Search

Measuring the quantumness of a system can be done with a variety of methods. In this article we compare different criteria, namely quantum discord, Bell inequality violation and non-separability, for systems placed in a Gaussian state. When the state is pure, these criteria are equivalent, while we find that they do not necessarily coincide when decoherence takes place. Finally, we prove that these criteria are essentially controlled by the semi-minor axis of the ellipse representing the state's Wigner function in phase space., Comment: 8 pages without appendix (total 19 pages), 5 figures. Matches published version in EPL

2009 MS9 is a trans-Neptunian object (TNO) whose perihelion brings it close to the distance where some long period comets are seen to become active. Knowing this, and the fact that this object appears to brighten in excess of it's predicted nucleus brightness suggests that 2009 MS9 has a delayed onset of activity brought on by the sublimation of a species more volatile than water. In this paper we characterize 2009 MS9's physical properties and investigate potential outgassing through composite images, sublimation models, and measurements of spectral reflectivity. We find that deep composite images of the object at various epochs along its orbit show no evidence of dust yet place sensitive limits to the dust production. We estimate the nucleus radius to be 11.5 km $\pm 3.5$ km using thermal IR modeling from NEOWISE data and use this and data pre-perihelion to estimate a geometric albedo of 0.25. We compare a CO-sublimation activity model to its post perihelion heliocentric light curve and find this data supports an active fractional area of $5 \times 10^{-6}$ assuming 2 $\mu$m sized grains and other typical comet parameters. The spectral reflectivity of the surface materials obtained with the Gemini Observatory and CFHT at different epochs shows a reddening spectral slope. We compare the physical properties of 2009 MS9 to both TNO and comet populations, and speculate that 2009 MS9's reddening may be due to the buildup of a dust mantle on the surface and could be an explanation of why TNOs exhibit a color bimodality., Comment: 25 pages, 8 figures, Accepted to PSJ

General relativity and its cosmological solution predicts the existence of tensor modes of perturbations evolving on top of our Friedman-Lema\^itre-Robertson-Walker expanding Universe. Being gauge invariant and not necessarily coupled to other quantum sources, they can be seen as representing pure gravity. Unambiguously showing they are indeed to be quantised would thus provide an unquestionable proof of the quantum nature of gravitation. This review will present a summary of the various theoretical issues that could lead to this conclusion., Comment: Invited chapter for the Section "Perturbative Quantum Gravity" of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023). New version matches the accepted version

Graph Echo State Networks (GESN) have already demonstrated their efficacy and efficiency in graph classification tasks. However, semi-supervised node classification brought out the problem of over-smoothing in end-to-end trained deep models, which causes a bias towards high homophily graphs. We evaluate for the first time GESN on node classification tasks with different degrees of homophily, analyzing also the impact of the reservoir radius. Our experiments show that reservoir models are able to achieve better or comparable accuracy with respect to fully trained deep models that implement ad hoc variations in the architectural bias, with a gain in terms of efficiency., Comment: Accepted for oral presentation at ESANN 2022

We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy., Comment: 66 pages, 6 figures

We present a novel data-driven distributionally robust Model Predictive Control formulation for unknown discrete-time linear time-invariant systems affected by unknown and possibly unbounded additive uncertainties. We use off-line collected data and an approximate model of the dynamics to formulate a finite-horizon optimization problem. To account for both the uncertainty related to the dynamics and the disturbance acting on the system, we resort to a distributionally robust formulation that optimizes the cost expectation while satisfying Conditional Value-at-Risk constraints with respect to the worst-case probability distributions of the uncertainties within an ambiguity set defined using the Wasserstein metric. Using results from the distributionally robust optimization literature we derive a tractable finite-dimensional convex optimization problem with finite-sample guarantees for the class of convex piecewise affine cost and constraint functions. The performance of the proposed algorithm is demonstrated in closed-loop simulation on a simple numerical example.

We are conducting a survey using twilight time on the Dark Energy Camera with the Blanco 4m telescope in Chile to look for objects interior to Earth's and Venus' orbits. To date we have discovered two rare Atira/Apohele asteroids, 2021 LJ4 and 2021 PH27, which have orbits completely interior to Earth's orbit. We also discovered one new Apollo type Near Earth Object (NEO) that crosses Earth's orbit, 2022 AP7. Two of the discoveries likely have diameters greater than 1 km. 2022 AP7 is likely the largest Potentially Hazardous Asteroid (PHA) discovered in about eight years. To date we have covered 624 square degrees of sky near to and interior to the orbit of Venus. The average images go to 21.3 mags in the r-band, with the best images near 22nd mag. Our new discovery 2021 PH27 has the smallest semi-major axis known for an asteroid, 0.4617 au, and the largest general relativistic effects (53 arcseconds/century) known for any body in the Solar System. The survey has detected about 15 percent of all known Atira NEOs. We put strong constraints on any stable population of Venus co-orbital resonance objects existing, as well as the Atira and Vatira asteroid classes. These interior asteroid populations are important to complete the census of asteroids near Earth, including some of the most likely Earth impactors that cannot easily be discovered in other surveys. Comparing the actual population of asteroids found interior to Earth and Venus with those predicted to exist by extrapolating from the known population exterior to Earth is important to better understand the origin, composition and structure of the NEO population., Comment: In Press at The Astronomical Journal

This paper addresses the question: Can spintronic circuits based on Magnetic Tunnel Junction (MTJ) transducers outperform their state-of-the-art CMOS counterparts? To this end, we use the EPFL combinational benchmark sets, synthesize them in 7 nm CMOS and in MTJ-based spintronic technologies, and compare the two implementation methods in terms of Energy-Delay-Product (EDP). To fully utilize the technologies potential, CMOS and spintronic implementations are built upon standard Boolean and Majority Gates, respectively. For the spintronic circuits, we assumed that domain conversion (electric/magnetic to magnetic/electric) is performed by means of MTJs and the computation is accomplished by domain wall based majority gates, and considered two EDP estimation scenarios: (i) Uniform Benchmarking, which ignores the circuit's internal structure and only includes domain transducers power and delay contributions into the calculations, and (ii) Majority-Inverter-Graph Benchmarking, which also embeds the circuit structure, the associated critical path delay and energy consumption by DW propagation. Our results indicate that for the uniform case, the spintronic route is better suited for the implementation of complex circuits with few inputs and outputs. On the other hand, when the circuit structure is also considered via majority and inverter synthesis, our analysis clearly indicates that in order to match and eventually outperform CMOS performance, MTJ efficiency has to be improved by 3-4 orders of magnitude. While it is clear that for the time being the MTJ-based-spintronic way cannot compete with CMOS, further transducer developments may tip the balance, which, when combined with information non-volatility, may make spintronic implementation for certain applications that require a large number of calculations and have a rather limited amount of interaction with the environment., Comment: This work was supported by imec Industrial Affiliation Program on Exploratory Logic Devices. It has also received funding from the European Union Horizon Europe research and innovation programme within the project SPIDER under grant agreement No 101070417

Deep reinforcement learning agents are notoriously sample inefficient, which considerably limits their application to real-world problems. Recently, many model-based methods have been designed to address this issue, with learning in the imagination of a world model being one of the most prominent approaches. However, while virtually unlimited interaction with a simulated environment sounds appealing, the world model has to be accurate over extended periods of time. Motivated by the success of Transformers in sequence modeling tasks, we introduce IRIS, a data-efficient agent that learns in a world model composed of a discrete autoencoder and an autoregressive Transformer. With the equivalent of only two hours of gameplay in the Atari 100k benchmark, IRIS achieves a mean human normalized score of 1.046, and outperforms humans on 10 out of 26 games, setting a new state of the art for methods without lookahead search. To foster future research on Transformers and world models for sample-efficient reinforcement learning, we release our code and models at https://github.com/eloialonso/iris., Comment: ICLR 2023 (notable top 5%)

Extremely similar heliocentric orbital elements of the main-belt objects (458271) 2010 UM26 and 2010 RN221 make them the tightest known pair and promise its very young age. We analyzed the conditions of its origin and determined its age. We conducted dedicated observations of (458271) 2010 UM26 and 2010 RN221 in summer 2022 that resulted in a high-accuracy astrometric set of data. Joining them with the previously available observations, we improved the precision of the orbit determination of both asteroids. We used numerical simulations backward in time to constrain the origin of this new pair by observing orbital convergence in the Cartesian space. Using a large number of possible clone variants of (458271) 2010 UM26 and 2010 RN221 we find they all converge in a narrow time interval around March 2003 having extremely tight minimum distances ($\leq 1000$ km) and minimum relative velocities ($\leq 3$ cm~s$^{-1}$). These conditions require to include mutual gravitational attraction of the asteroids constituting the pair for its age determination. Extending our model by this effect even improves the convergence results. We find there is more than $55$\% probability that the pair formed after the year 2000. However, quasi-satellite captures make the possible age uncertainty of this pair prolonged possibly to the 1960s. Still, this is by far the youngest known asteroid pair, a prime target for future astronomical observations., Comment: Accepted for publication in Astronomy and Astrophysics, 7 pages, 2 figures, 2 tables

Differential cryptanalysis famously uses statistical biases in the propagation of differences in a block cipher to attack the cipher. In this paper, we investigate the existence of more general statistical biases in the differences. To this end, we discuss the $c$-differential uniformity of S-boxes, which is a concept that was recently introduced in Ellingsen et. al. to measure certain statistical biases that could potentially be used in attacks similar to differential attacks. Firstly, we prove that a large class of potential candidates for S-boxes necessarily has large $c$-differential uniformity for all but at most $B$ choices of $c$, where $B$ is a constant independent of the size of the finite field $q$. This result implies that for a large class of functions, certain statistical differential biases are inevitable. In a second part, we discuss the practical possibility of designing a differential attack based on weaknesses of S-boxes related to their $c$-differential uniformity., Comment: 14 pages, 2 figures

Model Predictive Control is an extremely effective control method for systems with input and state constraints. Model Predictive Control performance heavily depends on the accuracy of the open-loop prediction. For systems with uncertainty this in turn depends on the information that is available about the properties of the model and disturbance uncertainties. Here we are interested in situations where such information is only available through realizations of the system trajectories. We propose a general scenario-based optimization framework for stochastic control of a linear system affected by additive disturbance, when the dynamics are only approximately known. The main contribution is in the derivation of an upper bound on the number of scenarios required to provide probabilistic guarantees on the quality of the solution to the deterministic scenario-based finite horizon optimal control problem. We provide a theoretical analysis of the sample complexity of the proposed method and demonstrate its performance on a simple simulation example. Since the proposed approach leverages sampling, it does not rely on the explicit knowledge of the model or disturbance distributions, making it applicable in a wide variety of contexts.

In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that allows to give a finer tuning of the minimum distance of the intermediate code (allowing larger dimension of the final code), and to remove restrictions on the arithmetic properties of $q$ compared with the size of the locality sets in the hierarchy. In turn, we manage to obtain codes with a wide set of parameters both for the size $q$ of the base field, and for the hierarchy size, while keeping the optimality of the codes we construct., Comment: Comments are welcome!

Correctness and robustness are essential for logic synthesis applications, but they are often only tested with a limited set of benchmarks. Moreover, when the application fails on a large benchmark, the debugging process may be tedious and time-consuming. In some fields such as compiler construction, automatic testing and debugging tools are well-developed to support developers and provide minimal guarantees on program quality. In this paper, we adapt fuzz testing and delta debugging techniques and specialize them for gate-level netlists commonly used in logic synthesis. Our toolkit improves over similar tools specialized for the AIGER format by supporting other gate-level netlist formats and by allowing a tight integration to provide 10x speed-up. Experimental results show that our fuzzer captures defects in mockturtle, ABC, and LSOracle with 10x smaller testcases and our testcase minimizer extracts minimal failure-inducing cores using 2x fewer oracle calls., Comment: originally accepted at Int'l Workshop on Logic & Synthesis 2022

Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state to prepare has a certain structure that allows for faster preparation. In this paper, we consider quantum states that can be efficiently represented by (reduced) decision diagrams, a versatile data structure for the representation and analysis of Boolean functions. We design an algorithm that utilises the structure of decision diagrams to prepare their associated quantum states. Our algorithm has a circuit complexity that is linear in the number of paths in the decision diagram. Numerical experiments show that our algorithm reduces the circuit complexity by up to 31.85% compared to the state-of-the-art algorithm, when preparing generic $n$-qubit states with different degrees of non-zero amplitudes. Additionally, for states with sparse decision diagrams, including the initial state of the quantum Byzantine agreement protocol, our algorithm reduces the number of CNOTs by 86.61% $\sim$ 99.9%., Comment: 9 pages, 6 figures; close to the published version

We present a new algorithm for the computation of the inverse Abel transform, a problem which emerges in many areas of physics and engineering. We prove that the Legendre coefficients of a given function coincide with the Fourier coefficients of a suitable periodic function associated with its Abel transform. This allows us to compute the Legendre coefficients of the inverse Abel transform in an easy, fast and accurate way by means of a single Fast Fourier Transform. The algorithm is thus appropriate also for the inversion of Abel integrals given in terms of samples representing noisy measurements. Rigorous stability estimates are proved and the accuracy of the algorithm is illustrated also by some numerical experiments., Comment: 19 pages, 4 figures

In a 1D Bose gas, there is no non-trivial scattering channel involving three Bogoliubov quasiparticles that conserves both energy and momentum. Nevertheless, we show that such 3-wave mixing processes (Beliaev and Landau damping) account for their decay via interactions with thermal fluctuations. Within an appropriate time window where the Fermi Golden Rule is expected to apply, the occupation number of the initially occupied mode decays exponentially and the rate takes a simple analytic form. The result is shown to compare favorably with simulations based on the Truncated Wigner Approximation. It is also shown that the same processes slow down the exponential growth of phonons induced by a parametric oscillation., Comment: 12 pages, 6 figures; Appendices: 16 pages, 8 figures; Version accepted for publication in Physical Review B

Brain-Computer Interfaces (BCIs) based on Steady State Visually Evoked Potentials (SSVEPs) have proven effective and provide significant accuracy and information-transfer rates. This family of strategies, however, requires external devices that provide the frequency stimuli required by the technique. This limits the scenarios in which they can be applied, especially when compared to other BCI approaches. In this work, we have investigated the possibility of obtaining frequency responses in the EEG output based on the pure visual imagination of SSVEP-eliciting stimuli. Our results show that not only that EEG signals present frequency-specific peaks related to the frequency the user is focusing on, but also that promising classification accuracy can be achieved, paving the way for a robust and reliable visual imagery BCI modality.

Recent years witnessed a remarkable increase in the availability of data and computing resources in communication networks. This contributed to the rise of data-driven over model-driven algorithms for network automation. This paper investigates a Minimization of Drive Tests (MDT)-driven Deep Reinforcement Learning (DRL) algorithm to optimize coverage and capacity by tuning antennas tilts on a cluster of cells from TIM's cellular network. We jointly utilize MDT data, electromagnetic simulations, and network Key Performance indicators (KPIs) to define a simulated network environment for the training of a Deep Q-Network (DQN) agent. Some tweaks have been introduced to the classical DQN formulation to improve the agent's sample efficiency, stability, and performance. In particular, a custom exploration policy is designed to introduce soft constraints at training time. Results show that the proposed algorithm outperforms baseline approaches like DQN and best-fist search in terms of long-term reward and sample efficiency. Our results indicate that MDT-driven approaches constitute a valuable tool for autonomous coverage and capacity optimization of mobile radio networks., Comment: 15 pages, 17 figures

Reinforcement learning competitions advance the field by providing appropriate scope and support to develop solutions toward a specific problem. To promote the development of more broadly applicable methods, organizers need to enforce the use of general techniques, the use of sample-efficient methods, and the reproducibility of the results. While beneficial for the research community, these restrictions come at a cost -- increased difficulty. If the barrier for entry is too high, many potential participants are demoralized. With this in mind, we hosted the third edition of the MineRL ObtainDiamond competition, MineRL Diamond 2021, with a separate track in which we permitted any solution to promote the participation of newcomers. With this track and more extensive tutorials and support, we saw an increased number of submissions. The participants of this easier track were able to obtain a diamond, and the participants of the harder track progressed the generalizable solutions in the same task., Comment: Under review for PMLR volume on NeurIPS 2021 competitions

The local to global principle for densities is a very convenient tool proposed by Poonen and Stoll to compute the density of a given subset of the integers. In this paper we provide an effective criterion to find all higher moments of the density (e.g. the mean, the variance) of a subset of a finite dimensional free module over the ring of algebraic integers of a number field. More precisely, we provide a local to global principle that allows the computation of all higher moments corresponding to the density, over a general number field $K$. This work advances the understanding of local to global principles for density computations in two ways: on one hand, it extends a result of Bright, Browning and Loughran, where they provide the local to global principle for densities over number fields; on the other hand, it extends the recent result on a local to global principle for expected values over the integers to both the ring of algebraic integers and to moments higher than the expected value. To show how effective and applicable our method is, we compute the density, mean and variance of Eisenstein polynomials and shifted Eisenstein polynomials over number fields. This extends (and fully covers) results in the literature that were obtained with ad-hoc methods., Comment: 21 pages. Comments welcome!

In quantum information theory, quantum discord has been proposed as a tool to characterise the presence of "quantum correlations" between the subparts of a given system. Whether a system behaves quantum-mechanically or classically is believed to be impacted by the phenomenon of decoherence, which originates from the unavoidable interaction between this system and an environment. Generically, decoherence is associated with a decrease of the state purity, i.e. a transition from a pure to a mixed state. In this paper, we investigate how quantum discord is modified by this quantum-to-classical transition. This study is carried out on systems described by quadratic Hamiltonians and Gaussian states, with generalised squeezing parameters. A generic parametrisation is also introduced to describe the way the system is partitioned into two subsystems. We find that the evolution of quantum discord in presence of an environment is a competition between the growth of the squeezing amplitude and the decrease of the state purity. In phase space, this corresponds to whether the semi-minor axis of the Wigner ellipse increases or decreases, which has a clear geometrical interpretation. Finally, these considerations are applied to primordial cosmological perturbations, thus allowing us to investigate how large-scale structures in our universe, which are believed to arise from quantum fluctuations, can exhibit classical properties., Comment: 35 pages without appendices (total 57 pages), 10 figures, typo corrected in the labels of figure 3

We study a multi-player stochastic differential game, where agents interact through their joint price impact on an asset that they trade to exploit a common trading signal. In this context, we prove that a closed-loop Nash equilibrium exists if the price impact parameter is small enough. Compared to the corresponding open-loop Nash equilibrium, both the agents' optimal trading rates and their performance move towards the central-planner solution, in that excessive trading due to lack of coordination is reduced. However, the size of this effect is modest for plausible parameter values., Comment: 41 pages, 5 figures, supplementary appendix

Asteroid pairs are genetically related asteroids that recently separated ($<$few million years), but still reside on similar heliocentric orbits. A few hundred of these systems have been identified, primarily in the asteroid main-belt. Here we studied a newly discovered pair of near-Earth objects (NEOs): 2019 PR2 and 2019 QR6. Based on broad-band photometry, we found these asteroids to be spectrally similar to D-types, a type rare amongst NEOs. We recovered astrometric observations for both asteroids from the Catalina Sky Survey from 2005, which significantly improved their fitted orbits. With these refinements we ran backwards orbital integrations to study formation and evolutionary history. We found that neither a pure gravitational model nor a model with the Yarkovsky effect could explain their current orbits. We thus implemented two models of comet-like non-gravitational forces based on water or CO sublimation. The first model assumed quasi-continuous, comet-like activity after separation, which suggested a formation time of the asteroid pair $300^{+120}_{-70}$ years ago. The second model assumed short-term activity for up to one heliocentric orbit ($\sim$13.9 years) after separation, which suggested that the pair formed 272$\pm$7 years ago. Image stacks showed no activity for 2019~PR2 during its last perihelion passage. These results strongly argue for a common origin that makes these objects the youngest asteroid pair known to date. Questions remain regarding whether these objects derived from a parent comet or asteroid, and how activity may have evolved since their separation.

Dynamic temporal graphs represent evolving relations between entities, e.g. interactions between social network users or infection spreading. We propose an extension of graph echo state networks for the efficient processing of dynamic temporal graphs, with a sufficient condition for their echo state property, and an experimental analysis of reservoir layout impact. Compared to temporal graph kernels that need to hold the entire history of vertex interactions, our model provides a vector encoding for the dynamic graph that is updated at each time-step without requiring training. Experiments show accuracy comparable to approximate temporal graph kernels on twelve dissemination process classification tasks., Comment: Accepted for oral presentation at ESANN 2021

The adiabatic quantum-flux parametron (AQFP) is a promising energy-efficient superconducting technology. Before technology mapping, additional buffer and splitter cells need to be inserted into AQFP circuits to fulfill two special constraints: (1) Input signals to a logic gate need to arrive at the same time, thus shorter paths need to be delayed with buffers. (2) The output signal of a logic gate has to be actively branched with splitters if it drives multiple fanouts. Buffers and splitters largely increase the area and delay in AQFP circuits. Na\"ive buffer and splitter insertion and light-weight optimization using retiming techniques have been used in related works, and it is not clear how much space there is for further optimization. In this paper, we develop (a) a linear-time algorithm to insert buffers and splitters irredundantly, and (b) optimization methods by scheduling and by moving groups of gates, called chunks, together. Experimental results show a reduction of up to 39% on buffer and splitter cost. Moreover, as the technology is still developing and assumptions on the physical constraints are not clear yet, we also discuss the impacts of different assumptions with experimental results to motivate future research on AQFP register design., Comment: originally accepted at Int'l Workshop on Logic & Synthesis 2021