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In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their applicability to real life situations such as control of epidemics, optimal decisions in financial markets, electricity grid management, or traffic control for self-driving cars. We start the tutorial by introducing stochastic optimal control problems for a single agent, in discrete time and in continuous time. Then, we present the framework of dynamic games with finite number of agents. To tackle games with a very large number of agents, we discuss the paradigm of mean field games, which provides an efficient way to compute approximate Nash equilibria. Based on this approach, we discuss machine learning algorithms for such problems. First in the context of discrete time games, we introduce fixed point based methods and related methods based on reinforcement learning. Second, we discuss machine learning methods that are specific to continuous time problems, by building on optimality conditions phrased in terms of stochastic or partial differential equations. Several examples and numerical illustrations of problems arising in operations research are provided along the way., Comment: 39 pages, 11 figures

Human Resources (HR) technology solutions encompass software and hardware tools designed to automate HR processes, gather, process, and analyze data, utilize it for strategic decision-making, and execute HR professionals' tasks while prioritizing security and privacy considerations. As with numerous other domains, Digital Transformation and emerging technologies have commenced integration into HR processes. These technologies are utilized by HR professionals and various stakeholders involved in HR operations. This study evaluates the utilization of Artificial Intelligence (AI), Virtual Reality (VR), Augmented Reality (VR), and the Metaverse within HR management, focusing on current trends and potential opportunities. A survey was conducted to gauge HR professionals' perceptions and critiques regarding these technologies. Participants were the HR department officers, academicians who specialized in HR and staff who had courses at diverse levels about HR. The acquired results were subjected to comparative analysis within this article., Comment: 10 pages, 10 tables

We study an approach to simulating the stochastic relativistic advection-diffusion equation based on the Metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random transfers of charge between fluid cells, interspersed with ideal hydrodynamic time steps. The random charge transfers are accepted or rejected in a Metropolis step using the entropy as a statistical weight. This procedure reproduces the expected strains of dissipative relativistic hydrodynamics in a specific (and non-covariant) hydrodynamic frame known as the density frame. Numerical results, both with and without noise, are presented and compared to relativistic kinetics and analytical expectations. An all order resummation of the density frame gradient expansion reproduces the covariant dynamics in a specific model. In contrast to all other numerical approaches to relativistic dissipative fluids, the dissipative fluid formalism presented here is strictly first order in gradients and has no non-hydrodynamic modes. The physical naturalness and simplicity of the Metropolis algorithm, together with its convergence properties, make it a promising tool for simulating stochastic relativistic fluids in heavy ion collisions and for critical phenomena in the relativistic domain., Comment: 30 pages, 6 figures. Version 2 discusses flow fields depending on space and time

While graph neural networks (GNNs) have gained popularity for learning circuit representations in various electronic design automation (EDA) tasks, they face challenges in scalability when applied to large graphs and exhibit limited generalizability to new designs. These limitations make them less practical for addressing large-scale, complex circuit problems. In this work we propose HOGA, a novel attention-based model for learning circuit representations in a scalable and generalizable manner. HOGA first computes hop-wise features per node prior to model training. Subsequently, the hop-wise features are solely used to produce node representations through a gated self-attention module, which adaptively learns important features among different hops without involving the graph topology. As a result, HOGA is adaptive to various structures across different circuits and can be efficiently trained in a distributed manner. To demonstrate the efficacy of HOGA, we consider two representative EDA tasks: quality of results (QoR) prediction and functional reasoning. Our experimental results indicate that (1) HOGA reduces estimation error over conventional GNNs by 46.76% for predicting QoR after logic synthesis; (2) HOGA improves 10.0% reasoning accuracy over GNNs for identifying functional blocks on unseen gate-level netlists after complex technology mapping; (3) The training time for HOGA almost linearly decreases with an increase in computing resources., Comment: Published as a conference paper at Design Automation Conference (DAC) 2024

The state-of-the-art theoretical formalism for a covariant description of non-Gaussian fluctuation dynamics in relativistic fluids is discussed., Comment: 4 pages, 1 figure. Contribution to the Proceedings of the XXXth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions (Quark Matter 2023)

Millimeter-wave (mmWave) spectrum is expected to support data-intensive applications that require ultra-reliable low-latency communications (URLLC). However, mmWave links are highly sensitive to blockage, which may lead to disruptions in the communication. Traditional techniques that build resilience against such blockages (among which are interleaving and feedback mechanisms) incur delays that are too large to effectively support URLLC. This calls for novel techniques that ensure resilient URLLC. In this paper, we propose to deploy multilevel codes over space and over time. These codes offer several benefits, such as they allow to control what information is received and they provide different reliability guarantees for different information streams based on their priority. We also show that deploying these codes leads to attractive trade-offs between rate, delay, and outage probability. A practically-relevant aspect of the proposed technique is that it offers resilience while incurring a low operational complexity.

Mean field games (MFG) and mean field control (MFC) problems have been introduced to study large populations of strategic players. They correspond respectively to non-cooperative or cooperative scenarios, where the aim is to find the Nash equilibrium and social optimum. These frameworks provide approximate solutions to situations with a finite number of players and have found a wide range of applications, from economics to biology and machine learning. In this paper, we study how the players can pass from a non-cooperative to a cooperative regime, and vice versa. The first direction is reminiscent of mechanism design, in which the game's definition is modified so that non-cooperative players reach an outcome similar to a cooperative scenario. The second direction studies how players that are initially cooperative gradually deviate from a social optimum to reach a Nash equilibrium when they decide to optimize their individual cost similar to the free rider phenomenon. To formalize these connections, we introduce two new classes of games which lie between MFG and MFC: $\lambda$-interpolated mean field games, in which the cost of an individual player is a $\lambda$-interpolation of the MFG and the MFC costs, and $p$-partial mean field games, in which a proportion $p$ of the population deviates from the social optimum by playing the game non-cooperatively. We conclude the paper by providing an algorithm for myopic players to learn a $p$-partial mean field equilibrium, and we illustrate it on a stylized model., Comment: 51 pages, 4 figures

We analyze the trajectory of the Lee-Yang edge singularities of the QCD equation of state in the complex baryon chemical potential ($\mu_B$) plane for different values of the temperature by using the recent lattice results for the Taylor expansion coefficients up to eighth order in $\mu_B$ and various resummation techniques that blend in Pade expansions and conformal maps. By extrapolating from this information, we estimate for the location of the QCD critical point, $ T_c \approx 100$ MeV, $\mu_c \approx 580$ MeV. We also estimate the crossover slope at the critical point to be $\alpha_1 \approx 9^\circ$ and further constrain the non-universal mapping parameters between the three dimensional Ising model and QCD equations of state., Comment: Journal version, new analysis using the Wuppertal Budapest data added, 14 pages, 12 figures, 2 table

We study the heavy-dense limit of QCD on the lattice with heavy quarks at high density. The effective three dimensional theory has a sign problem which is alleviated by sign optimization where the path integration domain is deformed in complex space in a way that minimizes the phase oscillations. We simulate the theory via a Hybrid-Monte-Carlo, for different volumes, both to leading order and next-to-next-to leading order in the hopping expansion, and show that sign optimization successfully mitigates the sign problem at large enough volumes where usual re-weighting methods fail. Finally we show that there is a significant overlap between the complex manifold generated by sign optimization and the Lefschetz thimbles associated with the theory., Comment: 13 pages, 17 figures

In this paper, we propose and study a mean field game model with multiple populations of minor players and multiple major players, motivated by applications to the regulation of carbon emissions. Each population of minor players represent a large group of electricity producers and each major player represents a regulator. We first characterize the minor players equilibrium controls using forward-backward differential equations, and show existence and uniqueness of the minor players equilibrium. We then express the major players' equilibrium controls through analytical formulas given the other players' controls. Finally, we then provide a method to solve the Nash equilibrium between all the players, and we illustrate numerically the sensitivity of the model to its parameters.

The interference from active to passive users is a well-recognized challenge in millimeter-wave (mmWave) communications. We propose a method that enables to limit the interference on passive users (whose presence may not be detected since they do not transmit) with a small penalty to the throughput of active users. Our approach abstracts away (in a simple, yet informative way) the physical layer component and it leverages the directivity of mmWave links and the available network path diversity. We provide linear programming formulations, lower bounds on active users rates, numerical evaluations, and we establish a connection with the problem of (information theoretically) secure communication over mmWave networks.

The changing level of haze is one of the main factors which affects the success of the proposed dehazing methods. However, there is a lack of controlled multi-level hazy dataset in the literature. Therefore, in this study, a new multi-level hazy color image dataset is presented. Color video data is captured for two real scenes with a controlled level of haze. The distance of the scene objects from the camera, haze level, and ground truth (clear image) are available so that different dehazing methods and models can be benchmarked. In this study, the dehazing performance of five different dehazing methods/models is compared on the dataset based on SSIM, PSNR, VSI and DISTS image quality metrics. Results show that traditional methods can generalize the dehazing problem better than many deep learning based methods. The performance of deep models depends mostly on the scene and is generally poor on cross-dataset dehazing., Comment: 13 pages

Condensation models describe the equilibrium distribution of elements between coexisting mineral solid solutions, silicate liquid, and vapor in a closed chemical system, vapor phase always present, using equations of state of the phases involved at a fixed total P (< 1 bar) and temperature T. The VAPORS code uses a CaO-MgO-Al$_2$O$_3$-SiO$_2$ liquid model at T above the stability field of olivine and the MELTS algorithm at lower T. Quenched high-T crystal + liquid assemblages are preserved in meteorites as Type B Ca-, Al-rich inclusions (CAIs) and olivine-rich ferromagnesian chondrules. Experimental tests of compositional regions may clarify the nature of the phases present, the phase boundaries, and the partition of trace elements among these phases. Twenty-three Pt-loop equilibrium experiments in seven phase fields on twelve bulk compositions at specific T and dust enrichment factors tested the predicted stability fields of forsteritic olivine (Mg$_2$SiO$_4$), enstatite (MgSiO$_3$), Cr-bearing spinel (MgAl$_2$O$_4$), perovskite (CaTiO$_3$), melilite (Ca$_2$Al$_2$SiO$_7$ - Ca$_2$Mg$_2$Si$_2$O$_7$) and/or grossite (CaAl4O7) crystallizing from liquid. Experimental results for forsterite, enstatite, and grossite are in very good agreement with predictions, both in chemistry and phase abundances. On the other hand, the stability of spinel with olivine, and stability of perovskite and gehlenite are quite different from predictions. Perovskite is absent in all experiments. Even at low oxygen fugacity (IW-3.4), the most TiO$_2$-rich experiments do not crystallize Al-, Ti-bearing calcic pyroxene. The stability of spinel and olivine together is limited to a smaller phase field than is predicted. The melilite stability field is much larger than predicted, indicating a deficiency of current liquid or melilite activity models. In that respect, these experiments contribute to improving the data for calibrating thermodynamic models including MELTS., Comment: 17 pages, 5 figures, 5 tables

We determined the mineral-melt partition coefficients (Di's) and the compositional and/or temperature dependency between grossite, melilite, hibonite, olivine and Ca-, Al-inclusion (CAI)-type liquids for a number of light (LE), high field strength (HFSE), large ion lithophile (LILE), and rare earth (REE) elements including Li, Be, B, Sr, Zr, Nb, Ba, La, Ce, Eu, Dy, Ho, Yb, Hf, Ta, Th. A series of isothermal crystallization experiments was conducted at 5 kbar pressure and IW+1 in graphite capsules. The starting compositions were selected based on the calculated and experimentally confirmed phase relations during condensation in CI dust-enriched systems (Ebel and Grossman, 2000; Ebel, 2006; Ustunisik et al., 2014). Partition coefficients between melt and gehlenite, hibonite, and grossite show that the trace element budget of igneous CAIs is controlled by these three major Al-bearing phases in addition to pyroxene. In general, LE, LILE, REE, and HFSE partition coefficients (by mass) decrease in the order of Di(Gehlenite-Melt) > Di(Hibonite-Melt) > Di(Grossite-Melt). Results suggest that Di(Gehlenite-Melt) vary by a factor of 2-3 in different melt compositions at the same T (~1500 C). Increased melt Al and Ca, relative to earlier work, increases the compatibility of Di(Gehlenite-Melt), and also the compatibility of Di(Hibonite-Melt), especially for La and Ce. Olivine partitioning experiments confirm that olivine contribution to the trace element budget of CAIs is small due to the low Di(Olivine-Melt) at a range of temperatures while D-Eu, Yb(Olivine-Melt) are sensitive to changes in T and oxygen fugacity. The development of a predictive model for partitioning in CAI-type systems would require more experimental data and the use of analytical instruments capable of obtaining single phase analyses for crystals < 5 micron., Comment: 23 pages, 15 figures, 5 tables

In this paper, we propose several approaches to learn the optimal population-dependent controls in order to solve mean field control problems (MFC). Such policies enable us to solve MFC problems with forms of common noises at a level of generality that was not covered by existing methods. We analyze rigorously the theoretical convergence of the proposed approximation algorithms. Of particular interest for its simplicity of implementation is the $N$-particle approximation. The effectiveness and the flexibility of our algorithms is supported by numerical experiments comparing several combinations of distribution approximation techniques and neural network architectures. We use three different benchmark problems from the literature: a systemic risk model, a price impact model, and a crowd motion model. We first show that our proposed algorithms converge to the correct solution in an explicitly solvable MFC problem. Then, we show that population-dependent controls outperform state-dependent controls. Along the way, we show that specific neural network architectures can improve the learning further., Comment: 23 pages, 6 figures

Many state-of-the art robotic applications utilize series elastic actuators (SEAs) with closed-loop force control to achieve complex tasks such as walking, lifting, and manipulation. Model-free PID control methods are more prone to instability due to nonlinearities in the SEA where cascaded model-based robust controllers can remove these effects to achieve stable force control. However, these model-based methods require detailed investigations to characterize the system accurately. Deep reinforcement learning (DRL) has proved to be an effective model-free method for continuous control tasks, where few works deal with hardware learning. This paper describes the training process of a DRL policy on hardware of an SEA pendulum system for tracking force control trajectories from 0.05 - 0.35 Hz at 50 N amplitude using the Proximal Policy Optimization (PPO) algorithm. Safety mechanisms are developed and utilized for training the policy for 12 hours (overnight) without an operator present within the full 21 hours training period. The tracking performance is evaluated showing improvements of $25$ N in mean absolute error when comparing the first 18 min. of training to the full 21 hours for a 50 N amplitude, 0.1 Hz sinusoid desired force trajectory. Finally, the DRL policy exhibits better tracking and stability margins when compared to a model-free PID controller for a 50 N chirp force trajectory., Comment: 8 pages, 5 figures, submitted to IROS 2023