Search

We consider the problem of online multi-agent Nash social welfare (NSW) maximization. While previous works of Hossain et al. [2021], Jones et al. [2023] study similar problems in stochastic multi-agent multi-armed bandits and show that $\sqrt{T}$-regret is possible after $T$ rounds, their fairness measure is the product of all agents' rewards, instead of their NSW (that is, their geometric mean). Given the fundamental role of NSW in the fairness literature, it is more than natural to ask whether no-regret fair learning with NSW as the objective is possible. In this work, we provide a complete answer to this question in various settings. Specifically, in stochastic $N$-agent $K$-armed bandits, we develop an algorithm with $\widetilde{\mathcal{O}}\left(K^{\frac{2}{N}}T^{\frac{N-1}{N}}\right)$ regret and prove that the dependence on $T$ is tight, making it a sharp contrast to the $\sqrt{T}$-regret bounds of Hossain et al. [2021], Jones et al. [2023]. We then consider a more challenging version of the problem with adversarial rewards. Somewhat surprisingly, despite NSW being a concave function, we prove that no algorithm can achieve sublinear regret. To circumvent such negative results, we further consider a setting with full-information feedback and design two algorithms with $\sqrt{T}$-regret: the first one has no dependence on $N$ at all and is applicable to not just NSW but a broad class of welfare functions, while the second one has better dependence on $K$ and is preferable when $N$ is small. Finally, we also show that logarithmic regret is possible whenever there exists one agent who is indifferent about different arms.

Morphological mapping is a fundamental step in studying the processes that shaped an asteroid surface. Yet, it is challenging and often requires multiple independent assessments by trained experts. Here, we present fast methods to detect and characterize meaningful terrains from the topographic roughness: entropy of information, and local mean surface orientation. We apply our techniques to Didymos and Dimorphos, the target asteroids of NASA's DART mission: first attempt to deflect an asteroid. Our methods reliably identify morphological units at multiple scales. The comparative study reveals various terrain types, signatures of processes that transformed Didymos and Dimorphos. Didymos shows the most heterogeneity and morphology that indicate recent resurfacing events. Dimorphos is comparatively rougher than Didymos, which may result from the formation process of the binary pair and past interaction between the two bodies. Our methods can be readily applied to other bodies and data sets., Comment: submitted to PSJ

We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erd\H{o}s-R\'enyi network. This is achieved by studying local spectral measures such as the level spacing and the level velocity statistics. A spectral form factor analysis is also performed as a global measure, probing energy level correlations at arbitrary spectral distances. Our findings show that these measures capture the breakdown of chaotic behavior upon varying the connectivity and strength of the transverse field in various regimes. We demonstrate that the level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks. The velocity statistics capture the surviving chaotic signatures in the sparse limit. However, these integrable-like regimes extend over a vanishingly small segment in the full range of connectivity.

Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. We use this insight to develop its geometrical description. In particular, we identify mutually orthogonal coherent and incoherent directions and give their physical interpretation. This understanding allows us to optimize the success rate for implementing non-Hermitian driving along prescribed trajectories. We show its significance for shortcuts to adiabaticity. We introduce the geometrical interpretation of a speed limit for non-Hermitian Hamiltonians and analyze its tightness. We derive the explicit expression that saturates such a speed limit and illustrate our results on a minimal example of a dissipative qubit.

The dynamics of quantum systems unfolds within a subspace of the state space or operator space, known as the Krylov space. This review presents the use of Krylov subspace methods to provide a compact and computationally efficient description of quantum evolution, with emphasis on nonequilibrium phenomena of many-body systems with a large Hilbert space. It provides a comprehensive update of recent developments, focused on the quantum evolution of operators in the Heisenberg picture as well as pure and mixed states. It further explores the notion of Krylov complexity and associated metrics as tools for quantifying operator growth, their bounds by generalized quantum speed limits, the universal operator growth hypothesis, and its relation to quantum chaos, scrambling, and generalized coherent states. A comparison of several generalizations of the Krylov construction for open quantum systems is presented. A closing discussion addresses the application of Krylov subspace methods in quantum field theory, holography, integrability, quantum control, and quantum computing, as well as current open problems., Comment: v2: 65 pages, 28 figures, Sec.IX.E. added, texts expanded, plots updated, references added

Shortcuts to adiabaticity (STA) make the fast preparation of many-body states possible, circumventing the limitations of adiabatic strategies. We propose a fast STA protocol for generating interacting states in the Tomonaga-Luttinger liquid by counter-diabatic driving, stirring the dynamics with an auxiliary control field. To this end, we exploit the equivalence between the time-dependent Tomonaga-Luttinger liquid and an ensemble of quantum oscillators with driven mass and frequency. We specify the closed-form expression of the counterdiabatic control and demonstrate its efficiency in suppressing excitations., Comment: 5+7, 1 figure

The brain is hierarchically organized to process sensory signals. But, to what extent do functional connections within and across areas shape this hierarchical order? We addressed this problem in the thalamocortical network, while monkeys judged the presence or absence of a vibrotactile stimulus. We quantified the variability by means of intrinsic timescales and Fano factor, and functional connectivity by means of a directionality measure in simultaneously recorded neurons sharing the same cutaneous receptive field from the somatosensory thalamus (VPL) and areas 3b and 1 from the somatosensory cortex. During the pre-stimulus periods, VPL and area 3b exhibited similarly fast dynamics while area 1 showed much slower timescales. Furthermore, during the stimulus presence, the Fano factor increased along the network VPL-3b-1. In parallel, VPL established two separate main feedforward pathways with areas 3b and 1 to process stimulus information. While feedforward interactions from VPL and area 3b were favored by neurons within specific Fano factor ranges, neural variability in area 1 was invariant to the incoming pathways. In contrast to VPL and area 3b, during the stimulus arrival, area 1 showed significant intra-area interactions, which mainly pointed to neurons with slow intrinsic timescales. Overall, our results suggest that the lower variability of VPL and area 3b regulates feedforward thalamocortical communication, while the higher variability of area 1 supports intra-cortical interactions during sensory processing. These results provide evidence of a hierarchical order along the thalamocortical network., Comment: 6 Main Figures, 6 Supplementary Figures

Within the framework of natural orbital functional theory, having a convenient representation of the occupation numbers and orbitals becomes critical for the computational performance of the calculations. Recognizing this, we propose an innovative parametrization of the occupation numbers that takes advantage of the electron-pairing approach used in Piris natural orbital functionals through the adoption of the softmax function, a pivotal component in modern deep-learning models. Our approach not only ensures adherence to the N-representability of the first-order reduced density matrix (1RDM) but also significantly enhances the computational efficiency of 1RDM functional theory calculations. The effectiveness of this alternative parameterization approach was assessed using the W4-17-MR molecular set, which demonstrated faster and more robust convergence compared to previous implementations., Comment: 13 pages, 6 Figures