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We report the experimental super-resolution of pairs of point-like fluorescent sources using a modified image inversion interferometer microscope. The technique is inspired by recent developments in the application of quantum parameter estimation theory to semiclassical imaging problems. We find that the image inversion technique requires special polarization filtering to account for the dipolar nature of the emission. Using an azimuthal polarizer, we obtain improvements in the Fisher information of point-source separation by over an order of magnitude relative to direct imaging. Unlike established super-resolution fluorescence techniques, the method does not require sequential photoswitching/blinking of the fluorophores, and thus could facilitate significant speed-ups for certain biological imaging/tracking tasks., Comment: v2 includes supplementary material and minor revisions to v1 main text

We study the problem of guarding the boundary of a simple polygon with a minimum number of guards such that each guard covers a contiguous portion of the boundary. First, we present a simple greedy algorithm for this problem that returns a guard set of size at most OPT + 1, where OPT is the number of guards in an optimal solution. Then, we present a polynomial-time exact algorithm. While the algorithm is not complicated, its correctness proof is rather involved. This result is interesting in the sense that guarding problems are typically NP-hard and, in particular, it is NP-hard to minimize the number of guards to see the boundary of a simple polygon, without the contiguous boundary guarding constraint. From the combinatorial point of view, we show that any $n$-vertex polygon can be guarded by at most $\lfloor \frac{n-2}{2}\rfloor$ guards. This bound is tight because there are polygons that require this many guards., Comment: 16 pages of body text; 3 pages of references; 13 figures

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators $\sigma$ and $\epsilon$, and the stress tensor $T_{\mu\nu}$. We obtain new precise determinations of scaling dimensions $(\Delta_\sigma, \Delta_\epsilon) = (0.518148806(24), 1.41262528(29))$ as well as OPE coefficients involving $\sigma$, $\epsilon$, and $T_{\mu\nu}$. We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap., Comment: 52 pages, 10 figures, 9 tables

Assume that a target is known to be present at an unknown point among a finite set of locations in the plane. We search for it using a mobile robot that has imperfect sensing capabilities. It takes time for the robot to move between locations and search a location; we have a total time budget within which to conduct the search. We study the problem of computing a search path/strategy for the robot that maximizes the probability of detection of the target. Considering non-uniform travel times between points (e.g., based on the distance between them) is crucial for search and rescue applications; such problems have been investigated to a limited extent due to their inherent complexity. In this paper, we describe fast algorithms with performance guarantees for this search problem and some variants, complement them with complexity results, and perform experiments to observe their performance., Comment: 10 pages, 6 figures, 3 algorithms

We study some variants of the $k$-\textsc{Watchman Routes} problem, the cooperative version of the classic \textsc{Watchman Routes} problem in a simple polygon. The watchmen may be required to see the whole polygon, or some pre-determined quota of area within the polygon, and we want to minimize the maximum length traveled by any watchman. While the single watchman version of the problem has received much attention is rather well understood, it is not the case for multiple watchmen version. We provide the first tight approximability results for the anchored $k$-\textsc{Watchman Routes} problem in a simple polygon, assuming $k$ is fixed, by a fully-polynomial time approximation scheme. The basis for the FPTAS is provided by an exact dynamic programming algorithm. If $k$ is a variable, we give constant-factor approximations., Comment: arXiv admin note: text overlap with arXiv:2405.21034

We perform a numerical bootstrap study of scalar operators in the critical 3d Gross-Neveu-Yukawa models, a family of conformal field theories containing N Majorana fermions in the fundamental representation of an O(N) global symmetry. We compute rigorous bounds on the scaling dimensions of the next-to-lowest parity-even and parity-odd singlet scalars at N = 2, 4, and 8. All of these dimensions have lower bounds greater than 3, implying that there are only two relevant singlet scalars and placing constraints on the RG flow structure of these theories., Comment: 13 pages, 4 figures

We study the Dispersive Art Gallery Problem with vertex guards: Given a polygon $\mathcal{P}$, with pairwise geodesic Euclidean vertex distance of at least $1$, and a rational number $\ell$; decide whether there is a set of vertex guards such that $\mathcal{P}$ is guarded, and the minimum geodesic Euclidean distance between any two guards (the so-called dispersion distance) is at least $\ell$. We show that it is NP-complete to decide whether a polygon with holes has a set of vertex guards with dispersion distance $2$. On the other hand, we provide an algorithm that places vertex guards in simple polygons at dispersion distance at least $2$. This result is tight, as there are simple polygons in which any vertex guard set has a dispersion distance of at most $2$., Comment: 13 pages, 14 figures; accepted at the 36th Canadian Conference on Computational Geometry (CCCG 2024)

The well-known \textsc{Watchman Route} problem seeks a shortest route in a polygonal domain from which every point of the domain can be seen. In this paper, we study the cooperative variant of the problem, namely the \textsc{$k$-Watchmen Routes} problem, in a simple polygon $P$. We look at both the version in which the $k$ watchmen must collectively see all of $P$, and the quota version in which they must see a predetermined fraction of $P$'s area. We give an exact pseudopolynomial time algorithm for the \textsc{$k$-Watchmen Routes} problem in a simple orthogonal polygon $P$ with the constraint that watchmen must move on axis-parallel segments, and there is a given common starting point on the boundary. Further, we give a fully polynomial-time approximation scheme and a constant-factor approximation for unconstrained movement. For the quota version, we give a constant-factor approximation in a simple polygon, utilizing the solution to the (single) \textsc{Quota Watchman Route} problem.

We propose precise notions of what it means to guard a domain "robustly", under a variety of models. While approximation algorithms for minimizing the number of (precise) point guards in a polygon is a notoriously challenging area of investigation, we show that imposing various degrees of robustness on the notion of visibility coverage leads to a more tractable (and realistic) problem for which we can provide approximation algorithms with constant factor guarantees., Comment: To appear in SoCG 2024

Given a geometric domain $P$, visibility-based search problems seek routes for one or more mobile agents ("watchmen") to move within $P$ in order to be able to see a portion (or all) of $P$, while optimizing objectives, such as the length(s) of the route(s), the size (e.g., area or volume) of the portion seen, the probability of detecting a target distributed within $P$ according to a prior distribution, etc. The classic watchman route problem seeks a shortest route for an observer, with omnidirectional vision, to see all of $P$. In this paper we study bicriteria optimization problems for a single mobile agent within a polygonal domain $P$ in the plane, with the criteria of route length and area seen. Specifically, we address the problem of computing a minimum length route that sees at least a specified area of $P$ (minimum length, for a given area quota). We also study the problem of computing a length-constrained route that sees as much area as possible. We provide hardness results and approximation algorithms. In particular, for a simple polygon $P$ we provide the first fully polynomial-time approximation scheme for the problem of computing a shortest route seeing an area quota, as well as a (slightly more efficient) polynomial dual approximation. We also consider polygonal domains $P$ (with holes) and the special case of a planar domain consisting of a union of lines. Our results yield the first approximation algorithms for computing a time-optimal search route in $P$ to guarantee some specified probability of detection of a static target within $P$, randomly distributed in $P$ according to a given prior distribution.

High throughput extraction and structured labeling of data from academic articles is critical to enable downstream machine learning applications and secondary analyses. We have embedded multimodal data curation into the academic publishing process to annotate segmented figure panels and captions. Natural language processing (NLP) was combined with human-in-the-loop feedback from the original authors to increase annotation accuracy. Annotation included eight classes of bioentities (small molecules, gene products, subcellular components, cell lines, cell types, tissues, organisms, and diseases) plus additional classes delineating the entities' roles in experiment designs and methodologies. The resultant dataset, SourceData-NLP, contains more than 620,000 annotated biomedical entities, curated from 18,689 figures in 3,223 articles in molecular and cell biology. We evaluate the utility of the dataset to train AI models using named-entity recognition, segmentation of figure captions into their constituent panels, and a novel context-dependent semantic task assessing whether an entity is a controlled intervention target or a measurement object. We also illustrate the use of our dataset in performing a multi-modal task for segmenting figures into panel images and their corresponding captions., Comment: Submitted to Journal for revision

Cloud compute adoption has been growing since its inception in the early 2000's with estimates that the size of this market in terms of worldwide spend will increase from \$700 billion in 2021 to \$1.3 trillion in 2025. While there is a significant research activity in many areas of cloud computing technologies, we see little attention being paid to advancing software engineering practices needed to support the current and next generation of cloud native applications. By cloud native, we mean software that is designed and built specifically for deployment to a modern cloud platform. This paper frames the landscape of Cloud Native Software Engineering from a practitioners standpoint, and identifies several software engineering research opportunities that should be investigated. We cover specific engineering challenges associated with software architectures commonly used in cloud applications along with incremental challenges that are expected with emerging IoT/Edge computing use cases.

We generalize the theory of resolving a mixture of two closely spaced spontaneous emission lifetimes to include pure dephasing contributions to decoherence, leading to the resurgence of Rayleigh's Curse at small lifetime separations. Considerable resolution enhancement remains possible when lifetime broadening is more significant than that due to pure dephasing. In the limit that lifetime broadening dominates, one can achieve super-resolution either by a tailored one-photon measurement or Hong-Ou-Mandel interferometry. We describe conditions for which either choice is superior., Comment: 6 pages, 5 figures

The Wiener index of a network, introduced by the chemist Harry Wiener, is the sum of distances between all pairs of nodes in the network. This index, originally used in chemical graph representations of the non-hydrogen atoms of a molecule, is considered to be a fundamental and useful network descriptor. We study the problem of constructing geometric networks on point sets in Euclidean space that minimize the Wiener index: given a set $P$ of $n$ points in $\mathbb{R}^d$, the goal is to construct a network, spanning $P$ and satisfying certain constraints, that minimizes the Wiener index among the allowable class of spanning networks. In this work, we focus mainly on spanning networks that are trees and we focus on problems in the plane ($d=2$). We show that any spanning tree that minimizes the Wiener index has non-crossing edges in the plane. Then, we use this fact to devise an $O(n^4)$-time algorithm that constructs a spanning tree of minimum Wiener index for points in convex position. We also prove that the problem of computing a spanning tree on $P$ whose Wiener index is at most $W$, while having total (Euclidean) weight at most $B$, is NP-hard. Computing a tree that minimizes the Wiener index has been studied in the area of communication networks, where it is known as the optimum communication spanning tree problem., Comment: 14 pages, 7 figures

Let $E=\{e_1,\ldots,e_n\}$ be a set of $C$-oriented disjoint segments in the plane, where $C$ is a given finite set of orientations that spans the plane, and let $s$ and $t$ be two points. %(We also require that for each orientation in $C$, its opposite orientation is also in $C$.) We seek a minimum-link $C$-oriented tour of $E$, that is, a polygonal path $\pi$ from $s$ to $t$ that visits the segments of $E$ in order, such that, the orientations of its edges are in $C$ and their number is minimum. We present an algorithm for computing such a tour in $O(|C|^2 \cdot n^2)$ time. This problem already captures most of the difficulties occurring in the study of the more general problem, in which $E$ is a set of not-necessarily-disjoint $C$-oriented polygons., Comment: Full version of paper to appear, CIAC 2023

Recent advances in deep learning have led to the development of models approaching the human level of accuracy. However, healthcare remains an area lacking in widespread adoption. The safety-critical nature of healthcare results in a natural reticence to put these black-box deep learning models into practice. This paper explores interpretable methods for a clinical decision support system called sleep staging, an essential step in diagnosing sleep disorders. Clinical sleep staging is an arduous process requiring manual annotation for each 30s of sleep using physiological signals such as electroencephalogram (EEG). Recent work has shown that sleep staging using simple models and an exhaustive set of features can perform nearly as well as deep learning approaches but only for some specific datasets. Moreover, the utility of those features from a clinical standpoint is ambiguous. On the other hand, the proposed framework, NormIntSleep demonstrates exceptional performance across different datasets by representing deep learning embeddings using normalized features. NormIntSleep performs 4.5% better than the exhaustive feature-based approach and 1.5% better than other representation learning approaches. An empirical comparison between the utility of the interpretations of these models highlights the improved alignment with clinical expectations when performance is traded-off slightly. NormIntSleep paired with a clinically meaningful set of features can best balance this trade-off by providing reliable, clinically relevant interpretation with robust performance., Comment: Spotlight paper at NeurIPS 2022 Workshop on Learning from Time Series for Health

Clinical Cohort Studies (CCS), such as randomized clinical trials, are a great source of documented clinical research. Ideally, a clinical expert inspects these articles for exploratory analysis ranging from drug discovery for evaluating the efficacy of existing drugs in tackling emerging diseases to the first test of newly developed drugs. However, more than 100 articles are published daily on a single prevalent disease like COVID-19 in PubMed. As a result, it can take days for a physician to find articles and extract relevant information. Can we develop a system to sift through the long list of these articles faster and document the crucial takeaways from each of these articles? In this work, we propose CCS Explorer, an end-to-end system for relevance prediction of sentences, extractive summarization, and patient, outcome, and intervention entity detection from CCS. CCS Explorer is packaged in a web-based graphical user interface where the user can provide any disease name. CCS Explorer then extracts and aggregates all relevant information from articles on PubMed based on the results of an automatically generated query produced on the back-end. For each task, CCS Explorer fine-tunes pre-trained language representation models based on transformers with additional layers. The models are evaluated using two publicly available datasets. CCS Explorer obtains a recall of 80.2%, AUC-ROC of 0.843, and an accuracy of 88.3% on sentence relevance prediction using BioBERT and achieves an average Micro F1-Score of 77.8% on Patient, Intervention, Outcome detection (PIO) using PubMedBERT. Thus, CCS Explorer can reliably extract relevant information to summarize articles, saving time by $\sim \text{660}\times$., Comment: Accepted at IEEE BigData 2022

The accuracy of recent deep learning based clinical decision support systems is promising. However, lack of model interpretability remains an obstacle to widespread adoption of artificial intelligence in healthcare. Using sleep as a case study, we propose a generalizable method to combine clinical interpretability with high accuracy derived from black-box deep learning. Clinician-determined sleep stages from polysomnogram (PSG) remain the gold standard for evaluating sleep quality. However, PSG manual annotation by experts is expensive and time-prohibitive. We propose SERF, interpretable Sleep staging using Embeddings, Rules, and Features to read PSG. SERF provides interpretation of classified sleep stages through meaningful features derived from the AASM Manual for the Scoring of Sleep and Associated Events. In SERF, the embeddings obtained from a hybrid of convolutional and recurrent neural networks are transposed to the interpretable feature space. These representative interpretable features are used to train simple models like a shallow decision tree for classification. Model results are validated on two publicly available datasets. SERF surpasses the current state-of-the-art for interpretable sleep staging by 2%. Using Gradient Boosted Trees as the classifier, SERF obtains 0.766 $\kappa$ and 0.870 AUC-ROC, within 2% of the current state-of-the-art black-box models., Comment: Accepted by CIKM 2022

The classical and extensively-studied Fr\'echet distance between two curves is defined as an inf max, where the infimum is over all traversals of the curves, and the maximum is over all concurrent positions of the two agents. In this article we investigate a "flipped" Fr\'echet measure defined by a sup min -- the supremum is over all traversals of the curves, and the minimum is over all concurrent positions of the two agents. This measure produces a notion of "social distance" between two curves (or general domains), where agents traverse curves while trying to stay as far apart as possible. We first study the flipped Fr\'echet measure between two polygonal curves in one and two dimensions, providing conditional lower bounds and matching algorithms. We then consider this measure on polygons, where it denotes the minimum distance that two agents can maintain while restricted to travel in or on the boundary of the same polygon. We investigate several variants of the problem in this setting, for some of which we provide linear time algorithms. Finally, we consider this measure on graphs. We draw connections between our proposed flipped Fr\'echet measure and existing related work in computational geometry, hoping that our new measure may spawn investigations akin to those performed for the Fr\'echet distance, and into further interesting problems that arise.

In this work we investigate the quantum information theoretical limits to several tasks related to lifetime estimation and discrimination of a two-level spontaneous optical emitter. We focus in particular on the model problem of resolving two mutually incoherent exponential decays with highly overlapping temporal probability profiles. Mirroring recent work on quantum-inspired super-resolution of point emitters, we find that direct lifetime measurement suffers from an analogue of "Rayleigh's Curse" when the time constants of the two decay channels approach one another. We propose alternative measurement schemes that circumvent this limit, and also demonstrate superiority to direct measurement for a related binary hypothesis test. Our findings add to a growing list of examples in which a quantum analysis uncovers significant information gains for certain tasks in opto-molecular metrology that do not rely on multiphoton interference, but evidently do benefit from a more thorough exploitation of the coherence properties of single photons., Comment: 13 pages, 13 figures

We give an overview of theoretical and practical aspects of finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of n points in the plane. Both problems are known to be NP-hard and were the subject of the 2019 Computational Geometry Challenge, which presented the quest of finding good solutions to more than 200 instances, ranging from n = 10 all the way to n = 1, 000, 000., Comment: 12 pages, 9 Futures, 1 table

Let $P$ be a crossing-free polygon and $\mathcal C$ a set of shortcuts, where each shortcut is a directed straight-line segment connecting two vertices of $P$. A shortcut hull of $P$ is another crossing-free polygon that encloses $P$ and whose oriented boundary is composed of elements from $\mathcal C$. Shortcut hulls find their application in geo-related problems such as the simplification of contour lines. We aim at a shortcut hull that linearly balances the enclosed area and perimeter. If no holes in the shortcut hull are allowed, the problem admits a straight-forward solution via shortest paths. For the more challenging case that the shortcut hull may contain holes, we present a polynomial-time algorithm that is based on computing a constrained, weighted triangulation of the input polygon's exterior. We use this problem as a starting point for investigating further variants, e.g., restricting the number of edges or bends. We demonstrate that shortcut hulls can be used for drawing the rough extent of point sets as well as for the schematization of polygons., Comment: Appears in the Proceedings of 33rd Canadian Conference on Computational Geometry, 2021

We give an overview of the 2021 Computational Geometry Challenge, which targeted the problem of optimally coordinating a set of robots by computing a family of collision-free trajectories for a set set S of n pixel-shaped objects from a given start configuration into a desired target configuration., Comment: 13 pages, 8 figures, 2 tables

We give a polynomial-time constant-factor approximation algorithm for maximum independent set for (axis-aligned) rectangles in the plane. Using a polynomial-time algorithm, the best approximation factor previously known is $O(\log\log n)$. The results are based on a new form of recursive partitioning in the plane, in which faces that are constant-complexity and orthogonally convex are recursively partitioned into a constant number of such faces.

Motivated by indoor localization by tripwire lasers, we study the problem of cutting a polygon into small-size pieces, using the chords of the polygon. Several versions are considered, depending on the definition of the "size" of a piece. In particular, we consider the area, the diameter, and the radius of the largest inscribed circle as a measure of the size of a piece. We also consider different objectives, either minimizing the maximum size of a piece for a given number of chords, or minimizing the number of chords that achieve a given size threshold for the pieces. We give hardness results for polygons with holes and approximation algorithms for multiple variants of the problem., Comment: This paper will appear in ESA2020, Track A proceedings

Given a set $P$ of $n$ red and blue points in the plane, a \emph{planar bichromatic spanning tree} of $P$ is a spanning tree of $P$, such that each edge connects between a red and a blue point, and no two edges intersect. In the bottleneck planar bichromatic spanning tree problem, the goal is to find a planar bichromatic spanning tree $T$, such that the length of the longest edge in $T$ is minimized. In this paper, we show that this problem is NP-hard for points in general position. Moreover, we present a polynomial-time $(8\sqrt{2})$-approximation algorithm, by showing that any bichromatic spanning tree of bottleneck $\lambda$ can be converted to a planar bichromatic spanning tree of bottleneck at most $8\sqrt{2}\lambda$.

We give an overview of the 2020 Computational Geometry Challenge, which targeted the problem of partitioning the convex hull of a given planar point set P into the smallest number of convex faces, such that no point of P is contained in the interior of a face., Comment: 8 pages, 3 figures, 1 table

We study a trajectory analysis problem we call the Trajectory Capture Problem (TCP), in which, for a given input set ${\cal T}$ of trajectories in the plane, and an integer $k\geq 2$, we seek to compute a set of $k$ points (``portals'') to maximize the total weight of all subtrajectories of ${\cal T}$ between pairs of portals. This problem naturally arises in trajectory analysis and summarization. We show that the TCP is NP-hard (even in very special cases) and give some first approximation results. Our main focus is on attacking the TCP with practical algorithm-engineering approaches, including integer linear programming (to solve instances to provable optimality) and local search methods. We study the integrality gap arising from such approaches. We analyze our methods on different classes of data, including benchmark instances that we generate. Our goal is to understand the best performing heuristics, based on both solution time and solution quality. We demonstrate that we are able to compute provably optimal solutions for real-world instances.