Search

In stochastic systems, risk-sensitive control balances performance with resilience to less likely events. Although existing methods rely on finite-horizon risk criteria, this paper introduces \textit{limiting-risk criteria} that capture long-term cumulative risks through probabilistic limiting theorems. Extending the Linear Quadratic Regulation (LQR) framework, we incorporate constraints on these limiting-risk criteria derived from the asymptotic behavior of cumulative costs, accounting for extreme deviations. Using tailored Functional Central Limit Theorems (FCLT), we demonstrate that the time-correlated terms in the limiting-risk criteria converge under strong ergodicity, and establish conditions for convergence in non-stationary settings while characterizing the distribution and providing explicit formulations for the limiting variance of the risk functional. The FCLT is developed by applying ergodic theory for Markov chains and obtaining \textit{uniform ergodicity} of the controlled process. For quadratic risk functionals on linear dynamics, in addition to internal stability, the uniform ergodicity requires the (possibly heavy-tailed) dynamic noise to have a finite fourth moment. This offers a clear path to quantifying long-term uncertainty. We also propose a primal-dual constrained policy optimization method that optimizes the average performance while ensuring limiting-risk constraints are satisfied. Our framework offers a practical, theoretically guaranteed approach for long-term risk-sensitive control, backed by convergence guarantees and validations through simulations.

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

Web-based Large Language Model (LLM) services have been widely adopted and have become an integral part of our Internet experience. Third-party plugins enhance the functionalities of LLM by enabling access to real-world data and services. However, the privacy consequences associated with these services and their third-party plugins are not well understood. Sensitive prompt data are stored, processed, and shared by cloud-based LLM providers and third-party plugins. In this paper, we propose Casper, a prompt sanitization technique that aims to protect user privacy by detecting and removing sensitive information from user inputs before sending them to LLM services. Casper runs entirely on the user's device as a browser extension and does not require any changes to the online LLM services. At the core of Casper is a three-layered sanitization mechanism consisting of a rule-based filter, a Machine Learning (ML)-based named entity recognizer, and a browser-based local LLM topic identifier. We evaluate Casper on a dataset of 4000 synthesized prompts and show that it can effectively filter out Personal Identifiable Information (PII) and privacy-sensitive topics with high accuracy, at 98.5% and 89.9%, respectively.

We study opinion dynamics over a directed multilayer network. In particular, we consider networks in which the impact of neighbors of agents on their opinions is proportional to their in-degree. Agents update their opinions over time to coordinate with their neighbors. However, the frequency of agents' interactions with neighbors in different network layers differs. Consequently, the multilayer network's adjacency matrices are time-varying. We aim to characterize how the frequency of activation of different layers impacts the convergence of the opinion dynamics process.

Discrete choice models (DCMs) have been widely utilized in various scientific fields, especially economics, for many years. These models consider a stochastic environment influencing each decision maker's choices. Extensive research has shown that the agents' socioeconomic characteristics, the chosen options' properties, and the conditions characterizing the decision-making environment all impact these models. However, the complex interactions between these factors, confidentiality concerns, time constraints, and costs, have made real experimentation impractical and undesirable. To address this, simulations have gained significant popularity among academics, allowing the study of these models in a controlled setting using simulated data. This paper presents multidisciplinary research to bridge the gap between DCMs, experimental design, and simulation. By reviewing related literature, the authors explore these interconnected areas. We then introduce a simulation method integrated with experimental design to generate synthetic data based on behavioral models of agents. A utility function is used to describe the developed simulation tool. The paper investigates the discrepancy between simulated data and real-world data.

We consider the situation when a learner faces a set of unknown discrete distributions $(p_k)_{k\in \mathcal K}$ defined over a common alphabet $\mathcal X$, and can build for each distribution $p_k$ an individual high-probability confidence set thanks to $n_k$ observations sampled from $p_k$. The set $(p_k)_{k\in \mathcal K}$ is structured: each distribution $p_k$ is obtained from the same common, but unknown, distribution q via applying an unknown permutation to $\mathcal X$. We call this \emph{permutation-equivalence}. The goal is to build refined confidence sets \emph{exploiting} this structural property. Like other popular notions of structure (Lipschitz smoothness, Linearity, etc.) permutation-equivalence naturally appears in machine learning problems, and to benefit from its potential gain calls for a specific approach. We present a strategy to effectively exploit permutation-equivalence, and provide a finite-time high-probability bound on the size of the refined confidence sets output by the strategy. Since a refinement is not possible for too few observations in general, under mild technical assumptions, our finite-time analysis establish when the number of observations $(n_k)_{k\in \mathcal K}$ are large enough so that the output confidence sets improve over initial individual sets. We carefully characterize this event and the corresponding improvement. Further, our result implies that the size of confidence sets shrink at asymptotic rates of $O(1/\sqrt{\sum_{k\in \mathcal K} n_k})$ and $O(1/\max_{k\in K} n_{k})$, respectively for elements inside and outside the support of q, when the size of each individual confidence set shrinks at respective rates of $O(1/\sqrt{n_k})$ and $O(1/n_k)$. We illustrate the practical benefit of exploiting permutation equivalence on a reinforcement learning task.

3D printing is considered the future of production systems and one of the physical elements of the Fourth Industrial Revolution. 3D printing will significantly impact the product lifecycle, considering cost, energy consumption, and carbon dioxide emissions, leading to the creation of sustainable production systems. Given the importance of these production systems and their effects on the quality of life for future generations, it is expected that 3D printing will soon become one of the global industry's fundamental needs. Although three decades have passed since the emergence of 3D printers, there has not yet been much research on production planning and mass production using these devices. Therefore, we aimed to identify the existing gaps in the planning of 3D printers and to propose a model for planning and scheduling these devices. In this research, several parts with different heights, areas, and volumes have been considered for allocation on identical 3D printers for various tasks. To solve this problem, a multi-objective mixed integer linear programming model has been proposed to minimize the earliness and tardiness of parts production, considering their order delivery times, and maximizing machine utilization. Additionally, a method has been proposed for the placement of parts in 3D printers, leading to the selection of the best edge as the height. Using a numerical example, we have plotted the Pareto curve obtained from solving the model using the epsilon constraint method for several parts and analyzed the impact of the method for selecting the best edge as the height, with and without considering it. Additionally, a comprehensive sensitivity and scenario analysis has been conducted to validate the results.

In this article we show that a large class of infinite measure preserving dynamical systems that do not admit physical measures nevertheless exhibit strong statistical properties. In particular, we give sufficient conditions for existence of a distinguished natural measure $\nu$ such that the pushforwards of any absolutely continuous probability measure converge to $\nu$. Moreover, we obtain a distributional limit law for empirical measures. We also extend existing results on the characterisation of the set of almost sure limit points for empirical measures. Our results apply to various intermittent maps with multiple neutral fixed points preserving an infinite $\sigma$-finite absolutely continuous measure.

This study sequentially investigates the enhancement of fracture behavior in adhesive joints. Initially, mechanical sanding techniques were explored, revealing significant improvements of 55% in fracture energy and 38% in load-bearing capacity with optimal 240-grit sanding. Subsequently, in a second stage, Multi-Walled Carbon Nanotubes (MWCNTs) were introduced at varying weight percentages (0.1%, 0.3%, and 0.5% by weight) into the adhesive joints. This combined approach aimed to synergistically examine the impact of surface pretreatments and nanoparticle integration on fracture behavior. Results highlight the potential for fracture resistance and enhanced load-carrying capabilities in reinforced specimens, with maximum load and fracture energy improvements of up to 92 % and 50 %, respectively, compared to unreinforced specimens and those subjected solely to sanding treatments. Furthermore, the fracture mode shifted from adhesive failure to cohesive substrate failure in reinforced specimens. This comprehensive investigation underscores the intricate interplay between mechanical preparation and nanomaterial incorporation in significantly improving adhesive joint performance

This survey explores the geometric perspective on policy optimization within the realm of feedback control systems, emphasizing the intrinsic relationship between control design and optimization. By adopting a geometric viewpoint, we aim to provide a nuanced understanding of how various ``complete parameterization'' -- referring to the policy parameters together with its Riemannian geometry -- of control design problems, influence stability and performance of local search algorithms. The paper is structured to address key themes such as policy parameterization, the topology and geometry of stabilizing policies, and their implications for various (non-convex) dynamic performance measures. We focus on a few iconic control design problems, including the Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) control, and $\mathcal{H}_\infty$ control. In particular, we first discuss the topology and Riemannian geometry of stabilizing policies, distinguishing between their static and dynamic realizations. Expanding on this geometric perspective, we then explore structural properties of the aforementioned performance measures and their interplay with the geometry of stabilizing policies in presence of policy constraints; along the way, we address issues such as spurious stationary points, symmetries of dynamic feedback policies, and (non-)smoothness of the corresponding performance measures. We conclude the survey with algorithmic implications of policy optimization in feedback design.

The formation of dark states is an important concept in quantum sciences, but its compatibility with strong interparticle interactions, for example, in a quantum degenerate gas is hardly explored. Here, we realize a dark state in one of the spins of a two-component, resonantly-interacting Fermi gas using a $\Lambda$ system within the $D_2$ transitions of $^6$Li at high magnetic field. The dark state is created in a micrometer-sized region within a one-dimensional channel connecting two superfluid reservoirs. The particle transport between the reservoirs is used as a probe. We observe that atoms are transported in the dark state and the superfluid-assisted fast current is preserved. If the dark state resonant condition is not met, the transport is suppressed by the spontaneous emission. We also uncover an asymmetry in the transport timescale across the two-photon resonance, which is absent in the non-interacting regime. This work raises questions on the interplay of dark states with interparticle interactions and opens up perspectives for optical manipulation of fermionic pairing., Comment: 18 pages, 10 figures

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the observer, embeds the data into low dimensions and learns the low-dimensional model parameters. Our algorithm enjoys a sample complexity guarantee of order $\tilde{\mathcal{O}}(n/\epsilon^2)$, where $n$ is the observation dimension. We further establish a fundamental lower bound indicating this complexity bound is optimal up to logarithmic factors and dimension-independent constants. We show that this inevitable linear factor of $n$ is due to the learning error of the observer's column space in the presence of high-dimensional noises. Extending our results, we consider a meta-learning problem inspired by various real-world applications, where the observer column space can be collectively learned from datasets of multiple LTI systems. An end-to-end algorithm is then proposed, facilitating learning LTI systems from a meta-dataset which breaks the sample complexity lower bound in certain scenarios.

Lead halide perovskites have emerged as platforms for exciton-polaritonic studies at room temperature thanks to their excellent photoluminescence efficiency and synthetic versatility. In this work we find proof of strong exciton-photon coupling in cavities formed by the layered crystals themselves, a phenomenon known as self-hybridization effect. We use multi-layers of high quality Ruddlesden-Popper perovskites in their 2D crystalline form, benefitting from their quantum-well excitonic resonances and the strong Fabry-Perot cavity modes resulting from the total-internal-reflection at their smooth surfaces. Optical spectroscopy reveals bending of the cavity modes typical for exciton-polariton formation, and photoluminescence spectroscopy shows thickness dependent splitting of the excitonic resonance. Strikingly, local optical excitation with energy below the excitonic resonance of the flakes in photoluminescence measurements unveils coupling of light to in-plane polaritonic modes with directed propagation. These exciton-polaritons exhibit high coupling efficiencies and extremely low loss propagation mechanisms which is confirmed by finite difference time domain simulations. We therefore prove that mesoscopic 2D Ruddlesden-Popper perovskites flakes represent an effective but simple system to study the rich physics of exciton-polaritons at room temperature.

Two-dimensional metals, such as graphene, have undergone extensive exploration, with graphene exhibiting a metallic response limited to the infrared spectral range. Overcoming the challenge of extending the electron mobility in two-dimensional metals to achieve plasmonic behaviors in the visible range necessitates innovative synthesis procedures. In this study, we showcase the successful realization of the phase of \c{hi}_3 borophene on diverse substrates using aluminum-based chemical vapor deposition. Leveraging first-principle density-functional theory alongside advanced deep-subwavelength cathodoluminescence spectroscopy, we reveal the extreme anisotropic response of this material in the visible range, transitioning from hyperbolic polaritonic to an elliptic wavefront. Our calculations substantiate the experimental findings, positioning borophene as an unprecedented candidate for the in-plane hyperbolic response in the visible range. These results open avenues for pioneering optoelectronic applications in the visible spectrum, particularly through the incorporation of borophene into hybrid metallic-semiconducting heterostructures.

Defect centers in hexagonal boron nitride have been extensively studied as room temperature single photon sources. The electronic structure of these defects exhibits strong coupling to phonons, as evidenced by the observation of phonon sidebands in both photoluminescence and cathodoluminescence spectra. However, the dynamics of the electron phonon coupling as well as phonon mediated dephasing of the color centers in hexagonal boron nitride remain unexplored. Here, we apply a novel time resolved CL spectroscopy technique to explore the population decay to phonon states and the dephasing time T2 with sub femtosecond time resolution. We demonstrate an ultrafast dephasing time of only 200 fs and a radiative decay of about 585 fs at room temperature, in contrast with all optical time resolved photoluminescence techniques that report a decay of a few nanoseconds. This behavior is attributed to efficient electron-beam excitation of coherent phonon polaritons in hexagonal boron nitride, resulting in faster dephasing of electronic transitions. Our results demonstrate the capability of our sequential cathodoluminescence spectroscopy technique to probe the ultrafast dephasing time of single emitters in quantum materials with sub femtosecond time resolution, heralding access to quantum path interferences in single emitters coupled to their complex environment.

Controlling free-electron momentum states is of high interest in electron microscopy to achieve momentum and energy resolved probing and manipulation of physical systems. Free-electron and light interactions have emerged as a powerful technique to accomplish this. Here, we demonstrate both longitudinal and transverse phase control of a slow electron wavepacket by extending the Kapitza-Dirac effect to spatially-structured pulsed laser beams. This extension enables both inelastic and elastic stimulated Compton scattering. The interaction reveals the formation of distinct electron transverse momentum orders, each demonstrating a comb-like electron energy spectrum. By exerting complete control over light parameters, including wavelength, field intensity, pulse duration, and spatial mode order, as well as their combinations, it is possible to coherently control the population of these electron energy-momentum states that are separated by a few meV energy and multiple photon momentum orders. This free-space electron-light interaction phenomenon possesses the capability to coherently control the energy and momentum of electron beams in electron microscopes. Moreover, it has the potential to facilitate the selective probing of various material excitations, including plasmons, excitons, and phonons, and performing Talbot-Lau matter-wave interferometry with transversely shaped electron beams.

We study the scaling properties of latent diffusion models (LDMs) with an emphasis on their sampling efficiency. While improved network architecture and inference algorithms have shown to effectively boost sampling efficiency of diffusion models, the role of model size -- a critical determinant of sampling efficiency -- has not been thoroughly examined. Through empirical analysis of established text-to-image diffusion models, we conduct an in-depth investigation into how model size influences sampling efficiency across varying sampling steps. Our findings unveil a surprising trend: when operating under a given inference budget, smaller models frequently outperform their larger equivalents in generating high-quality results. Moreover, we extend our study to demonstrate the generalizability of the these findings by applying various diffusion samplers, exploring diverse downstream tasks, evaluating post-distilled models, as well as comparing performance relative to training compute. These findings open up new pathways for the development of LDM scaling strategies which can be employed to enhance generative capabilities within limited inference budgets.

The transport properties of strongly interacting fermionic systems can reveal exotic states of matter, but experiments and theory have predominantly focused on bulk systems in the hydrodynamic limit describable with linear response coefficients such as electrical and thermal conductivity. In a ballistic channel connecting two superfluid reservoirs, recent experiments revealed a far-from-equilibrium regime beyond linear hydrodynamics where particle and entropy currents respond nonlinearly to biases of chemical potential and temperature, and their ratio is robust to the channel geometry. However, the origin of this robustness and its relation to the strong interparticle interactions remain unknown. Here, we study the coupled transport of particles and entropy tuning the interaction across the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover, the reservoir degeneracy across the superfluid phase transition, as well as the local potentials and confinement of the channel. Surprisingly, the entropy advectively transported per particle depends only on the interactions and reservoir degeneracy and not on the details of the channel, suggesting that this property has its origin in the universal equilibrium properties of the reservoirs. In contrast, the magnitudes of the advective and diffusive entropy currents vary significantly with the channel details. The advective current increases monotonically towards the BEC side, which can be largely explained by the estimated superfluid gap in the channel. The Wiedemann-Franz law that links the advective and diffusive currents in Fermi liquids is most egregiously violated at unitarity, suggesting a change in the nature of the excitations responsible for entropy diffusion near unitarity. These observations pose fundamental questions regarding transport phenomena in strongly interacting Fermi systems far from equilibrium., Comment: 14 pages, 7 figures

Doped semiconductors are capable of exhibiting metallic-like properties ranging from superconductivity to tunable localized surface plasmon resonances. Diamond is a wide-bandgap semiconductor that is rendered electronically active by incorporating a hole dopant, boron. While the effects of boron doping on the electronic band structure of diamond are well-studied, any link between charge carriers and plasmons, which could facilitate optical applications, has never been shown. Here, we report intervalence plasmons in boron-doped diamond, defined as collective electronic excitations between the valence subbands, opened up by the presence of holes. Evidence for these low energy excitations is provided by scanning transmission electron microscope-valence electron energy loss spectroscopy and photoinduced force infrared spectroscopy. The measured loss and absorbance spectra are subsequently reproduced by first-principles calculations based on the contribution of intervalence band transitions to the dielectric function. Remarkably, the calculations also reveal that the real part of the dielectric function exhibits a resonance characteristic of metallicity (narrow-banded negative values of the dielectric function). The energy of the zero-crossing and the position of the loss peak are found to coincide, and both increase with the carrier density. Our results provide insight into a new mechanism for inducing plasmon-like behavior in doped semiconductors from intervalence band transitions, and the possibility of attaining such properties in diamond, a key emerging material for biomedical and quantum information technologies.

This paper explores the critical domain of Revenue Management (RM) within Operations Research (OR), focusing on intricate pricing dynamics. Utilizing Mixed Integer Linear Programming (MILP) models, the study enhances revenue optimization by considering product prices as decision variables and emphasizing the interplay between demand and supply. Recent advancements in Discrete Choice Models (DCMs), particularly those rooted in Random Regret Minimization (RRM) theory, are investigated as potent alternatives to established Random Utility Maximization (RUM) based DCMs. Despite the widespread use of DCMs in RM, a significant gap exists between cutting-edge RRM-based models and their practical integration into RM strategies. The study addresses this gap by incorporating an advanced RRM-based DCM into MILP models, addressing pricing challenges in both capacitated and uncapacitated supply scenarios. The developed models demonstrate feasibility and offer diverse interpretations of consumer choice behavior, drawing inspiration from established RUM-based frameworks. This research contributes to bridging the existing gap in the application of advanced DCMs within practical RM implementations.

We delve into the dynamics of opinions within a multiplex network using coordination games, where agents communicate either in a one-way or two-way interactions, and where a designated leader may be present. By employing graph theory and Markov chains, we illustrate that despite non-positive diagonal elements in transition probability matrices or decomposable layers, opinions generally converge under specific conditions, leading to a consensus. We further scrutinize the convergence rates of opinion dynamics in networks with one-way versus two-way interactions. We find that in networks with a designated leader, opinions converge towards the initial opinion of the leader, whereas in networks without a designated leader, opinions converge to a convex combination of the opinions of agents. Moreover, we emphasize the crucial role of designated leaders in steering opinion convergence within the network. Our experimental findings corroborate that the presence of leaders expedites convergence, with mono-directional interactions exhibiting notably faster convergence rates compared to bidirectional interactions.

Recent progress in manufacturing high-electron-mobility transistors and optoelectronic devices highlights the necessity of understanding the charge dynamics and its impact on the optical properties inside heterostructures. Herein, we study the optical properties of GaN/AlGaN/GaN heterostructures using cathodoluminescence and photoluminescence spectroscopy. We explore the influence of generated secondary carriers after electron illumination and their penetration depth on the luminescence spectra. Our findings indicate that a higher laser power intensifies the photoluminescence response and establishes Fabry-Perot-like resonances. Furthermore, the intensity of the cathodoluminescence response shows a linear behavior versus the acceleration voltage and the current of electron beams for the yellow luminescence peak. A near-infrared cathodoluminescence peak (740 nm) is observed only when illuminating the sample with high currents that is attributed to the trapping of the secondary electrons within the Schottky barrier and the manipulation of the two-dimensional electron gas and the quantum-confined states within the barrier. Self-consistent Poisson-Schr\"odinger simulations verify this aspect. This research unveils the intricate charge dynamics associated with the interaction of electron beams with heterostructure systems, paving the way for innovative optoelectronic applications in semiconductor devices.

Text-driven diffusion models have become increasingly popular for various image editing tasks, including inpainting, stylization, and object replacement. However, it still remains an open research problem to adopt this language-vision paradigm for more fine-level image processing tasks, such as denoising, super-resolution, deblurring, and compression artifact removal. In this paper, we develop SPIRE, a Semantic and restoration Prompt-driven Image Restoration framework that leverages natural language as a user-friendly interface to control the image restoration process. We consider the capacity of prompt information in two dimensions. First, we use content-related prompts to enhance the semantic alignment, effectively alleviating identity ambiguity in the restoration outcomes. Second, our approach is the first framework that supports fine-level instruction through language-based quantitative specification of the restoration strength, without the need for explicit task-specific design. In addition, we introduce a novel fusion mechanism that augments the existing ControlNet architecture by learning to rescale the generative prior, thereby achieving better restoration fidelity. Our extensive experiments demonstrate the superior restoration performance of SPIRE compared to the state of the arts, alongside offering the flexibility of text-based control over the restoration effects., Comment: Accepted by ECCV 2024; Webpage: https://chenyangqiqi.github.io/tip