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In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the finite-state dimension (a finite-state version of algorithmic dimension) of a sequence $S \in Σ^\infty$ and, in 2018, Case and Lutz defined and investigated the mutual (algorithmic) dimension between two sequences $S \in Σ^\infty$ and $T \in Σ^\infty$. In this paper, we propose a definition for the lower and upper finite-state mutual dimensions $mdim_{FS}(S:T)$ and $Mdim_{FS}(S:T)$ between two sequences $S \in Σ^\infty$ and $T \in Σ^\infty$ over an alphabet $Σ$. Intuitively, the finite-state dimension of a sequence $S \in Σ^\infty$ represents the density of finite-state information contained within $S$, while the finite-state mutual dimension between two sequences $S \in Σ^\infty$ and $T \in Σ^\infty$ represents the density of finite-state information shared by $S$ and $T$. Thus ``finite-state mutual dimension'' can be viewed as a ``finite-state'' version of mutual dimension and as a ``mutual'' version of finite-state dimension. The main results of this investigation are as follows. First, we show that finite-state mutual dimension, defined using information-lossless finite-state compressors, has all of the pro
We introduce the notion of round surgery diagrams in $S^3$ for representing 3-manifolds similar to Dehn surgery diagrams. We give a correspondence between a certain class of round surgery diagrams and Dehn surgery diagrams for 3-manifolds. As a consequence, we recover Asimov's result, stating that any closed connected oriented 3-manifold can be obtained by a round surgery on a framed link in $S^3$. There may be more than one round surgery diagram giving rise to the same 3-manifold. Thus, it is natural to ask whether there is a version of Kirby Calculus for round surgery diagrams, similar to the case of Dehn surgery diagrams with integral framings. In this direction, we define four types of moves on round surgery diagrams such that any two round surgery diagrams corresponding to the same 3-manifold can be obtained one from another by a finite sequence of these moves, thereby establishing a version of Kirby Calculus. As an application, we prove the existence of taut foliations, hence the existence of tight contact structures on 3-manifolds obtained by round 1-surgery on fibred links with two components on $S^3$.
A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $γ(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a set $S$ is a $γ$-set. A generalization of this is partial domination which was introduced in 2017 by Case, Hedetniemi, Laskar, and Lipman [3,2] . In partial domination a set $S$ is a $p$-dominating set if it dominates a proportion $p$ of the vertices in $V$. The p-domination number $γ_{p}(G)$ is the minimum cardinality of a $p$-dominating set in $G$. In this paper, we investigate further properties of partial dominating sets, particularly ones related to graph products and locating partial dominating sets. We also introduce the concept of a $p$-influencing set as the union of all $p$-dominating sets for a fixed $p$ and investigate some of its properties.
With the advent of robot-assisted surgery, the role of data-driven approaches to integrate statistics and machine learning is growing rapidly with prominent interests in objective surgical skill assessment. However, most existing work requires translating robot motion kinematics into intermediate features or gesture segments that are expensive to extract, lack efficiency, and require significant domain-specific knowledge. We propose an analytical deep learning framework for skill assessment in surgical training. A deep convolutional neural network is implemented to map multivariate time series data of the motion kinematics to individual skill levels. We perform experiments on the public minimally invasive surgical robotic dataset, JHU-ISI Gesture and Skill Assessment Working Set (JIGSAWS). Our proposed learning model achieved a competitive accuracy of 92.5%, 95.4%, and 91.3%, in the standard training tasks: Suturing, Needle-passing, and Knot-tying, respectively. Without the need of engineered features or carefully-tuned gesture segmentation, our model can successfully decode skill information from raw motion profiles via end-to-end learning. Meanwhile, the proposed model is able to
Purpose: We investigated the utilization of privacy-preserving, locally-deployed, open-source Large Language Models (LLMs) to extract diagnostic information from free-text cardiovascular magnetic resonance (CMR) reports. Materials and Methods: We evaluated nine open-source LLMs on their ability to identify diagnoses and classify patients into various cardiac diagnostic categories based on descriptive findings in 109 clinical CMR reports. Performance was quantified using standard classification metrics including accuracy, precision, recall, and F1 score. We also employed confusion matrices to examine patterns of misclassification across models. Results: Most open-source LLMs demonstrated exceptional performance in classifying reports into different diagnostic categories. Google's Gemma2 model achieved the highest average F1 score of 0.98, followed by Qwen2.5:32B and DeepseekR1-32B with F1 scores of 0.96 and 0.95, respectively. All other evaluated models attained average scores above 0.93, with Mistral and DeepseekR1-7B being the only exceptions. The top four LLMs outperformed our board-certified cardiologist (F1 score of 0.94) across all evaluation metrics in analyzing CMR reports.
Concept erasure in text-to-image diffusion models is crucial for mitigating harmful content, yet existing methods often compromise generative quality. We introduce Semantic Surgery, a novel training-free, zero-shot framework for concept erasure that operates directly on text embeddings before the diffusion process. It dynamically estimates the presence of target concepts in a prompt and performs a calibrated vector subtraction to neutralize their influence at the source, enhancing both erasure completeness and locality. The framework includes a Co-Occurrence Encoding module for robust multi-concept erasure and a visual feedback loop to address latent concept persistence. As a training-free method, Semantic Surgery adapts dynamically to each prompt, ensuring precise interventions. Extensive experiments on object, explicit content, artistic style, and multi-celebrity erasure tasks show our method significantly outperforms state-of-the-art approaches. We achieve superior completeness and robustness while preserving locality and image quality (e.g., 93.58 H-score in object erasure, reducing explicit content to just 1 instance, and 8.09 H_a in style erasure with no quality degradation).
The recent Segment Anything Model (SAM) 2 has demonstrated remarkable foundational competence in semantic segmentation, with its memory mechanism and mask decoder further addressing challenges in video tracking and object occlusion, thereby achieving superior results in interactive segmentation for both images and videos. Building upon our previous empirical studies, we further explore the zero-shot segmentation performance of SAM 2 in robot-assisted surgery based on prompts, alongside its robustness against real-world corruption. For static images, we employ two forms of prompts: 1-point and bounding box, while for video sequences, the 1-point prompt is applied to the initial frame. Through extensive experimentation on the MICCAI EndoVis 2017 and EndoVis 2018 benchmarks, SAM 2, when utilizing bounding box prompts, outperforms state-of-the-art (SOTA) methods in comparative evaluations. The results with point prompts also exhibit a substantial enhancement over SAM's capabilities, nearing or even surpassing existing unprompted SOTA methodologies. Besides, SAM 2 demonstrates improved inference speed and less performance degradation against various image corruption. Although slightly u
Surgery on a knot in $S^3$ is said to be an alternating surgery if it yields the double branched cover of an alternating link. The main theoretical contribution is to show that the set of alternating surgery slopes is algorithmically computable and to establish several structural results. Furthermore, we calculate the set of alternating surgery slopes for many examples of knots, including all hyperbolic knots in the SnapPy census. These examples exhibit several interesting phenomena including strongly invertible knots with a unique alternating surgery and asymmetric knots with two alternating surgery slopes. We also establish upper bounds on the set of alternating surgeries, showing that an alternating surgery slope on a hyperbolic knot satisfies $|p/q| \leq 3g(K)+4$. Notably, this bound applies to lens space surgeries, thereby strengthening the known genus bounds from the conjecture of Goda and Teragaito.
The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hanselman reduced the problem to $\pm 2$ or $\pm 1/n$ surgeries being the only possible cosmetic surgeries. We remove the case of $\pm 1/n$-surgeries using the Chern-Simons filtration on Floer's original irreducible-only instanton homology, reducing the conjecture to the case of $\pm 2$ surgery on genus $2$ knots with trivial Alexander polynomial. We also prove some similar results for surgeries on knots in $S^2 \times S^1$. As key steps in establishing these results, we define invariants of the oriented homeomorphism type of three-manifolds derived from filtered instanton Floer homology and introduce a new surgery relationship for Floer's instanton homology.
BACKGROUND: Clinical factors influence surgery duration. This study also investigated non-clinical effects. METHODS: 22 months of data about thoracic operations in a large hospital in China were reviewed. Linear and nonlinear regression models were used to predict the duration of the operations. Interactions among predictors were also considered. RESULTS: Surgery duration decreased with the number of operations a surgeon performed in a day (P<0.001). Also, it was found that surgery duration decreased with the number of operations allocated to an OR as long as there were no more than four surgeries per day in the OR (P<0.001), but increased with the number of operations if it was more than four (P<0.01). The duration of surgery was affected by its position in a sequence of surgeries performed by a surgeon. In addition, surgeons exhibited different patterns of the effects of surgery type for surgeries in different positions in the day. CONCLUSIONS: Surgery duration was affected not only by clinical effects but also some non-clinical effects. Scheduling and allocation decisions significantly influenced surgery duration.
It is known that any contact 3-manifold can be obtained by rational contact Dehn surgery along a Legendrian link L in the standard tight contact 3-sphere. We define and study various versions of contact surgery numbers, the minimal number of components of a surgery link L describing a given contact 3-manifold under consideration. In the first part of the paper, we relate contact surgery numbers to other invariants in terms of various inequalities. In particular, we show that the contact surgery number of a contact manifold is bounded from above by the topological surgery number of the underlying topological manifold plus three. In the second part, we compute contact surgery numbers of all contact structures on the 3-sphere. Moreover, we completely classify the contact structures with contact surgery number one on $S^1\times S^2$, the Poincaré homology sphere, and the Brieskorn sphere $Σ(2,3,7)$. We conclude that there exist infinitely many non-isotopic contact structures on each of the above manifolds which cannot be obtained by a single rational contact surgery from the standard tight contact $3$-sphere. We further obtain results for the 3-torus and lens spaces. As one ingredient
The ability to estimate and predict pathogen variant dynamics can inform public health responses, including planning for increased transmission or severity, shifts in population immunity, or changes to vaccine or therapeutic effectiveness. The COVID-19 pandemic demonstrated the importance of monitoring SARS-CoV-2 variant evolution through viral genome sequencing, enabling predictive models to estimate variant frequencies in the recent past, present, and short-term future. Collaborative forecasting Hubs provided a valuable way to centralize predictive modeling of epidemiological indicators such as cases, hospitalizations, and deaths during the pandemic; however, none existed for variant dynamics. Here, we discuss the creation of the United States SARS-CoV-2 Variant Nowcast Hub, designed to solicit estimates of the relative abundance of a specified set of SARS-CoV-2 variants at the U.S. state level. We discuss the design decisions and challenges in building the Hub and its scoring procedures. Using submissions from the Hub's first respiratory virus season (nowcast dates October 9th, 2024 to June 4th, 2025), we evaluate five individual models and a baseline model. We found that the ba
For a nullhomologous Legendrian knot in a closed contact 3-manifold Y we consider a contact structure obtained by positive rational contact surgery. We prove that in this situation the Heegaard Floer contact invariant of Y is mapped by a surgery cobordism to the contact invariant of the result of contact surgery. In addition we characterize the spin-c structure on the cobordism that induces the relevant map. As a consequence we determine necessary and sufficient conditions for the nonvanishing of the contact invariant after rational surgery when Y is the standard 3-sphere, generalizing previous results of Lisca-Stipsicz and Golla. In fact our methods allow direct calculation of the contact invariant in terms of the rational surgery mapping cone of Ozsváth and Szabó. The proof involves a construction called reducible open book surgery, which reduces in special cases to the capping-off construction studied by Baldwin.
Purpose: Interventions at the otobasis operate in the narrow region of the temporal bone where several highly sensitive organs define obstacles with minimal clearance for surgical instruments. Nonlinear trajectories for potential minimally-invasive interventions can provide larger distances to risk structures and optimized orientations of surgical instruments, thus improving clinical outcomes when compared to existing linear approaches. In this paper, we present fast and accurate planning methods for such nonlinear access paths. Methods: We define a specific motion planning problem in SE(3) = R3 x SO(3) with notable constraints in computation time and goal pose that reflect the requirements of temporal bone surgery.We then present k-RRT-Connect: two suitable motion planners based on bidirectional Rapidly-exploring Random Trees (RRT) to solve this problem efficiently. Results: The benefits of k-RRT-Connect are demonstrated on real CT data of patients. Their general performance is shown on a large set of realistic synthetic anatomies. We also show that these new algorithms outperform state of the art methods based on circular arcs or Bezier-Splines when applied to this specific probl
Generating a surgical report in robot-assisted surgery, in the form of natural language expression of surgical scene understanding, can play a significant role in document entry tasks, surgical training, and post-operative analysis. Despite the state-of-the-art accuracy of the deep learning algorithm, the deployment performance often drops when applied to the Target Domain (TD) data. For this purpose, we develop a multi-layer transformer-based model with the gradient reversal adversarial learning to generate a caption for the multi-domain surgical images that can describe the semantic relationship between instruments and surgical Region of Interest (ROI). In the gradient reversal adversarial learning scheme, the gradient multiplies with a negative constant and updates adversarially in backward propagation, discriminating between the source and target domains and emerging domain-invariant features. We also investigate model calibration with label smoothing technique and the effect of a well-calibrated model for the penultimate layer's feature representation and Domain Adaptation (DA). We annotate two robotic surgery datasets of MICCAI robotic scene segmentation and Transoral Robotic
The portrayal of crowd accidents by the media can influence public understanding and emotional response, shaping societal perceptions and potentially impacting safety measures and preparedness strategies. This paper critically examines the portrayal of crowd accidents in news coverage by analyzing the texts of 372 media reports of crowd accidents spanning 26 diverse news sources from 1900 to 2019. We investigate how media representations of crowd accidents vary across time and geographical origins. Our methodology combines lexical analysis to unveil prevailing terminologies and sentiment analysis to discern the emotional tenor of the reports. The findings reveal the prevalence of the term "stampede" over "panic" in media descriptions of crowd accidents. Notably, divergent patterns are observable when comparing Western versus South Asian media (notably India and Pakistan), unveiling a cross-cultural dimension. Moreover, the analysis detects a gradual transition from "crowd stampede" to "crowd crush" in media and Wikipedia narratives in recent years, suggesting evolving lexical sensitivities. Sentiment analysis uncovers a consistent association with fear-related language, indicative
In medical imaging, access to data is commonly limited due to patient privacy restrictions and the issue that it can be difficult to acquire enough data in the case of rare diseases.[1] The purpose of this investigation was to develop a reusable open-source synthetic image generation pipeline, the GAN Image Synthesis Tool (GIST), that is easy to use as well as easy to deploy. The pipeline helps to improve and standardize AI algorithms in the digital health space by generating high quality synthetic image data that is not linked to specific patients. Its image generation capabilities include the ability to generate imaging of pathologies or injuries with low incidence rates. This improvement of digital health AI algorithms could improve diagnostic accuracy, aid in patient care, decrease medicolegal claims, and ultimately decrease the overall cost of healthcare. The pipeline builds on existing Generative Adversarial Networks (GANs) algorithms, and preprocessing and evaluation steps were included for completeness. For this work, we focused on ensuring the pipeline supports radiography, with a focus on synthetic knee and elbow x-ray images. In designing the pipeline, we evaluated the p
In this article, we explore phenomena relating to quasi-alternating surgeries on knots, where a quasi-alternating surgery on a knot is a Dehn surgery yielding the double branched cover of a quasi-alternating link. Since the double branched cover of a quasi-alternating link is an L-space, quasi-alternating surgeries are special examples of L-space surgeries. We show that all SnapPy census L-space knots admit quasi-alternating surgeries except for the knots t09847 and o9_30634, neither of which have any quasi-alternating surgeries. In particular, this finishes Dunfield's classification of the L-space knots among all SnapPy census knots. In addition, we show that all asymmetric census L-space knots have exactly two quasi-alternating slopes and that these are consecutive integers. Similar behavior is observed for some of the Baker-Luecke asymmetric L-space knots. We also classify the quasi-alternating surgeries on torus knots and show that the set of formal L-space slopes is either empty or infinite This allows us to give examples of asymmetric formal L-spaces.
Background Analyzing kinematic and video data can help identify potentially erroneous motions that lead to sub-optimal surgeon performance and safety-critical events in robot-assisted surgery. Methods We develop a rubric for identifying task and gesture-specific Executional and Procedural errors and evaluate dry-lab demonstrations of Suturing and Needle Passing tasks from the JIGSAWS dataset. We characterize erroneous parts of demonstrations by labeling video data, and use distribution similarity analysis and trajectory averaging on kinematic data to identify parameters that distinguish erroneous gestures. Results Executional error frequency varies by task and gesture, and correlates with skill level. Some predominant error modes in each gesture are distinguishable by analyzing error-specific kinematic parameters. Procedural errors could lead to lower performance scores and increased demonstration times but also depend on surgical style. Conclusions This study provides insights into context-dependent errors that can be used to design automated error detection mechanisms and improve training and skill assessment.
Purpose: Accurate estimation of the position and orientation (pose) of surgical instruments is crucial for delicate minimally invasive temporal bone surgery. Current techniques lack in accuracy and/or line-of-sight constraints (conventional tracking systems) or expose the patient to prohibitive ionizing radiation (intra-operative CT). A possible solution is to capture the instrument with a c-arm at irregular intervals and recover the pose from the image. Methods: i3PosNet infers the position and orientation of instruments from images using a pose estimation network. Said framework considers localized patches and outputs pseudo-landmarks. The pose is reconstructed from pseudo-landmarks by geometric considerations. Results: We show i3PosNet reaches errors less than 0.05mm. It outperforms conventional image registration-based approaches reducing average and maximum errors by at least two thirds. i3PosNet trained on synthetic images generalizes to real x-rays without any further adaptation. Conclusion: The translation of Deep Learning based methods to surgical applications is difficult, because large representative datasets for training and testing are not available. This work empirica