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We study finite-player dynamic stochastic games with heterogeneous interactions and non-Markovian linear-quadratic objective functionals. We derive the Nash equilibrium explicitly by converting the first-order conditions into a coupled system of stochastic Fredholm equations, which we solve in terms of operator resolvents. When the agents' interactions are modeled by a weighted graph, we formulate the corresponding non-Markovian continuum-agent game, where interactions are modeled by a graphon. We also derive the Nash equilibrium of the graphon game explicitly by first reducing the first-order conditions to an infinite-dimensional coupled system of stochastic Fredholm equations, then decoupling it using the spectral decomposition of the graphon operator, and finally solving it in terms of operator resolvents. Moreover, we show that the Nash equilibria of finite-player games on graphs converge to those of the graphon game as the number of agents increases. This holds both when a given graph sequence converges to the graphon in the cut norm and when the graph sequence is sampled from the graphon. We also bound the convergence rate, which depends on the cut norm in the former case and on the sampling method in the latter. Finally, we apply our results to various stochastic games with heterogeneous interactions, including systemic risk models with delays and stochastic network games., Comment: 58 pages

The COVID-19 pandemic has profoundly impacted global economies and healthcare systems, revealing critical vulnerabilities in both. In response, our study introduces a groundbreaking method for the detection of SARS-CoV-2 cDNA, leveraging Luminescence resonance energy transfer (LRET) between upconversion nanoparticles (UCNPs) and gold nanoparticles (AuNPs) to achieve an unprecedented detection limit of 242 femtomolar (fM). This innovative sensing platform utilizes UCNPs conjugated with one primer and AuNPs with another, targeting the 5' and 3' ends of the SARS-CoV-2 cDNA, respectively, enabling precise differentiation of mismatched DNA sequences and significantly enhancing detection specificity. Through rigorous experimental analysis, we established a quenching efficiency range from 10.4\% to 73.6\%, with an optimal midpoint of 42\%, thereby demonstrating the superior sensitivity of our method. By comparing the quenching efficiency of mismatched DNAs to the target DNA, we identified an optimal DNA:UCNP:AuNP ratio that ensures accurate detection. Our comparative analysis with existing SARS-CoV-2 detection methods revealed that our approach not only provides a lower detection limit but also offers higher specificity and potential for rapid, on-site testing. This study demonstrates the superior sensitivity and specificity of using UCNPs and AuNPs for SARS-CoV-2 cDNA detection, offering a significant advancement in rapid, accessible diagnostic technologies. Our method, characterized by its low detection limit and high precision, represents a critical step forward in managing current and future viral outbreaks, contributing to the enhancement of global healthcare responsiveness and infectious disease control., Comment: 14 pages, 5 figs

Achieving reliable multidimensional Vehicle-to-Vehicle (V2V) channel state information (CSI) prediction is both challenging and crucial for optimizing downstream tasks that depend on instantaneous CSI. This work extends traditional prediction approaches by focusing on four-dimensional (4D) CSI, which includes predictions over time, bandwidth, and antenna (TX and RX) space. Such a comprehensive framework is essential for addressing the dynamic nature of mobility environments within intelligent transportation systems, necessitating the capture of both temporal and spatial dependencies across diverse domains. To address this complexity, we propose a novel context-conditioned spatiotemporal predictive learning method. This method leverages causal convolutional long short-term memory (CA-ConvLSTM) to effectively capture dependencies within 4D CSI data, and incorporates context-conditioned attention mechanisms to enhance the efficiency of spatiotemporal memory updates. Additionally, we introduce an adaptive meta-learning scheme tailored for recurrent networks to mitigate the issue of accumulative prediction errors. We validate the proposed method through empirical studies conducted across three different geometric configurations and mobility scenarios. Our results demonstrate that the proposed approach outperforms existing state-of-the-art predictive models, achieving superior performance across various geometries. Moreover, we show that the meta-learning framework significantly enhances the performance of recurrent-based predictive models in highly challenging cross-geometry settings, thus highlighting its robustness and adaptability.

The end of Moore's Law and Dennard Scaling has combined with advances in agile hardware design to foster a golden age of domain-specific acceleration. However, this new frontier of computing opportunities is not without pitfalls. As computer architects approach unfamiliar domains, we have seen common themes emerge in the challenges that can hinder progress in the development of useful acceleration. In this work, we present the Magnificent Seven Challenges in domain-specific accelerator design that can guide adventurous architects to contribute meaningfully to novel application domains. Although these challenges appear across domains ranging from ML to genomics, we examine them through the lens of autonomous systems as a motivating example in this work. To that end, we identify opportunities for the path forward in a successful domain-specific accelerator design from these challenges., Comment: Presented at DAC 2024

Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In the present study we prove that, in the limit of small and frequent orders, the discrete system indeed converges to the fluid limit, which is characterized by a system of coupled nonlinear ODEs with singular coefficients at the origin. Moreover, we establish that the fluid system is asymptotically stable for an arbitrary number of limit order books in that, over time, it converges to the stationary equilibrium state studied by Maglaras et al. (2021).

We consider a central trading desk which aggregates the inflow of clients' orders with unobserved toxicity, i.e. persistent adverse directionality. The desk chooses either to internalise the inflow or externalise it to the market in a cost effective manner. In this model, externalising the order flow creates both price impact costs and an additional market feedback reaction for the inflow of trades. The desk's objective is to maximise the daily trading P&L subject to end of the day inventory penalization. We formulate this setting as a partially observable stochastic control problem and solve it in two steps. First, we derive the filtered dynamics of the inventory and toxicity, projected to the observed filtration, which turns the stochastic control problem into a fully observed problem. Then we use a variational approach in order to derive the unique optimal trading strategy. We illustrate our results for various scenarios in which the desk is facing momentum and mean-reverting toxicity. Our implementation shows that the P&L performance gap between the partially observable problem and the full information case are of order $0.01\%$ in all tested scenarios., Comment: 52 pages, 10 figures

In this work, we explore the dynamical sampling problem on $\ell^2(\mathbb{Z})$ driven by a convolution operator defined by a convolution kernel. This problem is inspired by the need to recover a bandlimited heat diffusion field from space-time samples and its discrete analogue. In this book chapter, we review recent results in the finite-dimensional case and extend these findings to the infinite-dimensional case, focusing on the study of the density of space-time sampling sets.

We study the learning problem associated with spiking neural networks. Specifically, we consider hypothesis sets of spiking neural networks with affine temporal encoders and decoders and simple spiking neurons having only positive synaptic weights. We demonstrate that the positivity of the weights continues to enable a wide range of expressivity results, including rate-optimal approximation of smooth functions or approximation without the curse of dimensionality. Moreover, positive-weight spiking neural networks are shown to depend continuously on their parameters which facilitates classical covering number-based generalization statements. Finally, we observe that from a generalization perspective, contrary to feedforward neural networks or previous results for general spiking neural networks, the depth has little to no adverse effect on the generalization capabilities.

In recent years, a scientific approach to reading education has gained traction due to the joint efforts of educators, parents, and state leaders. This movement for better reading instruction has helped to fuel a wave of legislation to address widespread and persistent reading deficits of American students. While reading difficulties cut across socioeconomic lines, they disproportionately affect students living in poverty as well as those from black, brown, and indigenous communities. This report aims to investigate how states have responded to this increased pressure for improved reading outcomes. Specifically, the authors analyzed reading-related state legislation enacted between 2019 and 2022. The study involved categorizing 223 bills enacted in 45 states and the District of Columbia during this period and examining over 40 dimensions, such as teacher preparation, professional development and curriculum. The objective was to provide a granular description of states' efforts to enhance reading instruction, with the following goals: (1) Foster constructive discussions that support states in developing effective roadmaps for advancing reading reform; (2) Encourage states to devise supplementary policies (e.g., guidance, additional legislation) to address the areas needing improvement identified in this report; and (3) Appeal to the research community for assistance in filling legislative gaps, not only to align with current evidence-based principles, but also to adapt to the evolving nature of scientific research. [This report is based on research funded in part by the Ibis Group.]

We generalize the characterization theorem going back to Mercer and Young, which states that a symmetric and continuous kernel is positive definite if and only if it is integrally positive definite. More precisely, we extend the result from real-valued kernels on compact intervals to matrix-valued kernels on separable metric spaces. We also demonstrate the applications of the generalized theorem to the field of convex optimization., Comment: 12 pages, 2 figures

We consider a class of optimal portfolio choice problems in continuous time where the agent's transactions create both transient cross-impact driven by a matrix-valued Volterra propagator, as well as temporary price impact. We formulate this problem as the maximization of a revenue-risk functional, where the agent also exploits available information on a progressively measurable price predicting signal. We solve the maximization problem explicitly in terms of operator resolvents, by reducing the corresponding first order condition to a coupled system of stochastic Fredholm equations of the second kind and deriving its solution. We then give sufficient conditions on the matrix-valued propagator so that the model does not permit price manipulation. We also provide an implementation of the solutions to the optimal portfolio choice problem and to the associated optimal execution problem. Our solutions yield financial insights on the influence of cross-impact on the optimal strategies and its interplay with alpha decays., Comment: 44 pages, 5 figures

Controlling electrically-stimulated quantum light sources (QLS) is key for developing integrated and low-scale quantum devices. The mechanisms leading to quantum emission are complex, as a large number of electronic states of the system impacts the emission dynamics. Here, we use a scanning tunneling microscope (STM) to excite a model QLS, namely a single molecule. The luminescence spectra reveal two lines, associated to the emission of the neutral and positively charged molecule, both exhibiting single-photon source behavior. In addition, we find a correlation between the charged and neutral molecule's emission, the signature of a photon cascade. By adjusting the charging/discharging rate, we can control these emission statistics. This generic strategy is further established by a rate equation model revealing the complex internal dynamics of the molecular junction.

Machine learning models with inputs in a Euclidean space $\mathbb{R}^d$, when implemented on digital computers, generalize, and their {\it generalization gap} converges to $0$ at a rate of $c/N^{1/2}$ concerning the sample size $N$. However, the constant $c>0$ obtained through classical methods can be large in terms of the ambient dimension $d$ and the machine precision, posing a challenge when $N$ is small to realistically large. In this paper, we derive a family of generalization bounds $\{c_m/N^{1/(2\vee m)}\}_{m=1}^{\infty}$ tailored for learning models on digital computers, which adapt to both the sample size $N$ and the so-called geometric {\it representation dimension} $m$ of the discrete learning problem. Adjusting the parameter $m$ according to $N$ results in significantly tighter generalization bounds for practical sample sizes $N$, while setting $m$ small maintains the optimal dimension-free worst-case rate of $\mathcal{O}(1/N^{1/2})$. Notably, $c_{m}\in \mathcal{O}(\sqrt{m})$ for learning models on discretized Euclidean domains. Furthermore, our adaptive generalization bounds are formulated based on our new non-asymptotic result for concentration of measure in discrete optimal transport, established via leveraging metric embedding arguments.

The development and application of upconversion nanoparticles (UCNPs) have garnered significant attention due to their unique optical properties and potential uses in bioimaging, drug delivery, and solar cells. However, the hydrophobic nature of UCNPs presents challenges in their synthesis and application, particularly in aqueous environments. We provide an overview of UCNPs, their synthesis challenges, and the importance of surface modification. Furthermore, we discuss the properties of \textit{LiYF_{4}:Yb, Er, Tm} UCNPs synthesized using novel 2,2-[ethylenebis(oxy)] bisacetic acid (EBAA) method and their versatile applications. Notably, the first Dynamic Light Scattering measurement on 05/22/2022 showed a size of 11.39 nm, and after 348 days on 04/05/2023, the same batch maintained a size of 13.8 nm, indicating excellent stability and no particle agglomeration over this extended period. This remarkable stability underscores the potential of UCNPs synthesized with the EBAA method for long-term applications. Finally, we compare the EBAA method with other surface modification techniques, exploring challenges and future perspectives for the use of hydrophilic UCNPs in various applications. This review aims to emphasize the significance of the EBAA method in advancing the field of upconversion nanoparticles and broadening their potential integration into diverse applications., Comment: 21 Pages, 1 table, 13 figures

Real-world networks have a complex topology comprising many elements often structured into communities. Revealing these communities helps researchers uncover the organizational and functional structure of the system that the network represents. However, detecting community structures in complex networks requires selecting a community detection method among a multitude of alternatives with different network representations, community interpretations, and underlying mechanisms. This review and tutorial focuses on a popular community detection method called the map equation and its search algorithm Infomap. The map equation framework for community detection describes communities by analyzing dynamic processes on the network. Thanks to its flexibility, the map equation provides extensions that can incorporate various assumptions about network structure and dynamics. To help decide if the map equation is a suitable community detection method for a given complex system and problem at hand -- and which variant to choose -- we review the map equation's theoretical framework and guide users in applying the map equation to various research problems.

Single-molecule tip-enhanced Raman spectroscopy (TERS) under ultra-high vacuum (UHV) and cryogenic conditions enables exploration of the relations between the adsorption geometry, electronic state, and vibrational fingerprints of individual molecules. TERS capability of reflecting spin states in open-shell molecular configurations is yet unexplored. Here we use the tip of a scanning probe microscope to lift a perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecule from a metal surface to bring it into an open-shell spin one-half anionic state. We reveal a correlation between the appearance of a Kondo resonance in the differential conductance spectroscopy and concurrent characteristic changes captured by the TERS measurements. Through a detailed investigation of various adsorbed and tip-contacted PTCDA scenarios, we infer that the Raman scattering on the suspended PTCDA is resonant with a higher excited state. Theoretical simulation of the vibrational spectra enables a precise assignment of the individual TERS peaks to high-symmetry Ag modes, including the fingerprints of the observed spin state. These findings highlight the potential of TERS in capturing complex interactions between charge, spin, and photophysical properties in nanoscale molecular systems, and suggest a pathway for designing spin-optical devices using organic molecules.

We introduce RobotPerf, a vendor-agnostic benchmarking suite designed to evaluate robotics computing performance across a diverse range of hardware platforms using ROS 2 as its common baseline. The suite encompasses ROS 2 packages covering the full robotics pipeline and integrates two distinct benchmarking approaches: black-box testing, which measures performance by eliminating upper layers and replacing them with a test application, and grey-box testing, an application-specific measure that observes internal system states with minimal interference. Our benchmarking framework provides ready-to-use tools and is easily adaptable for the assessment of custom ROS 2 computational graphs. Drawing from the knowledge of leading robot architects and system architecture experts, RobotPerf establishes a standardized approach to robotics benchmarking. As an open-source initiative, RobotPerf remains committed to evolving with community input to advance the future of hardware-accelerated robotics.

We consider an offline learning problem for an agent who first estimates an unknown price impact kernel from a static dataset, and then designs strategies to liquidate a risky asset while creating transient price impact. We propose a novel approach for a nonparametric estimation of the propagator from a dataset containing correlated price trajectories, trading signals and metaorders. We quantify the accuracy of the estimated propagator using a metric which depends explicitly on the dataset. We show that a trader who tries to minimise her execution costs by using a greedy strategy purely based on the estimated propagator will encounter suboptimality due to so-called spurious correlation between the trading strategy and the estimator and due to intrinsic uncertainty resulting from a biased cost functional. By adopting an offline reinforcement learning approach, we introduce a pessimistic loss functional taking the uncertainty of the estimated propagator into account, with an optimiser which eliminates the spurious correlation, and derive an asymptotically optimal bound on the execution costs even without precise information on the true propagator. Numerical experiments are included to demonstrate the effectiveness of the proposed propagator estimator and the pessimistic trading strategy., Comment: 12 figures

Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained network can swap in information from a different graph without retraining and retain its accuracy. A recent method of capturing transferability of GNNs is through the use of graphons, which are symmetric, measurable functions representing the limit of large dense graphs. In this work, we contribute to the application of graphons to GNNs by presenting an explicit two-layer graphon neural network (WNN) architecture. We prove its ability to approximate bandlimited graphon signals within a specified error tolerance using a minimal number of network weights. We then leverage this result, to establish the transferability of an explicit two-layer GNN over all sufficiently large graphs in a convergent sequence. Our work addresses transferability between both deterministic weighted graphs and simple random graphs and overcomes issues related to the curse of dimensionality that arise in other GNN results. The proposed WNN and GNN architectures offer practical solutions for handling graph data of varying sizes while maintaining performance guarantees without extensive retraining.