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We give a sufficient condition for the local limit theorem. To construct it, we employ infinite times of convolutions of probability density functions.

In this work we investigate the two-neutron decay of 13Li and of the excited states of 11Li populated via one-proton removal from 14Be and 12Be, respectively. A phenomenological model is used to describe the decay of 11Li and 13Li. While the first one displays important sequential components, the second one appears dominated by the direct two-neutron decay. A microscopic three-body model is used to extract information on the spatial configuration of the emitted neutrons before the decay and shows that the average distance between the neutrons increases going from 11Li to 13Li.

Skyrmions, merons, bimerons, and skyrmionic hopfions are quasiparticles which have stable topological textures. They have been observed across multiple physical domains including nucleons, water waves, magnetic materials, electromagnetic fields, condensed-matter physics, liquid crystals, and Bose-Einstein condensates. The nontrivial topological texture of these quasiparticles exhibited promising applications across several research fields including cosmology, particle physics, superfluids, high-energy physics, optics, condensed matter, early-universe cosmology, cold quantum matter, and liquid crystals. These quasiparticles have most recently been observed in paraxial vector beams. Due to the inhomogeneous polarization distribution of vector beams, the quasiparticle textures reside in the Stokes vector fields. Here, we review recent developments in paraxial quasiparticle research and provide detailed information on their fundamental properties and future prospects. We discuss various techniques which have been used to experimentally generate these quasiparticles and we examine a number of their proposed applications. Notably, this review offers insight into the concepts and techniques which can be applied to the generation of optical skyrmions in paraxial laser beams, and investigates their intriguing applications across both fundamental and applied optics., Comment: 43 pages, 29 figures, topical review

Treatment effect estimation, which helps understand the causality between treatment and outcome variable, is a central task in decision-making across various domains. While most studies focus on treatment effect estimation on individual targets, in specific contexts, there is a necessity to comprehend the treatment effect on a group of targets, especially those that have relationships represented as a graph structure between them. In such cases, the focus of treatment assignment is prone to depend on a particular node of the graph, such as the one with the highest degree, thus resulting in an observational bias from a small part of the entire graph. Whereas a bias tends to be caused by the small part, straightforward extensions of previous studies cannot provide efficient bias mitigation owing to the use of the entire graph information. In this study, we propose Graph-target Treatment Effect Estimation (GraphTEE), a framework designed to estimate treatment effects specifically on graph-structured targets. GraphTEE aims to mitigate observational bias by focusing on confounding variable sets and consider a new regularization framework. Additionally, we provide a theoretical analysis on how GraphTEE performs better in terms of bias mitigation. Experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our proposed method.

The Compton Spectrometer and Imager balloon payload (COSI-Balloon) is a wide-field-of-view Compton ${\gamma}$-ray telescope that operates in the 0.2 - 5 MeV bandpass. COSI-Balloon had a successful 46-day flight in 2016 during which the instrument observed the Crab Nebula, Cygnus X-1, and Centaurus A. Using the data collected by the COSI-Balloon instrument during this flight, we present the source flux extraction of signals from the variable balloon background environment and produce images of these background-dominated sources by performing Richardson-Lucy deconvolutions. We also present the spectra measured by the COSI-Balloon instrument, compare and combine them with measurements from other instruments, and fit the data. The Crab Nebula was observed by COSI-Balloon and we obtain a measured flux in the energy band 325 - 480 keV of (4.5 ${\pm}$ 1.6) ${\times}$ 10$^{-3}$ ph cm$^{-2}$ s$^{-1}$. The model that best fits the COSI-Balloon data combined with measurements from NuSTAR and Swift-BAT is a broken power law with a measured photon index ${\Gamma}$ = 2.20 ${\pm}$ 0.02 above the 43 keV break. Cygnus X-1 was also observed during this flight, and we obtain a measured flux of (1.4 ${\pm}$ 0.2) ${\times}$ 10$^{-3}$ ph cm$^{-2}$ s$^{-1}$ in the same energy band and a best-fit result (including data from NuSTAR, Swift-BAT, and INTEGRAL/ IBIS) was to a cutoff power law with a high-energy cutoff energy of 138.3 ${\pm}$ 1.0 keV and a photon index of ${\Gamma}$ = 1.358 ${\pm}$ 0.002. Lastly, we present the measured spectrum of Centaurus A and our best model fit to a power law with a photon index of ${\Gamma}$ = 1.73 ${\pm}$ 0.01.

The first spectroscopy of $^{52}$K was investigated via in-beam $\gamma$-ray spectroscopy at the RIKEN Radioactive Isotope Beam Factory after one-proton and one-neutron knockout from $^{53}$Ca and $^{53}$K beams impinging on a 15-cm liquid hydrogen target at $\approx$ 230~MeV/nucleon. The energy level scheme of $^{52}$K was built using single $\gamma$ and $\gamma$-$\gamma$ coincidence spectra. The spins and parities of the excited states were established based on momentum distributions of the fragment after the knockout reaction and based on exclusive cross sections. The results were compared to state-of-the-art shell model calculations with the SDPF-Umod interaction and ab initio IMSRG calculations with chiral effective field theory nucleon-nucleon and three-nucleon forces.

Finding the chromatic number of large graphs is known to be NP-hard. Although various algorithms have been developed to efficiently compute chromatic numbers, they still take an enormous amount of time for large graphs. In this paper, we propose the recurrence relation to obtain the expected value of the chromatic number of random graphs in a short time.

The isotopic compositions of samples returned from Cb-type asteroid Ryugu and Ivuna-type (CI) chondrites are distinct from other carbonaceous chondrites, which has led to the suggestion that Ryugu and CI chondrites formed in a different region of the accretion disk, possibly around the orbits of Uranus and Neptune. We show that, like for Fe, Ryugu and CI chondrites also have indistinguishable Ni isotope anomalies, which differ from those of other carbonaceous chondrites. We propose that this unique Fe and Ni isotopic composition reflects different accretion efficiencies of small FeNi metal grains among the carbonaceous chondrite parent bodies. The CI chondrites incorporated these grains more efficiently, possibly because they formed at the end of the disk's lifetime, when planetesimal formation was also triggered by photoevaporation of the disk. Isotopic variations among carbonaceous chondrites may thus reflect fractionation of distinct dust components from a common reservoir, implying CI chondrites and Ryugu may have formed in the same region of the accretion disk as other carbonaceous chondrites., Comment: Published open access in Science Advances

We consider arbitrary bounded discrete time series originating from dynamical system with recursivity. More precisely, we provide an explicit construction of recurrent neural networks which effectively approximate the corresponding discrete dynamical systems.

Humans naturally obtain intuition about the interactions between and the stability of rigid objects by observing and interacting with the world. It is this intuition that governs the way in which we regularly configure objects in our environment, allowing us to build complex structures from simple, everyday objects. Robotic agents, on the other hand, traditionally require an explicit model of the world that includes the detailed geometry of each object and an analytical model of the environment dynamics, which are difficult to scale and preclude generalization. Instead, robots would benefit from an awareness of intuitive physics that enables them to similarly reason over the stable interaction of objects in their environment. Towards that goal, we propose StackGen, a diffusion model that generates diverse stable configurations of building blocks matching a target silhouette. To demonstrate the capability of the method, we evaluate it in a simulated environment and deploy it in the real setting using a robotic arm to assemble structures generated by the model.

GRAMS (Gamma-Ray and AntiMatter Survey) is a next-generation balloon/satellite experiment utilizing a LArTPC (Liquid Argon Time Projection Chamber), to simultaneously target astrophysical observations of cosmic MeV gamma-rays and conduct an indirect dark matter search using antimatter. While LArTPCs are widely used in particle physics experiments, they have never been operated at balloon altitudes. An engineering balloon flight with a small-scale LArTPC (eGRAMS) was conducted on July 27th, 2023, to establish a system for safely operating a LArTPC at balloon altitudes and to obtain cosmic-ray data from the LArTPC. The flight was launched from the Japan Aerospace Exploration Agency's (JAXA) Taiki Aerospace Research Field in Hokkaido, Japan. The total flight duration was 3 hours and 12 minutes, including a level flight of 44 minutes at a maximum altitude of 28.9 km. The flight system was landed on the sea and successfully recovered. The LArTPC was successfully operated throughout the flight, and about 0.5 million events of the cosmic-ray data including muons, protons, and Compton scattering gamma-ray candidates, were collected. This pioneering flight demonstrates the feasibility of operating a LArTPC in high-altitude environments, paving the way for future GRAMS missions and advancing our capabilities in MeV gamma-ray astronomy and dark matter research.

Since the invention of the laser nonlinear effects such as filamentation, Rabi-cycling and collective emission have been explored in the optical regime leading to a wide range of scientific and industrial applications. X-ray free electron lasers (XFELs) have led to the extension of many optical techniques to X-rays for their advantages of angstrom scale spatial resolution and elemental specificity. One such example is XFEL driven population inversion of 1s core hole states resulting in inner-shell K${\alpha}$ (2p to 1s) X-ray lasing in elements ranging from neon to copper, which has been utilized for nonlinear spectroscopy and development of next generation X-ray laser sources. Here we show that strong lasing effects, similar to those observed in the optical regime, can occur at 1.5 to 2.1 angstrom wavelengths during high intensity (> ${10^{19}}$ W/cm${^{2}}$) XFEL driven inner-shell lasing and superfluorescence of copper and manganese. Depending on the temporal substructure of the XFEL pump pulses, the resulting inner-shell X-ray laser pulses can exhibit strong spatial inhomogeneities as well as spectral inhomogeneities and broadening. Through 3D Maxwell Bloch theory we show that the observed spatial inhomogeneities result from X-ray filamentation, and that the spectral broadening is driven by Rabi cycling with sub-femtosecond periods. These findings indicate that we have generated Angstrom-wavelength x-ray pulses (containing ${10^{6}}$ - ${10^{8}}$ photons) in the strong lasing regime, some of them with pulse lengths of less than 100 attoseconds.

Heralded by the initial success in speech recognition and image classification, learning-based approaches with neural networks, commonly referred to as deep learning, have spread across various fields. A primitive form of a neural network functions as a deterministic mapping from one vector to another, parameterized by trainable weights. This is well suited for point estimation in which the model learns a one-to-one mapping (e.g., mapping a front camera view to a steering angle) that is required to solve the task of interest. Although learning such a deterministic, one-to-one mapping is effective, there are scenarios where modeling \emph{multimodal} data distributions, namely learning one-to-many relationships, is helpful or even necessary. In this thesis, we adopt a generative modeling perspective on robotics problems. Generative models learn and produce samples from multimodal distributions, rather than performing point estimation. We will explore the advantages this perspective offers for three topics in robotics., Comment: arXiv admin note: text overlap with arXiv:2302.12244

We measure and analyze noise-induced energy-fluctuations of spin qubits defined in quantum dots made of isotopically natural silicon. Combining Ramsey, time-correlation of single-shot measurements, and CPMG experiments, we cover the qubit noise power spectrum over a frequency range of nine orders of magnitude without any gaps. We find that the low-frequency noise spectrum is similar across three different devices suggesting that it is dominated by the hyperfine coupling to nuclei. The effects of charge noise are smaller, but not negligible, and are device dependent as confirmed from the noise cross-correlations. We also observe differences to spectra reported in GaAs {[Phys. Rev. Lett. 118, 177702 (2017), Phys. Rev. Lett. 101, 236803 (2008)]}, which we attribute to the presence of the valley degree of freedom in silicon. Finally, we observe $T_2^*$ to increase upon increasing the external magnetic field, which we speculate is due to the increasing field-gradient of the micromagnet suppressing nuclear spin diffusion., Comment: 12 pages, 10 figures

In this paper, we prove that a local weak solution to the $d$-dimensional incompressible Navier-Stokes equations ($d \geq 2$) can be constructed by taking the hydrodynamic limit of a velocity-discretized Boltzmann equation with a simplified BGK collision operator. Moreover, in the case when the dimension is $d=2,3$, we characterize the combinations of finitely many particle velocities and probabilities that lead to the incompressible Navier-Stokes equations in the hydrodynamic limit. Numerical computations conducted in 2D provide information about the rate with which this hydrodynamic limit is achieved when the Knudsen number tends to zero., Comment: 49 pages, 3 figures

The neutron-rich unbound fluorine isotope $^{30}$F$_{21}$ has been observed for the first time by measuring its neutron decay at the SAMURAI spectrometer (RIBF, RIKEN) in the quasi-free proton knockout reaction of $^{31}$Ne nuclei at 235 MeV/nucleon. The mass and thus one-neutron-separation energy of $^{30}$F has been determined to be $S_n = -472\pm 58 \mathrm{(stat.)} \pm 33 \mathrm{(sys.)}$ keV from the measurement of its invariant-mass spectrum. The absence of a sharp drop in $S_n$($^{30}$F) shows that the ``magic'' $N=20$ shell gap is not restored close to $^{28}$O, which is in agreement with our shell-model calculations that predict a near degeneracy between the neutron $d$ and $fp$ orbitals, with the $1p_{3/2}$ and $1p_{1/2}$ orbitals becoming more bound than the $0f_{7/2}$ one. This degeneracy and reordering of orbitals has two potential consequences: $^{28}$O behaves like a strongly superfluid nucleus with neutron pairs scattering across shells, and both $^{29,31}$F appear to be good two-neutron halo-nucleus candidates., Comment: 9 pages, 2 figures, accepted for publication in Physical Review Letters

In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lema\^itre--Robertson--Walker spacetime. To evaluate the numerical stability, we calculate the constraint amplification factor by the eigenvalue analysis of the evolution of the constraint. We propose a modification to the time evolution equations of the cBSSN formulation for a higher numerical stability. Furthermore, we perform numerical simulations using the modified formulation to confirm its improved stability., Comment: 16 pages, 3 figures

This paper will examine the cognitive processes involved in palpation in order to develop an appropriate remote palpation system. In a conventional remote palpation system, the tactile condition of the patient is conveyed to the doctors using a force feedback system. A clarification of the cognitive process during palpation suggests that the purpose of palpation is to formulate a clear idea about the patient's medical problems using the tactile sensation as a trigger to combine the results of other assessments, past experience and memory, and patient reactions to the doctor's touch. This is in contrast to the objective of acquiring the detailed tactile condition of the affected body part. In order to demonstrate this purpose, we will describe the two significant signal pathways for the perception of tactile sensation, both in doctors and patients. The perception of doctors progresses as the result of active touch to the affected part, thereby implying that the simultaneous stimulation of kinaesthetic and tactile sensation is necessary. Conversely, the tactile sensation experienced by patients is the result of passive touch, which evokes a more subjective and emotional response. Patients both explicitly and implicitly perceive the stimulation, and doctors use these perceptions as reactions of the pain to the doctors' touch. This paper proposes the fundamental concept of a remote palpation system, ``Palpation Reality beyond Real'', to achieve the purpose of palpation. Palpation reality implies a system in which the whole cognitive process progresses at the same level or better than palpation in the standard examination, rather than presenting the real tactile sensation.

The calcium isotopes are an ideal system to investigate the evolution of shell structure and magic numbers. Although the properties of surface nucleons in calcium have been well studied, probing the structure of deeply bound nucleons remains a challenge. Here, we report on the first measurement of unbound states in $^{53}$Ca and $^{55}$Ca, populated from \ts{54,56}Ca($p,pn$) reactions at a beam energy of around 216 MeV/nucleon at the RIKEN Radioactive Isotopes Beam Factory. The resonance properties, partial cross sections, and momentum distributions of these unbound states were analyzed. Orbital angular momentum $l$ assignments were extracted from momentum distributions based on calculations using the distorted wave impulse approximation (DWIA) reaction model. The resonances at excitation energies of 5516(41)\,keV in $^{53}$Ca and 6000(250)\,keV in $^{55}$Ca indicate a significant $l$\, =\,3 component, providing the first experimental evidence for the $\nu 0f_{7/2}$ single-particle strength of unbound hole states in the neutron-rich Ca isotopes. The observed excitation energies and cross-sections point towards extremely localized and well separated strength distributions, with some fragmentation for the $\nu 0f_{7/2}$ orbital in $^{55}$Ca. These results are in good agreement with predictions from shell-model calculations using the effective GXPF1Bs interaction and \textit{ab initio} calculations and diverge markedly from the experimental distributions in the nickel isotones at $Z=28$., Comment: 13 pages, 7 figures

Commercially impactful quantum algorithms such as quantum chemistry and Shor's algorithm require a number of qubits and gates far beyond the capacity of any existing quantum processor. Distributed architectures, which scale horizontally by networking modules, provide a route to commercial utility and will eventually surpass the capability of any single quantum computing module. Such processors consume remote entanglement distributed between modules to realize distributed quantum logic. Networked quantum computers will therefore require the capability to rapidly distribute high fidelity entanglement between modules. Here we present preliminary demonstrations of some key distributed quantum computing protocols on silicon T centres in isotopically-enriched silicon. We demonstrate the distribution of entanglement between modules and consume it to apply a teleported gate sequence, establishing a proof-of-concept for T centres as a distributed quantum computing and networking platform., Comment: 14 pages, 13 figures

We consider the problem of coloring a 3-colorable graph in polynomial time using as few colors as possible. This is one of the most challenging problems in graph algorithms. In this paper using Blum's notion of ``progress'', we develop a new combinatorial algorithm for the following: Given any 3-colorable graph with minimum degree $\ds>\sqrt n$, we can, in polynomial time, make progress towards a $k$-coloring for some $k=\sqrt{n/\ds}\cdot n^{o(1)}$. We balance our main result with the best-known semi-definite(SDP) approach which we use for degrees below $n^{0.605073}$. As a result, we show that $\tO(n^{0.19747})$ colors suffice for coloring 3-colorable graphs. This improves on the previous best bound of $\tO(n^{0.19996})$ by Kawarabayashi and Thorup in 2017., Comment: To appear in STOC'24

Deep-sea archives that include intermediate-lived radioactive $^{60}\mathrm{Fe}$ particles suggest the occurrence of several recent supernovae inside the present-day volume of the Local Bubble during the last $\sim 10$ Myr. The isotope $^{60}\mathrm{Fe}$ is mainly produced in massive stars and ejected in supernova explosions, which should always result in a sizeable yield of $^{26}\mathrm{Al}$ from the same objects. $^{60}\mathrm{Fe}$ and $^{26}\mathrm{Al}$ decay with lifetimes of 3.82 and 1.05 Myr, and emit $\gamma$-rays at 1332 and 1809 keV, respectively. These $\gamma$-rays have been measured as diffuse glow of the Milky Way, and would also be expected from inside the Local Bubble as foreground emission. Based on two scenarios, one employing a geometrical model and the other state-of-the-art hydrodynamics simulations, we estimate the expected fluxes of the 1332 and 1809 keV $\gamma$-ray lines, as well as the resulting 511 keV line from positron annihilation due to the $^{26}\mathrm{Al}$ $\beta^+$-decay. We find fluxes in the range of $10^{-6}$-$10^{-5}\,\mathrm{ph\,cm^{-2}\,s^{-1}}$ for all three lines with isotropic contributions of 10-50%. We show that these fluxes are within reach for the upcoming COSI-SMEX $\gamma$-ray telescope over its nominal satellite mission duration of 2 yr. Given the Local Bubble models considered, we conclude that in the case of 10-20 Myr-old superbubbles, the distributions of $^{60}\mathrm{Fe}$ and $^{26}\mathrm{Al}$ are not co-spatial - an assumption usually made in $\gamma$-ray data analyses. In fact, this should be taken into account however when analysing individual nearby targets for their $^{60}\mathrm{Fe}$ to $^{26}\mathrm{Al}$ flux ratio as this gauges the stellar evolution models and the age of the superbubbles. A flux ratio measured for the Local Bubble could further constrain models of $^{60}\mathrm{Fe}$ deposition on Earth and its moon., Comment: accepted in A&A, 18 pages, 13 figures, 2 tables

To detect and track structural changes in atomic nuclei, the systematic study of nuclear levels with firm spin-parity assignments is important. While linear polarization measurements have been applied to determine the electromagnetic character of gamma-ray transitions, the applicable range is strongly limited due to the low efficiency of the detection system. The multi-layer Cadmium-Telluride (CdTe) Compton camera can be a state-of-the-art gamma-ray polarimeter for nuclear spectroscopy with the high position sensitivity and the detection efficiency. We demonstrated the capability to operate this detector as a reliable gamma-ray polarimeter by using polarized 847-keV gamma rays produced by the $^{56}\rm{Fe}({\it p},{\it p'}\gamma)$ reaction. By combining the experimental data and simulated calculations, the modulation curve for the gamma ray was successfully obtained. A remarkably high polarization sensitivity was achieved, compatible with a reasonable detection efficiency. Based on the obtained results, a possible future gamma-ray polarimetery is discussed.

The structure and decay of the most neutron-rich beryllium isotope, $^{16}$Be, has been investigated following proton knockout from a high-energy $^{17}$B beam. Two relatively narrow resonances were observed for the first time, with energies of $0.84(3)$ and $2.15(5)$ MeV above the two-neutron decay threshold and widths of $0.32(8)$ and $0.95(15)$ MeV respectively. These were assigned to be the ground ($J^{\pi}=0^+$) and first excited ($2^+$) state, with $E_x=1.31(6)$ MeV. The mass excess of $^{16}$Be was thus deduced to be $56.93(13)$ MeV, some $0.5$ MeV more bound than the only previous measurement. Both states were observed to decay by direct two-neutron emission. Calculations incorporating the evolution of the wavefunction during the decay as a genuine three-body process reproduced the principal characteristics of the neutron-neutron energy spectra for both levels, indicating that the ground state exhibits a strong spatially compact dineutron component, while the 2$^+$ level presents a far more diffuse neutron-neutron distribution.

The present study aims to reinforce the evidence for the ~9 s pulsation in the gamma-ray binary LS 5039, derived with a Suzaku observation in 2007 and that with NuSTAR in 2016 (Yoneda et al 2000). Through a reanalysis of the NuSTAR data incorporating the orbital Doppler correction, the 9.0538 s pulsation was confirmed successfully even in the 3--10 keV range, where it was undetectable previously. This was attained by perceiving an energy-dependent drift in the pulse phase below 10 keV, and correcting the pulse timing of individual photons for that effect. Similarly, an archival 0.7--12 keV data set of LS 5039, taken with the ASCA GIS in 1999 October, was analyzed. The data showed possible periodicity at about 8.882 s, but again the energy-dependent phase drift was noticed below 10 keV. By correcting for this effect, and for the orbital Doppler delays in the LS 5039 system, the 2.8--12 keV periodicity became statistically significant at 8.891+- 0.001 s. The periods measured with ASCA, Suzaku, and NuSTAR approximately follow an average period derivative of dP/dt = 3.0 e-10 s/s. These results provide further evidence for the pulsation in this object, and strengthen the scenario by (Yoneda et al 2000), that the compact object in LS 5039 is a strongly magnetized neutron star., Comment: 20 pages, 16 figures, accepted for publication in The Astrophysical Journal

A core capability for robot manipulation is reasoning over where and how to stably place objects in cluttered environments. Traditionally, robots have relied on object-specific, hand-crafted heuristics in order to perform such reasoning, with limited generalizability beyond a small number of object instances and object interaction patterns. Recent approaches instead learn notions of physical interaction, namely motion prediction, but require supervision in the form of labeled object information or come at the cost of high sample complexity, and do not directly reason over stability or object placement. We present 6-DoFusion, a generative model capable of generating 3D poses of an object that produces a stable configuration of a given scene. Underlying 6-DoFusion is a diffusion model that incrementally refines a randomly initialized SE(3) pose to generate a sample from a learned, context-dependent distribution over stable poses. We evaluate our model on different object placement and stacking tasks, demonstrating its ability to construct stable scenes that involve novel object classes as well as to improve the accuracy of state-of-the-art 3D pose estimation methods., Comment: In submission

Learning from demonstrations (LfD) has successfully trained robots to exhibit remarkable generalization capabilities. However, many powerful imitation techniques do not prioritize the feasibility of the robot behaviors they generate. In this work, we explore the feasibility of plans produced by LfD. As in prior work, we employ a temporal diffusion model with fixed start and goal states to facilitate imitation through in-painting. Unlike previous studies, we apply cold diffusion to ensure the optimization process is directed through the agent's replay buffer of previously visited states. This routing approach increases the likelihood that the final trajectories will predominantly occupy the feasible region of the robot's state space. We test this method in simulated robotic environments with obstacles and observe a significant improvement in the agent's ability to avoid these obstacles during planning.

While reinforcement learning (RL) has shown promising performance, its sample complexity continues to be a substantial hurdle, restricting its broader application across a variety of domains. Imitation learning (IL) utilizes oracles to improve sample efficiency, yet it is often constrained by the quality of the oracles deployed. which actively interleaves between IL and RL based on an online estimate of their performance. RPI draws on the strengths of IL, using oracle queries to facilitate exploration, an aspect that is notably challenging in sparse-reward RL, particularly during the early stages of learning. As learning unfolds, RPI gradually transitions to RL, effectively treating the learned policy as an improved oracle. This algorithm is capable of learning from and improving upon a diverse set of black-box oracles. Integral to RPI are Robust Active Policy Selection (RAPS) and Robust Policy Gradient (RPG), both of which reason over whether to perform state-wise imitation from the oracles or learn from its own value function when the learner's performance surpasses that of the oracles in a specific state. Empirical evaluations and theoretical analysis validate that RPI excels in comparison to existing state-of-the-art methodologies, demonstrating superior performance across various benchmark domains.

We consider arbitrary bounded discrete time series originating from dynamical system. Without any use of the Fourier transform, we find periodic points which suitably characterizes (i.e. independent of Lyapunov exponent) the corresponding time series. In particular, bounded discrete time series generated by the autoregressive model (without the white noise) is equivalent to a quasi periodic function.