The efficient construction of an anatomical model is one of the major challenges of patient-specific in-silico models of the human heart. Current methods frequently rely on linear statistical models, allowing no advanced topological changes, or requiring medical image segmentation followed by a meshing pipeline, which strongly depends on image resolution, quality, and modality. These approaches are therefore limited in their transferability to other imaging domains. In this work, the cardiac shape is reconstructed by means of three-dimensional deep signed distance functions with Lipschitz regularity. For this purpose, the shapes of cardiac MRI reconstructions are learned from public databases to model the spatial relation of multiple chambers in Cartesian space. We demonstrate that this approach is also capable of reconstructing anatomical models from partial data, such as point clouds from a single ventricle, or modalities different from the trained MRI, such as electroanatomical mapping, and in addition, allows us to generate new anatomical shapes by randomly sampling latent vectors.
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Large transformer models have achieved state-of-the-art results in numerous natural language processing tasks. Among the pivotal components of the transformer architecture, the attention mechanism plays a crucial role in capturing token interactions within sequences through the utilization of softmax function. Conversely, linear attention presents a more computationally efficient alternative by approximating the softmax operation with linear complexity. However, it exhibits substantial performance degradation when compared to the traditional softmax attention mechanism. In this paper, we bridge the gap in our theoretical understanding of the reasons behind the practical performance gap between softmax and linear attention. By conducting a comprehensive comparative analysis of these two attention mechanisms, we shed light on the underlying reasons for why softmax attention outperforms linear attention in most scenarios.
We revisit the recent polynomial-time algorithm for the MAX WEIGHT INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a fixed graph whose every component is a subdivided claw as an induced subgraph [Abrishami, Dibek, Chudnovsky, Rz\k{a}\.zewski, SODA 2022]. First, we show that with an arguably simpler approach we can obtain a faster algorithm with running time $n^{\mathcal{O}(\Delta^2)}$, where $n$ is the number of vertices of the instance and $\Delta$ is the maximum degree. Then we combine our technique with known results concerning tree decompositions and provide a polynomial-time algorithm for MWIS in graphs excluding a fixed graph whose every component is a subdivided claw as an induced subgraph, and a fixed biclique as a subgraph.
The topic of inverse problems, related to Maxwell's equations, in the presence of nonlinear materials is quite new in literature. The lack of contributions in this area can be ascribed to the significant challenges that such problems pose. Retrieving the spatial behaviour of some unknown physical property, starting from boundary measurements, is a nonlinear and highly ill-posed problem even in the presence of linear materials. And the complexity exponentially grows when the focus is on nonlinear material properties. Recently, the Monotonicity Principle has been extended to nonlinear materials under very general assumptions. Starting from the theoretical background given by this extension, we develop a first real-time inversion method for the inverse obstacle problem in the presence of nonlinear materials. The Monotonicity Principle is the foundation of a class of non-iterative algorithms for tomography of linear materials. It has been successfully applied to various problems, governed by different PDEs. In the linear case, MP based inversion methods ensure excellent performances and compatibility with real-time applications. We focus on problems governed by elliptical PDEs and, as an example of application, we treat the Magnetostatic Permeability Tomography problem, in which the aim is to retrieve the spatial behaviour of magnetic permeability through boundary measurements in DC operations. In this paper, we provide some preliminary results giving the foundation of our method and extended numerical examples.
The Graded of Membership (GoM) model is a powerful tool for inferring latent classes in categorical data, which enables subjects to belong to multiple latent classes. However, its application is limited to categorical data with nonnegative integer responses, making it inappropriate for datasets with continuous or negative responses. To address this limitation, this paper proposes a novel model named the Weighted Grade of Membership (WGoM) model. Compared with GoM, our WGoM relaxes GoM's distribution constraint on the generation of a response matrix and it is more general than GoM. We then propose an algorithm to estimate the latent mixed memberships and the other WGoM parameters. We derive the error bounds of the estimated parameters and show that the algorithm is statistically consistent. The algorithmic performance is validated in both synthetic and real-world datasets. The results demonstrate that our algorithm is accurate and efficient, indicating its high potential for practical applications. This paper makes a valuable contribution to the literature by introducing a novel model that extends the applicability of the GoM model and provides a more flexible framework for analyzing categorical data with weighted responses.
Empirical research on perception and cognition has laid the foundation for visualization design, often yielding useful design guidelines for practitioners. However, it remains uncertain how well practitioners stay informed about the latest findings in visualization research. In this paper, we employed a mixed-method approach to explore the knowledge gap between visualization research and real-world design guidelines. We initially collected existing design guidelines from various sources and empirical studies from major publishing venues, analyzing their alignment and uncovering missing links and contradictory knowledge. Subsequently, we conducted surveys and interviews with practitioners and researchers to gain further insights into their experiences and attitudes towards design guidelines and empirical studies, and their views on the knowledge gap between research and practice. Our findings highlight the similarities and differences in their perspectives and propose strategies to bridge the divide in visualization design knowledge.
This work is concerned with cone-beam computed tomography with circular source trajectory, where the reconstruction inverse problem requires an accurate knowledge of source, detector and rotational axis relative positions and orientations. We address this problem as a preceding step of the reconstruction process directly from the acquired projections. The method estimates both the detector shift (orthogonal to focal and rotational axes) and the in-plane detector rotation, relative to source and rotational axis. The obtained algorithm is based on a fan-beam symmetry condition and the variable projection optimization approach with a low computational cost. Therefore, the alignment problem for fan-beam tomography is addressed as well. The methods are validated with simulated and real industrial tomographic data with code examples available for both fan- and cone-beam geometries.
In contrast to numerous NLP and 2D computer vision foundational models, the learning of a robust and highly generalized 3D foundational model poses considerably greater challenges. This is primarily due to the inherent data variability and the diversity of downstream tasks. In this paper, we introduce a comprehensive 3D pre-training framework designed to facilitate the acquisition of efficient 3D representations, thereby establishing a pathway to 3D foundational models. Motivated by the fact that informative 3D features should be able to encode rich geometry and appearance cues that can be utilized to render realistic images, we propose a novel universal paradigm to learn point cloud representations by differentiable neural rendering, serving as a bridge between 3D and 2D worlds. We train a point cloud encoder within a devised volumetric neural renderer by comparing the rendered images with the real images. Notably, our approach demonstrates the seamless integration of the learned 3D encoder into diverse downstream tasks. These tasks encompass not only high-level challenges such as 3D detection and segmentation but also low-level objectives like 3D reconstruction and image synthesis, spanning both indoor and outdoor scenarios. Besides, we also illustrate the capability of pre-training a 2D backbone using the proposed universal methodology, surpassing conventional pre-training methods by a large margin. For the first time, PonderV2 achieves state-of-the-art performance on 11 indoor and outdoor benchmarks. The consistent improvements in various settings imply the effectiveness of the proposed method. Code and models will be made available at //github.com/OpenGVLab/PonderV2.
Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful supercomputers today. However, whether the current approach limited by photon loss and noise in such experiments prescribes a scalable path to quantum advantage is an open question. To understand the effect of photon loss on the scalability of Gaussian boson sampling, we analytically derive the asymptotic operator entanglement entropy scaling, which relates to the simulation complexity. As a result, we observe that efficient tensor network simulations are likely possible under the $N_\text{out}\propto\sqrt{N}$ scaling of the number of surviving photons orange$N_\text{out}$ in the number of input photons $N$. We numerically verify this result using a tensor network algorithm with $U(1)$ symmetry, and overcome previous challenges due to the large local Hilbert space dimensions in Gaussian boson sampling with hardware acceleration. Additionally, we observe that increasing the photon number through larger squeezing does not increase the entanglement entropy significantly. Finally, we numerically find the bond dimension necessary for fixed accuracy simulations, providing more direct evidence for the complexity of tensor networks.
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the idea of equivalence taking values in a quantale V, which covers the cases of (in)equations and (ultra)metric equations among others. Our main result is the introduction of a V-equational deductive system for linear {\lambda}-calculus together with a proof that it is sound and complete. In fact we go further than this, by showing that linear {\lambda}-theories based on this V-equational system form a category that is equivalent to a category of autonomous categories enriched over 'generalised metric spaces'. If we instantiate this result to inequations, we get an equivalence with autonomous categories enriched over partial orders. In the case of (ultra)metric equations, we get an equivalence with autonomous categories enriched over (ultra)metric spaces. We additionally show that this syntax-semantics correspondence extends to the affine setting. We use our results to develop examples of inequational and metric equational systems for higher-order programming in the setting of real-time, probabilistic, and quantum computing.
Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.
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