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Recent work has applied supervised deep learning to derive continuous symmetry transformations that preserve the data labels and to obtain the corresponding algebras of symmetry generators. This letter introduces two improved algorithms that significantly speed up the discovery of these symmetry transformations. The new methods are demonstrated by deriving the complete set of generators for the unitary groups U(n) and the exceptional Lie groups $G_2$, $F_4$, and $E_6$. A third post-processing algorithm renders the found generators in sparse form. We benchmark the performance improvement of the new algorithms relative to the standard approach. Given the significant complexity of the exceptional Lie groups, our results demonstrate that this machine-learning method for discovering symmetries is completely general and can be applied to a wide variety of labeled datasets., Comment: 11 pages, 7 figures

We present a new family of logit-Q dynamics for efficient learning in stochastic games by combining the log-linear learning (also known as logit dynamics) for the repeated play of normal-form games with Q-learning for unknown Markov decision processes within the auxiliary stage-game framework. In this framework, we view stochastic games as agents repeatedly playing some stage game associated with the current state of the underlying game while the agents' Q-functions determine the payoffs of these stage games. We show that the logit-Q dynamics presented reach (near) efficient equilibrium in stochastic teams with unknown dynamics and quantify the approximation error. We also show the rationality of the logit-Q dynamics against agents following pure stationary strategies and the convergence of the dynamics in stochastic games where the stage-payoffs induce potential games, yet only a single agent controls the state transitions beyond stochastic teams. The key idea is to approximate the dynamics with a fictional scenario where the Q-function estimates are stationary over epochs whose lengths grow at a sufficiently slow rate. We then couple the dynamics in the main and fictional scenarios to show that these two scenarios become more and more similar across epochs due to the vanishing step size and growing epoch lengths.

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie algebras. We show that our method reproduces the canonical (sparse) representations of the generators of the Lorentz group, as well as the $U(n)$ and $SU(n)$ families of Lie groups. This approach is completely general and can be used to find the infinitesimal generators for any Lie group., Comment: 14 pages, 6 figures

We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully connected neural networks trained with a specially constructed loss function ensuring the desired symmetry properties. The two new elements in this work are the use of a reduced-dimensionality latent space and the generalization to transformations invariant with respect to high-dimensional oracles. The method is demonstrated with several examples on the MNIST digit dataset., Comment: 9 pages, 8 figures

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding generators. We construct loss functions that ensure that the applied transformations are symmetries and that the corresponding set of generators forms a closed (sub)algebra. Our procedure is validated with several examples illustrating different types of conserved quantities preserved by symmetry. In the process of deriving the full set of symmetries, we analyze the complete subgroup structure of the rotation groups $SO(2)$, $SO(3)$, and $SO(4)$, and of the Lorentz group $SO(1,3)$. Other examples include squeeze mapping, piecewise discontinuous labels, and $SO(10)$, demonstrating that our method is completely general, with many possible applications in physics and data science. Our study also opens the door for using a machine learning approach in the mathematical study of Lie groups and their properties., Comment: 21 pages, 26 figures with 47 panels

Clinical identification and fundamental study of viruses rely on the detection of viral proteins or viral nucleic acids. Yet, amplification-based and antigen-based methods are not able to provide precise compositional information of individual virions due to small particle size and low-abundance chemical contents (e.g., ~ 5000 proteins in a vesicular stomatitis virus). Here, we report a widefield interferometric defocus-enhanced mid-infrared photothermal (WIDE-MIP) microscope for high-throughput fingerprinting of single viruses. With the identification of feature absorption peaks, WIDE-MIP reveals the contents of viral proteins and nucleic acids in single DNA vaccinia viruses and RNA vesicular stomatitis viruses. Different nucleic acids signatures of thymine and uracil residue vibrations are obtained to differentiate DNA and RNA viruses. WIDE-MIP imaging further reveals an enriched \b{eta} sheet components in DNA varicella-zoster virus proteins. Together, these advances open a new avenue for compositional analysis of viral vectors and elucidating protein function in an assembled virion.

It can be easy and even fun to sketch humans in different poses. In contrast, creating those same poses on a 3D graphics "mannequin" is comparatively tedious. Yet 3D body poses are necessary for various downstream applications. We seek to preserve the convenience of 2D sketching while giving users of different skill levels the flexibility to accurately and more quickly pose\slash refine a 3D mannequin. At the core of the interactive system, we propose a machine-learning model for inferring the 3D pose of a CG mannequin from sketches of humans drawn in a cylinder-person style. Training such a model is challenging because of artist variability, a lack of sketch training data with corresponding ground truth 3D poses, and the high dimensionality of human pose-space. Our unique approach to synthesizing vector graphics training data underpins our integrated ML-and-kinematics system. We validate the system by tightly coupling it with a user interface, and by performing a user study, in addition to quantitative comparisons., Comment: accepted and published at 3DV 2022

Illumination uniformity is a critical parameter for excitation and data extraction quality in widefield biological imaging applications. However, typical imaging systems suffer from spatial and spectral non-uniformity due to non-ideal optical elements, thus require complex solutions for illumination corrections. We present Effective Uniform Color-Light Integration Device (EUCLID), a simple and cost-effective illumination source for uniformity corrections. EUCLID employs a diffuse-reflective, adjustable hollow cavity that allows for uniform mixing of light from discrete light sources and modifies the source field distribution to compensate for spatial non-uniformity introduced by optical components in the imaging system. In this study, we characterize the light coupling efficiency of the proposed design and compare the uniformity performance with the conventional method. EUCLID demonstrates a remarkable illumination improvement for multi-spectral imaging in both Nelsonian and Koehler alignment with a maximum spatial deviation of ~1% across a wide field-of-view.

A system of linear integral equations is presented, which is the analog of the system of Marchenko integral equations, to solve the inverse scattering problem for the linear system associated with the derivative NLS equations. The corresponding direct and inverse scattering problems are analyzed, and the recovery of the potentials and the Jost solutions from the solution to the Marchenko system is described. When the reflection coefficients are zero, some explicit solution formulas are provided for the potentials and the Jost solutions in terms of a pair of constant matrix triplets representing the bound-state information for any number of bound states and any multiplicities. In the reduced case, when the two potentials in the linear system are related to each other through complex conjugation, the corresponding reduced Marchenko integral equation is obtained. The solution to the derivative NLS equation is obtained from the solution to the reduced Marchenko integral equation. The theory presented is illustrated with some explicit examples., Comment: 50 pages, 6 figures

Sequence diversity is one of the major challenges in the design of diagnostic, prophylactic and therapeutic interventions against viruses. DiMA is a novel tool that is big data-ready and designed to facilitate the dissection of sequence diversity dynamics for viruses. DiMA stands out from other diversity analysis tools by offering various unique features. DiMA provides a quantitative overview of sequence (nucleotide/protein) diversity by use of Shannon's entropy corrected for size bias, applied via a user-defined k-mer sliding window to an input alignment file, and each k-mer position is dissected to various diversity motifs. The motifs are defined based on the probability of distinct sequences at a given k-mer position, whereby an index is the predominant sequence, while all the others are (total) variants to the index. The total variants are sub-classified into the major (most common) variant, minor variants (occurring more than once and of frequency lower than the major), and the unique (singleton) variants. DiMA allows user-defined, sequence metadata enrichment for analyses of the motifs. The application of DiMA was demonstrated for the alignment data of the relatively conserved Spike protein (2,106,985 sequences) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the relatively highly diverse Pol protein (3,874) of human immunodeficiency virus-1 (HIV-1). The tool is publicly available as a web server (https://dima.bezmialem.edu.tr), as a Python library (via PyPi) and as a command line client (Via GitHub)., Comment: 18 pages, 2 figures, 50 references

We present new learning dynamics combining (independent) log-linear learning and value iteration for stochastic games within the auxiliary stage game framework. The dynamics presented provably attain the efficient equilibrium (also known as optimal equilibrium) in identical-interest stochastic games, beyond the recent concentration of progress on provable convergence to some (possibly inefficient) equilibrium. The dynamics are also independent in the sense that agents take actions consistent with their local viewpoint to a reasonable extent rather than seeking equilibrium. These aspects can be of practical interest in the control applications of intelligent and autonomous systems. The key challenges are the convergence to an inefficient equilibrium and the non-stationarity of the environment from a single agent's viewpoint due to the adaptation of others. The log-linear update plays an important role in addressing the former. We address the latter through the play-in-episodes scheme in which the agents update their Q-function estimates only at the end of the episodes.

Although cardiovascular diseases are the leading cause of death globally, non-invasive and inexpensive diagnostic tools for the identification of associated unstable atherosclerotic plaques are not yet available. Scanning acoustic microscopy offers a high potential to fill this critical gap in patient care. However, convincing validation and calibration of this technique requires high resolution maps of Ca concentrations of atherosclerotic plaques. Here, we demonstrate that synchrotron radiation-based X-ray fluorescence imaging with micrometer spatial resolution can provide such a gold standard.

A method is presented to obtain the change in the potential and in the relevant wavefunction of a linear system of ordinary differential equations containing a spectral parameter, when that linear system is perturbed and a finite number of discrete eigenvalues are added to or removed from the spectrum. Some explicit formulas are derived for those changes by introducing certain fundamental linear integral equations for the corresponding unperturbed and perturbed linear systems. This generalized method is applicable in a unified manner on a wide class of linear systems. This is in contrast to the standard method for a Darboux transformation, which is specific to the particular linear system on which it applies. A comparison is provided in some special cases between this generalized method and the standard method for the Darboux transformation. In particular, when a bound state is added to the discrete spectrum, some Darboux transformation formulas are presented for the full-line Schr\"odinger equation, where those formulas resemble the Darboux transformation formulas for the half-line Schr\"odinger equation. The theory presented is illustrated with some explicit examples., Comment: 39 pages

Do quasi-experimental (QE) studies conducted with baseline covariates that are typically available in the longitudinal administrative state databases yield unbiased effect estimates? This paper conducts a within-study comparison (WSC) study that compares experimental impacts of early college high school (ECHS) attendance with QE impacts drawn from the state and locales. We find that (1) QE models for outcomes with natural (matching) pretests replicated the randomized benchmarks quite well; (2) the replication bias is not sensitive to type of propensity score model or method; and (3) imposing locational restrictions (i.e., local matching) on the comparison students--specifically choosing them from among non-treatment students who came from the same feeder middle schools as the treatment students--does not decrease the QE bias; on the contrary, it performed worse than the models that did not impose this restriction for most outcomes. The first two findings are generally consistent with other education WSCs while the third one is not, suggesting that in cases where selection may be driven by individual-level factors, such as this one, local matching may yield biased treatment effect estimates by greatly reducing the pool of potential comparison units and distorting balance on unobservable confounders while prioritizing balance on observable factors. [This paper was published in "Journal of Policy Analysis and Management" v40 n2 p572-613 2021.]

Building on a growing literature showing that early college high schools substantially improve educational outcomes, we investigate possible spillover impacts of this intervention on civic outcomes in North Carolina, which houses an early college in most of its counties. We present both lottery and observational impacts on voting and criminal convictions. Our results suggest a modest increase in voting during early adulthood of about 4 to 5 percent, though lottery estimates do not rule out a null effect. For criminal convictions, lottery estimates are imprecise due to very low conviction rates, but observational evidence suggests a moderate decrease in convictions. We additionally identify stronger impacts on voting and conviction outcomes for key student subgroups, particularly black males and economically-disadvantaged white students. These results suggest that scaling up the early college program can improve youth civic outcomes and help to close key civic and political participation gaps. [This paper was published in "Social Sciences Research" v99 Article 10258 2021.]