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We present Modular Polynomial (MP) Codes for Secure Distributed Matrix Multiplication (SDMM). The construction is based on the observation that one can decode certain proper subsets of the coefficients of a polynomial with fewer evaluations than is necessary to interpolate the entire polynomial. These codes are proven to outperform, in terms of recovery threshold, the currently best-known polynomial codes for the inner product partition. We also present Generalized Gap Additive Secure Polynomial (GGASP) codes for the grid partition. These two families of codes are shown experimentally to perform favorably in terms of recovery threshold when compared to other comparable polynomials codes for SDMM. Both MP and GGASP codes achieve the recovery threshold of Entangled Polynomial Codes for robustness against stragglers, but MP codes can decode below this recovery threshold depending on the set of worker nodes which fails. The decoding complexity of MP codes is shown to be lower than other approaches in the literature, due to the user not being tasked with interpolating an entire polynomial.

Modern radio telescopes will daily generate data sets on the scale of exabytes for systems like the Square Kilometre Array (SKA). Massive data sets are a source of unknown and rare astrophysical phenomena that lead to discoveries. Nonetheless, this is only plausible with the exploitation of intensive machine intelligence to complement human-aided and traditional statistical techniques. Recently, there has been a surge in scientific publications focusing on the use of artificial intelligence in radio astronomy, addressing challenges such as source extraction, morphological classification, and anomaly detection. This study presents a succinct, but comprehensive review of the application of machine intelligence techniques on radio images with emphasis on the morphological classification of radio galaxies. It aims to present a detailed synthesis of the relevant papers summarizing the literature based on data complexity, data pre-processing, and methodological novelty in radio astronomy. The rapid advancement and application of computer intelligence in radio astronomy has resulted in a revolution and a new paradigm shift in the automation of daunting data processes. However, the optimal exploitation of artificial intelligence in radio astronomy, calls for continued collaborative efforts in the creation of annotated data sets. Additionally, in order to quickly locate radio galaxies with similar or dissimilar physical characteristics, it is necessary to index the identified radio sources. Nonetheless, this issue has not been adequately addressed in the literature, making it an open area for further study.

In this paper we consider the generalized inverse iteration for computing ground states of the Gross-Pitaevskii eigenvector problem (GPE). For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross-Pitaevskii operator, recovering the same rates as for linear eigenvector problems. With this we establish the first local convergence result for the basic inverse iteration for the GPE without damping. We also show how our findings directly generalize to extended inverse iterations, such as the Gradient Flow Discrete Normalized (GFDN) proposed in [W. Bao, Q. Du, SIAM J. Sci. Comput., 25 (2004)] or the damped inverse iteration suggested in [P. Henning, D. Peterseim, SIAM J. Numer. Anal., 53 (2020)]. Our analysis also reveals why the inverse iteration for the GPE does not react favourably to spectral shifts. This empirical observation can now be explained with a blow-up of a weighting function that crucially contributes to the convergence rates. Our findings are illustrated by numerical experiments.

We consider \emph{Gibbs distributions}, which are families of probability distributions over a discrete space $\Omega$ with probability mass function of the form $\mu^\Omega_\beta(\omega) \propto e^{\beta H(\omega)}$ for $\beta$ in an interval $[\beta_{\min}, \beta_{\max}]$ and $H( \omega ) \in \{0 \} \cup [1, n]$. The \emph{partition function} is the normalization factor $Z(\beta)=\sum_{\omega \in\Omega}e^{\beta H(\omega)}$. Two important parameters of these distributions are the log partition ratio $q = \log \tfrac{Z(\beta_{\max})}{Z(\beta_{\min})}$ and the counts $c_x = |H^{-1}(x)|$. These are correlated with system parameters in a number of physical applications and sampling algorithms. Our first main result is to estimate the counts $c_x$ using roughly $\tilde O( \frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and $\tilde O( \frac{n^2}{\varepsilon^2} )$ samples for integer-valued distributions (ignoring some second-order terms and parameters), and we show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs, independent sets, and perfect matchings. As a key subroutine, we also develop algorithms to compute the partition function $Z$ using $\tilde O(\frac{q}{\varepsilon^2})$ samples for general Gibbs distributions and using $\tilde O(\frac{n^2}{\varepsilon^2})$ samples for integer-valued distributions.

Recent studies show that stable distributions are successful in modeling heavy-tailed or impulsive noise. Investigation of the stability of a probability distribution can be greatly facilitated if the corresponding characteristic function (CF) has a closed-form expression. We explore a new family of distribution called the Vertically-Drifted First Arrival Position (VDFAP) distribution, which can be viewed as a generalization of symmetric alpha-stable (S$\alpha$S) distribution with stability parameter $\alpha=1$. In addition, VDFAP distribution has a clear physical interpretation when we consider first-hitting problems of particles following Brownian motion with a driving drift. Inspired by the Fourier relation between the probability density function and CF of Student's $t$-distribution, we extract an integral representation for the VDFAP probability density function. Then, we exploit the Hankel transform to derive a closed-form expression for the CF of VDFAP. From the CF, we discover that VDFAP possesses some interesting stability properties, which are in a weaker form than S$\alpha$S. This calls for a generalization of the theory on alpha-stable distributions.

Future collaborative robots must be capable of finding objects. As such a fundamental skill, we expect object search to eventually become an off-the-shelf capability for any robot, similar to e.g., object detection, SLAM, and motion planning. However, existing approaches either make unrealistic compromises (e.g., reduce the problem from 3D to 2D), resort to ad-hoc, greedy search strategies, or attempt to learn end-to-end policies in simulation that are yet to generalize across real robots and environments. This thesis argues that through using Partially Observable Markov Decision Processes (POMDPs) to model object search while exploiting structures in the human world (e.g., octrees, correlations) and in human-robot interaction (e.g., spatial language), a practical and effective system for generalized object search can be achieved. In support of this argument, I develop methods and systems for (multi-)object search in 3D environments under uncertainty due to limited field of view, occlusion, noisy, unreliable detectors, spatial correlations between objects, and possibly ambiguous spatial language (e.g., "The red car is behind Chase Bank"). Besides evaluation in simulators such as PyGame, AirSim, and AI2-THOR, I design and implement a robot-independent, environment-agnostic system for generalized object search in 3D and deploy it on the Boston Dynamics Spot robot, the Kinova MOVO robot, and the Universal Robots UR5e robotic arm, to perform object search in different environments. The system enables, for example, a Spot robot to find a toy cat hidden underneath a couch in a kitchen area in under one minute. This thesis also broadly surveys the object search literature, proposing taxonomies in object search problem settings, methods and systems.

Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors follow some geometric structure in the latent space. In this paper, we consider random dot product graphs, in which an edge is formed between two nodes with probability given by the inner product of their respective latent positions. We assume that the latent position vectors lie on an unknown one-dimensional curve and are coupled with a response covariate via a regression model. Using the geometry of the underlying latent position vectors, we propose a manifold learning and graph embedding technique to predict the response variable on out-of-sample nodes, and we establish convergence guarantees for these responses. Our theoretical results are supported by simulations and an application to Drosophila brain data.

The analysis of large-scale time-series network data, such as social media and email communications, remains a significant challenge for graph analysis methodology. In particular, the scalability of graph analysis is a critical issue hindering further progress in large-scale downstream inference. In this paper, we introduce a novel approach called "temporal encoder embedding" that can efficiently embed large amounts of graph data with linear complexity. We apply this method to an anonymized time-series communication network from a large organization spanning 2019-2020, consisting of over 100 thousand vertices and 80 million edges. Our method embeds the data within 10 seconds on a standard computer and enables the detection of communication pattern shifts for individual vertices, vertex communities, and the overall graph structure. Through supporting theory and synthesis studies, we demonstrate the theoretical soundness of our approach under random graph models and its numerical effectiveness through simulation studies.

Deep learning-based approaches have produced models with good insect classification accuracy; Most of these models are conducive for application in controlled environmental conditions. One of the primary emphasis of researchers is to implement identification and classification models in the real agriculture fields, which is challenging because input images that are wildly out of the distribution (e.g., images like vehicles, animals, humans, or a blurred image of an insect or insect class that is not yet trained on) can produce an incorrect insect classification. Out-of-distribution (OOD) detection algorithms provide an exciting avenue to overcome these challenge as it ensures that a model abstains from making incorrect classification prediction of non-insect and/or untrained insect class images. We generate and evaluate the performance of state-of-the-art OOD algorithms on insect detection classifiers. These algorithms represent a diversity of methods for addressing an OOD problem. Specifically, we focus on extrusive algorithms, i.e., algorithms that wrap around a well-trained classifier without the need for additional co-training. We compared three OOD detection algorithms: (i) Maximum Softmax Probability, which uses the softmax value as a confidence score, (ii) Mahalanobis distance-based algorithm, which uses a generative classification approach; and (iii) Energy-Based algorithm that maps the input data to a scalar value, called energy. We performed an extensive series of evaluations of these OOD algorithms across three performance axes: (a) \textit{Base model accuracy}: How does the accuracy of the classifier impact OOD performance? (b) How does the \textit{level of dissimilarity to the domain} impact OOD performance? and (c) \textit{Data imbalance}: How sensitive is OOD performance to the imbalance in per-class sample size?

Out-of-distribution (OOD) detection is critical to ensuring the reliability and safety of machine learning systems. For instance, in autonomous driving, we would like the driving system to issue an alert and hand over the control to humans when it detects unusual scenes or objects that it has never seen before and cannot make a safe decision. This problem first emerged in 2017 and since then has received increasing attention from the research community, leading to a plethora of methods developed, ranging from classification-based to density-based to distance-based ones. Meanwhile, several other problems are closely related to OOD detection in terms of motivation and methodology. These include anomaly detection (AD), novelty detection (ND), open set recognition (OSR), and outlier detection (OD). Despite having different definitions and problem settings, these problems often confuse readers and practitioners, and as a result, some existing studies misuse terms. In this survey, we first present a generic framework called generalized OOD detection, which encompasses the five aforementioned problems, i.e., AD, ND, OSR, OOD detection, and OD. Under our framework, these five problems can be seen as special cases or sub-tasks, and are easier to distinguish. Then, we conduct a thorough review of each of the five areas by summarizing their recent technical developments. We conclude this survey with open challenges and potential research directions.