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In this paper, we consider the relationship between the Mahler measure of a polynomial and its separation. In 1964, Mahler proved that if $f(x) \in \mathbb{Z}[x]$ is separable of degree $n$, then $\operatorname{sep}(f) \gg_n M(f)^{-(n-1)}$. This spurred further investigations into the implicit constant involved in that relation, and it led to questions about the optimal exponent on $M(f)$ in that relation. However, there has been relatively little study concerning upper bounds on $\operatorname{sep}(f)$ in terms of $M(f)$. In this paper, we prove that if $f(x) \in \mathbb{C}[x]$ has degree $n$, then $\operatorname{sep}(f) \ll n^{-1/2}M(f)^{1/(n-1)}$. Moreover, this bound is sharp up to the implied constant factor. We further investigate the constant factor under various additional assumptions on $f(x)$, for example, if it only has real roots., Comment: 11 pages

Depth perception is essential for a robot's spatial and geometric understanding of its environment, with many tasks traditionally relying on hardware-based depth sensors like RGB-D or stereo cameras. However, these sensors face practical limitations, including issues with transparent and reflective objects, high costs, calibration complexity, spatial and energy constraints, and increased failure rates in compound systems. While monocular depth estimation methods offer a cost-effective and simpler alternative, their adoption in robotics is limited due to their output of relative rather than metric depth, which is crucial for robotics applications. In this paper, we propose a method that utilizes a single calibrated camera, enabling the robot to act as a ``measuring stick" to convert relative depth estimates into metric depth in real-time as tasks are performed. Our approach employs an LSTM-based metric depth regressor, trained online and refined through probabilistic filtering, to accurately restore the metric depth across the monocular depth map, particularly in areas proximal to the robot's motion. Experiments with real robots demonstrate that our method significantly outperforms current state-of-the-art monocular metric depth estimation techniques, achieving a 22.1% reduction in depth error and a 52% increase in success rate for a downstream task., Comment: 8 pages, 5 figures

Recently, Alon initiated the study of graph codes and their linear variants in analogy to the study of error correcting codes in theoretical computer science. Alon related the maximum density of a linear graph code which avoids images of a small graph $H$ to the following variant of the Erd\H{o}s-Gy\'arf\'as problem on edge-colourings of $K_n$. A copy of $H$ in an edge-colouring of $K_n$ is even-chromatic if each colour occupies an even number of edges in the copy. We seek an edge-colouring of $K_n$ using $n^{o(1)}$ colours such that there are no even-chromatic copies of $H$. Such an edge-colouring is conjectured to exist for all cliques $K_t$ with an even number of edges. To date, edge-colourings satisfying this property have been constructed for $K_4$ and $K_5$. We construct an edge-colouring using $n^{o(1)}$ colours which avoids even-chromatic copies of $K_8$. This was the smallest open case of the above conjecture, as $K_6, K_7$ each has an odd number of edges. We also study a stronger condition on edge-colourings, where for each copy of $H$, there is a colour occupying exactly one edge in the copy. We conjecture that an edge-colouring using $n^{o(1)}$ colours and satisfying this stronger requirement exists for all cliques $K_t$ regardless of the parity of the number of its edges. We construct edge-colourings satisfying this stronger property for $K_4$ and $K_5$. These constructions also improve upon the number of colours needed for the original problem of avoiding even-chromatic copies of $K_4$ and $K_5$., Comment: 15 pages

Current emotional text-to-speech (TTS) systems face challenges in mimicking a broad spectrum of human emotions due to the inherent complexity of emotions and limitations in emotional speech datasets and models. This paper proposes a TTS framework that facilitates control over pleasure, arousal, and dominance, and can synthesize a diversity of emotional styles without requiring any emotional speech data during TTS training. We train an emotional attribute predictor using only categorical labels from speech data, aligning with psychological research and incorporating anchored dimensionality reduction on self-supervised learning (SSL) features. The TTS framework converts text inputs into phonetic tokens via an autoregressive language model and uses pseudo-emotional dimensions to guide the parallel prediction of fine-grained acoustic details. Experiments conducted on the LibriTTS dataset demonstrate that our framework can synthesize speech with enhanced naturalness and a variety of emotional styles by effectively controlling emotional dimensions, even without the inclusion of any emotional speech during TTS training., Comment: submitted to ICASSP 2025

Neural codecs have become crucial to recent speech and audio generation research. In addition to signal compression capabilities, discrete codecs have also been found to enhance downstream training efficiency and compatibility with autoregressive language models. However, as extensive downstream applications are investigated, challenges have arisen in ensuring fair comparisons across diverse applications. To address these issues, we present a new open-source platform ESPnet-Codec, which is built on ESPnet and focuses on neural codec training and evaluation. ESPnet-Codec offers various recipes in audio, music, and speech for training and evaluation using several widely adopted codec models. Together with ESPnet-Codec, we present VERSA, a standalone evaluation toolkit, which provides a comprehensive evaluation of codec performance over 20 audio evaluation metrics. Notably, we demonstrate that ESPnet-Codec can be integrated into six ESPnet tasks, supporting diverse applications., Comment: Accepted by SLT

Surgical automation holds immense potential to improve the outcome and accessibility of surgery. Recent studies use reinforcement learning to learn policies that automate different surgical tasks. However, these policies are developed independently and are limited in their reusability when the task changes, making it more time-consuming when robots learn to solve multiple tasks. Inspired by how human surgeons build their expertise, we train surgical automation policies through Surgical Incremental Reinforcement Learning (SurgIRL). SurgIRL aims to (1) acquire new skills by referring to external policies (knowledge) and (2) accumulate and reuse these skills to solve multiple unseen tasks incrementally (incremental learning). Our SurgIRL framework includes three major components. We first define an expandable knowledge set containing heterogeneous policies that can be helpful for surgical tasks. Then, we propose Knowledge Inclusive Attention Network with mAximum Coverage Exploration (KIAN-ACE), which improves learning efficiency by maximizing the coverage of the knowledge set during the exploration process. Finally, we develop incremental learning pipelines based on KIAN-ACE to accumulate and reuse learned knowledge and solve multiple surgical tasks sequentially. Our simulation experiments show that KIAN-ACE efficiently learns to automate ten surgical tasks separately or incrementally. We also evaluate our learned policies on the da Vinci Research Kit (dVRK) and demonstrate successful sim-to-real transfers.

We present a new approach for investigating the Markovian to non-Markovian transition in quantum aggregates strongly coupled to a vibrational bath through the analysis of linear absorption spectra. Utilizing hierarchical algebraic equations in the frequency domain, we elucidate how these spectra can effectively reveal transitions between Markovian and non-Markovian regimes, driven by the complex interplay of dissipation, aggregate-bath coupling, and intra-aggregate dipole-dipole interactions. Our results demonstrate that reduced dissipation induces spectral peak splitting, signaling the emergence of bath-induced non-Markovian effects. The spectral peak splitting can also be driven by enhanced dipole-dipole interactions, although the underlying mechanism differs from that of dissipation-induced splitting. Additionally, with an increase in aggregate-bath coupling strength, initially symmetric or asymmetric peaks with varying spectral amplitudes may merge under weak dipole-dipole interactions, whereas strong dipole-dipole interactions are more likely to cause peak splitting. Moreover, we find that spectral features serve as highly sensitive indicators for distinguishing the geometric structures of aggregates, while also unveiling the critical role geometry plays in shaping non-Markovian behavior. This study not only deepens our understanding of the Markovian to non-Markovian transition but also provides a robust framework for optimizing and controlling quantum systems., Comment: 13 pages, 9 figures

Surgical automation has the capability to improve the consistency of patient outcomes and broaden access to advanced surgical care in underprivileged communities. Shared autonomy, where the robot automates routine subtasks while the surgeon retains partial teleoperative control, offers great potential to make an impact. In this paper we focus on one important skill within surgical shared autonomy: Automating robotic assistance to maximize visual exposure and apply tissue tension for dissection and cautery. Ensuring consistent exposure to visualize the surgical site is crucial for both efficiency and patient safety. However, achieving this is highly challenging due to the complexities of manipulating deformable volumetric tissues that are prevalent in surgery.To address these challenges we propose \methodname, a framework for autonomous surgical robotic assistance to \methodfullname. We integrate a differentiable physics model with perceptual feedback to achieve our two key objectives: 1) Maximizing tissue exposure and applying tension for a specified dissection site through visual-servoing conrol and 2) Selecting optimal control positions for a dissection target based on deformable Jacobian analysis. We quantitatively assess our method through repeated real robot experiments on a tissue phantom, and showcase its capabilities through dissection experiments using shared autonomy on real animal tissue., Comment: Submitted to ICRA 2025

Chronic wounds, including diabetic ulcers, pressure ulcers, and ulcers secondary to venous hypertension, affects more than 6.5 million patients and a yearly cost of more than $25 billion in the United States alone. Chronic wound treatment is currently a manual process, and we envision a future where robotics and automation will aid in this treatment to reduce cost and improve patient care. In this work, we present the development of the first robotic system for wound dressing removal which is reported to be the worst aspect of living with chronic wounds. Our method leverages differentiable physics-based simulation to perform gradient-based Model Predictive Control (MPC) for optimized trajectory planning. By integrating fracture mechanics of adhesion, we are able to model the peeling effect inherent to dressing adhesion. The system is further guided by carefully designed objective functions that promote both efficient and safe control, reducing the risk of tissue damage. We validated the efficacy of our approach through a series of experiments conducted on both synthetic skin phantoms and real human subjects. Our results demonstrate the system's ability to achieve precise and safe dressing removal trajectories, offering a promising solution for automating this essential healthcare procedure., Comment: Submitted to ICRA 2025

Human-robot physical interaction (pHRI) is a rapidly evolving research field with significant implications for physical therapy, search and rescue, and telemedicine. However, a major challenge lies in accurately understanding human constraints and safety in human-robot physical experiments without an IRB and physical human experiments. Concerns regarding human studies include safety concerns, repeatability, and scalability of the number and diversity of participants. This paper examines whether a physical approximation can serve as a stand-in for human subjects to enhance robot autonomy for physical assistance. This paper introduces the SHULDRD (Shoulder Haptic Universal Limb Dynamic Repositioning Device), an economical and anatomically similar device designed for real-time testing and deployment of pHRI planning tasks onto robots in the real world. SHULDRD replicates human shoulder motion, providing crucial force feedback and safety data. The device's open-source CAD and software facilitate easy construction and use, ensuring broad accessibility for researchers. By providing a flexible platform able to emulate infinite human subjects, ensure repeatable trials, and provide quantitative metrics to assess the effectiveness of the robotic intervention, SHULDRD aims to improve the safety and efficacy of human-robot physical interactions., Comment: Submitted to ICRA '25

How do people use their faces and bodies to test the interactive abilities of a robot? Making lively, believable agents is often seen as a goal for robots and virtual agents but believability can easily break down. In this Wizard-of-Oz (WoZ) study, we observed 1169 nonverbal interactions between 20 participants and 6 types of agents. We collected the nonverbal behaviors participants used to challenge the characters physically, emotionally, and socially. The participants interacted freely with humanoid and non-humanoid forms: a robot, a human, a penguin, a pufferfish, a banana, and a toilet. We present a human behavior codebook of 188 unique nonverbal behaviors used by humans to test the virtual characters. The insights and design strategies drawn from video observations aim to help build more interaction-aware and believable robots, especially when humans push them to their limits., Comment: 8 pages, 4 figures, Accepted to International Conference on Intelligent Robots and Systems (IROS 2024), project website: https://rosielab.github.io/react-to-this/

A graph $G$ with an even number of edges is called even-decomposable if there is a sequence $V(G)=V_0\supset V_1\supset \dots \supset V_k=\emptyset$ such that for each $i$, $G[V_i]$ has an even number of edges and $V_i\setminus~V_{i+1}$ is an independent set in $G$. The study of this property was initiated recently by Versteegen, motivated by connections to a Ramsey-type problem and questions about graph codes posed by Alon. Resolving a conjecture of Versteegen, we prove that all but an $e^{-\Omega(n^2)}$ proportion of the $n$-vertex graphs with an even number of edges are even-decomposable. Moreover, answering one of his questions, we determine the order of magnitude of the smallest $p=p(n)$ for which the probability that the random graph $G(n,1-p)$ is even-decomposable (conditional on it having an even number of edges) is at least $1/2$. We also study the following closely related property. A graph is called even-degenerate if there is an ordering $v_1,v_2,\dots,v_n$ of its vertices such that each $v_i$ has an even number of neighbours in the set $\{v_{i+1},\dots,v_n\}$. We prove that all but an $e^{-\Omega(n)}$ proportion of the $n$-vertex graphs with an even number of edges are even-degenerate, which is tight up to the implied constant., Comment: 23 pages

We present the first general-relativistic resistive magnetohydrodynamics simulations of self-consistent, rotating neutron stars with mixed poloidal and toroidal magnetic fields. Specifically, we investigate the role of resistivity in the dynamical evolution of neutron stars over a period of up to 100 ms and its effects on their quasi-equilibrium configurations. Our results demonstrate that resistivity can significantly influence the development of magnetohydrodynamic instabilities, resulting in markedly different magnetic field geometries. Additionally, resistivity suppresses the growth of these instabilities, leading to a reduction in the amplitude of emitted gravitational waves. Despite the variations in magnetic field geometries, the ratio of poloidal to toroidal field energies remains consistently 9:1 throughout the simulations, for the models we investigated.

Camera-to-robot calibration is crucial for vision-based robot control and requires effort to make it accurate. Recent advancements in markerless pose estimation methods have eliminated the need for time-consuming physical setups for camera-to-robot calibration. While the existing markerless pose estimation methods have demonstrated impressive accuracy without the need for cumbersome setups, they rely on the assumption that all the robot joints are visible within the camera's field of view. However, in practice, robots usually move in and out of view, and some portion of the robot may stay out-of-frame during the whole manipulation task due to real-world constraints, leading to a lack of sufficient visual features and subsequent failure of these approaches. To address this challenge and enhance the applicability to vision-based robot control, we propose a novel framework capable of estimating the robot pose with partially visible robot manipulators. Our approach leverages the Vision-Language Models for fine-grained robot components detection, and integrates it into a keypoint-based pose estimation network, which enables more robust performance in varied operational conditions. The framework is evaluated on both public robot datasets and self-collected partial-view datasets to demonstrate our robustness and generalizability. As a result, this method is effective for robot pose estimation in a wider range of real-world manipulation scenarios., Comment: 7 pages, 5 figures, project website: https://sites.google.com/ucsd.edu/ctrnet-x

Given a small spherical particle, we consider flow of a nematic liquid crystal in the corresponding exterior domain. Our focus is on precise far field asymptotic behavior of the flow in a parameter regime when the governing equations can be reduced to a system of linear partial differential equations. We are able to analytically characterize the velocity of the flow and compare it to the classical expression for the Stokes flow. The expression for velocity away from the particle can be computed either numerically or symbolically.

Automating suturing during robotically-assisted surgery reduces the burden on the operating surgeon, enabling them to focus on making higher-level decisions rather than fatiguing themselves in the numerous intricacies of a surgical procedure. Accurate suture thread reconstruction and grasping are vital prerequisites for suturing, particularly for avoiding entanglement with surgical tools and performing complex thread manipulation. However, such methods must be robust to heavy perceptual degradation resulting from heavy noise and thread feature sparsity from endoscopic images. We develop a reconstruction algorithm that utilizes quadratic programming optimization to fit smooth splines to thread observations, satisfying reliability bounds estimated from measured observation noise. Additionally, we craft a grasping policy that generates gripper trajectories that maximize the probability of a successful grasp. Our full image-to-grasp pipeline is rigorously evaluated with over 400 grasping trials, exhibiting state-of-the-art accuracy. We show that this strategy can be applied to the various techniques in autonomous suture needle manipulation to achieve autonomous surgery in a generalizable way., Comment: 8 pages, 6 figures, Submitted to RAL

Gradient-based meta-learning algorithms have gained popularity for their ability to train models on new tasks using limited data. Empirical observations indicate that such algorithms are able to learn a shared representation across tasks, which is regarded as a key factor in their success. However, the in-depth theoretical understanding of the learning dynamics and the origin of the shared representation remains underdeveloped. In this work, we investigate the meta-learning dynamics of the non-linear two-layer neural networks trained on streaming tasks in the teach-student scenario. Through the lens of statistical physics analysis, we characterize the macroscopic behavior of the meta-training processes, the formation of the shared representation, and the generalization ability of the model on new tasks. The analysis also points to the importance of the choice of certain hyper-parameters of the learning algorithms.

Assume that $\alpha>1$ is an algebraic number and $\xi\neq0$ is a real number. We are concerned with the distribution of the fractional parts of the sequence $(\xi \alpha^{n})$. Under various Diophantine conditions on $\xi$ and $\alpha$, we obtain lower bounds on the number $n$ with $1\leq n\leq N $ for which the fractional part of the sequence $(\xi \alpha^{n})_{n\geq1}$ fall into a prescribed region $I\subset [0,1]$, extending several results in the literature. As an application, we show that the Fourier decay rate of some self-similar measures is logarithmic, generalizing a result of Varj\'{u} and Yu., Comment: 12 pages

Safe operation of machine learning models requires architectures that explicitly delimit their operational ranges. We evaluate the ability of anomaly detection algorithms to provide indicators correlated with degraded model performance. By placing acceptance thresholds over such indicators, hard boundaries are formed that define the model's coverage. As a use case, we consider the extraction of exoplanetary spectra from transit light curves, specifically within the context of ESA's upcoming Ariel mission. Isolation Forests are shown to effectively identify contexts where prediction models are likely to fail. Coverage/error trade-offs are evaluated under conditions of data and concept drift. The best performance is seen when Isolation Forests model projections of the prediction model's explainability SHAP values., Comment: To appear in "Proceedings of SPAICE 2024: 1st ESA/IAA conference on AI in and for Space". Conference page at https://spaice.esa.int/

Heavy fermion quantum criticality is an extremely rich domain of research which represents a framework to understand strange metals as a consequence of a Kondo breakdown transition. Here we provide an experimental realization of such systems in terms of organic radicals on a metallic surface. The ground state of organic radicals is a Kramer's doublet that can be modeled by a spin 1/2 degree of freedom. Using on-surface synthesis and scanning tunneling microscopy (STM) tip manipulation, one can controllably engineer and characterize chains of organic radicals on a Au(111) surface. The spatial-resolved differential conductance reveals site-dependent low-energy excitations, which support the picture of emergent many-body Kondo physics. Using quantum Monte Carlo simulations, we show that a Kondo lattice model of spin chains on a metallic surface reproduces accurately the experimental results. This allows us to interpret the experimental results in terms of a heavy fermion metal, below the coherence temperature. We foresee that the tunability of these systems will pave the way to realize quantum simulators of heavy fermion criticality.

Let $p$ be a prime, $q=p^n$, and $D \subset \mathbb{F}_q^*$. A celebrated result of McConnel states that if $D$ is a proper subgroup of $\mathbb{F}_q^*$, and $f:\mathbb{F}_q \to \mathbb{F}_q$ is a function such that $(f(x)-f(y))/(x-y) \in D$ whenever $x \neq y$, then $f(x)$ necessarily has the form $ax^{p^j}+b$. In this notes, we give a sufficient condition on $D$ to obtain the same conclusion on $f$. In particular, we show that McConnel's theorem extends if $D$ has small doubling., Comment: short notes, 5 pages, typos corrected

Critical parameters are the key to superconductivity research, and reliable instrumentations can facilitate the study. Traditionally, one has to use several different measurement techniques to measure critical parameters separately. In this work, we develop the use of a single species of quantum sensor to determine and estimate several critical parameters with the help of independent simulation data. We utilize the nitrogen-vacancy (NV) center in the diamond, which recently emerged as a promising candidate for probing exotic features in condensed matter physics. The non-invasive and highly stable nature provides extraordinary opportunities to solve scientific problems in various systems. Using a high-quality single-crystalline YBa$_{2}$Cu$_{4}$O$_{8}$ (YBCO) as a platform, we demonstrate the use of diamond particles and a bulk diamond to probe the Meissner effect. The evolution of the vector magnetic field, the $H-T$ phase diagram, and the map of fluorescence contour are studied via NV sensing. Our results reveal different critical parameters, including lower critical field $H_{c1}$, upper critical field $H_{c2}$, and critical current density $j_{c}$, as well as verifying the unconventional nature of this high-temperature superconductor YBCO. Therefore, NV-based quantum sensing techniques have huge potential in condensed matter research.

With the James Webb Space Telescope (JWST) offering higher resolution data in space-based transmission spectroscopy, understanding the capabilities of our current atmospheric retrieval pipelines is essential. These new data cover wider wavelength ranges and at much higher spectral resolution than previous instruments have been able to offer. Therefore, it is often appealing to bin spectra to fewer points, better constrained in their transit depth, before using them as inputs for atmospheric retrievals. However, little quantitative analysis of the trade-off between spectral resolution and signal-to-noise ratio has been conducted thus far. As such, we produce a simulation replicating the observations of WASP-39b by the NIRSpec PRISM instrument on board JWST and assess the accuracy and consistency of retrievals while varying resolution and the average photometric error. While this probes a specific case we also plot `binning paths' in the resulting sensitivity maps to demonstrate the best attainable atmospheric parameter estimations starting from the position of the real JWST Early Release Science observation. We repeat this analysis on three different simulation setups where each includes an opaque cloud layer at a different height in the atmosphere. We find that a much greater resolution is needed in the case of a high cloud deck since features are already heavily muted by the presence of the clouds. In the other two cases, there are large `safe zones' in the parameter space. If these maps can be generalised, binning paths could inform future observations on how to achieve the most accurate retrieval results., Comment: Submitted to Monthly Notices of the Royal Astronomical Society, 25 pages, 27 figures

This work introduces an approach to enhancing the computational efficiency of 3D atmospheric simulations by integrating a machine-learned surrogate model into the OASIS global circulation model (GCM). Traditional GCMs, which are based on repeatedly numerically integrating physical equations governing atmospheric processes across a series of time-steps, are time-intensive, leading to compromises in spatial and temporal resolution of simulations. This research improves upon this limitation, enabling higher resolution simulations within practical timeframes. Speeding up 3D simulations holds significant implications in multiple domains. Firstly, it facilitates the integration of 3D models into exoplanet inference pipelines, allowing for robust characterisation of exoplanets from a previously unseen wealth of data anticipated from JWST and post-JWST instruments. Secondly, acceleration of 3D models will enable higher resolution atmospheric simulations of Earth and Solar System planets, enabling more detailed insights into their atmospheric physics and chemistry. Our method replaces the radiative transfer module in OASIS with a recurrent neural network-based model trained on simulation inputs and outputs. Radiative transfer is typically one of the slowest components of a GCM, thus providing the largest scope for overall model speed-up. The surrogate model was trained and tested on the specific test case of the Venusian atmosphere, to benchmark the utility of this approach in the case of non-terrestrial atmospheres. This approach yields promising results, with the surrogate-integrated GCM demonstrating above 99.0% accuracy and 101 factor GPU speed-up of the entire simulation compared to using the matched original GCM under Venus-like conditions., Comment: 17 pages, 11 figures

Continual Learning (CL) involves fine-tuning pre-trained models with new data while maintaining the performance on the pre-trained data. This is particularly relevant for expanding multilingual ASR (MASR) capabilities. However, existing CL methods, mainly designed for computer vision and reinforcement learning tasks, often yield sub-optimal results when directly applied to MASR. We hypothesise that this is because CL of the auto-regressive decoder in the MASR model is difficult. To verify this, we propose four optimizations on the decoder. They include decoder-layer gradient surgery, freezing unused token embeddings, suppressing output of newly added tokens, and learning rate re-scaling. Our experiments on adapting Whisper to 10 unseen languages from the Common Voice dataset demonstrate that these optimizations reduce the Average Word Error Rate (AWER) of pretrained languages from 14.2% to 12.4% compared with Experience Replay, without compromising the AWER of new languages., Comment: Proceedings of Interspeech

We characterise graphs that have three distinct eigenvalues and coherent ranks 8 and 9, linking the former to certain symmetric 2-designs and the latter to specific quasi-symmetric 2-designs. This characterisation leads to the discovery of a new biregular graph with three distinct eigenvalues. Additionally, we demonstrate that the coherent rank of a triregular graph with three distinct eigenvalues is at least 14. Finally, we introduce a conjecturally infinite family of biregular graphs with three distinct eigenvalues, obtained by switching the block graphs of orthogonal arrays., Comment: 36 pages

Cohort studies are of significant importance in the field of healthcare analysis. However, existing methods typically involve manual, labor-intensive, and expert-driven pattern definitions or rely on simplistic clustering techniques that lack medical relevance. Automating cohort studies with interpretable patterns has great potential to facilitate healthcare analysis but remains an unmet need in prior research efforts. In this paper, we propose a cohort auto-discovery model, CohortNet, for interpretable healthcare analysis, focusing on the effective identification, representation, and exploitation of cohorts characterized by medically meaningful patterns. CohortNet initially learns fine-grained patient representations by separately processing each feature, considering both individual feature trends and feature interactions at each time step. Subsequently, it classifies each feature into distinct states and employs a heuristic cohort exploration strategy to effectively discover substantial cohorts with concrete patterns. For each identified cohort, it learns comprehensive cohort representations with credible evidence through associated patient retrieval. Ultimately, given a new patient, CohortNet can leverage relevant cohorts with distinguished importance, which can provide a more holistic understanding of the patient's conditions. Extensive experiments on three real-world datasets demonstrate that it consistently outperforms state-of-the-art approaches and offers interpretable insights from diverse perspectives in a top-down fashion., Comment: 10 pages, 12 figures

Recent improvements in neural audio codec (NAC) models have generated interest in adopting pre-trained codecs for a variety of speech processing applications to take advantage of the efficiencies gained from high compression, but these have yet been applied to the speech separation (SS) task. SS can benefit from high compression because the compute required for traditional SS models makes them impractical for many edge computing use cases. However, SS is a waveform-masking task where compression tends to introduce distortions that severely impact performance. Here we propose a novel task of Audio Codec-based SS, where SS is performed within the embedding space of a NAC, and propose a new model, Codecformer, to address this task. At inference, Codecformer achieves a 52x reduction in MAC while producing separation performance comparable to a cloud deployment of Sepformer. This method charts a new direction for performing efficient SS in practical scenarios., Comment: This paper was accepted by Interspeech 2024

We propose using mechanistic interpretability -- techniques for reverse engineering model weights into human-interpretable algorithms -- to derive and compactly prove formal guarantees on model performance. We prototype this approach by formally proving lower bounds on the accuracy of 151 small transformers trained on a Max-of-$K$ task. We create 102 different computer-assisted proof strategies and assess their length and tightness of bound on each of our models. Using quantitative metrics, we find that shorter proofs seem to require and provide more mechanistic understanding. Moreover, we find that more faithful mechanistic understanding leads to tighter performance bounds. We confirm these connections by qualitatively examining a subset of our proofs. Finally, we identify compounding structureless noise as a key challenge for using mechanistic interpretability to generate compact proofs on model performance., Comment: accepted to ICML 2024 Workshop on Mechanistic Interpretability (Spotlight)

This paper proposes a hierarchical spatial-temporal model for modelling the spectrograms of animal calls. The motivation stems from analyzing recordings of the so-called grunt calls emitted by various lemur species. Our goal is to identify a latent spectral shape that characterizes each species and facilitates measuring dissimilarities between them. The model addresses the synchronization of animal vocalizations, due to varying time-lengths and speeds, with non-stationary temporal patterns and accounts for periodic sampling artifacts produced by the time discretization of analog signals. The former is achieved through a synchronization function, and the latter is modeled using a circular representation of time. To overcome the curse of dimensionality inherent in the model's implementation, we employ the Nearest Neighbor Gaussian Process, and posterior samples are obtained using the Markov Chain Monte Carlo method. We apply the model to a real dataset comprising sounds from 8 different species. We define a representative sound for each species and compare them using a simple distance measure. Cross-validation is used to evaluate the predictive capability of our proposal and explore special cases. Additionally, a simulation example is provided to demonstrate that the algorithm is capable of retrieving the true parameters., Comment: 33 pages, 11 figures

Recent language model-based text-to-speech (TTS) frameworks demonstrate scalability and in-context learning capabilities. However, they suffer from robustness issues due to the accumulation of errors in speech unit predictions during autoregressive language modeling. In this paper, we propose a phonetic enhanced language modeling method to improve the performance of TTS models. We leverage self-supervised representations that are phonetically rich as the training target for the autoregressive language model. Subsequently, a non-autoregressive model is employed to predict discrete acoustic codecs that contain fine-grained acoustic details. The TTS model focuses solely on linguistic modeling during autoregressive training, thereby reducing the error propagation that occurs in non-autoregressive training. Both objective and subjective evaluations validate the effectiveness of our proposed method., Comment: Accepted by Interspeech 2024

Let $n$ be a non-zero integer. A set $S$ of positive integers is a Diophantine tuple with the property $D(n)$ if $ab+n$ is a perfect square for each $a,b \in S$ with $a \neq b$. It is of special interest to estimate the quantity $M_n$, the maximum size of a Diophantine tuple with the property $D(n)$. In this notes, we show the contribution of intermediate elements is $O(\log \log |n|)$, improving a result by Dujella. As a consequence, we deduce that $M_n\leq (2+o(1))\log |n|$, improving the best-known upper bound on $M_n$ by Becker and Murty., Comment: 4 pages, revised based on referee comments

Let $k \geq 2$, $q$ be an odd prime power, and $F \in \mathbb{F}_q[x_1, \ldots, x_k]$ be a polynomial. An $F$-Diophantine set over a finite field $\mathbb{F}_q$ is a set $A \subset \mathbb{F}_q^*$ such that $F(a_1, a_2, \ldots, a_k)$ is a square in $\mathbb{F}_q$ whenever $a_1, a_2, \ldots, a_k$ are distinct elements in $A$. In this paper, we provide a strategy to construct a large $F$-Diophantine set, provided that $F$ has a nice property in terms of its monomial expansion. In particular, when $F=x_1x_2\ldots x_k+1$, our construction gives a $k$-Diophantine tuple over $\mathbb{F}_q$ with size $\gg_k \log q$, significantly improving the $\Theta((\log q)^{1/(k-1)})$ lower bound in a recent paper by Hammonds-Kim-Miller-Nigam-Onghai-Saikia-Sharma., Comment: 7 pages

Surgical automation can improve the accessibility and consistency of life saving procedures. Most surgeries require separating layers of tissue to access the surgical site, and suturing to reattach incisions. These tasks involve deformable manipulation to safely identify and alter tissue attachment (boundary) topology. Due to poor visual acuity and frequent occlusions, surgeons tend to carefully manipulate the tissue in ways that enable inference of the tissue's attachment points without causing unsafe tearing. In a similar fashion, we propose JIGGLE, a framework for estimation and interactive sensing of unknown boundary parameters in deformable surgical environments. This framework has two key components: (1) a probabilistic estimation to identify the current attachment points, achieved by integrating a differentiable soft-body simulator with an extended Kalman filter (EKF), and (2) an optimization-based active control pipeline that generates actions to maximize information gain of the tissue attachments, while simultaneously minimizing safety costs. The robustness of our estimation approach is demonstrated through experiments with real animal tissue, where we infer sutured attachment points using stereo endoscope observations. We also demonstrate the capabilities of our method in handling complex topological changes such as cutting and suturing., Comment: Accepted at RSS 2024

Change-point detection and estimation procedures have been widely developed in the literature. However, commonly used approaches in change-point analysis have mainly been focusing on detecting change-points within an entire time series (off-line methods), or quickest detection of change-points in sequentially observed data (on-line methods). Both classes of methods are concerned with change-points that have already occurred. The arguably more important question of when future change-points may occur, remains largely unexplored. In this paper, we develop a novel statistical model that describes the mechanism of change-point occurrence. Specifically, the model assumes a latent process in the form of a random walk driven by non-negative innovations, and an observed process which behaves differently when the latent process belongs to different regimes. By construction, an occurrence of a change-point is equivalent to hitting a regime threshold by the latent process. Therefore, by predicting when the latent process will hit the next regime threshold, future change-points can be forecasted. The probabilistic properties of the model such as stationarity and ergodicity are established. A composite likelihood-based approach is developed for parameter estimation and model selection. Moreover, we construct the predictor and prediction interval for future change points based on the estimated model., Comment: 37 pages, 4 figures

Paley graphs and Paley sum graphs are classical examples of quasi-random graphs. In this paper, we provide new constructions of families of quasi-random graphs that behave like Paley graphs but are neither Cayley graphs nor Cayley sum graphs. These graphs give a unified perspective of studying various graphs arising from polynomials over finite fields such as Paley graphs, Paley sum graphs, and graphs coming from Diophantine tuples and their generalizations. We also provide new lower bounds on the clique number and independence number of general quasi-random graphs. In particular, we give a sufficient condition for the clique number of quasi-random graphs of $n$ vertices to be at least $(1-o(1)\log_{3.008}n$. Such a condition applies to many classical quasi-random graphs, including Paley graphs and Paley sum graphs, as well as some new Paley-like graphs we construct., Comment: 26 pages

We provide a general framework to construct colorings avoiding short monochromatic arithmetic progressions in Euclidean Ramsey theory. Specifically, if $\ell_m$ denotes $m$ collinear points with consecutive points of distance one apart, we say that $\mathbb{E}^n \not \to (\ell_r,\ell_s)$ if there is a red/blue coloring of $n$-dimensional Euclidean space that avoids red congruent copies of $\ell_r$ and blue congruent copies of $\ell_s$. We show that $\mathbb{E}^n \not \to (\ell_3, \ell_{20})$, improving the best-known result $\mathbb{E}^n \not \to (\ell_3, \ell_{1177})$ by F\"uhrer and T\'oth, and also establish $\mathbb{E}^n \not \to (\ell_4, \ell_{18})$ and $\mathbb{E}^n \not \to (\ell_5, \ell_{10})$ in the spirit of the classical result $\mathbb{E}^n \not \to (\ell_6, \ell_{6})$ due to Erd{\H{o}}s et. al. We also show a number of similar $3$-coloring results, as well as $\mathbb{E}^n \not \to (\ell_3, \alpha\ell_{6889})$, where $\alpha$ is an arbitrary positive real number. This final result answers a question of F\"uhrer and T\'oth in the positive., Comment: 12 pages

We consider the vestigial phase with broken time-reversal symmetry above the superconducting transition temperature of a two-component superconductor in two spatial dimensions. We show that, in contrast to 3D, a vestigial phase is in general allowed within Ginzburg-Landau theory. The vestigial phase occupies an increasing temperature region if the parameters in the Ginzburg-Landau theory gives a larger energy difference between the broken time reversal symmetry phase and the other ordered phase., Comment: 7 pages, 2 figures

We present a population study of 20 exoplanets, ranging from Neptune-like to inflated hot-Jupiter planets, observed during transit with the STIS and WFC3 instruments aboard the Hubble Space Telescope. To obtain spectral information from the near-UV to the near-infrared, we reanalysed sixteen WFC3 and over fifty STIS archival data sets with our dedicated HST pipeline. We also include twenty-four WFC3 data sets previously reduced with the same software. Across our target sample we observe significant divergence among multiple observations conducted with the same STIS grating at various epochs, whilst we do not detect variations in the WFC3 data sets. These results are suggestive of stellar contamination, which we have investigated further using known Bayesian tools and other tailored metrics, facilitating a more objective assessment of stellar activity intensity within each system. Our findings reveal that stellar activity contaminates up to half of the studied exoplanet atmospheres, albeit at varying extents. Accounting for stellar activity can significantly alter planetary atmospheric parameters like molecular abundances (up to 6 orders of magnitude) and temperature (up to 145 %), contrasting with the results of analyses that neglect activity. Our results emphasise the importance of considering the effects of stellar contamination in exoplanet transit studies; this issue is particularly true for data sets obtained with facilities that do not cover the optical and/or UV spectral range where the activity is expected to be more impactful but also more easily detectable. Our results also provide a catalogue of potentially active stars for further investigation and monitoring., Comment: 68 pages, 18 figures, 25 tables, submitted to ApJS

Inspired by the works of L. Carlitz and Z.-W. Sun on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which can be viewed as finite field analogues of certain matrices related to the Gamma function. For example, let $q=p^n$ be an odd prime power with $p$ prime and $n\in\mathbb{Z}^+$. Let $\zeta_p=e^{2\pi{\bf i}/p}$ and let $\chi$ be a generator of the group of all mutiplicative characters of the finite field $\mathbb{F}_q$. For the Gauss sum $$G_q(\chi^{r})=\sum_{x\in\mathbb{F}_q}\chi^{r}(x)\zeta_p^{{\rm Tr}_{\mathbb{F}_q/\mathbb{F}_p}(x)},$$ we prove that $$\det \left[G_q(\chi^{2i+2j})\right]_{0\le i,j\le (q-3)/2}=(-1)^{\alpha_p}\left(\frac{q-1}{2}\right)^{\frac{q-1}{2}}2^{\frac{p^{n-1}-1}{2}},$$ where $$\alpha_p= \begin{cases} 1 & \mbox{if}\ n\equiv 1\pmod 2, (p^2+7)/8 & \mbox{if}\ n\equiv 0\pmod 2. \end{cases}$$, Comment: 15 pages. Comments are very welcome

This study introduces a novel BERT-LSH model that incorporates Locality Sensitive Hashing (LSH) to approximate the attention mechanism in the BERT architecture. We examine the computational efficiency and performance of this model compared to a standard baseline BERT model. Our findings reveal that BERT-LSH significantly reduces computational demand for the self-attention layer while unexpectedly outperforming the baseline model in pretraining and fine-tuning tasks. These results suggest that the LSH-based attention mechanism not only offers computational advantages but also may enhance the model's ability to generalize from its training data. For more information, visit our GitHub repository: https://github.com/leo4life2/algoml-final, Comment: 10 pages, 5 figures

Given two irreducible conics $C$ and $D$ over a finite field $\mathbb{F}_q$ with $q$ odd, we show that there are $q^2/4+O(q^{3/2})$ points $P$ in $\mathbb{P}^2(\mathbb{F}_q)$ such that $P$ is external to $C$ and internal to $D$. This answers a question of Korchm\'{a}ros. We also prove the analogous result for higher-dimensional smooth quadric hypersurfaces over $\mathbb{P}^{n-1}$ with $n$ odd, where the answer is $q^{n-1}/4+O(q^{n-\frac{3}{2}})$., Comment: 10 pages

A Diophantine $m$-tuple over a finite field $\mathbb{F}_q$ is a set $\{a_1,\ldots, a_m\}$ of $m$ distinct elements in $\mathbb{F}_{q}^{*}$ such that $a_{i}a_{j}+1$ is a square in $\mathbb{F}_q$ whenever $i\neq j$. In this paper, we study $M(q)$, the maximum size of a Diophantine tuple over $\mathbb{F}_q$, assuming the characteristic of $\mathbb{F}_q$ is fixed and $q \to \infty$. By explicit constructions, we improve the lower bound on $M(q)$. In particular, this improves a recent result of Dujella and Kazalicki by a multiplicative factor., Comment: 9 pages

Inaccurate tool localization is one of the main reasons for failures in automating surgical tasks. Imprecise robot kinematics and noisy observations caused by the poor visual acuity of an endoscopic camera make tool tracking challenging. Previous works in surgical automation adopt environment-specific setups or hard-coded strategies instead of explicitly considering motion and observation uncertainty of tool tracking in their policies. In this work, we present SURESTEP, an uncertainty-aware trajectory optimization framework for robust surgical automation. We model the uncertainty of tool tracking with the components motivated by the sources of noise in typical surgical scenes. Using a Gaussian assumption to propagate our uncertainty models through a given tool trajectory, SURESTEP provides a general framework that minimizes the upper bound on the entropy of the final estimated tool distribution. We compare SURESTEP with a baseline method on a real-world suture needle regrasping task under challenging environmental conditions, such as poor lighting and a moving endoscopic camera. The results over 60 regrasps on the da Vinci Research Kit (dVRK) demonstrate that our optimized trajectories significantly outperform the un-optimized baseline.

Gauge fields are ubiquitous in modern quantum physics. In superfluids, quantized vortices can be induced by gauge fields. Here we demonstrate the first experimental observation of vortex nucleations in spinor Bose-Einstein Condensates under radially-localized synthetic magnetic fields. The associated gauge potentials $\vec{A}$ are azimuthal and created by light-induced spin-orbital-angular-momentum coupling, generating circulating azimuthal velocity fields $\propto \vec{p}-\vec{A}$ even when the canonical momentum $\vec{p}= 0$. A sufficiently large azimuthal velocity peaked near the condensate center results in a dynamically unstable localized excitation that initiates vortex nucleations. This excitation appears as a spontaneously-formed vortex-antivortex pair near the cloud center. Following the initially developed instability, the dynamics is governed by the asymmetry and dissipation, where the atomic orbital angular momentum evolves and can reach the value of the ground state. Our system exhibits dynamical and Landau instabilities and agrees reasonably with time-dependent Gross-Pitaevskii simulations.