Search

With the large diversity of platforms and devices used by students, web applications increasingly suggest themselves as the solution of choice. Developing adequate educational programming environments in the browser, however, remains a challenge and often involves trade-offs between desired functionalities and navigating the limitations of web applications, in particular the blocking single-threaded execution model. We introduce a fully browser-based Python programming environment that explores the possibilities and demonstrates that a web application can indeed support a rich and mature set of features, ranging from Turtle graphics over educational robotics to data processing.

We study convolutional neural networks with monomial activation functions. Specifically, we prove that their parameterization map is regular and is an isomorphism almost everywhere, up to rescaling the filters. By leveraging on tools from algebraic geometry, we explore the geometric properties of the image in function space of this map -- typically referred to as neuromanifold. In particular, we compute the dimension and the degree of the neuromanifold, which measure the expressivity of the model, and describe its singularities. Moreover, for a generic large dataset, we derive an explicit formula that quantifies the number of critical points arising in the optimization of a regression loss.

We demonstrate the Patterns of Life Simulation to create realistic simulations of human mobility in a city. This simulation has recently been used to generate massive amounts of trajectory and check-in data. Our demonstration focuses on using the simulation twofold: (1) using the graphical user interface (GUI), and (2) running the simulation headless by disabling the GUI for faster data generation. We further demonstrate how the Patterns of Life simulation can be used to simulate any region on Earth by using publicly available data from OpenStreetMap. Finally, we also demonstrate recent improvements to the scalability of the simulation allows simulating up to 100,000 individual agents for years of simulation time. During our demonstration, as well as offline using our guides on GitHub, participants will learn: (1) The theories of human behavior driving the Patters of Life simulation, (2) how to simulate to generate massive amounts of synthetic yet realistic trajectory data, (3) running the simulation for a region of interest chosen by participants using OSM data, (4) learn the scalability of the simulation and understand the properties of generated data, and (5) manage thousands of parallel simulation instances running concurrently., Comment: Accepted paper to SIGSPATIAL 2024 main conference

We propose a seasonal AR model with time-varying parameter processes in both the regular and seasonal parameters. The model is parameterized to guarantee stability at every time point and can accommodate multiple seasonal periods. The time evolution is modeled by dynamic shrinkage processes to allow for long periods of essentially constant parameters, periods of rapid change as well as abrupt jumps. A Gibbs sampler is developed with a particle Gibbs update step for the AR parameter trajectories. The near-degeneracy of the model, caused by the dynamic shrinkage processes, is shown to pose a challenge for particle methods. To address this, a more robust, faster and accurate approximate sampler based on the extended Kalman filter is proposed. The model and the numerical effectiveness of the Gibbs sampler are investigated on simulated and real data. An application to more than a century of monthly US industrial production data shows interesting clear changes in seasonality over time, particularly during the Great Depression and the recent Covid-19 pandemic. Keywords: Bayesian inference; Extended Kalman filter; Locally stationary processes; Particle MCMC; Seasonality.

We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case.

Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to follow an autoregressive integrated moving average (ARIMA) model, or seasonal variants thereof, which are unable to capture a long-range dependency structure of the error process. We propose a novel dynamic linear regression model that incorporates the long-range dependency feature of the errors. We demonstrate that the proposed error process may (i) have a significant impact on the posterior uncertainty of the estimated regression parameters and (ii) improve the model's forecasting ability. We develop a Markov chain Monte Carlo method to fit general dynamic linear regression models based on a frequency domain approach that enables fast, asymptotically exact Bayesian inference for large datasets. We demonstrate that our approximate algorithm is faster than the traditional time domain approaches, such as the Kalman filter and the multivariate Gaussian likelihood, while retaining a high accuracy when approximating the posterior distribution. We illustrate the method in simulated examples and two energy forecasting applications.

Symbolic data analysis (SDA) aggregates large individual-level datasets into a small number of distributional summaries, such as random rectangles or random histograms. Inference is carried out using these summaries in place of the original dataset, resulting in computational gains at the loss of some information. In likelihood-based SDA, the likelihood function is characterised by an integral with a large exponent, which limits the method's utility as for typical models the integral unavailable in closed form. In addition, the likelihood function is known to produce biased parameter estimates in some circumstances. Our article develops a Bayesian framework for SDA methods in these settings that resolves the issues resulting from integral intractability and biased parameter estimation using pseudo-marginal Markov chain Monte Carlo methods. We develop an exact but computationally expensive method based on path sampling and the block-Poisson estimator, and a much faster, but approximate, method based on Taylor expansion. Through simulation and real-data examples we demonstrate the performance of the developed methods, showing large reductions in computation time compared to the full-data analysis, with only a small loss of information.

This Letter reports the first measurement of the oscillation amplitude and frequency of reactor antineutrinos at Daya Bay via neutron capture on hydrogen using 1958 days of data. With over 3.6 million signal candidates, an optimized candidate selection, improved treatment of backgrounds and efficiencies, refined energy calibration, and an energy response model for the capture-on-hydrogen sensitive region, the relative $\overline{\nu}_{e}$ rates and energy spectra variation among the near and far detectors gives $\mathrm{sin}^22\theta_{13} = 0.0759_{-0.0049}^{+0.0050}$ and $\Delta m^2_{32} = (2.72^{+0.14}_{-0.15})\times10^{-3}$ eV$^2$ assuming the normal neutrino mass ordering, and $\Delta m^2_{32} = (-2.83^{+0.15}_{-0.14})\times10^{-3}$ eV$^2$ for the inverted neutrino mass ordering. This estimate of $\sin^2 2\theta_{13}$ is consistent with and essentially independent from the one obtained using the capture-on-gadolinium sample at Daya Bay. The combination of these two results yields $\mathrm{sin}^22\theta_{13}= 0.0833\pm0.0022$, which represents an 8% relative improvement in precision regarding the Daya Bay full 3158-day capture-on-gadolinium result.

Directed acyclic graph (DAG) learning is a rapidly expanding field of research. Though the field has witnessed remarkable advances over the past few years, it remains statistically and computationally challenging to learn a single (point estimate) DAG from data, let alone provide uncertainty quantification. Our article addresses the difficult task of quantifying graph uncertainty by developing a Bayesian variational inference framework based on novel distributions that have support directly on the space of DAGs. The distributions, which we use to form our prior and variational posterior, are induced by a projection operation, whereby an arbitrary continuous distribution is projected onto the space of sparse weighted acyclic adjacency matrices (matrix representations of DAGs) with probability mass on exact zeros. Though the projection constitutes a combinatorial optimization problem, it is solvable at scale via recently developed techniques that reformulate acyclicity as a continuous constraint. We empirically demonstrate that our method, ProDAG, can deliver accurate inference and often outperforms existing state-of-the-art alternatives.

This paper reports on the integration of runtime monitoring into fully-electric aircraft designed by Volocopter, a German aircraft manufacturer of electric multi-rotor helicopters. The runtime monitor recognizes hazardous situations and system faults. Since the correct operation of the monitor is critical for the safety of the aircraft, the development of the monitor must follow strict aeronautical standards. This includes the integration of the monitor into different development environments, such as log-file analysis, hardware/software-in-the-loop testing, and test flights. We have used the stream-based monitoring framework RTLola to generate monitors for a range of requirements. In this paper, we present representative monitoring specifications and our lessons learned from integrating the generated monitors. Our main finding is that the specification and the integration need to be decoupled, because the specification remains stable throughout the development process, whereas the different development stages require a separate integration of the monitor into each environment. We achieve this decoupling with a novel abstraction layer in the monitoring framework that adapts the monitor to each environment without affecting the core component generated from the specification. The decoupling of the integration has also allowed us to react quickly to the frequent changes in the hardware and software environment of the monitor due to the fast-paced development of the aircraft in a startup company.

This Letter presents results of a search for the mixing of a sub-eV sterile neutrino with three active neutrinos based on the full data sample of the Daya Bay Reactor Neutrino Experiment, collected during 3158 days of detector operation, which contains $5.55 \times 10^{6}$ reactor \anue candidates identified as inverse beta-decay interactions followed by neutron-capture on gadolinium. The analysis benefits from a doubling of the statistics of our previous result and from improvements of several important systematic uncertainties. No significant oscillation due to mixing of a sub-eV sterile neutrino with active neutrinos was found. Exclusion limits are set by both Feldman-Cousins and CLs methods. Light sterile neutrino mixing with $\sin^2 2\theta_{14} \gtrsim 0.01$ can be excluded at 95\% confidence level in the region of $0.01$ eV$^2 \lesssim |\Delta m^{2}_{41}| \lesssim 0.1 $ eV$^2$. This result represents the world-leading constraints in the region of $2 \times 10^{-4}$ eV$^2 \lesssim |\Delta m^{2}_{41}| \lesssim 0.2 $ eV$^2$., Comment: 7 pages, 4 figures, 1 table

We present an analysis on Physics Club's supremacy over the Astronomy Club at the University of Arizona. Through a thorough investigation of each club's history and content, and subsequent diligent calculations, we have proven without a doubt that the Physics Club is superior to Astronomy Club., Comment: 3 pages. Happy April Fools Day

Rolling shutter (RS) cameras dominate consumer and smartphone markets. Several methods for computing the absolute pose of RS cameras have appeared in the last 20 years, but the relative pose problem has not been fully solved yet. We provide a unified theory for the important class of order-one rolling shutter (RS$_1$) cameras. These cameras generalize the perspective projection to RS cameras, projecting a generic space point to exactly one image point via a rational map. We introduce a new back-projection RS camera model, characterize RS$_1$ cameras, construct explicit parameterizations of such cameras, and determine the image of a space line. We classify all minimal problems for solving the relative camera pose problem with linear RS$_1$ cameras and discover new practical cases. Finally, we show how the theory can be used to explain RS models previously used for absolute pose computation., Comment: 36 pages, 6 figures, 3 ancillary files

We study certain "geometric-invariant resonant cavitie"' introduced by Liberal et. al in a 2016 Nature Comm. paper, modeled using the transverse magnetic reduction of Maxwell's equations. The cross-section consists of a dielectric inclusion surrounded by an "epsilon-near-zero" (ENZ) shell. When the shell has the right area, its interaction with the inclusion produces a resonance. Mathematically, the resonance is a nontrivial solution of a 2D divergence-form Helmoltz equation $\nabla \cdot \left(\varepsilon^{-1}(x,\omega) \nabla u \right) + \omega^2 \mu u = 0$, where $\varepsilon(x,\omega)$ is the (complex-valued) dielectric permittivity, $\omega$ is the frequency, $\mu$ is the magnetic permeability, and a homogeneous Neumann condition is imposed at the outer boundary of the shell. This is a nonlinear eigenvalue problem, since $\varepsilon$ depends on $\omega$. Use of an ENZ material in the shell means that $\varepsilon(x,\omega)$ is nearly zero there, so the PDE is rather singular. Working with a Lorentz model for the dispersion of the ENZ material, we put the discussion of Liberal et.~al.~on a sound foundation by proving the existence of the anticipated resonance when the loss is sufficiently small. Our analysis is perturbative in character despite the apparently singular form of the PDE. While the existence of the resonance depends only on the area of the ENZ shell, the rate at which it decays depends on the shape of the shell. We consider an associated optimal design problem: what shape shell gives the slowest-decaying resonance? We prove that if the dielectric inclusion is a ball then the optimal shell is a concentric annulus. For an inclusion of any shape, we study a convex relaxation of the design problem using tools from convex duality, and discuss the conjecture that our relaxed problem amounts to considering homogenization-like limits of nearly optimal designs., Comment: 44 pages, 2 Figures. Revised version incorporating referee suggestions with a few more references