arXiv subjects

Joseph Chen

Publications and source records attributed to Joseph Chen.

11 recordsLinked to original sources

arXiv2026

The limit shape and emergence of the Discrete Gaussian level lines

Consider the $(2+1)$D Discrete Gaussian model (ZGFF) on an $L\times L$ box with a hard floor at height zero and zero boundary conditions, at low temperature. The second author, Martinelli and Sly (2016) showed that the surface has a plateau, filling nearly the full square, at height either $H$ or $H+1$ for an explicit function $H(L)$. In a companion paper, we studied the local laws of the top level lines near the four sides of the box, and showed that after rescaling each by $(L^{2/3-o(1)},L^{1/3-o(1)})$, they converge to a product of Ferrari--Spohn diffusions. Two key features of the top level lines remained unaddressed: their global limit shape, and the critical window marking the transition from a top plateau at height $H$ to one at height $H+1$. These features are intrinsically linked: deriving the global limit of the top level line is needed for determining whether it is preferable to be at height $H$ or $H+1$ near criticality. This work completes this picture as follows. First, we obtain the global limit of the top level lines: for every fixed $n$, the $n$-th from-the-top level line converges in Hausdorff distance to a deterministic shape $\mathscr{L}_n$ that features the Wulff shape at scale $N_n=L^{1-o(1)}$ near the four corners of the box. Second, we identify, for every $h$, the point of emergence of a macroscopic $h$ level line: the probability of this event is monotone increasing in $L$ (up to a $o(1)$ error), and undergoes a sharp transition from near $0$ to near $1$ in a critical window of width $\leq L^{1/2+o(1)}$ around a side length $L=L_c^{(h)}$. This transition is discontinuous in that, once a macroscopic level $h$ emerges, it immediately occupies nearly all the box, and the above global and local scaling limits (Wulff, Ferrari--Spohn) hold for it. The new results extend to the $(2+1)$D $|\nabla\phi|^p$-models (ZGFF is the case $p=2$) for every fixed $p> 1$.

math.PR↗

arXiv2026

On the universal definition of intelligence

This paper aims to propose a universal definition of intelligence that enables fair and consistent comparison of human and artificial intelligence (AI). With the rapid development of AI technology in recent years, how to compare and evaluate human and AI intelligence has become an important theoretical issue. However, existing definitions of intelligence are anthropocentric and unsuitable for empirical comparison, resulting in a lack of consensus in the research field. This paper first introduces four criteria for evaluating intelligence definitions based on R. Carnap's methodology of conceptual clarification: similarity to explicandum, exactness, fruitfulness, and simplicity. We then examine six representative definitions: IQ testing, complex problem-solving ability, reward optimization, environmental adaptation, learning efficiency, and predictive ability, and clarify their theoretical strengths and limitations. The results show that while definitions based on predictive ability have high explanatory power and empirical feasibility, they suffer from an inability to adequately explain the relationship between predictions and behavior/benefits. This paper proposes the Extended Predictive Hypothesis (EPH), which views intelligence as a combination of the ability to accurately predict the future and the ability to benefit from those predictions. Furthermore, by distinguishing predictive ability into spontaneous and reactive predictions and adding the concept of gainability, we present a unified framework for explaining various aspects of intelligence, such as creativity, learning, and future planning. In conclusion, this paper argues that the EPH is the most satisfactory and universal definition for comparing human and AI intelligence.

cs.AI↗

arXiv2025

Towards Autonomous Robotic Electrosurgery via Thermal Imaging

Electrosurgery is a surgical technique that can improve tissue cutting by reducing cutting force and bleeding. However, electrosurgery adds a risk of thermal injury to surrounding tissue. Expert surgeons estimate desirable cutting velocities based on experience but have no quantifiable reference to indicate if a particular velocity is optimal. Furthermore, prior demonstrations of autonomous electrosurgery have primarily used constant tool velocity, which is not robust to changes in electrosurgical tissue characteristics, power settings, or tool type. Thermal imaging feedback provides information that can be used to reduce thermal injury while balancing cutting force by controlling tool velocity. We introduce Thermography for Electrosurgical Rate Modulation via Optimization (ThERMO) to autonomously reduce thermal injury while balancing cutting force by intelligently controlling tool velocity. We demonstrate ThERMO in tissue phantoms and compare its performance to the constant velocity approach. Overall, ThERMO improves cut success rate by a factor of three and can reduce peak cutting force by a factor of two. ThERMO responds to varying environmental disturbances, reduces damage to tissue, and completes cutting tasks that would otherwise result in catastrophic failure for the constant velocity approach.

cs.RO↗

arXiv2025

The limiting law of the Discrete Gaussian level lines

Consider the $(2+1)$D Discrete Gaussian (ZGFF, integer-valued Gaussian free field) model in an $L\times L$ box above a hard floor. Bricmont, El-Mellouki and Fr\"ohlich (1986) established that, at low enough temperature, this random surface exhibits entropic repulsion: the floor propels the average height to be poly-logarithmic in $L$. The second author, Martinelli and Sly (2016) showed that, for all but exceptional values of $L$, the surface has a plateau whose height concentrates on an explicit integer $H(L)$, and fills nearly the full square. It was conjectured there that the boundary of this plateau -- the top level-line of the surface -- should have random fluctuations of $L^{1/3+o(1)}$. We confirm this conjecture of [LMS16] and further recover the limiting law of the top level-line: there exists an explicit sequence $N=L^{1-o(1)}$ such that the distance of the top level-line from $I$, the interval of length $N^{2/3}$ centered along the side boundary, converges, after rescaling it by $N^{1/3}$ and the width of the interval by $N^{2/3}$, to a Ferrari--Spohn diffusion. In particular, the level-line fluctuations at, say, the center of $I$, have a limit law involving the Airy function rescaled by $N^{1/3}$. This gives the first example of one of the $(2+1)$D $|\nabla \phi|^p$ models (approximating 3D Ising and crystal formation) where a Ferrari--Spohn limit law of its level-lines is confirmed (ZGFF is the case $p=2$). More generally, we find the joint limit law of any finite number of top level-lines: rescaling their distances from the side boundary, each by its $(N_n^{2/3},N_n^{1/3})$, yields a product of Ferrari--Spohn laws. These new results extend to the full universality class of $|\nabla\phi|^p$ models for any fixed $p>1$.

math.PR↗

arXiv2025

Towards Fluorescence-Guided Autonomous Robotic Partial Nephrectomy on Novel Tissue-Mimicking Hydrogel Phantoms

Autonomous robotic systems hold potential for improving renal tumor resection accuracy and patient outcomes. We present a fluorescence-guided robotic system capable of planning and executing incision paths around exophytic renal tumors with a clinically relevant resection margin. Leveraging point cloud observations, the system handles irregular tumor shapes and distinguishes healthy from tumorous tissue based on near-infrared imaging, akin to indocyanine green staining in partial nephrectomy. Tissue-mimicking phantoms are crucial for the development of autonomous robotic surgical systems for interventions where acquiring ex-vivo animal tissue is infeasible, such as cancer of the kidney and renal pelvis. To this end, we propose novel hydrogel-based kidney phantoms with exophytic tumors that mimic the physical and visual behavior of tissue, and are compatible with electrosurgical instruments, a common limitation of silicone-based phantoms. In contrast to previous hydrogel phantoms, we mix the material with near-infrared dye to enable fluorescence-guided tumor segmentation. Autonomous real-world robotic experiments validate our system and phantoms, achieving an average margin accuracy of 1.44 mm in a completion time of 69 sec.

cs.RO↗

arXiv2024

Logarithmic delocalization of low temperature 3D Ising and Potts interfaces above a hard floor

We study the entropic repulsion of the low temperature 3D Ising and Potts interface in an $n\times n \times n$ box with blue boundary conditions on its bottom face (the hard floor), and red boundary conditions on its other five faces. For Ising, Frohlich and Pfister proved in 1987 that the typical interface height above the origin diverges (non-quantitatively), via correlation inequalities special to the Ising model; no such result was known for Potts. We show for both the Ising and Potts models that the entropic repulsion fully overcomes the potentially attractive interaction with the floor, and obtain a logarithmically diverging lower bound on the typical interface height. This is complemented by a conjecturally sharp upper bound of $\lfloor \xi^{-1}\log n\rfloor$ where $\xi$ is the rate function for a point-to-plane non-red connection under the infinite volume red measure. The proof goes through a coupled random-cluster interface to overcome the potential attractive interaction with the boundary, and a coupled fuzzy Potts model to reduce the upper bound to a simpler setting where the repulsion is attained by conditioning a no-floor interface to lie in the upper half-space.

math.PR↗

arXiv2024

Vectoring Languages

Recent breakthroughs in large language models (LLM) have stirred up global attention, and the research has been accelerating non-stop since then. Philosophers and psychologists have also been researching the structure of language for decades, but they are having a hard time finding a theory that directly benefits from the breakthroughs of LLMs. In this article, we propose a novel structure of language that reflects well on the mechanisms behind language models and go on to show that this structure is also better at capturing the diverse nature of language compared to previous methods. An analogy of linear algebra is adapted to strengthen the basis of this perspective. We further argue about the difference between this perspective and the design philosophy for current language models. Lastly, we discuss how this perspective can lead us to research directions that may accelerate the improvements of science fastest.

cs.CL↗

arXiv2024

Critical wetting in the (2+1)D Solid-On-Solid model

In this note, we study the low temperature $(2+1)$D SOS interface above a hard floor with critical pinning potential $\lambda_w= \log (\frac{1}{1-e^{-4\beta}})$. At $\lambda<\lambda_w$ entropic repulsion causes the surface to delocalize and be rigid at height $\frac1{4\beta}\log n+O(1)$; at $\lambda>\lambda_w$ it is localized at some $O(1)$ height. We show that at $\lambda=\lambda_w$, there is delocalization, with rigidity now at height $\lfloor \frac1{6\beta}\log n+\frac13\rfloor$, confirming a conjecture of Lacoin.

math.PR↗

arXiv2023

Extrema of 3D Potts interfaces

The interface between the plus and minus phases in the low temperature 3D Ising model has been intensely studied since Dobrushin's pioneering works in the early 1970's established its rigidity. Advances in the last decade yielded the tightness of the maximum of the interface of this Ising model on the cylinder of side length $n$, around a mean that is asymptotically $c\log n$ for an explicit $c$ (temperature dependent). In this work, we establish analogous results for the 3D Potts and random cluster (FK) models. Compared to 3D Ising, the Potts model and its lack of monotonicity form obstacles for existing methods, calling for new proof ideas, while its interfaces (and associated extrema) exhibit richer behavior. We show that the maxima and minima of the interface bounding the blue component in the 3D Potts interface, and those of the interface bounding the bottom component in the 3D FK model, are governed by 4 different large deviation rates, whence the corresponding global extrema feature 4 distinct constants $c$ as above. Due to the above obstacles, our methods are initially only applicable to 1 of these 4 interface extrema, and additional ideas are needed to recover the other 3 rates given the behavior of the first one.

math.PR↗

arXiv2021

Robust Voxelization and Visualization by Improved Tetrahedral Mesh Generation

When obtaining interior 3D voxel data from triangular meshes, most existing methods fail to handle low quality meshes which happens to take up a big portion on the internet. In this work we present a robust voxelization method that is based on tetrahedral mesh generation within a user defined error bound. Comparing to other tetrahedral mesh generation methods, our method produces much higher quality tetrahedral meshes as the intermediate outcome, which allows us to utilize a faster voxelization algorithm that is based on a stronger assumption. We show the results comparing to various methods including the state-of-the-art. Our contribution includes a framework which takes triangular mesh as an input and produces voxelized data, a proof to an unproved algorithm that performs better than the state-of-the-art, and various experiments including parallelization built on the GPU and CPU. We further tested our method on various dataset including Princeton ModelNet and Thingi10k to show the robustness of the framework, where near 100% availability is achieved, while others can only achieve around 50%.

cs.GR↗

arXiv2019

Deploying a Top-100 Supercomputer for Large Parallel Workloads: the Niagara Supercomputer

Niagara is currently the fastest supercomputer accessible to academics in Canada. It was deployed at the beginning of 2018 and has been serving the research community ever since. This homogeneous 60,000-core cluster, owned by the University of Toronto and operated by SciNet, was intended to enable large parallel jobs and has a measured performance of 3.02 petaflops, debuting at #53 in the June 2018 TOP500 list. It was designed to optimize throughput of a range of scientific codes running at scale, energy efficiency, and network and storage performance and capacity. It replaced two systems that SciNet operated for over 8 years, the Tightly Coupled System (TCS) and the General Purpose Cluster (GPC). In this paper we describe the transition process from these two systems, the procurement and deployment processes, as well as the unique features that make Niagara a one-of-a-kind machine in Canada.

cs.DC↗