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We consider the training of the first layer of vision models and notice the clear relationship between pixel values and gradient update magnitudes: the gradients arriving at the weights of a first layer are by definition directly proportional to (normalized) input pixel values. Thus, an image with low contrast has a smaller impact on learning than an image with higher contrast, and a very bright or very dark image has a stronger impact on the weights than an image with moderate brightness. In this work, we propose performing gradient descent on the embeddings produced by the first layer of the model. However, switching to discrete inputs with an embedding layer is not a reasonable option for vision models. Thus, we propose the conceptual procedure of (i) a gradient descent step on first layer activations to construct an activation proposal, and (ii) finding the optimal weights of the first layer, i.e., those weights which minimize the squared distance to the activation proposal. We provide a closed form solution of the procedure and adjust it for robust stochastic training while computing everything efficiently. Empirically, we find that TrAct (Training Activations) speeds up training by factors between 1.25x and 4x while requiring only a small computational overhead. We demonstrate the utility of TrAct with different optimizers for a range of different vision models including convolutional and transformer architectures., Comment: Published at NeurIPS 2024

Smart cities have been a very active research area in the past 20 years, while continuously adapting to new technological advancements and keeping up with the times regarding sustainability and climate change. In this context, there have been numerous proposals to expand the scope of smart cities, focusing on resilience and sustainability, among other aspects, resulting in terms like smart sustainable cities. At the same time, there is an ongoing discussion regarding the degree in which smart cities put people at their centre. In this work, we argue toward expanding the current smart city definition by integrating the circular economy as one of its central pillars and adopting the term smart (and) circular city. We discuss the ways a smart and circular city encompasses both sustainability and smartness in an integral manner, while also being well-positioned to foster novel business activity and models and helping to place citizens at the heart of the smart city. In this sense, we also argue that previous research in smart cities and technologies, such as those related to Industry 4.0, can serve as a cornerstone to implement circular economy activities within cities, at a scale that exceeds current activities that are based on more conventional approaches. We also outline current open challenges in this domain and research questions that still need to be addressed., Comment: Preprint submitted to the 10th IEEE International Smart Cities Conference 2024 (ISC2 2024)

When training neural networks with custom objectives, such as ranking losses and shortest-path losses, a common problem is that they are, per se, non-differentiable. A popular approach is to continuously relax the objectives to provide gradients, enabling learning. However, such differentiable relaxations are often non-convex and can exhibit vanishing and exploding gradients, making them (already in isolation) hard to optimize. Here, the loss function poses the bottleneck when training a deep neural network. We present Newton Losses, a method for improving the performance of existing hard to optimize losses by exploiting their second-order information via their empirical Fisher and Hessian matrices. Instead of training the neural network with second-order techniques, we only utilize the loss function's second-order information to replace it by a Newton Loss, while training the network with gradient descent. This makes our method computationally efficient. We apply Newton Losses to eight differentiable algorithms for sorting and shortest-paths, achieving significant improvements for less-optimized differentiable algorithms, and consistent improvements, even for well-optimized differentiable algorithms., Comment: Published at NeurIPS 2024

Scanning objects with a more tightly focused beam (for example of photons or electrons) can provide higher-resolution images. However the stronger localisation of energy deposition can damage tissues in organic samples or may rearrange the chemical structure or physical properties of inorganic materials. Scanning an object with a broad beam can deliver an equivalent probe energy but spreads it over a much wider footprint. Sharp images can be reconstructed from the diffuse implanted signal when a decoding step can recover a delta-like impulse response. Huffman sequences, by design, have the optimal delta-like autocorrelation for aperiodic (non-cyclic) convolution and are well-conditioned. Here we adapt 1D Huffman sequences to design 2D Huffman-like discrete arrays that have spatially broad, relatively thin and uniform intensity profiles that retain excellent aperiodic autocorrelation metrics. Examples of broad shaped diffuse beams were developed for the case of x-ray imaging. A variety of masks were fabricated by the deposition of finely structured layers of tantalum on a silicon oxide wafer. The layers form a pattern of discrete pixels that modify the shape of an incident uniform beam of low energy x-rays as it passes through the mask. The intensity profiles of the x-ray beams after transmission through these masks were validated, first by acquiring direct-detector x-ray images of the masks, and second by raster scanning a pinhole over each mask pattern, pixel-by-pixel, collecting "bucket" signals as applied in traditional ghost imaging. The masks were then used to raster scan the shaped x-ray beam over several simple binary and "gray" test objects, again producing bucket signals, from which sharp reconstructed object images were obtained by deconvolving their bucket images.

In this paper, we quantify voltage and current phasor-based measurement requirements for the unique identification of the electric grid topology and admittance parameters. Our approach is underpinned by the concept of a rigidity matrix that has been extensively studied in graph rigidity theory. Specifically, we show that the rank of the rigidity matrix is the same as that of a voltage coefficient matrix in a corresponding electric power system. Accordingly, we show that there is a minimum number of measurements required to uniquely identify the admittance matrix and corresponding grid topology. By means of a numerical example on the IEEE 4-node radial network, we demonstrate that our approach is suitable for applications in electric power grids.

We describe observations of low energy excess (LEE) events (background events observed in all light dark matter direct detection calorimeters) and noise in a two-channel silicon athermal phonon detector with 375 meV baseline energy resolution. We measure two distinct LEE populations: ``shared'' multichannel events with a pulse shape consistent with athermal phonon events, and sub-eV events which couple nearly exclusively to a single channel with a significantly faster pulse shape. These ``singles'' are consistent with events occurring within the aluminum athermal phonon collection fins. Similarly, our measured detector noise is higher than the theoretical expectation. Measured noise can be split into an uncorrelated component, consistent with shot noise from small energy depositions within the athermal phonon sensor itself, and a correlated component, consistent with shot noise from energy depositions within the silicon crystal's phonon system., Comment: 6 pages, 5 figures

The first FASER search for a light, long-lived particle decaying into a pair of photons is reported. The search uses LHC proton-proton collision data at $\sqrt{s}=13.6~\text{TeV}$ collected in 2022 and 2023, corresponding to an integrated luminosity of $57.7\text{fb}^{-1}$. A model with axion-like particles (ALPs) dominantly coupled to weak gauge bosons is the primary target. Signal events are characterised by high-energy deposits in the electromagnetic calorimeter and no signal in the veto scintillators. One event is observed, compared to a background expectation of $0.44 \pm 0.39$ events, which is entirely dominated by neutrino interactions. World-leading constraints on ALPs are obtained for masses up to $300~\text{MeV}$ and couplings to the Standard Model W gauge boson, $g_{aWW}$, around $10^{-4}$ GeV$^{-1}$, testing a previously unexplored region of parameter space. Other new particle models that lead to the same experimental signature, including ALPs coupled to gluons or photons, U(1)$_B$ gauge bosons, up-philic scalars, and a Type-I two-Higgs doublet model, are also considered for interpretation, and new constraints on previously viable parameter space are presented in this paper., Comment: 37 pages, 22 figures

The notion of defects in crystalline phases of matter has been extremely powerful for understanding crystal growth, deformation and melting. These discontinuities in the periodic order of crystals are mathematically described by the Burgers vector, derived from the particle displacements, which encapsulates the direction and magnitude of slip relative to the undeformed state. Since the reference structure of the crystal is known a priori, the Burgers vector can be determined experimentally using both imaging and diffraction methods to measure the lattice distortion, and thus infer the particle displacements. Glasses have structures that lack the periodicity of crystals, and thus a well-defined reference state. Yet, measurable structural parameters can still be obtained from diffraction from a glass. Here we examine the usefulness of these parameters to probe deformation in glasses. We find that coordinated transformations in the centrosymmetry of local particle arrangements are a strong marker of plastic events. Moreover, we investigate two geometric indicators that can be derived from distortions in local diffraction patterns, namely the continuous Burgers vector and the quadrupolar strain. We find that the Burgers vector again emerges as a robust and sensitive metric for understanding local structural transformations due to mechanical deformation, even in structural glasses., Comment: 13 pages 5 figures

We deal with the problem of gradient estimation for stochastic differentiable relaxations of algorithms, operators, simulators, and other non-differentiable functions. Stochastic smoothing conventionally perturbs the input of a non-differentiable function with a differentiable density distribution with full support, smoothing it and enabling gradient estimation. Our theory starts at first principles to derive stochastic smoothing with reduced assumptions, without requiring a differentiable density nor full support, and we present a general framework for relaxation and gradient estimation of non-differentiable black-box functions $f:\mathbb{R}^n\to\mathbb{R}^m$. We develop variance reduction for gradient estimation from 3 orthogonal perspectives. Empirically, we benchmark 6 distributions and up to 24 variance reduction strategies for differentiable sorting and ranking, differentiable shortest-paths on graphs, differentiable rendering for pose estimation, as well as differentiable cryo-ET simulations.

'lintsampler' provides a Python implementation of a technique we term 'linear interpolant sampling': an algorithm to efficiently draw pseudo-random samples from an arbitrary probability density function (PDF). First, the PDF is evaluated on a grid-like structure. Then, it is assumed that the PDF can be approximated between grid vertices by the (multidimensional) linear interpolant. With this assumption, random samples can be efficiently drawn via inverse transform sampling. lintsampler is primarily written with 'numpy', drawing some additional functionality from 'scipy'. Under the most basic usage of lintsampler, the user provides a Python function defining the target PDF and some parameters describing a grid-like structure to the 'LintSampler' class, and is then able to draw samples via the 'sample' method. Additionally, there is functionality for the user to set the random seed, employ quasi-Monte Carlo sampling, or sample within a premade grid ('DensityGrid') or tree ('DensityTree') structure., Comment: Accepted by Journal of Open Source Software. Describes code repository at https://github.com/aneeshnaik/lintsampler

We introduce a conceptual framework for numerically solving linear elliptic, parabolic, and hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural networks. The PDEs are recast as minimization of a least-squares (LSQ for short) residual of an equivalent, well-posed first-order system, over parametric families of deep neural networks. The associated LSQ residual is a) equal or proportional to a weak residual of the PDE, b) additive in terms of contributions from localized subnetworks, indicating locally ``out-of-equilibrium'' of neural networks with respect to the PDE residual, c) serves as numerical loss function for neural network training, and d) constitutes, even with incomplete training, a computable, (quasi-)optimal numerical error estimator in the context of adaptive LSQ finite element methods. In addition, an adaptive neural network growth strategy is proposed which, assuming exact numerical minimization of the LSQ loss functional, yields sequences of neural networks with realizations that converge rate-optimally to the exact solution of the first order system LSQ formulation.

In this paper we solve mixed-integer linear programs (MILPs) via distributed asynchronous saddle point computation. This work is motivated by the MILPs being able to model problems in multi-agent autonomy, such as task assignment problems and trajectory planning with collision avoidance constraints in multi-robot systems. To solve a MILP, we relax it with a linear program approximation. We first show that if the linear program relaxation satisfies Slater's condition, then relaxing the problem, solving it, and rounding the relaxed solution produces a point that is guaranteed to satisfy the constraints of the original MILP. Next, we form a Lagrangian saddle point problem that is equivalent to the linear program relaxation, and then we regularize the Lagrangian in both the primal and dual spaces. Doing so gives a regularized Lagrangian that is strongly convex-strongly concave. We then develop a parallelized algorithm to compute saddle points of the regularized Lagrangian, and we show that it is tolerant to asynchrony in the computations and communications of primal and dual variables. Suboptimality bounds and convergence rates are presented for convergence to a saddle point. The suboptimality bound accounts for (i) the error induced by regularizing the Lagrangian and (ii) the suboptimality gap between the solution to the original MILP and the solution to its relaxed form. Simulation results illustrate these theoretical developments in practice, and show that relaxation and regularization combined typically have only a mild impact on the suboptimality of the solution obtained., Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:2211.11842

Due to climate change the frequency and intensity of extreme rainfall events, which contribute to urban flooding, are expected to increase in many places. These floods can damage transport infrastructure and disrupt mobility, highlighting the need for cities to adapt to escalating risks. Reinforcement learning (RL) serves as a powerful tool for uncovering optimal adaptation strategies, determining how and where to deploy adaptation measures effectively, even under significant uncertainty. In this study, we leverage RL to identify the most effective timing and locations for implementing measures, aiming to reduce both direct and indirect impacts of flooding. Our framework integrates climate change projections of future rainfall events and floods, models city-wide motorized trips, and quantifies direct and indirect impacts on infrastructure and mobility. Preliminary results suggest that our RL-based approach can significantly enhance decision-making by prioritizing interventions in specific urban areas and identifying the optimal periods for their implementation.

We study the problem of approximating and estimating classification functions that have their decision boundary in the $RBV^2$ space. Functions of $RBV^2$ type arise naturally as solutions of regularized neural network learning problems and neural networks can approximate these functions without the curse of dimensionality. We modify existing results to show that every $RBV^2$ function can be approximated by a neural network with bounded weights. Thereafter, we prove the existence of a neural network with bounded weights approximating a classification function. And we leverage these bounds to quantify the estimation rates. Finally, we present a numerical study that analyzes the effect of different regularity conditions on the decision boundaries.

This paper is concerned with open quantum harmonic oscillators with position-momentum system variables, whose internal dynamics and interaction with the environment are governed by linear quantum stochastic differential equations. A recently proposed approach to such systems as Heisenberg picture quantum memories exploits their ability to approximately retain initial conditions over a decoherence horizon. Using the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation of the system variables from their initial values, we apply this approach to a partially isolated subsystem of the oscillator, which is not directly affected by the external fields. The partial isolation leads to an appropriate system decomposition and a qualitatively different short-horizon asymptotic behaviour of the deviation, which yields a longer decoherence time in the high-fidelity limit. The resulting approximate decoherence time maximization over the energy parameters for improving the quantum memory performance is discussed for a coherent feedback interconnection of such systems., Comment: 9 pages, 3 figures, submitted to ANZCC 2025

Business Process Management (BPM) is mostly centered around finding technical solutions. Nudging is an approach from psychology and behavioral economics to guide people's behavior. In this paper, we show how nudging can be integrated into the different phases of the BPM lifecycle. Further, we outline how nudging can be an alternative strategy for more sustainable business processes. We show how the integration of nudging offers significant opportunities for process mining and business process management in general to be more human-centric. We also discuss challenges that come with the adoption of nudging.

Process models may be automatically generated from event logs that contain as-is data of a business process. While such models generalize over the control-flow of specific, recorded process executions, they are often also annotated with behavioural statistics, such as execution frequencies.Based thereon, once a model is published, certain insights about the original process executions may be reconstructed, so that an external party may extract confidential information about the business process. This work is the first to empirically investigate such reconstruction attempts based on process models. To this end, we propose different play-out strategies that reconstruct the control-flow from process trees, potentially exploiting frequency annotations. To assess the potential success of such reconstruction attacks on process models, and hence the risks imposed by publishing them, we compare the reconstructed process executions with those of the original log for several real-world datasets.

The noncommutative nature of quantum mechanics imposes fundamental constraints on system dynamics, which, in the linear realm, are manifested through the physical realizability conditions on system matrices. These restrictions give system matrices a unique structure. This paper aims to study this structure by investigating the zeros and poles of linear quantum systems. Firstly, it is shown that -s_0 is a transmission zero if and only if s_0 is a pole of the transfer function, and -s_0 is an invariant zero if and only if s_0 is an eigenvalue of the A-matrix, of a linear quantum system. Moreover, s_0 is an output-decoupling zero if and only if -s_0 is an input-decoupling zero. Secondly, based on these zero-pole correspondences, we show that a linear quantum system must be Hurwitz unstable if it is strongly asymptotically left invertible. Two types of stable input observers are constructed for unstable linear quantum systems. Finally, the sensitivity of a coherent feedback network is investigated; in particular, the fundamental tradeoff between ideal input squeezing and system robustness is studied on the basis of system sensitivity analysis., Comment: 16 pages, 2 figures, comments are welcome. arXiv admin note: text overlap with arXiv:2408.03177

Diffusion models have a tendency to exactly replicate their training data, especially when trained on small datasets. Most prior work has sought to mitigate this problem by imposing differential privacy constraints or masking parts of the training data, resulting in a notable substantial decrease in image quality. We present CPSample, a method that modifies the sampling process to prevent training data replication while preserving image quality. CPSample utilizes a classifier that is trained to overfit on random binary labels attached to the training data. CPSample then uses classifier guidance to steer the generation process away from the set of points that can be classified with high certainty, a set that includes the training data. CPSample achieves FID scores of 4.97 and 2.97 on CIFAR-10 and CelebA-64, respectively, without producing exact replicates of the training data. Unlike prior methods intended to guard the training images, CPSample only requires training a classifier rather than retraining a diffusion model, which is computationally cheaper. Moreover, our technique provides diffusion models with greater robustness against membership inference attacks, wherein an adversary attempts to discern which images were in the model's training dataset. We show that CPSample behaves like a built-in rejection sampler, and we demonstrate its capabilities to prevent mode collapse in Stable Diffusion.

The topological Hochschild homology of a ring (or ring spectrum) $R$ is an $S^1$-spectrum, and the fixed points of THH($R$) for subgroups $C_n\subset S^1$ have been widely studied due to their use in algebraic K-theory computations. Hesselholt and Madsen proved that the fixed points of topological Hochschild homology are closely related to Witt vectors. Further, they defined the notion of a Witt complex, and showed that it captures the algebraic structure of the homotopy groups of the fixed points of THH. Recent work of Angeltveit, Blumberg, Gerhardt, Hill, Lawson and Mandell defines a theory of twisted topological Hochschild homology for equivariant rings (or ring spectra) that builds upon Hill, Hopkins and Ravenel's work on equivariant norms. In this paper, we study the algebraic structure of the equivariant homotopy groups of twisted THH. In particular, we define an equivariant Witt complex and prove that the equivariant homotopy of twisted THH has this structure. Our definition of equivariant Witt complexes contributes to a growing body of research in the subject of equivariant algebra., Comment: 35 pages

To study any dynamical system it is useful to find a partition that allows essentially faithful encoding (injective, up to a small exceptional set) into a subshift. Most topological and measure-theoretic systems can be represented by Bratteli-Vershik (or adic, or BV) systems. So it is natural to ask when can a BV system be encoded essentially faithfully. We show here that for BV diagrams defined by homogeneous positive integer multivariable polynomials, and a wide family of their generalizations, which we call polynomial shape diagrams, for every choice of the edge ordering the coding according to initial path segments of a fixed finite length is injective off of a negligible exceptional set.

Individuals with Intellectual and Developmental Disabilities (IDD) have unique needs and challenges when working with data. While visualization aims to make data more accessible to a broad audience, our understanding of how to design cognitively accessible visualizations remains limited. In this study, we engaged 20 participants with IDD as co-designers to explore how they approach and visualize data. Our preliminary investigation paired four participants as data pen-pals in a six-week online asynchronous participatory design workshop. In response to the observed conceptual, technological, and emotional struggles with data, we subsequently organized a two-day in-person co-design workshop with 16 participants to further understand relevant visualization authoring and sensemaking strategies. Reflecting on how participants engaged with and represented data, we propose two strategies for cognitively accessible data visualizations: transforming numbers into narratives and blending data design with everyday aesthetics. Our findings emphasize the importance of involving individuals with IDD in the design process, demonstrating their capacity for data analysis and expression, and underscoring the need for a narrative and tangible approach to accessible data visualization.

Many interventions are both beneficial to initiate and harmful to stop. Traditionally, to determine whether to deploy that intervention in a time-limited way depends on if, on average, the increase in the benefits of starting it outweigh the increase in the harms of stopping it. We propose a novel causal estimand that provides a more nuanced understanding of the effects of such treatments, particularly, how response to an earlier treatment (e.g., treatment initiation) modifies the effect of a later treatment (e.g., treatment discontinuation), thus learning if there are effects among the (un)affected. Specifically, we consider a marginal structural working model summarizing how the average effect of a later treatment varies as a function of the (estimated) conditional average effect of an earlier treatment. We allow for estimation of this conditional average treatment effect using machine learning, such that the causal estimand is a data-adaptive parameter. We show how a sequentially randomized design can be used to identify this causal estimand, and we describe a targeted maximum likelihood estimator for the resulting statistical estimand, with influence curve-based inference. Throughout, we use the Adaptive Strategies for Preventing and Treating Lapses of Retention in HIV Care trial (NCT02338739) as an illustrative example, showing that discontinuation of conditional cash transfers for HIV care adherence was most harmful among those who most had an increase in benefits from them initially.

To promote sustainable business practices, and to achieve climate neutrality by 2050, the EU has developed the taxonomy of sustainable activities, which describes when exactly business practices can be considered sustainable. While the taxonomy has only been recently established, progressively more companies will have to report how much of their revenue was created via sustainably executed business processes. To help companies prepare to assess whether their business processes comply with the constraints outlined in the taxonomy, we investigate in how far these criteria can be used for conformance checking, that is, assessing in a data-driven manner, whether business process executions adhere to regulatory constraints. For this, we develop a few-shot learning pipeline to characterize the constraints of the taxonomy with the help of an LLM as to the process dimensions they relate to. We find that many constraints of the taxonomy are useable for conformance checking, particularly in the sectors of energy, manufacturing, and transport. This will aid companies in preparing to monitor regulatory compliance with the taxonomy automatically, by characterizing what kind of information they need to extract, and by providing a better understanding of sectors where such an assessment is feasible and where it is not.

In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the $3^{rd}$ order Upwind and the $5^{th}$ order Upwind and WENO reconstruction schemes in the TT format. It is shown in detail that the linear upwind schemes can be implemented by directly manipulating the TT cores while the WENO scheme requires the use of TT cross interpolation for the nonlinear reconstruction. In the development of numerical fluxes, we directly compute the flux for the linear SWEs without using TT rounding or cross interpolation. For the nonlinear SWEs where the TT reciprocal of the shallow water layer thickness is needed for fluxes, we develop an approximation algorithm using Taylor series to compute the TT reciprocal. The performance of the TT finite volume solver with linear and nonlinear reconstruction options is investigated under a physically relevant set of validation problems. In all test cases, the TT finite volume method maintains the formal high-order accuracy of the corresponding traditional finite volume method. In terms of speed, the TT solver achieves up to 124x acceleration of the traditional full-tensor scheme.

Visualization, from simple line plots to complex high-dimensional visual analysis systems, has established itself throughout numerous domains to explore, analyze, and evaluate data. Applying such visualizations in the context of simulation science where High-Performance Computing (HPC) produces ever-growing amounts of data that is more complex, potentially multidimensional, and multimodal, takes up resources and a high level of technological experience often not available to domain experts. In this work, we present DaVE -- a curated database of visualization examples, which aims to provide state-of-the-art and advanced visualization methods that arise in the context of HPC applications. Based on domain- or data-specific descriptors entered by the user, DaVE provides a list of appropriate visualization techniques, each accompanied by descriptions, examples, references, and resources. Sample code, adaptable container templates, and recipes for easy integration in HPC applications can be downloaded for easy access to high-fidelity visualizations. While the database is currently filled with a limited number of entries based on a broad evaluation of needs and challenges of current HPC users, DaVE is designed to be easily extended by experts from both the visualization and HPC communities., Comment: 4 + 1 pages, 4 figures, to be published at VIS 2024

This manuscript explores the intersection of surrogate outcomes and adaptive designs in statistical research. While surrogate outcomes have long been studied for their potential to substitute long-term primary outcomes, current surrogate evaluation methods do not directly account for the potential benefits of using surrogate outcomes to adapt randomization probabilities in adaptive randomized trials that aim to learn and respond to treatment effect heterogeneity. In this context, surrogate outcomes can benefit participants in the trial directly (i.e. improve expected outcome of newly-enrolled participants) by allowing for more rapid adaptation of randomization probabilities, particularly when surrogates enable earlier detection of heterogeneous treatment effects and/or indicate the optimal (individualized) treatment with stronger signals. Our study introduces a novel approach for surrogate evaluation that quantifies both of these benefits in the context of sequential adaptive experiment designs. We also propose a new Covariate-Adjusted Response-Adaptive (CARA) design that incorporates an Online Superlearner to assess and adaptively choose surrogate outcomes for updating treatment randomization probabilities. We introduce a Targeted Maximum Likelihood Estimator that addresses data dependency challenges in adaptively collected data and achieves asymptotic normality under reasonable assumptions without relying on parametric model assumptions. The robust performance of our adaptive design with Online Superlearner is presented via simulations. Our framework not only contributes a method to more comprehensively quantifying the benefits of candidate surrogate outcomes and choosing between them, but also offers an easily generalizable tool for evaluating various adaptive designs and making inferences, providing insights into alternative choices of designs.

Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$, the number of curves per subject, is often much larger than the sample size $n$. In this setting of high-dimensional functional data, much of developed methodology relies on preliminary estimates of the unknown mean functions and the auto- and cross-covariance functions. This paper investigates the convergence rates of local linear estimators in terms of the maximal error across components and pairs of components for mean and covariance functions, respectively, in both $L^2$ and uniform metrics. The local linear estimators utilize a generic weighting scheme that can adjust for differing numbers of discrete observations $N_{ij}$ across curves $j$ and subjects $i$, where the $N_{ij}$ vary with $n$. Particular attention is given to the equal weight per observation (OBS) and equal weight per subject (SUBJ) weighting schemes. The theoretical results utilize novel applications of concentration inequalities for functional data and demonstrate that, similar to univariate functional data, the order of the $N_{ij}$ relative to $p$ and $n$ divides high-dimensional functional data into three regimes (sparse, dense, and ultra-dense), with the high-dimensional parametric convergence rate of $\left\{\log(p)/n\right\}^{1/2}$ being attainable in the latter two., Comment: 27 pages, Journal of Multivariate Analysis (accepted)

Combining machine learning and formal methods (FMs) provides a possible solution to overcome the safety issue of autonomous driving (AD) vehicles. However, there are gaps to be bridged before this combination becomes practically applicable and useful. In an attempt to facilitate researchers in both FMs and AD areas, this paper proposes a framework that combines two well-known tools, namely CommonRoad and UPPAAL. On the one hand, CommonRoad can be enhanced by the rigorous semantics of models in UPPAAL, which enables a systematic and comprehensive understanding of the AD system's behaviour and thus strengthens the safety of the system. On the other hand, controllers synthesised by UPPAAL can be visualised by CommonRoad in real-world road networks, which facilitates AD vehicle designers greatly adopting formal models in system design. In this framework, we provide automatic model conversions between CommonRoad and UPPAAL. Therefore, users only need to program in Python and the framework takes care of the formal models, learning, and verification in the backend. We perform experiments to demonstrate the applicability of our framework in various AD scenarios, discuss the advantages of solving motion planning in our framework, and show the scalability limit and possible solutions., Comment: 20 pages, 5 figures, ISoLA 2024

Hyperspectral imaging captures both spectral and spatial information from a sample. The near infrared (NIR, > 800 nm) is advantageous for biomedical imaging as it falls into the tissue transparency window but also contains vibrational overtone and combination modes useful for molecular fingerprinting. Here, we demonstrate hyperspectral NIR imaging using a spectral phasor transformation (HyperNIR). This method employs a liquid crystal variable retarder (LCVR) for tunable, wavelength-dependent sine-, cosine and no filtering that transforms optical signals into phasor space. Spectral information is thus obtained with just three images. The LCVR can be adjusted to cover a spectral range from 900 nm to 1600 nm in windows tunable from 50 nm to 700 nm. This approach enables distinguishing NIR fluorophores with emission peaks less than 5 nm apart. Furthermore, we demonstrate label-free hyperspectral NIR reflectance imaging to identify plastic polymers and to monitor in vivo plant health. The approach uses the full camera resolution and reaches hyperspectral frame rates of 0.2 per second, limited only by the switching rate of the LCVR. HyperNIR facilitates straightforward hyperspectral imaging with standard NIR cameras for applications in biomedical imaging and environmental monitoring., Comment: Main Manuscript (15 pages, 5 figures) + Supplementary Information (15 pages, 14 figures)

We propose and evaluate a question-answering system that uses decomposed prompting to classify and answer student questions on a course discussion board. Our system uses a large language model (LLM) to classify questions into one of four types: conceptual, homework, logistics, and not answerable. This enables us to employ a different strategy for answering questions that fall under different types. Using a variant of GPT-3, we achieve $81\%$ classification accuracy. We discuss our system's performance on answering conceptual questions from a machine learning course and various failure modes., Comment: 6 pages. Published at International Conference on Artificial Intelligence in Education 2023. Code repository: https://github.com/brandonjaipersaud/piazza-qabot-gpt

We consider the problem of synthesizing safety strategies for control systems, also known as shields. Since the state space is infinite, shields are typically computed over a finite-state abstraction, with the most common abstraction being a rectangular grid. However, for many systems, such a grid does not align well with the safety property or the system dynamics. That is why a coarse grid is rarely sufficient, but a fine grid is typically computationally infeasible to obtain. In this paper, we show that appropriate state-space transformations can still allow to use a coarse grid at almost no computational overhead. We demonstrate in three case studies that our transformation-based synthesis outperforms a standard synthesis by several orders of magnitude. In the first two case studies, we use domain knowledge to select a suitable transformation. In the third case study, we instead report on results in engineering a transformation without domain knowledge.

The validity of medical studies based on real-world clinical data, such as observational studies, depends on critical assumptions necessary for drawing causal conclusions about medical interventions. Many published studies are flawed because they violate these assumptions and entail biases such as residual confounding, selection bias, and misalignment between treatment and measurement times. Although researchers are aware of these pitfalls, they continue to occur because anticipating and addressing them in the context of a specific study can be challenging without a large, often unwieldy, interdisciplinary team with extensive expertise. To address this expertise gap, we explore the use of large language models (LLMs) as co-pilot tools to assist researchers in identifying study design flaws that undermine the validity of causal inferences. We propose a conceptual framework for LLMs as causal co-pilots that encode domain knowledge across various fields, engaging with researchers in natural language interactions to provide contextualized assistance in study design. We provide illustrative examples of how LLMs can function as causal co-pilots, propose a structured framework for their grounding in existing causal inference frameworks, and highlight the unique challenges and opportunities in adapting LLMs for reliable use in epidemiological research.

This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural network theory. Serving as a guide for students and researchers in mathematics and related fields, the book aims to equip readers with foundational knowledge on the topic. It prioritizes simplicity over generality, and presents rigorous yet accessible results to help build an understanding of the essential mathematical concepts underpinning deep learning.

Business process management (BPM) has been widely used to discover, model, analyze, and optimize organizational processes. BPM looks at these processes with analysis techniques that assume a clearly defined start and end. However, not all processes adhere to this logic, with the consequence that their behavior cannot be appropriately captured by BPM analysis techniques. This paper addresses this research problem at a conceptual level. More specifically, we introduce the notion of vitalizing business processes that target the lifecycle process of one or more entities. We show the existence of lifecycle processes in many industries and that their appropriate conceptualizations pave the way for the definition of suitable modeling and analysis techniques. This paper provides a set of requirements for their analysis, and a conceptualization of lifecycle and vitalizing processes.

In this study, high pressure synchrotron powder X-ray diffraction is used to investigate the compression of two high pressure polymorphs of \ce{CrSb2}. The first is the \ce{CuAl2}-type polymorph with an eight-fold coordinated Cr, which can be quenched to ambient conditions from high-pressure high-temperature conditions. The second is the recently discovered \ce{MoP2}-type polymorph, which is induced by compression at room temperature, with a seven-fold coordinated Cr. Here, the assigned structure is unambiguously confirmed by solving it from single-crystal X-ray diffraction. Furthermore, the electrical properties of the \ce{MoP2}-type polymorph were investigated theoretically and the resistance calculations under pressure were accompanied by resistance measurements under high pressure on a single crystal of \ce{CrSb2}. The calculated electronic band structure for the \ce{MoP2}-type phase is discussed and we show that the polymorph is semimetallic and possesses type-I Weyl points. No further phase transitions were observed for the \ce{CuAl2}-type structure up to 50 GPa and 40 GPa for the \ce{MoP2}-type structure. Even though the \ce{CuAl2}-phase has the highest coordination number of Cr, it was found to be less compressible than the \ce{MoP2}-phase having a seven-fold coordinated Cr, which was attributed to the longer Cr-Sb distance in the \ce{CuAl2}-type phase. The discovery of a type-I Weyl semimetallic phase in \ce{CrSb2} opens up for discovering other Weyl semimetals in the transition metal di-pnictides under high pressure., Comment: 20 pages, 4 tables, 6 figures

Virtual interventions enable the physics-based simulation of device deployment within coronary arteries. This framework allows for counterfactual reasoning by deploying the same device in different arterial anatomies. However, current methods to create such counterfactual arteries face a trade-off between controllability and realism. In this study, we investigate how Latent Diffusion Models (LDMs) can custom synthesize coronary anatomy for virtual intervention studies based on mid-level anatomic constraints such as topological validity, local morphological shape, and global skeletal structure. We also extend diffusion model guidance strategies to the context of morpho-skeletal conditioning and propose a novel guidance method for continuous attributes that adaptively updates the negative guiding condition throughout sampling. Our framework enables the generation and editing of coronary anatomy in a controllable manner, allowing device designers to derive mechanistic insights regarding anatomic variation and simulated device deployment., Comment: Accepted to ECCV 2024

As longitudinal data becomes more available in many settings, policy makers are increasingly interested in the effect of time-varying treatments (e.g. sustained treatment strategies). In settings such as this, the preferred analysis techniques are the g-methods, however these require the untestable assumption of no unmeasured confounding. Instrumental variable analyses can minimise bias through unmeasured confounding. Of these methods, the Two Stage Least Squares technique is one of the most well used in Econometrics, but it has not been fully extended, and evaluated, in full time-varying settings. This paper proposes a robust two stage least squares method for the econometric evaluation of time-varying treatment. Using a simulation study we found that, unlike standard two stage least squares, it performs relatively well across a wide range of circumstances, including model misspecification. It compares well with recent time-varying instrument approaches via g-estimation. We illustrate the methods in an evaluation of treatment intensification for Type-2 Diabetes Mellitus, exploring the exogeneity in prescribing preferences to operationalise a time-varying instrument., Comment: 34 Pages, 4 Figures, and 7 Tables

In the dynamic field of Software Engineering (SE), where practice is constantly evolving and adapting to new technologies, conducting research is a daunting quest. This poses a challenge for researchers: how to stay relevant and effective in their studies? Empirical Software Engineering (ESE) has emerged as a contending force aiming to critically evaluate and provide knowledge that informs practice in adopting new technologies. Empirical research requires a rigorous process of collecting and analyzing data to obtain evidence-based findings. Challenges to this process are numerous, and many researchers, novice and experienced, found difficulties due to many complexities involved in designing their research. The core of this chapter is to teach foundational skills in research design, essential for educating software engineers and researchers in ESE. It focuses on developing a well-structured research design, which includes defining a clear area of investigation, formulating relevant research questions, and choosing appropriate methodologies. While the primary focus is on research design, this chapter also covers aspects of research scoping and selecting research methods. This approach prepares students to handle the complexities of the ever-changing technological landscape in SE, making it a critical component of their educational curriculum.

Beyond individual languages, multilingual natural language processing (NLP) research increasingly aims to develop models that perform well across languages generally. However, evaluating these systems on all the world's languages is practically infeasible. To attain generalizability, representative language sampling is essential. Previous work argues that generalizable multilingual evaluation sets should contain languages with diverse typological properties. However, 'typologically diverse' language samples have been found to vary considerably in this regard, and popular sampling methods are flawed and inconsistent. We present a language sampling framework for selecting highly typologically diverse languages given a sampling frame, informed by language typology. We compare sampling methods with a range of metrics and find that our systematic methods consistently retrieve more typologically diverse language selections than previous methods in NLP. Moreover, we provide evidence that this affects generalizability in multilingual model evaluation, emphasizing the importance of diverse language sampling in NLP evaluation.

Magnetic resonance is a prime method for the study of chemical and biological structures and their dynamical processes. The interpretation of many of these experiments relies on understanding how the spin of unpaired electrons exchanges energy with their environment, or lattice, and relaxes to equilibrium. In this work, we overcome the common use of effective spin Hamiltonians to describe spin-lattice relaxation in spin-1/2 and apply ab initio open quantum systems theory to their full molecular electronic wavefunction. Simulations for two Cr(V) coordination compounds under this framework show a dramatic improvement in accuracy and demonstrate that relaxation in spin-1/2 molecules is enabled by virtual transitions to molecular excited states with energy approaching 20,000 cm$^{-1}$. This work establishes a connection between the original theory of Van Vleck and modern electronic structure methods, ultimately exemplifying the urgency of further advancing an ab initio approach to spin-lattice relaxation.

Bacterial sensor systems can be used for the detection and measurement of molecular signal concentrations. The dynamics of the sensor directly depend on the biological properties of the bacterial sensor cells; manipulation of these features in the wet lab enables the engineering and optimization of the bacterial sensor kinetics. This necessitates the development of biologically meaningful computational models for bacterial sensors comprising a variety of different molecular mechanisms, which further facilitates a systematic and quantitative evaluation of optimization strategies. In this work, we dissect the detection chain of bacterial sensors from a mathematical perspective from which we derive, supported by wet-lab data, a complete computational model for a Streptococcus mutans-based bacterial sensor as a case example. We address the engineering of bacterial sensors by investigating the impact of altered bacterial cell properties on the sensor response characteristics, specifically sensor sensitivity and response signal intensity. This is achieved through a sensitivity analysis targeting both the steady-state and transient sensor response characteristics. Alongside the demonstration of suitability of our methodological approach, our analysis shows that an increase of sensor sensitivity, through a targeted manipulation of bacterial physiology, often comes at the cost of generally diminished sensor response intensity.

We propose a discrete-time integral resonant control (IRC) approach for negative imaginary (NI) systems, which overcomes several limitations of continuous-time IRC. We show that a discrete-time IRC has a step-advanced negative imaginary property. A zero-order hold-sampled NI system can be asymptotically stabilized using a discrete-time IRC with suitable parameters. A hardware experiment is conducted where a high-speed flexure-guided nanopositioner is efficiently damped using the proposed discrete-time IRC with the discrete-time controller being implemented in FPGA hardware at the sampling rate of 1.25 MHz., Comment: 10 pages, 10 figures

Measuring the rate of innovation in academia and industry is fundamental to monitoring the efficiency and competitiveness of the knowledge economy. To this end, a disruption index (CD) was recently developed and applied to publication and patent citation networks (Wu et al., Nature 2019; Park et al., Nature 2023). Here we show that CD systematically decreases over time due to secular growth in research and patent production, following two distinct mechanisms unrelated to innovation -- one behavioral and the other structural. Whereas the behavioral explanation reflects shifts associated with techno-social factors (e.g. self-citation practices), the structural explanation follows from `citation inflation' (CI), an inextricable feature of real citation networks attributable to increasing reference list lengths, which causes CD to systematically decrease. We demonstrate this causal link by way of mathematical deduction, computational simulation, multi-variate regression, and quasi-experimental comparison of the disruptiveness of PNAS versus PNAS Plus articles, which differ only in their lengths. Accordingly, we analyze CD data available in the SciSciNet database and find that disruptiveness incrementally increased from 2005-2015, and that the negative relationship between disruption and team-size is remarkably small in overall magnitude effect size, and shifts from negative to positive for team size $\geq$ 8 coauthors., Comment: 9 pages, 4 figures; SI: 4 figures and 4 tables

We consider labelings of a finite regular tree by a finite alphabet subject to restrictions specified by a nonnegative transition matrix, propose an algorithm for determining whether the set of possible configurations on the last row of the tree is independent of the symbol at the root, and prove that the algorithm succeeds in a bounded number of steps, provided that the dimension of the tree is greater than or equal to the maximum row sum of the transition matrix. (The question was motivated by calculation of topological pressure on trees and is an extension of the idea of primitivity for nonnegative matrices.), Comment: Slight reorganization and light editing

Machine learning models have achieved high overall accuracy in medical image analysis. However, performance disparities on specific patient groups pose challenges to their clinical utility, safety, and fairness. This can affect known patient groups - such as those based on sex, age, or disease subtype - as well as previously unknown and unlabeled groups. Furthermore, the root cause of such observed performance disparities is often challenging to uncover, hindering mitigation efforts. In this paper, to address these issues, we leverage Slice Discovery Methods (SDMs) to identify interpretable underperforming subsets of data and formulate hypotheses regarding the cause of observed performance disparities. We introduce a novel SDM and apply it in a case study on the classification of pneumothorax and atelectasis from chest x-rays. Our study demonstrates the effectiveness of SDMs in hypothesis formulation and yields an explanation of previously observed but unexplained performance disparities between male and female patients in widely used chest X-ray datasets and models. Our findings indicate shortcut learning in both classification tasks, through the presence of chest drains and ECG wires, respectively. Sex-based differences in the prevalence of these shortcut features appear to cause the observed classification performance gap, representing a previously underappreciated interaction between shortcut learning and model fairness analyses., Comment: MICCAI 2024 Workshop on Fairness of AI in Medical Imaging

The European Commission's new definition of green hydrogen provides clear guidelines and legal certainty for producers and consumers. However, the strict criteria for electrolysis production, requiring additionality, temporal correlation, and geographical correlation, could increase hydrogen costs, affecting its competitiveness as an energy carrier. This study examines the impact of these European regulations using a stochastic capacity expansion model for the European energy market up to 2048. We analyze how these requirements influence costs and investment decisions. Our results show that green hydrogen production requirements will raise system costs by 82 Euro billion from 2024 to 2048, driven mainly by a rapid transition from fossil fuels to renewable energy. The additionality requirement, which mandates the use of new renewable energy installations for electrolysis, emerges as the most expensive to comply with but also the most effective in accelerating the transition to renewable power, particularly before 2030.

Identifying predictive biomarkers, which forecast individual treatment effectiveness, is crucial for personalized medicine and informs decision-making across diverse disciplines. These biomarkers are extracted from pre-treatment data, often within randomized controlled trials, and have to be distinguished from prognostic biomarkers, which are independent of treatment assignment. Our study focuses on the discovery of predictive imaging biomarkers, aiming to leverage pre-treatment images to unveil new causal relationships. Previous approaches relied on labor-intensive handcrafted or manually derived features, which may introduce biases. In response, we present a new task of discovering predictive imaging biomarkers directly from the pre-treatment images to learn relevant image features. We propose an evaluation protocol for this task to assess a model's ability to identify predictive imaging biomarkers and differentiate them from prognostic ones. It employs statistical testing and a comprehensive analysis of image feature attribution. We explore the suitability of deep learning models originally designed for estimating the conditional average treatment effect (CATE) for this task, which previously have been primarily assessed for the precision of CATE estimation, overlooking the evaluation of imaging biomarker discovery. Our proof-of-concept analysis demonstrates promising results in discovering and validating predictive imaging biomarkers from synthetic outcomes and real-world image datasets., Comment: 19 pages, 12 figures

In the transition to achieving net zero emissions, it has been suggested that a substantial expansion of electric power grids will be necessary to support emerging renewable energy zones. In this paper, we propose employing battery-based feedback control and nonlinear negative imaginary (NI) systems theory to reduce the need for such expansion. By formulating a novel Lur\'e-Postnikov-like Lyapunov function, stability results are presented for the feedback interconnection of two single nonlinear NI systems, while output feedback consensus results are established for the feedback interconnection of two networked nonlinear NI systems based on a network topology. This theoretical framework underpins our design of battery-based control in power transmission systems. We demonstrate that the power grid can be gradually transitioned into the proposed NI systems, one transmission line at a time., Comment: 8 pages, 2 figures, 26th International Symposium on Mathematical Theory of Networks and Systems