Random matrix theory has become a widely useful tool in high-dimensional statistics and theoretical machine learning. However, random matrix theory is largely focused on the proportional asymptotics in which the number of columns grows proportionally to the number of rows of the data matrix. This is not always the most natural setting in statistics where columns correspond to covariates and rows to samples. With the objective to move beyond the proportional asymptotics, we revisit ridge regression ($\ell_2$-penalized least squares) on i.i.d. data $(x_i, y_i)$, $i\le n$, where $x_i$ is a feature vector and $y_i = \beta^\top x_i +\epsilon_i \in\mathbb{R}$ is a response. We allow the feature vector to be high-dimensional, or even infinite-dimensional, in which case it belongs to a separable Hilbert space, and assume either $z_i := \Sigma^{-1/2}x_i$ to have i.i.d. entries, or to satisfy a certain convex concentration property. Within this setting, we establish non-asymptotic bounds that approximate the bias and variance of ridge regression in terms of the bias and variance of an `equivalent' sequence model (a regression model with diagonal design matrix). The approximation is up to multiplicative factors bounded by $(1\pm \Delta)$ for some explicitly small $\Delta$. Previously, such an approximation result was known only in the proportional regime and only up to additive errors: in particular, it did not allow to characterize the behavior of the excess risk when this converges to $0$. Our general theory recovers earlier results in the proportional regime (with better error rates). As a new application, we obtain a completely explicit and sharp characterization of ridge regression for Hilbert covariates with regularly varying spectrum. Finally, we analyze the overparametrized near-interpolation setting and obtain sharp `benign overfitting' guarantees.

This work contributes to developing an agent based on deep reinforcement learning capable of acting in a beyond visual range (BVR) air combat simulation environment. The paper presents an overview of building an agent representing a high-performance fighter aircraft that can learn and improve its role in BVR combat over time based on rewards calculated using operational metrics. Also, through self-play experiments, it expects to generate new air combat tactics never seen before. Finally, we hope to examine a real pilot's ability, using virtual simulation, to interact in the same environment with the trained agent and compare their performances. This research will contribute to the air combat training context by developing agents that can interact with real pilots to improve their performances in air defense missions.

The evolutionary success of bacteria lies in their ability to form complex surface-associated communities in diverse biophysical settings. However, it remains poorly understood how compliance of soft surfaces, measured in terms of their elastic deformability, impacts the dynamics and self-organization of bacterial cells proliferating into colonies. Using experiments and biomechanical modelling, here we study the expansion and self-organization of bacterial cells into sessile colonies on soft substrates. The dynamics and spatiotemporal structures were captured by visualising growing bacterial colonies on nutrient-rich, soft agarose pads, with elastic modulus in the range ~0.3 kPA to ~100 kPA by varying the concentration of the agarose in the underlying substrate. Our results show that, at the scale of the colonies, significant differences emerge in the spreading dynamics and colony geometry as the substrate stiffness is altered: softer substrates promote distinct, multilayered colony structures, and as revealed by fractal analysis of the colony boundaries, they exhibit higher boundary roughness. In contrast, colonies growing on harder substrates first grow up to large monolayers, before undergoing the mono-to-multilayer transition (MTMT), showing nearly 300% increase in the overall colony area at MTMT. A simple biomechanical model captures the role of effective drag forces at different scales, acting on the colonies as they spread on substrates with different stiffness: higher drag in soft substrates drive early verticalisation of the colonies, while lower effective drag delays the MTMT, resulting in larger colony areas. Based on the results and biomechanical insights, a comprehensive data-backed numerical model is currently being developed. Our findings highlight the role of surface stiffness in determining the self-organization of bacterial cells into an expanding multi-scale colony.

We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation. We analyze the algorithm under a new expressivity assumption that we call "optimistic closure," which is strictly weaker than assumptions from prior analyses for the linear setting. With optimistic closure, we prove that our algorithm enjoys a regret bound of $\tilde{O}(\sqrt{d^3 T})$ where $d$ is the dimensionality of the state-action features and $T$ is the number of episodes. This is the first statistically and computationally efficient algorithm for reinforcement learning with generalized linear functions.

In this paper, we introduce an alternative approach to enhancing Multi-Agent Reinforcement Learning (MARL) through the integration of domain knowledge and attention-based policy mechanisms. Our methodology focuses on the incorporation of domain-specific expertise into the learning process, which simplifies the development of collaborative behaviors. This approach aims to reduce the complexity and learning overhead typically associated with MARL by enabling agents to concentrate on essential aspects of complex tasks, thus optimizing the learning curve. The utilization of attention mechanisms plays a key role in our model. It allows for the effective processing of dynamic context data and nuanced agent interactions, leading to more refined decision-making. Applied in standard MARL scenarios, such as the Stanford Intelligent Systems Laboratory (SISL) Pursuit and Multi-Particle Environments (MPE) Simple Spread, our method has been shown to improve both learning efficiency and the effectiveness of collaborative behaviors. The results indicate that our attention-based approach can be a viable approach for improving the efficiency of MARL training process, integrating domain-specific knowledge at the action level.

Disc accretion onto astrophysical objects with a material surface proceeds through the boundary layer (BL) -- a radially narrow region in the inner disc where the incoming gas must slow down its rotation before settling onto the surface of the accretor. Here we numerically study a BL in which the angular momentum transport in the layer is accomplished via the excitation of global acoustic waves. While the earlier studies of such wave-mediated BLs typically modeled the internal structure of the central object as a globally isothermal sphere with sharply rising density profile, here we explore the effect of other internal density and temperature profiles on the mode operation. We model the inner structure of an accretor as a polytropic sphere, allowing a shallower increase of density and a non-trivial temperature profile inside the object. While the mix of acoustic modes observed in our long-duration (1000 inner orbits long) 2D hydrodynamic simulations is a weak function of the polytropic index $n$ of the accretor's structure, the mass accretion rate and the angular momentum flux across the BL show a clear dependence on $n$, both decreasing in amplitude as $n$ is lowered. Interestingly, in 2D these transport metrics are better correlated not with $n$ but with a total mass inside the central object contained within the simulation domain. These results improve our understanding of the wave-mediated BL accretion by quantifying the effect of the inner structure of the accretor on the excitation and propagation of acoustic modes mediating the BL transport.

We study the evolutionary trend of the total density profile of early-type galaxies (ETGs) in IllustrisTNG. To this end, we trace ETGs from $z=0$ to $z=4$ and measure the power-law slope $\gamma^{\prime}$ of the total density profile for their main progenitors. We find that their $\gamma^{\prime}$ steepen on average during $z\sim4-2$, then becoming shallower until $z=1$, after which they remain almost constant, aside from a residual trend of becoming shallower towards $z=0$. We also compare to a statistical sample of ETGs at different redshifts, selected based on their luminosity profiles and stellar masses. Due to different selection effects, the average slopes of the statistical samples follow a modified evolutionary trend. They monotonically decrease since $z=3$, and after $z\approx 1$, they remain nearly invariant with a mild increase towards $z=0$. These evolutionary trends are mass-dependent for both samples, with low-mass galaxies having in general steeper slopes than their more massive counterparts. Galaxies that transitioned to ETGs more recently have steeper mean slopes as they tend to be smaller and more compact at any given redshift. By analyzing the impact of mergers and AGN feedback on the progenitors' evolution, we conjecture a multi-phase path leading to isothermality in ETGs: dissipation associated with rapid wet mergers tends to steepen $\gamma^{\prime}$ from $z=4$ to $z=2$, whereas subsequent AGN feedback (especially in the kinetic mode) makes $\gamma^{\prime}$ shallower again from $z=2$ to $z=1$. Afterwards, passive evolution from $z=1$ to $z=0$, mainly through gas-poor mergers, mildly decreases $\gamma^{\prime}$ and maintains the overall mass distribution close to isothermal.

We propose a mechanism in which, using an eightbrane, a sixbrane ends on a NS brane in type IIA superstring theory. We use this mechanism to construct N=1 supersymmetric gauge theories in four dimensions with chiral matter localized in different points in space. Anomaly cancellation for the gauge theories is satisfied by requiring RR charge conservation for the various type IIA fields. The construction allows us to study a curious phase transition in which the number of flavors in supersymmetric QCD depends on the value of the ten dimensional cosmological constant. These phenomena are related to the fact that every time a D8-brane crosses a NS brane, a D6-brane is created in between them.

Surface-to-Air Missiles (SAMs) are crucial in modern air defense systems. A critical aspect of their effectiveness is the Engagement Zone (EZ), the spatial region within which a SAM can effectively engage and neutralize a target. Notably, the EZ is intrinsically related to the missile's maximum range; it defines the furthest distance at which a missile can intercept a target. The accurate computation of this EZ is essential but challenging due to the dynamic and complex factors involved, which often lead to high computational costs and extended processing times when using conventional simulation methods. In light of these challenges, our study investigates the potential of machine learning techniques, proposing an approach that integrates machine learning with a custom-designed simulation tool to train supervised algorithms. We leverage a comprehensive dataset of pre-computed SAM EZ simulations, enabling our model to accurately predict the SAM EZ for new input parameters. It accelerates SAM EZ simulations, enhances air defense strategic planning, and provides real-time insights, improving SAM system performance. The study also includes a comparative analysis of machine learning algorithms, illuminating their capabilities and performance metrics and suggesting areas for future research, highlighting the transformative potential of machine learning in SAM EZ simulations.

We show that several aspects of the low-temperature hydrodynamics of a discrete Gross-Pitaevskii equation (GPE) can be understood by mapping it to a nonlinear version of fluctuating hydrodynamics. This is achieved by first writing the GPE in a hydrodynamic form of a continuity and an Euler equation. Respecting conservation laws, dissipation and noise due to the system's chaos are added, thus giving us a nonlinear stochastic field theory in general and the Kardar-Parisi-Zhang (KPZ) equation in our particular case. This mapping to KPZ is benchmarked against exact Hamiltonian numerics on discrete GPE by investigating the non-zero temperature dynamical structure factor and its scaling form and exponent. Given the ubiquity of the Gross-Pitaevskii equation (a.k.a. nonlinear Schrodinger equation), ranging from nonlinear optics to cold gases, we expect this remarkable mapping to the KPZ equation to be of paramount importance and far reaching consequences.

We introduce the notion of "binary" positive and complex geometries, giving a completely rigid geometric realization of the combinatorics of generalized associahedra attached to any Dynkin diagram. We also define open and closed "cluster string integrals" associated with these "cluster configuration spaces". The binary geometry of type ${\cal A}$ gives a gauge-invariant description of the usual open and closed string moduli spaces for tree scattering, making no explicit reference to a worldsheet. The binary geometries and cluster string integrals for other Dynkin types provide a generalization of particle and string scattering amplitudes. Both the binary geometries and cluster string integrals enjoy remarkable factorization properties at finite $\alpha'$, obtained simply by removing nodes of the Dynkin diagram. As $\alpha'\to 0$ these cluster string integrals reduce to the canonical forms of the ABHY generalized associahedron polytopes. For classical Dynkin types these are associated with $n$-particle scattering in the bi-adjoint $\phi^3$ theory through one-loop order.

The fast-growing demand for fully autonomous aerial operations in shared spaces necessitates developing trustworthy agents that can safely and seamlessly navigate in crowded, dynamic spaces. In this work, we propose Social Robot Tree Search (SoRTS), an algorithm for the safe navigation of mobile robots in social domains. SoRTS aims to augment existing socially-aware trajectory prediction policies with a Monte Carlo Tree Search planner for improved downstream navigation of mobile robots. To evaluate the performance of our method, we choose the use case of social navigation for general aviation. To aid this evaluation, within this work, we also introduce X-PlaneROS, a high-fidelity aerial simulator, to enable more research in full-scale aerial autonomy. By conducting a user study based on the assessments of 26 FAA certified pilots, we show that SoRTS performs comparably to a competent human pilot, significantly outperforming our baseline algorithm. We further complement these results with self-play experiments in scenarios with increasing complexity.

We consider the incompressible, two dimensional Navier Stokes equation with periodic boundary conditions under the effect of an additive, white in time, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we show that any finite dimensional projection of the solution possesses a smooth density with respect to Lebesgue measure. We also show that under natural assumptions the density of such a projection is everywhere strictly positive. In particular, our conditions are viscosity independent. We are mainly interested in forcing which excites a very small number of modes. All of the results rely on the nondegeneracy of the infinite dimensional Malliavin matrix.

The Lojasiewicz inequalities for real analytic functions on Euclidean space were first proved by Stanislaw Lojasiewicz (1965) using methods of semianalytic and subanalytic sets, arguments later simplified by Bierstone and Milman (1988). In this article, we first give an elementary geometric, coordinate-based proof of the Lojasiewicz inequalities in the special case where the function is $C^1$ with simple normal crossings. We then prove, partly following Bierstone and Milman (1997) and using resolution of singularities for real analytic varieties, that the gradient inequality for an arbitrary real or complex analytic function follows from the special case where it has simple normal crossings. In addition, we prove the Lojasiewicz inequalities when a function is $C^N$ and generalized Morse-Bott of order $N \geq 3$; we gave an elementary proof of the Lojasiewicz inequalities when a function is $C^2$ and Morse-Bott in arXiv:1708.09775v4 (finite-dimensional case) and arXiv:1706.09349 (infinite-dimensional case).

The effect of the dipole polarization on the quantum dipole dipole interaction near an Ag nanosphere (ANS) is investigated. A theoretical formalism in terms of classical Green function is developed for the transfer rate and the potential energy of the dipole dipole interaction (DDI) between two polarized dipoles. It is found that a linear transition dipole can couple to a left circularly polarized transition dipole much stronger than to a right circularly polarized transition dipole. This polarization selectivity exists over a wide frequency range and is robust against the variation of the dipoles' position or the radius of the ANS. In contrast, a right circularly polarized transition dipole, can change sharply from coupling strongly to another right circularly polarized dipole to coupling strongly to a left circularly polarized dipole with varying frequency. However, if the two dipoles are placed in the same radial direction of the sphere, the right circularly polarized transition dipole can only couple to the dipole with the same polarization while not to the left circularly polarized transition dipole. These findings may be used in solid-state quantum-information processing based on the DDI.

We propose developing an integrated system to keep autonomous unmanned aircraft safely separated and behave as expected in conjunction with manned traffic. The main goal is to achieve safe manned-unmanned vehicle teaming to improve system performance, have each (robot/human) teammate learn from each other in various aircraft operations, and reduce the manning needs of manned aircraft. The proposed system anticipates and reacts to other aircraft using natural language instructions and can serve as a co-pilot or operate entirely autonomously. We point out the main technical challenges where improvements on current state-of-the-art are needed to enable Visual Flight Rules to fully autonomous aerial operations, bringing insights to these critical areas. Furthermore, we present an interactive demonstration in a prototypical scenario with one AI pilot and one human pilot sharing the same terminal airspace, interacting with each other using language, and landing safely on the same runway. We also show a demonstration of a vision-only aircraft detection system.

The Aerospace Simulation Environment (Ambiente de Simula\c{c}\~ao Aeroespacial -- ASA in Portuguese) is a custom-made object-oriented simulation framework developed mainly in C++ that enables the modeling and simulation of military operational scenarios to support the development of tactics and procedures in the aerospace context for the Brazilian Air Force. This work describes the ASA framework, bringing its distributed architecture for managing multiple simulation machines, a data analysis platform for post-processing simulation data, the capability of loading models at simulation runtime, and a batch mode execution platform to perform multiple independent executions simultaneously. In addition, we present a list of recent works using the ASA framework as a simulation tool in the air combat context.

This work compares supervised machine learning methods using reliable data from constructive simulations to estimate the most effective moment for launching missiles during air combat. We employed resampling techniques to improve the predictive model, analyzing accuracy, precision, recall, and f1-score. Indeed, we could identify the remarkable performance of the models based on decision trees and the significant sensitivity of other algorithms to resampling techniques. The models with the best f1-score brought values of 0.379 and 0.465 without and with the resampling technique, respectively, which is an increase of 22.69%. Thus, if desirable, resampling techniques can improve the model's recall and f1-score with a slight decline in accuracy and precision. Therefore, through data obtained through constructive simulations, it is possible to develop decision support tools based on machine learning models, which may improve the flight quality in BVR air combat, increasing the effectiveness of offensive missions to hit a particular target.

The fast-growing demand for fully autonomous aerial operations in shared spaces necessitates developing trustworthy agents that can safely and seamlessly navigate in crowded, dynamic spaces. In this work, we propose Social Robot Tree Search (SoRTS), an algorithm for the safe navigation of mobile robots in social domains. SoRTS aims to augment existing socially-aware trajectory prediction policies with a Monte Carlo Tree Search planner for improved downstream navigation of mobile robots. To evaluate the performance of our method, we choose the use case of social navigation for general aviation. To aid this evaluation, within this work, we also introduce X-PlaneROS, a high-fidelity aerial simulator, to enable more research in full-scale aerial autonomy. By conducting a user study based on the assessments of 26 FAA certified pilots, we show that SoRTS performs comparably to a competent human pilot, significantly outperforming our baseline algorithm. We further complement these results with self-play experiments in scenarios with increasing complexity.

This report discusses several topics in both top quark physics and QCD at an International Linear Collider (ILC). Issues such as measurements at the $t\bar{t}$ threshold, including both theoretical and machine requirements, and the determination of electroweak top quark couplings, are reviewed. New results concerning the potential of a 500 GeV $e^+e^-$ collider for measuring $Wtb$ couplings and the top quark Yukawa coupling are presented. The status of higher order QCD corrections to jet production cross sections, heavy quark form factors, and longitudinal gauge boson scattering, needed for percent-level studies at the ILC, are reviewed. A new study of the measurement of the hadronic structure of the photon at a $\gamma\gamma$ collider is presented. The effects on top quark properties from several models of new physics, including composite models, Little Higgs theories, and CPT violation, are studied.