arXiv subjects

Paul Liu

Publications and source records attributed to Paul Liu.

At least 19 recordsLinked to original sources

arXiv2025

Two-stage Respiratory Motion-resolved Radial MR Image Reconstruction Using an Interpretable Deep Unrolled Network

Due to the prolonged MRI encoding process, respiratory motion can cause undesired artifacts and image blurring, degrading image quality and limiting clinical applications in abdominal and pulmonary imaging. In this work, we develop a two-stage respiratory motion-resolved radial MR image reconstruction pipeline using an interpretable deep unrolled network (MoraNet), enabling high-quality imaging under free-breathing conditions. Firstly, low-resolution images are reconstructed from the central region of successive golden-angle radial k-space to extract respiratory motion signals. The binned k-space data based on the respiratory signal are then used to reconstruct the motion-resolved high-resolution image for each motion state. The MoraNet applies nonuniform fast Fourier transform (NUFFT) to operate radial encoding and convolutional neural network (CNN) modules to conduct image regularizations. The MoraNet was trained on retrospectively acquired lung MRI images for both fully sampled and undersampled acquisitions. The performance of the proposed method was evaluated on digital CT/MRI breathing XCAT (CoMBAT) phantom data, QUASAR motion phantom data acquired from a 1.0T MRI scanner and volunteer chest data acquired from a 1.5T MRI scanner. The MoraNet pipeline was compared with motion-averaged reconstruction and a conventional compressed sensing (CS)-based method in terms of SSIM, RMSE and computation time. Simulation and experimental results demonstrated that the proposed network could provide accurate respiratory signal estimation and enable effective motion correction. Compared with the CS method, the MoraNet preserved better structural details with lower RMSE and higher SSIM values at acceleration factor of 4, and meanwhile took ten-fold faster inference time.

physics.med-ph↗

arXiv2025

Design and Construction of a Dedicated Radiolucent 8-element Flexible Radiofrequency (RF) Torso Coil for the 1.0T Australian MRI-Linac System

Magnetic resonance imaging-guided linear accelerators (MRI-Linacs) are an emerging treatment technology that enable online soft-tissue visualisation and adaptive radiotherapy. The Australian 1.0 T MRI-Linac employs a fixed, inline beamline, with treatment angles achieved via patient couch rotation, and currently relies on a radiolucent whole-body radiofrequency (RF) coil. However, the large coil-patient separation limits signal-to-noise ratio (SNR) and constrains the fast imaging required for real-time tumour tracking. Here, we show the design and validation of a dedicated, flexible 8-element receive-only RF torso array tailored to the geometry and beam access requirements of the Australian MRI-Linac. Electromagnetic simulations, bench measurements, and phantom imaging demonstrate approximately three-fold SNR improvement at the centre and eight-fold improvement at superficial regions compared with the whole-body coil. In vivo abdominal imaging confirms enhanced anatomical detail and sharper tissue boundaries, and the increased SNR enables parallel imaging with GRAPPA acceleration factors up to three without severe artefacts. Dosimetry measurements and dynamic beam-on noise analysis confirm that the coil array is effectively radiolucent, with dose differences below 1% and no measurable degradation in image noise. This work demonstrates a practical RF solution for accelerated, high-SNR imaging compatible with patient rotation and beam delivery on the Australian MRI-Linac.

physics.med-ph↗

arXiv2025

OceanAI: A Conversational Platform for Accurate, Transparent, Near-Real-Time Oceanographic Insights

Artificial intelligence is transforming the sciences, yet general conversational AI systems often generate unverified "hallucinations" undermining scientific rigor. We present OceanAI, a conversational platform that integrates the natural-language fluency of open-source large language models (LLMs) with real-time, parameterized access to authoritative oceanographic data streams hosted by the National Oceanic and Atmospheric Administration (NOAA). Each query such as "What was Boston Harbor's highest water level in 2024?" triggers real-time API calls that identify, parse, and synthesize relevant datasets into reproducible natural-language responses and data visualizations. In a blind comparison with three widely used AI chat-interface products, only OceanAI produced NOAA-sourced values with original data references; others either declined to answer or provided unsupported results. Designed for extensibility, OceanAI connects to multiple NOAA data products and variables, supporting applications in marine hazard forecasting, ecosystem assessment, and water-quality monitoring. By grounding outputs and verifiable observations, OceanAI advances transparency, reproducibility, and trust, offering a scalable framework for AI-enabled decision support within the oceans. A public demonstration is available at https://oceanai.ai4ocean.xyz.

cs.CL↗

arXiv2025

Inference Scaled GraphRAG: Improving Multi Hop Question Answering on Knowledge Graphs

Large Language Models (LLMs) have achieved impressive capabilities in language understanding and generation, yet they continue to underperform on knowledge-intensive reasoning tasks due to limited access to structured context and multi-hop information. Retrieval-Augmented Generation (RAG) partially mitigates this by grounding generation in retrieved context, but conventional RAG and GraphRAG methods often fail to capture relational structure across nodes in knowledge graphs. We introduce Inference-Scaled GraphRAG, a novel framework that enhances LLM-based graph reasoning by applying inference-time compute scaling. Our method combines sequential scaling with deep chain-of-thought graph traversal, and parallel scaling with majority voting over sampled trajectories within an interleaved reasoning-execution loop. Experiments on the GRBench benchmark demonstrate that our approach significantly improves multi-hop question answering performance, achieving substantial gains over both traditional GraphRAG and prior graph traversal baselines. These findings suggest that inference-time scaling is a practical and architecture-agnostic solution for structured knowledge reasoning with LLMs

cs.CL↗

arXiv2025

Uncertainty-Driven Modeling of Microporosity and Permeability in Clastic Reservoirs Using Random Forest

Predicting microporosity and permeability in clastic reservoirs is a challenge in reservoir quality assessment, especially in formations where direct measurements are difficult or expensive. These reservoir properties are fundamental in determining a reservoir's capacity for fluid storage and transmission, yet conventional methods for evaluating them, such as Mercury Injection Capillary Pressure (MICP) and Scanning Electron Microscopy (SEM), are resource-intensive. The aim of this study is to develop a cost-effective machine learning model to predict complex reservoir properties using readily available field data and basic laboratory analyses. A Random Forest classifier was employed, utilizing key geological parameters such as porosity, grain size distribution, and spectral gamma-ray (SGR) measurements. An uncertainty analysis was applied to account for natural variability, expanding the dataset, and enhancing the model's robustness. The model achieved a high level of accuracy in predicting microporosity (93%) and permeability levels (88%). By using easily obtainable data, this model reduces the reliance on expensive laboratory methods, making it a valuable tool for early-stage exploration, especially in remote or offshore environments. The integration of machine learning with uncertainty analysis provides a reliable and cost-effective approach for evaluating key reservoir properties in siliciclastic formations. This model offers a practical solution to improve reservoir quality assessments, enabling more informed decision-making and optimizing exploration efforts.

physics.geo-ph↗

arXiv2025

Minimum-Length Coordinated Motions For Two Convex Centrally-Symmetric Robots

We study the problem of determining coordinated motions, of minimum total length, for two arbitrary convex centrally-symmetric (CCS) robots in an otherwise obstacle-free plane. Using the total path length traced by the two robot centres as a measure of distance, we give an exact characterization of a (not necessarily unique) shortest collision-avoiding motion for all initial and goal configurations of the robots. The individual paths are composed of at most six convex pieces, and their total length can be expressed as a simple integral with a closed form solution depending only on the initial and goal configuration of the robots. The path pieces are either straight segments or segments of the boundary of the Minkowski sum of the two robots (circular arcs, in the special case of disc robots). Furthermore, the paths can be parameterized in such a way that (i) only one robot is moving at any given time (decoupled motion), or (ii) the orientation of the robot configuration changes monotonically.

cs.CG↗

arXiv2024

Dynamic Data Layout Optimization with Worst-case Guarantees

Many data analytics systems store and process large datasets in partitions containing millions of rows. By mapping rows to partitions in an optimized way, it is possible to improve query performance by skipping over large numbers of irrelevant partitions during query processing. This mapping is referred to as a data layout. Recent works have shown that customizing the data layout to the anticipated query workload greatly improves query performance, but the performance benefits may disappear if the workload changes. Reorganizing data layouts to accommodate workload drift can resolve this issue, but reorganization costs could exceed query savings if not done carefully. In this paper, we present an algorithmic framework OReO that makes online reorganization decisions to balance the benefits of improved query performance with the costs of reorganization. Our framework extends results from Metrical Task Systems to provide a tight bound on the worst-case performance guarantee for online reorganization, without prior knowledge of the query workload. Through evaluation on real-world datasets and query workloads, our experiments demonstrate that online reorganization with OReO can lead to an up to 32% improvement in combined query and reorganization time compared to using a single, optimized data layout for the entire workload.

cs.DB↗

arXiv2023

On the Complexity of Sampling Redistricting Plans

A crucial task in the political redistricting problem is to sample redistricting plans i.e. a partitioning of the graph of census blocks into districts. We show that Recombination [DeFord-Duchin-Solomon'21]-a popular Markov chain to sample redistricting plans-is exponentially slow mixing on simple subgraph of $\mathbb{Z}_2.$ We show an alternative way to sample balance, compact and contiguous redistricting plans using a "relaxed" version of ReCom and rejection sampling.

cs.DS↗

arXiv2023

Faster Submodular Maximization for Several Classes of Matroids

The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint has been investigated extensively due to its algorithmic properties and expressive power. Recent progress has focused on fast algorithms for important classes of matroids given in explicit form. Currently, nearly-linear time algorithms only exist for graphic and partition matroids [ICALP '19]. In this work, we develop algorithms for monotone submodular maximization constrained by graphic, transversal matroids, or laminar matroids in time near-linear in the size of their representation. Our algorithms achieve an optimal approximation of $1-1/e-ε$ and both generalize and accelerate the results of Ene and Nguyen [ICALP '19]. In fact, the running time of our algorithm cannot be improved within the fast continuous greedy framework of Badanidiyuru and Vondrák [SODA '14]. To achieve near-linear running time, we make use of dynamic data structures that maintain bases with approximate maximum cardinality and weight under certain element updates. These data structures need to support a weight decrease operation and a novel FREEZE operation that allows the algorithm to freeze elements (i.e. force to be contained) in its basis regardless of future data structure operations. For the laminar matroid, we present a new dynamic data structure using the top tree interface of Alstrup, Holm, de Lichtenberg, and Thorup [TALG '05] that maintains the maximum weight basis under insertions and deletions of elements in $O(\log n)$ time. For the transversal matroid the FREEZE operation corresponds to requiring the data structure to keep a certain set $S$ of vertices matched, a property that we call $S$-stability.

cs.DS↗

arXiv2022

MonoTrack: Shuttle trajectory reconstruction from monocular badminton video

Trajectory estimation is a fundamental component of racket sport analytics, as the trajectory contains information not only about the winning and losing of each point, but also how it was won or lost. In sports such as badminton, players benefit from knowing the full 3D trajectory, as the height of shuttlecock or ball provides valuable tactical information. Unfortunately, 3D reconstruction is a notoriously hard problem, and standard trajectory estimators can only track 2D pixel coordinates. In this work, we present the first complete end-to-end system for the extraction and segmentation of 3D shuttle trajectories from monocular badminton videos. Our system integrates badminton domain knowledge such as court dimension, shot placement, physical laws of motion, along with vision-based features such as player poses and shuttle tracking. We find that significant engineering efforts and model improvements are needed to make the overall system robust, and as a by-product of our work, improve state-of-the-art results on court recognition, 2D trajectory estimation, and hit recognition.

cs.CV↗

arXiv2022

Streaming Submodular Maximization under Matroid Constraints

Recent progress in (semi-)streaming algorithms for monotone submodular function maximization has led to tight results for a simple cardinality constraint. However, current techniques fail to give a similar understanding for natural generalizations, including matroid constraints. This paper aims at closing this gap. For a single matroid of rank $k$ (i.e., any solution has cardinality at most $k$), our main results are: 1) a single-pass streaming algorithm that uses $\widetilde{O}(k)$ memory and achieves an approximation guarantee of $0.3178$, and 2) a multi-pass streaming algorithm that uses $\widetilde{O}(k)$ memory and achieves an approximation guarantee of $(1-1/e - \varepsilon)$ by taking a constant (depending on $\varepsilon$) number of passes over the stream. This improves on the previously best approximation guarantees of $1/4$ and $1/2$ for single-pass and multi-pass streaming algorithms, respectively. In fact, our multi-pass streaming algorithm is tight in that any algorithm with a better guarantee than $1/2$ must make several passes through the stream and any algorithm that beats our guarantee of $1-1/e$ must make linearly many passes (as well as an exponential number of value oracle queries). Moreover, we show how the approach we use for multi-pass streaming can be further strengthened if the elements of the stream arrive in uniformly random order, implying an improved result for $p$-matchoid constraints.

cs.DS↗

arXiv2021

Cardinality constrained submodular maximization for random streams

We consider the problem of maximizing submodular functions in single-pass streaming and secretaries-with-shortlists models, both with random arrival order. For cardinality constrained monotone functions, Agrawal, Shadravan, and Stein gave a single-pass $(1-1/e-\varepsilon)$-approximation algorithm using only linear memory, but their exponential dependence on $\varepsilon$ makes it impractical even for $\varepsilon=0.1$. We simplify both the algorithm and the analysis, obtaining an exponential improvement in the $\varepsilon$-dependence (in particular, $O(k/\varepsilon)$ memory). Extending these techniques, we also give a simple $(1/e-\varepsilon)$-approximation for non-monotone functions in $O(k/\varepsilon)$ memory. For the monotone case, we also give a corresponding unconditional hardness barrier of $1-1/e+\varepsilon$ for single-pass algorithms in randomly ordered streams, even assuming unlimited computation. Finally, we show that the algorithms are simple to implement and work well on real world datasets.

cs.DS↗

arXiv2021

Coordinated Motion Planning Through Randomized k-Opt

This paper examines the approach taken by team gitastrophe in the CG:SHOP 2021 challenge. The challenge was to find a sequence of simultaneous moves of square robots between two given configurations that minimized either total distance travelled or makespan (total time). Our winning approach has two main components: an initialization phase that finds a good initial solution, and a $k$-opt local search phase which optimizes this solution. This led to a first place finish in the distance category and a third place finish in the makespan category.

cs.CG↗

arXiv2021

An Elo-like System for Massive Multiplayer Competitions

Rating systems play an important role in competitive sports and games. They provide a measure of player skill, which incentivizes competitive performances and enables balanced match-ups. In this paper, we present a novel Bayesian rating system for contests with many participants. It is widely applicable to competition formats with discrete ranked matches, such as online programming competitions, obstacle courses races, and some video games. The simplicity of our system allows us to prove theoretical bounds on robustness and runtime. In addition, we show that the system aligns incentives: that is, a player who seeks to maximize their rating will never want to underperform. Experimentally, the rating system rivals or surpasses existing systems in prediction accuracy, and computes faster than existing systems by up to an order of magnitude.

cs.IR↗

arXiv2020

Improved Algorithms for Edge Colouring in the W-Streaming Model

In the W-streaming model, an algorithm is given $O(n \mathrm{polylog} n)$ space and must process a large graph of up to $O(n^2)$ edges. In this short note we give two algorithms for edge colouring under the W-streaming model. For edge colouring in W-streaming, a colour for every edge must be determined by the time all the edges are streamed. Our first algorithm uses $Δ+ o(Δ)$ colours in $O(n \log^2 n)$ space when the edges arrive according to a uniformly random permutation. The second algorithm uses $(1 + o(1))Δ^2 / s$ colours in $\tilde{O}(n s)$ space when edges arrival adversarially.

cs.DS↗

arXiv2020

A simple bipartite graph projection model for clustering in networks

Graph datasets are frequently constructed by a projection of a bipartite graph, where two nodes are connected in the projection if they share a common neighbor in the bipartite graph; for example, a coauthorship graph is a projection of an author-publication bipartite graph. Analyzing the structure of the projected graph is common, but we do not have a good understanding of the consequences of the projection on such analyses. Here, we propose and analyze a random graph model to study what properties we can expect from the projection step. Our model is based on a Chung-Lu random graph for constructing the bipartite representation, which enables us to rigorously analyze the projected graph. We show that common network properties such as sparsity, heavy-tailed degree distributions, local clustering at nodes, the inverse relationship between node degree, and global transitivity can be explained and analyzed through this simple model. We also develop a fast sampling algorithm for our model, which we show is provably optimal for certain input distributions. Numerical simulations where model parameters come from real-world datasets show that much of the clustering behavior in some datasets can just be explained by the projection step.

cs.SI↗

arXiv2020

A polynomial lower bound on adaptive complexity of submodular maximization

In large-data applications, it is desirable to design algorithms with a high degree of parallelization. In the context of submodular optimization, adaptive complexity has become a widely-used measure of an algorithm's "sequentiality". Algorithms in the adaptive model proceed in rounds, and can issue polynomially many queries to a function $f$ in each round. The queries in each round must be independent, produced by a computation that depends only on query results obtained in previous rounds. In this work, we examine two fundamental variants of submodular maximization in the adaptive complexity model: cardinality-constrained monotone maximization, and unconstrained non-mono-tone maximization. Our main result is that an $r$-round algorithm for cardinality-constrained monotone maximization cannot achieve an approximation factor better than $1 - 1/e - Ω(\min \{ \frac{1}{r}, \frac{\log^2 n}{r^3} \})$, for any $r < n^c$ (where $c>0$ is some constant). This is the first result showing that the number of rounds must blow up polynomially large as we approach the optimal factor of $1-1/e$. For the unconstrained non-monotone maximization problem, we show a positive result: For every instance, and every $δ>0$, either we obtain a $(1/2-δ)$-approximation in $1$ round, or a $(1/2+Ω(δ^2))$-approximation in $O(1/δ^2)$ rounds. In particular (and in contrast to the cardinality-constrained case), there cannot be an instance where (i) it is impossible to achieve an approximation factor better than $1/2$ regardless of the number of rounds, and (ii) it takes $r$ rounds to achieve a factor of $1/2-O(1/r)$.

cs.DS↗

arXiv2019

Retrieving Top Weighted Triangles in Graphs

Pattern counting in graphs is a fundamental primitive for many network analysis tasks, and a number of methods have been developed for scaling subgraph counting to large graphs. Many real-world networks carry a natural notion of strength of connection between nodes, which are often modeled by a weighted graph, but existing scalable graph algorithms for pattern mining are designed for unweighted graphs. Here, we develop a suite of deterministic and random sampling algorithms that enable the fast discovery of the 3-cliques (triangles) with the largest weight in a graph, where weight is measured by a generalized mean of a triangle's edges. For example, one of our proposed algorithms can find the top-1000 weighted triangles of a weighted graph with billions of edges in thirty seconds on a commodity server, which is orders of magnitude faster than existing "fast" enumeration schemes. Our methods thus open the door towards scalable pattern mining in weighted graphs.

cs.SI↗