\pm_{}$. In this letter, we present the calculation of the full next-to-leading order (NLO) QCD corrections to $hH$ and $AA$ production at the LHC in the 2HDM at small values of the ratio of the vacuum expectation values, $\tan\beta$, including the exact top-mass dependence everywhere in the calculation. Using techniques applied in the NLO QCD SM Higgs pair production calculation, we present results for the total cross section as well as for the invariant Higgs-pair-mass distribution at the LHC. We also provide the top-quark scale and scheme uncertainties which are found to be sizeable., Comment: 13 pages, 10 figures. V2: minor typos corrected, identical to published version

Strong coupling between molecules and quantized fields has emerged as an effective methodology to engineer molecular properties. New hybrid states are formed when molecules interact with quantized fields. Since the properties of these states can be modulated by fine-tuning the field features, an exciting and new side of chemistry can be explored. In particular, significant modifications of the molecular properties can be achieved in plasmonic nanocavities, where the field quantization volume is reduced to sub-nanometric volumes. Intriguing applications of nanoplasmonics include the possibility of coupling the plasmons with a single molecule, instrumental for sensing, high-resolution spectroscopy, and single-molecule imaging. In this work, we focus on phenomena where the simultaneous effects of multiple plasmonic modes are critical. We propose a theoretical methodology to account for many plasmonic modes simultaneously while retaining computational feasibility. Our approach is conceptually simple and allows us to accurately account for the multimode effects and rationalize the nature of the interaction between multiple plasmonic excitations and molecules., Comment: 27 pages, 6 figures

A fascinating feature of metallic glasses is their ability to explore different configurations under mechanical deformations. This effect is usually observed through macroscopic observables, while little is known on the consequence of the deformation at atomic level. Using the new generation of synchrotrons, we probe the atomic motion and structure in a metallic glass under hydrostatic compression, from the onset of the perturbation up to a severely-compressed state. While the structure indicates reversible densification under compression, the dynamic is dramatically accelerated and exhibits a hysteresis with two regimes. At low pressures, the atomic motion is heterogeneous with avalanche-like rearrangements suggesting rejuvenation, while under further compression, aging leads to a super-diffusive dynamics triggered by internal stresses inherent to the glass. These results highlight the complexity of the atomic motion in non-ergodic systems and support a theory recently developed to describe the surprising rejuvenation and strain hardening of metallic glasses under compression., Comment: 16 pages, 5 figures + Supplementary Information (7 pages, 9 figures). First submitted version of manuscript

We present the first calculation of the complete set of NNLO QED corrections for muon-electron scattering. This includes leptonic, non-perturbative hadronic, and photonic contributions. All fermionic corrections as well as the photonic subset that only corrects the electron or the muon line are included with full mass dependence. The genuine four-point two-loop topologies are computed as an expansion in the small electron mass, taking into account both, logarithmically enhanced as well as constant mass effects using massification. A fast and stable implementation of the numerically delicate real-virtual contribution is achieved by combining OpenLoops with next-to-soft stabilisation. All matrix elements are implemented in the McMule framework, which allows for the fully-differential calculation of any infrared-safe observable. This calculation is to be viewed in the context of the MUonE experiment requiring a background prediction at the level of 10 ppm. Our results thus represent a major milestone towards this ambitious precision goal., Comment: 31 pages, 6 figures, 3 tables

Every automaton can be decomposed into a cascade of basic prime automata. This is the Prime Decomposition Theorem by Krohn and Rhodes. Guided by this theory, we propose automata cascades as a structured, modular, way to describe automata as complex systems made of many components, each implementing a specific functionality. Any automaton can serve as a component; using specific components allows for a fine-grained control of the expressivity of the resulting class of automata; using prime automata as components implies specific expressivity guarantees. Moreover, specifying automata as cascades allows for describing the sample complexity of automata in terms of their components. We show that the sample complexity is linear in the number of components and the maximum complexity of a single component, modulo logarithmic factors. This opens to the possibility of learning automata representing large dynamical systems consisting of many parts interacting with each other. It is in sharp contrast with the established understanding of the sample complexity of automata, described in terms of the overall number of states and input letters, which implies that it is only possible to learn automata where the number of states is linear in the amount of data available. Instead our results show that one can learn automata with a number of states that is exponential in the amount of data available., Comment: Full version with appendix of a paper with the same title that appears in the proceedings of AAAI 2023

The future of space missions beyond low-Earth orbit presents exciting opportunities but may come with formidable health challenges. Astronauts face a unique combination of space stressors capable of exerting effects on the central nervous system (CNS) with possible sex-dependent differences. The interaction of these combined spaceflight stressors may induce oxidative stress, thereby altering brain integrity and behavioral performance. Understanding these changes is critical for safeguarding astronaut health and enabling successful exploration. By understanding the physiological responses to the combined effects of ionizing radiation (IR) and social isolation in the brain through immunohistochemistry (IHC), proteomics and cytokine expression analyses, we aim to identify CNS pathways ripe for countermeasure development to mitigate adverse brain changes with future deep space exploration. Here, we study the combined effects of simulated 5-ion galactic cosmic radiation (GCRsim) at acute dosage (5, 15, and 50 cGy) and social isolation on crew age-matched male and female mice at 124 days post-irradiation. We conducted analyses of hippocampal cytokine biomarkers and proteomic profiling on hippocampal lysates. Our findings reveal sex-specific regulation of hippocampal cytokines and proteomic profiles. Ongoing immunohistochemistry findings on the hippocampus will provide qualitative information regarding key protein expression and cellular changes such as microglial activation, blood brain barrier integrity, and neuroinflammation. With future plans for long-duration space missions, such as Mars exploration, understanding CNS changes over extended periods in mice can provide insights into potential long-term health impacts on astronauts. This project will provide us with valuable insights into sex-differences in neurobiological processes and disease mechanisms impacting men and women in space.

Thriving In DEep Space (TIDES) initiative aims to comprehensively understand how hostile environments such as the Moon and Mars affect human physiology. Here we present two NASA-selected spaceflight experiments under the TIDES portfolio, iGCE (Integrated Gravity Continuum Experiment) and MitoFlyght (Mitochondrial Investigation of Oxidative Stress in Flies). We hypothesize that exposure to spaceflight conditions induces oxidative stress responses that negatively impact physiology. The iGCE mission employs two well-established spaceflight models, Drosophila melanogaster and C.elegans, using Redwire’s Multi-use Variable-g Platform (MVP) hardware to assess changes in cardiac, muscle, and nervous systems across five different gravities: Hypergravity (2g), Earth (1g), Mars (0.37g), Moon (0.16g), and microgravity (ug). This mission focuses on uncovering alterations in protein homeostasis, autophagy, and mitochondrial function conserved across species. In the MitoFlyght mission to the ISS, Drosophila will be housed in the Vented Fly Box (VFB). This mission evaluates the oxidative stress response and autophagic pathway in muscle, heart, and nervous system. Additionally, we will (a) use the genetic mutant, Tor7/P to test whether increased autophagy is beneficial or a maladaptive response to the spaceflight stressors, and (b) utilize fly lines with tissue-specific expression (neuronal, muscle, and cardiac) of an antioxidant gene, SOD2 (superoxide dismutase) as a potential countermeasure. Data from these missions will be compared with previous LEO-based datasets to identify shared signatures. Furthermore, cross-species analysis of the transcriptomic data from other invertebrate and vertebrate spaceflight studies will help determine evolutionarily conserved pathways perturbed by space stressors. Overall, both these missions aim to provide crucial insights into the mechanisms underlying oxidative stress responses, synaptic changes, and heart and muscle deficits, facilitating the identification of diagnostic and therapeutic targets to mitigate the adverse health effects of long-duration space habitation. Ultimately, this research will enhance our ability to thrive in deep space and inform future missions.

Historically, only 75 women have flown in space and while this inequity has been recently addressed with astronaut candidates about 50% female, research defining female biological responses to spaceflight remain limited. The NASA Artemis Campaign aims to land the first woman on the Moon for purposes of scientific discovery, technology advancement, and learning how to live and work on another world in preparation for human missions to Mars. The need to understand how sex and gender affect a wide range of physiological functions, impacting numerous health outcomes is critical. The purpose of this chapter is to summarize recent findings in women’s health in spaceflight, past studies examining female mammalian responses to spaceflight and highlight the need for additional studies to help reduce risk and enhance countermeasure development specific to female astronauts. The promise of artificial intelligence approaches for advancing the pace of research is discussed with the caveat that, at present, fundamental research on women’s health in space and sex-specificity of response to spaceflight stressors is not sufficiently robust to achieve this goal.

Intermolecular van der Waals interactions are central to chemical and physical phenomena ranging from biomolecule binding to soft-matter phase transitions. However, there are currently very limited approaches to manipulate van der Waals interactions. In this work, we demonstrate that strong light-matter coupling can be used to tune van der Waals interactions, and, thus, control the thermodynamic properties of many-molecule systems. Our analyses reveal orientation dependent single molecule energies and interaction energies for van der Waals molecules (for example, H$_{2}$). For example, we find intermolecular interactions that depend on the distance between the molecules $R$ as $R^{-3}$ and $R^{0}$. Moreover, we employ non-perturbative \textit{ab initio} cavity quantum electrodynamics calculations to develop machine learning-based interaction potentials for molecules inside optical cavities. By simulating systems ranging from $12$ H$_2$ to $144$ H$_2$ molecules, we demonstrate that strong light-matter coupling can tune the structural and thermodynamic properties of molecular fluids. In particular, we observe varying degrees of orientational order as a consequence of cavity-modified interactions, and we explain how quantum nuclear effects, light-matter coupling strengths, number of cavity modes, molecular anisotropies, and system size all impact the extent of orientational order. These simulations and analyses demonstrate both local and collective effects induced by strong light-matter coupling and open new paths for controlling the properties of molecular clusters., Comment: 7 pages and 3 figures in main text - 16 pages and 13 figures supplemental material

The development of efficient techniques to distinguish mirror images of chiral molecules (enantiomers) is very important in both chemistry and physics. Enantiomers share most molecular properties except, for instance, the absorption of circularly polarized light. Enantiomer purification is therefore a challenging task that requires specialized equipment. Strong coupling between quantized fields and matter (e.g. in optical cavities) is a promising technique to modify molecular processes in a non-invasive way. The modulation of molecular properties is achieved by changing the field characteristics. In this work, we investigate whether strong coupling to circularly polarized electromagnetic fields is a viable way to discriminate chiral molecules. To this end, we develop a nonperturbative framework to calculate the behavior of molecules in chiral cavities. We show that in this setting the enantiomers have different energies -- that is, one is more stable than the other. The field-induced energy differences are also shown to give rise to enantiospecific signatures in rotational spectra., Comment: 18 pages and 14 figures

Our work aims at developing reinforcement learning algorithms that do not rely on the Markov assumption. We consider the class of Non-Markov Decision Processes where histories can be abstracted into a finite set of states while preserving the dynamics. We call it a Markov abstraction since it induces a Markov Decision Process over a set of states that encode the non-Markov dynamics. This phenomenon underlies the recently introduced Regular Decision Processes (as well as POMDPs where only a finite number of belief states is reachable). In all such kinds of decision process, an agent that uses a Markov abstraction can rely on the Markov property to achieve optimal behaviour. We show that Markov abstractions can be learned during reinforcement learning. Our approach combines automata learning and classic reinforcement learning. For these two tasks, standard algorithms can be employed. We show that our approach has PAC guarantees when the employed algorithms have PAC guarantees, and we also provide an experimental evaluation., Comment: IJCAI 2022

We present the first full analytic evaluation of the scattering amplitude for the process $q {\bar q} \to Q {\bar Q}$ up-to two loops in Quantum Chromodynamics, for a massless $(q)$ and a massive $(Q)$ quark flavour. The interference terms of the one- and two-loop amplitudes with the Born amplitude, decomposed in terms of gauge invariant form factors depending on the colour and flavour structure, are analytically calculated by keeping complete dependence on the squared center-of-mass energy, the squared momentum transfer, and the heavy-quark mass. The results are expressed as Laurent series around four space-time dimensions, with coefficients given in terms of generalised polylogarithms and transcendental constants up-to weight four. Our results validate the known, purely numerical calculations of the squared amplitude, and extend the analytic knowledge, previously limited to a subset of form factors, to their whole set, coming from both planar and non-planar diagrams, up-to the second order corrections in the strong coupling constant., Comment: 19 pages, 12 figures, 1 table