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Stochastic Representation of the Quantum Quartic Oscillator

Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results. Recent experimental advances have inspired the development of theoretical tools to describe the non-equilibrium dynamics of quantum systems. Among them an exact representation of quantum spin systems in terms of classical stochastic processes has been proposed. Here we provide first steps towards the extension of this stochastic approach to bosonic systems by considering the one-dimensional quantum quartic oscillator. We show how to exactly parameterize the time evolution of this prototypical model via the dynamics of a set of classical variables. We interpret these variables as stochastic processes, which allows us to propose a novel way to numerically simulate the time evolution of the system. We benchmark our findings by considering analytically solvable limits and providing alternative derivations of known results.

Authors: Gennaro Tucci, Stefano De Nicola, Sascha Wald, Andrea Gambassi.

Star Formation Variability as a Probe for the Baryon Cycle within Galaxies

We investigate the connection of the regulation of star formation and the cycling of baryons within and in and out of galaxies. We use idealized numerical simulations of Milky Way-mass galaxies, in which we systemically vary the galaxy morphology (bulge-to-total mass ratio) and stellar feedback strength (total eight setups with 80 simulations). We conclude that measurements of the temporal and spatial PSD of the SFH can provide constraints on the baryon cycle and the star formation process.

We investigate the connection of the regulation of star formation and the cycling of baryons within and in and out of galaxies. We use idealized numerical simulations of Milky Way-mass galaxies, in which we systemically vary the galaxy morphology (bulge-to-total mass ratio) and stellar feedback strength (total eight setups with 80 simulations). By following individual gas parcels through the disk, spiral arms, and massive star-forming clumps, we quantify how gas moves and oscillates through the different phases of the interstellar medium (ISM) and forms stars. We show that the residence time of gas in the dense ISM phase ($\tau_{\rm SF}$), the nature of spiral arms (strength, number), and the clump properties (number, mass function, and young star fraction) depend on both the galaxy morphology and stellar feedback. Based on these results, we quantify signatures of the baryon cycle within galaxies using the temporal and spatial power spectrum density (PSD) of the star formation history (SFH). Stronger stellar feedback leads to more bursty star formation while the correlation timescale of the SFH is longer, because stronger feedback dissolves the dense, star-forming ISM phase, leading to a more homogeneous ISM and a decrease in $\tau_{\rm SF}$. The bulge strength has a similar effect: the deep gravitational potential in a bulge-dominant galaxy imposes a strong shear force that effectively breaks apart gas clumps in the ISM; this subsequently inhibits the fragmentation of cool gas and therefore the star formation in the disk, leading to a decrease in the spatial power on scales of $\sim$ 1 kpc. We conclude that measurements of the temporal and spatial PSD of the SFH can provide constraints on the baryon cycle and the star formation process.

Authors: Eun-jin Shin, Sandro Tacchella, Ji-hoon Kim, Kartheik G. Iyer, Vadim A. Semenov.

On Estimation and Inference of Large Approximate Dynamic Factor Models via the Principal Component Analysis

(2009). A series of useful complementary results is also given. The issue of testing multiple restrictions on the loadings as well as building joint confidence intervals for the factors is discussed. This paper revisits and provides an alternative derivation of the asymptotic results for the Principal Components estimator of a large approximate factor model as considered in Stock and Watson (2002), Bai (2003), and Forni et al. (2009). Results are derived under a minimal set of assumptions with a special focus on the time series setting, which is usually considered in almost all recent empirical applications. Hence, $n$ and $T$ are not treated symmetrically, the former being the dimension of the considered vector of time series, while the latter being the sample size and, therefore, being relevant only for estimation purposes, but not when it comes to just studying the properties of the model at a population level. As a consequence, following Stock and Watson (2002) and Forni et al. (2009), estimation is based on the classical $n \times n$ sample covariance matrix. As expected, all asymptotic results we derive are equivalent to those stated in Bai (2003), where, however, a $T\times T$ covariance matrix is considered as a starting point. A series of useful complementary results is also given. In particular, we give some alternative sets of primitive conditions for mean-squared consistency of the sample covariance matrix of the factors, of the idiosyncratic components, and of the observed time series. We also give more intuitive asymptotic expansions for the estimators showing that PCA is equivalent to OLS as long as $\sqrt{T}/n\to 0$ and $\sqrt{n}/T\to 0$, that is loadings are estimated in a time series regression as if the factors were known, while factors are estimated in a cross-sectional regression as if the loadings were known. The issue of testing multiple restrictions on the loadings as well as building joint confidence intervals for the factors is discussed.

Authors: Matteo Barigozzi.

Two weight L^{p} inequalities for smooth Calderón-Zygmund operators and doubling measures

We also show that these quadratic triple testing conditions can be relaxed to scalar testing conditions, quadratic offset Muckenhoupt conditions, and a quadratic weak boundedness property.

If T is a smooth Stein elliptic fractional singular integral, 1<p<infinity, and sigma and omega are doubling measures, then the two weight L^{p} norm inequality holds if and only if the quadratic triple testing conditions of Hyt\"onen and Vuorinen hold. We also show that these quadratic triple testing conditions can be relaxed to scalar testing conditions, quadratic offset Muckenhoupt conditions, and a quadratic weak boundedness property.

Authors: Eric T. Sawyer, Brett D. Wick.

Non-local corrections to dynamical mean-field theory from the two-particle self-consistent method

Theoretical methods that are accurate for both short-distance observables and long-wavelength collective modes are still being developed for the Hubbard model. The DMFT double occupancy determines the spin and charge vertices through local spin and charge sum rules. The TPSC self-energy is also improved by replacing its local part with the local DMFT self-energy. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks. TPSC+DMFT can be used in regimes where quantum Monte Carlo is inaccessible. Theoretical methods that are accurate for both short-distance observables and long-wavelength collective modes are still being developed for the Hubbard model. Here, we benchmark against published diagrammatic quantum Monte Carlo results an approach that combines local observables from dynamical mean-field theory (DMFT) with the two-particle self-consistent theory (TPSC). This method (TPSC+DMFT) is relevant for weak to intermediate interaction, satisfies the local Pauli principle and allows us to compute a spin susceptibility that satisfies the Mermin-Wagner theorem. The DMFT double occupancy determines the spin and charge vertices through local spin and charge sum rules. The TPSC self-energy is also improved by replacing its local part with the local DMFT self-energy. With this method, we find improvements for both spin and charge fluctuations and for the self-energy. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks. TPSC+DMFT can be used in regimes where quantum Monte Carlo is inaccessible. In addition, this method paves the way to multi-band generalizations of TPSC that could be used in advanced electronic structure codes that include DMFT.

Authors: N. Martin, C. Gauvin-Ndiaye, A. -M. S. Tremblay.

A Dynamic Observer for a Class of Infinite-Dimensional Vibrating Flexible Structures

Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. Sufficient conditions for the convergence of the constructed observer are obtained on the basis of the invariance principle. The estimation error decay is illustrated with numerical simulations of finite-dimensional approximations of the observer dynamics.

Infinite-dimensional control systems with outputs are considered in the Hamiltonian formulation with generalized coordinates. An explicit scheme for constructing a dynamic observer for this class of systems is proposed with arbitrary gain coefficients. Sufficient conditions for the convergence of the constructed observer are obtained on the basis of the invariance principle. This result is applied to a flexible beam model attached to a mass-spring system with lumped and distributed actuators. The estimation error decay is illustrated with numerical simulations of finite-dimensional approximations of the observer dynamics.

Authors: Alexander Zuyev, Julia Kalosha.

Expanding Accurate Person Recognition to New Altitudes and Ranges: The BRIAR Dataset

These applications require lower resolution, longer ranges, and elevated viewpoints. Thus far, the dataset includes more than 350,000 still images and over 1,300 hours of video footage of approximately 1,000 subjects. The goal is to support the development of algorithms capable of accurately recognizing people at ranges up to 1,000 m and from high angles of elevation. This paper describes methods used to collect and curate the dataset, and the dataset's characteristics at the current stage. Face recognition technology has advanced significantly in recent years due largely to the availability of large and increasingly complex training datasets for use in deep learning models. These datasets, however, typically comprise images scraped from news sites or social media platforms and, therefore, have limited utility in more advanced security, forensics, and military applications. These applications require lower resolution, longer ranges, and elevated viewpoints. To meet these critical needs, we collected and curated the first and second subsets of a large multi-modal biometric dataset designed for use in the research and development (R&D) of biometric recognition technologies under extremely challenging conditions. Thus far, the dataset includes more than 350,000 still images and over 1,300 hours of video footage of approximately 1,000 subjects. To collect this data, we used Nikon DSLR cameras, a variety of commercial surveillance cameras, specialized long-rage R&D cameras, and Group 1 and Group 2 UAV platforms. The goal is to support the development of algorithms capable of accurately recognizing people at ranges up to 1,000 m and from high angles of elevation. These advances will include improvements to the state of the art in face recognition and will support new research in the area of whole-body recognition using methods based on gait and anthropometry. This paper describes methods used to collect and curate the dataset, and the dataset's characteristics at the current stage.

Authors: David Cornett III, Joel Brogan, Nell Barber, Deniz Aykac, Seth Baird, Nick Burchfield, Carl Dukes, Andrew Duncan, Regina Ferrell, Jim Goddard, Gavin Jager, Matt Larson, Bart Murphy, Christi Johnson, Ian Shelley, Nisha Srinivas, Brandon Stockwell, Leanne Thompson, Matt Yohe, Robert Zhang, Scott Dolvin, Hector J. Santos-Villalobos, David S. Bolme.

Improved Analysis of Score-based Generative Modeling: User-Friendly Bounds under Minimal Smoothness Assumptions

In this paper, we focus on the theoretical analysis of diffusion-based generative modeling. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. Our theoretical analysis also provides quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

In this paper, we focus on the theoretical analysis of diffusion-based generative modeling. Under an $L^2$-accurate score estimator, we provide convergence guarantees with polynomial complexity for any data distribution with second-order moment, by either employing an early stopping technique or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in KL divergence in $\epsilon$-accuracy can be done in $\tilde O\left(\frac{d^2 \log^2 (1/\delta)}{\epsilon^2}\right)$ steps: 1) the variance-$\delta$ Gaussian perturbation of any data distribution; 2) data distributions with $1/\delta$-smooth score functions. Our theoretical analysis also provides quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

Authors: Hongrui Chen, Holden Lee, Jianfeng Lu.

Uncertainty Quantification for Rule-Based Models

Rule-based classification models described in the language of logic directly predict boolean values, rather than modeling a probability and translating it into a prediction as done in statistical models. The vast majority of existing uncertainty quantification approaches rely on models providing continuous output not available to rule-based models. The confidence is based on how well that input region is explored and is designed to work in any OOD scenario. We demonstrate the usefulness of this uncertainty model by building an abstaining classifier powered by it and observing its performance in various scenarios. Rule-based classification models described in the language of logic directly predict boolean values, rather than modeling a probability and translating it into a prediction as done in statistical models. The vast majority of existing uncertainty quantification approaches rely on models providing continuous output not available to rule-based models. In this work, we propose an uncertainty quantification framework in the form of a meta-model that takes any binary classifier with binary output as a black box and estimates the prediction accuracy of that base model at a given input along with a level of confidence on that estimation. The confidence is based on how well that input region is explored and is designed to work in any OOD scenario. We demonstrate the usefulness of this uncertainty model by building an abstaining classifier powered by it and observing its performance in various scenarios.

Authors: Yusik Kim.

FedGen: Generalizable Federated Learning

In many real-world distributed settings, spurious correlations exist due to biases and data sampling issues on distributed devices or clients that can erroneously influence models. Current generalization approaches are designed for centralized training and attempt to identify features that have an invariant causal relationship with the target, thereby reducing the effect of spurious features. However, such invariant risk minimization approaches rely on apriori knowledge of training data distributions which is hard to obtain in many applications. We evaluate our approach on real-world datasets from different domains and show that FedGen results in models that achieve significantly better generalization than current federated learning approaches.

Existing federated learning models that follow the standard risk minimization paradigm of machine learning often fail to generalize in the presence of spurious correlations in the training data. In many real-world distributed settings, spurious correlations exist due to biases and data sampling issues on distributed devices or clients that can erroneously influence models. Current generalization approaches are designed for centralized training and attempt to identify features that have an invariant causal relationship with the target, thereby reducing the effect of spurious features. However, such invariant risk minimization approaches rely on apriori knowledge of training data distributions which is hard to obtain in many applications. In this work, we present a generalizable federated learning framework called FedGen, which allows clients to identify and distinguish between spurious and invariant features in a collaborative manner without prior knowledge of training distributions. We evaluate our approach on real-world datasets from different domains and show that FedGen results in models that achieve significantly better generalization than current federated learning approaches.

Authors: Praveen Venkateswaran, Vatche Isahagian, Vinod Muthusamy, Nalini Venkatasubramanian.