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We investigate connected posets $C$ of height one as retracts of finite posets $P$. We define two multigraphs: a multigraph $\mathfrak{F}(P)$ reflecting the network of so-called improper 4-crown bundles contained in the extremal points of $P$, and a multigraph $\mathfrak{C}(C)$ depending on $C$ but not on $P$. There exists a close interdependence between $C$ being a retract of $P$ and the existence of a graph homomorphism of a certain type from $\mathfrak{F}(P)$ to $\mathfrak{C}(C)$. In particular, if $C$ is an ordinal sum of two antichains, then $C$ is a retract of $P$ iff such a graph homomorphism exists. Returning to general connected posets $C$ of height one, we show that the image of such a graph homomorphism can be a clique in $\mathfrak{C}(C)$ iff the improper 4-crowns in $P$ contain only a sparse subset of the edges of $C$., Comment: 16 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:2111.09588

As the signatories of this manifesto, we denounce the attention economy as inhumane and a threat to our sociopolitical and ecological well-being. We endorse policymakers' efforts to address the negative consequences of the attention economy's technology, but add that these approaches are often limited in their criticism of the systemic context of human attention. Starting from Buddhist philosophy, we advocate a broader approach: an ecology of attending, that centers on conceptualizing, designing, and using attention (1) in an embedded way and (2) focused on the alleviating of suffering. With 'embedded' we mean that attention is not a neutral, isolated mechanism but a meaning-engendering part of an 'ecology' of bodily, sociotechnical and moral frameworks. With 'focused on the alleviation of suffering' we explicitly move away from the (often implicit) conception of attention as a tool for gratifying desires., Comment: 21 pages, 1 figure

We introduce a spatial form factor (SFF) for the characterization of spatial patterns associated with point processes. Specifically, the SFF is defined in terms of the averaged even Fourier transform of the distance between any pair of points. We focus on homogeneous Poisson point processes and derive the explicit expression for the SFF in $d$-spatial dimensions. The SFF can then be found in terms of the even Fourier transform of the probability distribution for the distance between two independent and uniformly distributed random points on a $d$-dimensional ball, arising in the ball line picking problem. The relation between the SFF and the set of $n$-order spacing distributions is further established. The SFF is analyzed in detail for $d=1,2,3$ and in the infinite-dimensional case, as well as for the $d$-dimensional Coulomb gas, as an interacting point process. We also introduce a generalization of the SFF applicable to arbitrary sets in a metric space., Comment: 15 pages, 6 figures

We investigate the efficiency of approximate counterdiabatic driving (CD) in accelerating adiabatic passage through a first-order quantum phase transition. Specifically, we analyze a minimal spin-glass bottleneck model that is analytically tractable and exhibits both an exponentially small gap at the transition point and a change in the ground state that involves a macroscopic rearrangement of spins. Using the variational Floquet-Krylov expansion to construct CD terms, we find that while the formation of excitations is significantly suppressed, achieving fully adiabatic evolution remains challenging, necessitating high-order nonlocal terms in the expansion. Our results demonstrate that local CD strategies have limited effectiveness when crossing the extremely small gaps characteristic of NP-hard Ising problems. To address this limitation, we propose an alternative method, termed quantum brachistochrone counterdiabatic driving (QBCD), which significantly increases the fidelity to the target state over the expansion method by directly addressing the gap-closing point and the associated edge states.

We introduce a quantum algorithm integrating counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to tackle combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces the dependence on extensive higher-order CD terms and classical optimization techniques, rendering it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum computing.

The present work aims to measure speeds of sound $c$ in a biogas mixture of $CH_{4}$ + $N_{2}$ + $CO_{2}$ + $CO$, at $p$ = (1-12) MPa and $T$ = (273, 300 and 325) K, using a spherical acoustical resonator. The results are fitted to the virial acoustic equation of state, and the virial acoustic coefficients are obtained, $\beta_{a}$ and $\gamma_{a}$ and extrapolated to zero pressure, determining the adiabatic coefficient as perfect gas, $\gamma^{pg}$, and the isobaric and isochoric heat capacities as perfect gas, $C_{p}^{pg}$ and $C_{V}^{pg}$, respectively. The speeds of sound are acquired with a mean expanded relative uncertainty of 165 parts in $10^{6}$ ($k$ = 2) and are compared with the results predicted by the reference equation of state for this kind of mixture (natural gas-like mixtures), EoS GERG-2008. Relative deviations between experimental data and values estimated by this model were less than 700 parts in $10^{6}$ at $T$ = 325 K, and below 400 parts in $10^{6}$, and within measurement uncertainty of at $T$ = 300 K, although appreciably higher at isotherm $T$ = 273 K at the highest pressure data for this work, and even reaching values above 3 400 parts in $10^{6}$.

A new determination of the molar gas constant was performed from measurements of the speed of sound in argon at the triple point of water and extrapolation to zero pressure. A new resonant cavity was used. This is a triaxial ellipsoid whose walls are gold-coated steel and which is divided into two identical halves that are bolted and sealed with an O-ring. Microwave and electroacoustic traducers are located in the northern and southern parts of the cavity, respectively, so that measurements of microwave and acoustic frequencies are carried out in the same experiment. Measurements were taken at pressures from 600 kPa to 60 kPa and at 273.16 K. The internal equivalent radius of the cavity was accurately determined by microwave measurements and the first four radial symmetric acoustic modes were simultaneously measured and used to calculate the speed of sound. The improvements made using the new cavity have reduced by half the main contributions to the uncertainty due to the radius determination using microwave measurements which amounts to 4.7 parts in $10^{6}$ and the acoustic measurements, 4.4 parts in $10^{6}$, where the main contribution (3.7 parts in $10^{6}$) is the relative excess half-widths associated with the limit of our acoustic model, compared with our previous measurements. As a result of all the improvements with the new cavity and the measurements performed, we determined the molar gas constant $R$ = (8.314 449 $\pm$ 0.000 056) J/(K mol) which corresponds to a relative standard uncertainty of 6.7 parts in $10^{6}$. The value reported in this paper lies -1.3 parts in $10^{6}$ below the recommended value of CODATA 2014, although still within the range consistent with it.

We settle the problem of K-stability of quasi-smooth Fano 3-fold hypersurfaces with Fano index 1 by providing lower bounds for their delta invariants. We use the method introduced by Abban and Zhuang for computing lower bounds of delta invariants on flags of hypersurfaces in the Fano 3-fold., Comment: 102 pages

The development of a novel technique based on a cylindrical microwave resonator for high pressure phase equilibrium determination is described. Electric permittivity or dielectric constant is a physical property that depends on temperature and pressure $\epsilon$($p$,$T$). Based on this property, a measuring technique consisting of a cylindrical resonant cavity that works in the microwave spectrum has been developed. Equilibrium data of fluid mixtures are measured at high pressure using a synthetic method, where phase transition is determined under isothermal conditions due to the change of the dielectric constant. This technique may be a more accurate alternative to conventional visual synthetic methods. The technique was validated measuring pure $CO_{2}$, and phase behaviour was then determined for two binary mixtures [$CO_{2}$ (0.6) + $CH_{4}$ (0.4)] and [$CO_{2}$ (0.4) + $CH_{4}$ (0.6)], results for which are presented. These systems are interesting for the study of biogas-like mixtures. In addition, data were compared with the equation of state used for natural gas GERG-2008, and also, they were modelled using Peng-Robinson equation of state and Wong-Sandler mixing rules, which are widely employed in chemical industries and which give good results.

In an era marked by a demographic change towards an older population, there is an urgent need to improve nutritional monitoring in view of the increase in frailty. This research aims to enhance the identification of meal-taking activities by combining K-Means, GMM, and DBSCAN techniques. Using the Davies-Bouldin Index (DBI) for the optimal meal taking activity clustering, the results show that K-Means seems to be the best solution, thanks to its unrivalled efficiency in data demarcation, compared with the capabilities of GMM and DBSCAN. Although capable of identifying complex patterns and outliers, the latter methods are limited by their operational complexities and dependence on precise parameter configurations. In this paper, we have processed data from 4 houses equipped with sensors. The findings indicate that applying the K-Means method results in high performance, evidenced by a particularly low Davies-Bouldin Index (DBI), illustrating optimal cluster separation and cohesion. Calculating the average duration of each activity using the GMM algorithm allows distinguishing various categories of meal-taking activities. Alternatively, this can correspond to different times of the day fitting to each meal-taking activity. Using K-Means, GMM, and DBSCAN clustering algorithms, the study demonstrates an effective strategy for thoroughly understanding the data. This approach facilitates the comparison and selection of the most suitable method for optimal meal-taking activity clustering.

Krylov subspace methods in quantum dynamics identify the minimal subspace in which a process unfolds. To date, their use is restricted to time evolutions governed by time-independent generators. We introduce a generalization valid for driven quantum systems governed by a time-dependent Hamiltonian that maps the evolution to a diffusion problem in a one-dimensional lattice with nearest-neighbor hopping probabilities that are inhomogeneous and time-dependent. This representation is used to establish a novel class of fundamental limits to the quantum speed of evolution and operator growth. We also discuss generalizations of the algorithm, adapted to discretized time evolutions and periodic Hamiltonians, with applications to many-body systems., Comment: 6+13 pages, 3 figures

We explore the near adiabatic dynamics in a non-Hermitian quantum many-body system by investigating a finite-time ramp of the imaginary vector potential in the interacting Hatano-Nelson model. The excess energy, the Loschmidt echo, and the density imbalance are analyzed using bosonization and exact diagonalization. The energy becomes complex valued, despite the instantaneous Hamiltonian having the same real spectrum throughout. The adiabatic limit is approached very slowly through damped oscillations. The decay scales with $\tau^{-1}$ with $\tau$ the ramp duration, while the oscillation period is $2L/v$ with $v$ the Fermi velocity and $L$ the system length. Yet, without the need for auxiliary controls, a shortcut to adiabaticity is found for ramp times commensurate with the period. Our work highlights the intricate interplay of adiabaticity and non-Hermitian many-body physics., Comment: 11 pages, 4 figures

We consider the optimal driving of the ground state of a many-body quantum system across a quantum phase transition in finite time. In this context, excitations caused by the breakdown of adiabaticity can be minimized by adjusting the schedule of the control parameter that drives the transition. Drawing inspiration from the Kibble-Zurek mechanism, we characterize the timescale of onset of adiabaticity for several optimal control procedures. Our analysis reveals that schedules relying on local adiabaticity, such as Roland-Cerf's local adiabatic driving and the quantum adiabatic brachistochrone, fail to provide a significant speedup over the adiabatic evolution in the transverse-field Ising and long-range Kitaev models. As an alternative, we introduce a novel framework, Non-Adiabatic Quantum Optimization (NAQO), that, by exploiting the Landau-Zener formula and taking into account the role of higher-excited states, outperforms schedules obtained via both local adiabaticity and state-of-the-art numerical optimization. NAQO is not restricted to exactly solvable models, and we further confirm its superior performance in a disordered non-integrable model., Comment: 24 pages, 15 figures, comments welcome

The spin-vector Monte Carlo model is widely used as a benchmark for the classicality of quantum annealers but severely restricts the time evolution. The spin-vector Langevin (SVL) model has been proposed and tested as an alternative, closely reproducing the real-time dynamics of physical quantum annealers such as D-Wave machines in the dissipative regime. We investigate the SVL annealing dynamics of classical O(2) rotors on regular graphs, identifying universal features in the nonequilibrium dynamics when changing the range of interactions and the topology of the graph. Regular graphs with low connectance or edge density exhibit universal scaling dynamics consistent with the Kibble-Zurek mechanism, which leads to a power-law dependence of the density of defects and the residual energy as a function of the annealing time. As the interaction range is increased, the power-law scaling is suppressed, and an exponential scaling with the annealing time sets in. Our results establish a universal breakdown of the Kibble-Zurek mechanism in classical systems characterized by long-range interactions, in sharp contrast with previous findings in the quantum domain.

We study the quantum dynamics generated by a non-Hermitian Hamiltonian subject to stochastic perturbations in its anti-Hermitian part, describing fluctuating gains and losses. The master equation governing the noise-average dynamics describes a new form of dephasing. We characterize the resulting state evolution and analyze its purity. The novel properties of such dynamics are illustrated in a stochastic dissipative qubit. Our analytical results show that adding noise allows for a rich control of the dynamics, with a greater diversity of steady states and the possibility of state purification., Comment: 4+6 pages, 3 + 4 figures, Comments are welcome!

Short-Term object-interaction Anticipation (STA) consists of detecting the location of the next-active objects, the noun and verb categories of the interaction, and the time to contact from the observation of egocentric video. We propose STAformer, a novel attention-based architecture integrating frame-guided temporal pooling, dual image-video attention, and multi-scale feature fusion to support STA predictions from an image-input video pair. Moreover, we introduce two novel modules to ground STA predictions on human behavior by modeling affordances. First, we integrate an environment affordance model which acts as a persistent memory of interactions that can take place in a given physical scene. Second, we predict interaction hotspots from the observation of hands and object trajectories, increasing confidence in STA predictions localized around the hotspot. On the test set, our results obtain a final 33.5 N mAP, 17.25 N+V mAP, 11.77 N+{\delta} mAP and 6.75 Overall top-5 mAP metric when trained on the v2 training dataset., Comment: arXiv admin note: substantial text overlap with arXiv:2406.01194

General-purpose programmable photonic processors provide a versatile platform for integrating diverse functionalities on a single chip. Leveraging a two-dimensional hexagonal waveguide mesh of Mach-Zehnder interferometers, these systems have demonstrated significant potential in microwave photonics applications. Additionally, they are a promising platform for creating unitary linear transformations, which are key elements in quantum computing and photonic neural networks. However, a general procedure for implementing these transformations on such systems has not been established yet. This work demonstrates the programming of universal unitary transformations on a general-purpose programmable photonic circuit with a hexagonal topology. We detail the steps to split the light on-chip, demonstrate that an equivalent structure to the Mach-Zehnder interferometer with one internal and one external phase shifter can be built in the hexagonal mesh, and program both the triangular and rectangular architectures for matrix multiplication. We recalibrate the system to account for passive phase deviations. Experimental programming of 3x3 and 4x4 random unitary matrices yields fidelities > 98% and bit precisions over 5 bits. To the best of our knowledge, this is the first time that random unitary matrices are demonstrated on a general-purpose photonic processor and pave the way for the implementation of programmable photonic circuits in optical computing and signal processing systems.

Photonic neural networks offer a promising alternative to traditional electronic systems for machine learning accelerators due to their low latency and energy efficiency. However, the challenge of implementing the backpropagation algorithm during training has limited their development. To address this, alternative machine learning schemes, such as extreme learning machines (ELMs), have been proposed. ELMs use a random hidden layer to increase the feature space dimensionality, requiring only the output layer to be trained through linear regression, thus reducing training complexity. Here, we experimentally demonstrate a programmable photonic extreme learning machine (PPELM) using a hexagonal waveguide mesh, and which enables to program directly on chip the input feature vector and the random hidden layer. Our system also permits to apply the nonlinearity directly on-chip by using the systems integrated photodetecting elements. Using the PPELM we solved successfully three different complex classification tasks. Additioanlly, we also propose and demonstrate two techniques to increase the accuracy of the models and reduce their variability using an evolutionary algorithm and a wavelength division multiplexing approach, obtaining excellent performance. Our results show that programmable photonic processors may become a feasible way to train competitive machine learning models on a versatile and compact platform.

Quantum machine learning has gained considerable attention as quantum technology advances, presenting a promising approach for efficiently learning complex data patterns. Despite this promise, most contemporary quantum methods require significant resources for variational parameter optimization and face issues with vanishing gradients, leading to experiments that are either limited in scale or lack potential for quantum advantage. To address this, we develop a general-purpose, gradient-free, and scalable quantum reservoir learning algorithm that harnesses the quantum dynamics of neutral-atom analog quantum computers to process data. We experimentally implement the algorithm, achieving competitive performance across various categories of machine learning tasks, including binary and multi-class classification, as well as timeseries prediction. Effective and improving learning is observed with increasing system sizes of up to 108 qubits, demonstrating the largest quantum machine learning experiment to date. We further observe comparative quantum kernel advantage in learning tasks by constructing synthetic datasets based on the geometric differences between generated quantum and classical data kernels. Our findings demonstrate the potential of utilizing classically intractable quantum correlations for effective machine learning. We expect these results to stimulate further extensions to different quantum hardware and machine learning paradigms, including early fault-tolerant hardware and generative machine learning tasks., Comment: 10 + 14 pages, 4 + 7 figures

Smart home automation systems aim to improve the comfort and convenience of users in their living environment. However, adapting automation to user needs remains a challenge. Indeed, many systems still rely on hand-crafted routines for each smart object.This paper presents an original smart home architecture leveraging Large Language Models (LLMs) and user preferences to push the boundaries of personalisation and intuitiveness in the home environment.This article explores a human-centred approach that uses the general knowledge provided by LLMs to learn and facilitate interactions with the environment.The advantages of the proposed model are demonstrated on a set of scenarios, as well as a comparative analysis with various LLM implementations. Some metrics are assessed to determine the system's ability to maintain comfort, safety, and user preferences. The paper details the approach to real-world implementation and evaluation.The proposed approach of using preferences shows up to 52.3% increase in average grade, and with an average processing time reduced by 35.6% on Starling 7B Alpha LLM. In addition, performance is 26.4% better than the results of the larger models without preferences, with processing time almost 20 times faster.

Recent advancements in robotics, including applications like self-driving cars, unmanned systems, and medical robots, have had a significant impact on the job market. On one hand, big robotics companies offer training programs based on the job requirements. However, these training programs may not be as beneficial as general robotics programs offered by universities or community colleges. On the other hand, community colleges and universities face challenges with required resources, especially qualified instructors, to offer students advanced robotics education. Furthermore, the diverse backgrounds of undergraduate students present additional challenges. Some students bring extensive industry experiences, while others are newcomers to the field. To address these challenges, we propose a student-centered personalized learning framework for robotics. This framework allows a general instructor to teach undergraduate-level robotics courses by breaking down course topics into smaller components with well-defined topic dependencies, structured as a graph. This modular approach enables students to choose their learning path, catering to their unique preferences and pace. Moreover, our framework's flexibility allows for easy customization of teaching materials to meet the specific needs of host institutions. In addition to teaching materials, a frequently-asked-questions document would be prepared for a general instructor. If students' robotics questions cannot be answered by the instructor, the answers to these questions may be included in this document. For questions not covered in this document, we can gather and address them through collaboration with the robotics community and course content creators. Our user study results demonstrate the promise of this method in delivering undergraduate-level robotics education tailored to individual learning outcomes and preferences., Comment: 11 pages, 3 figures, 1 table, 2024 ASEE Conference

Using holography, we study the universal scaling laws governing the coarsening dynamics of strongly coupled domain walls. Specifically, we studied the universal dependence of the length of the domain wall interfaces on the quench rate. The relation satisfies the Kibble-Zurek scaling shortly after the critical point. However, as time goes by, the coarsening dynamics suppresses the Kibble-Zurek scaling in favor of a universal dynamical scaling of the characteristic length and the adiabatic growth of the system. Theoretical predictions of the universal scaling laws are consistent with numerical findings in both regimes for both weak and strongly coupled systems., Comment: 9 pages, 9 figures

The superfluid phase transition dynamics and associated spontaneous vortex formation with the crossing of the critical temperature in a disk geometry is studied in the framework of the $AdS/CFT$ correspondence by solving the Einstein-Abelian-Higgs model in an $AdS_4$ black hole. For a slow quench, the vortex density admits a universal scaling law with the cooling rate as predicted by the Kibble-Zurek mechanism (KZM), while for fast quenches, the density shows a universal scaling behavior as a function of the final temperature, that lies beyond the KZM prediction. The vortex number distribution in both the power-law and saturation regimes can be approximated by a normal distribution. However, the study of the universal scaling of the cumulants reveals non-normal features and indicates that vortex statistics in the newborn superfluid is best described by the Poisson binomial distribution, previously predicted in the KZM regime [Phys. Rev. Lett. 124, 240602 (2020)]. This is confirmed by studying the cumulant scalings as a function of the quench time and the quench depth. Our work supports the existence of a universal defect number distribution that accommodates the KZM scaling, its breakdown at fast quenches, and the additional universal scaling laws as a function of the final value of the control parameter., Comment: 13 pages, 7 figures

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