Computing Topological Persistence for Simplicial Maps

Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $\mathbb{Z}_2$ coefficients for a sequence of general simplicial maps and show how these maps arise naturally in some applications of topological data analysis. First, we observe that it is not hard to simulate simplicial maps by inclusion maps but not necessarily in a monotone direction. This, combined with the known algorithms for zigzag persistence, provides an algorithm for computing the persistence induced by simplicial maps. Our main result is that the above simple minded approach can be improved for a sequence of simplicial maps given in a monotone direction. A simplicial map can be decomposed into a set of elementary inclusions and vertex collapses--two atomic operations that can be supported efficiently with the notion of simplex annotations for computing persistent homology. A consistent annotation through these atomic operations implies the maintenance of a consistent cohomology basis, hence a homology basis by duality. While the idea of maintaining a cohomology basis through an inclusion is not new, maintaining them through a vertex collapse is new, which constitutes an important atomic operation for simulating simplicial maps. Annotations support the vertex collapse in addition to the usual inclusion quite naturally. Finally, we exhibit an application of this new tool in which we approximate the persistence diagram of a filtration of Rips complexes where vertex collapses are used to tame the blow-up in size.Comment: This is the revised and full version of the paper that is going to appear in the Proceedings of 30th Annual Symposium on Computational Geometr

Dimension Detection with Local Homology

Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena associated to the data. Among the many dimension detection algorithms proposed in various fields, a few can provide theoretical guarantee on the correctness of the estimated dimension. However, the correctness usually requires certain regularity of the input: the input points are either uniformly randomly sampled in a statistical setting, or they form the so-called $(\varepsilon,\delta)$-sample which can be neither too dense nor too sparse. Here, we propose a purely topological technique to detect dimensions. Our algorithm is provably correct and works under a more relaxed sampling condition: we do not require uniformity, and we also allow Hausdorff noise. Our approach detects dimension by determining local homology. The computation of this topological structure is much less sensitive to the local distribution of points, which leads to the relaxation of the sampling conditions. Furthermore, by leveraging various developments in computational topology, we show that this local homology at a point $z$ can be computed \emph{exactly} for manifolds using Vietoris-Rips complexes whose vertices are confined within a local neighborhood of $z$. We implement our algorithm and demonstrate the accuracy and robustness of our method using both synthetic and real data sets

Topological analysis of scalar fields with outliers

Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field

Large Language Model Based Automated Labeling of Keypoints in Images of Rooms

Spatial applications require accurate geometrical measurements of physical spaces. Typically, room geometry can be determined based on the position of various corners in the room. A room keypoints model can provide the locations of corners in an image of a room. However, there is a dearth of diverse types of suitable images with labeled keypoints that can be employed to train keypoint models. Manual labeling does not scale because it is tedious, slow, and expensive. This disclosure describes an LLM-based agent to automate the labeling of keypoints, such as corners within room images at scale, thus enabling speedy generation of ground truth training data at scale. The agent can be fine-tuned to output pixel coordinates within an image corresponding to the locations of various keypoints within the room based on the image and a prompt specifying the task. The techniques can be enhanced by appropriately incorporating Reinforcement Learning from Human Feedback (RLHF)

Semantic Information Based Device Localization Using Artificial Intelligence

This disclosure describes techniques for device localization based on semantic information available in the environment. A semantic data source is identified by performing landmark identification using an artificial intelligence (AI) model trained to identify landmarks. Image(s) of the semantic data source are provided to a text recognition module. The detected text is provided to a semantic aware localizer. An estimated surface normal and estimated depth of the semantic data source are additionally provided as inputs to the semantic aware localizer. When device localization is being performed, live semantic information captured by the device can be utilized in conjunction with a 2D map of the environment to accurately estimate the location and spatial orientation of the device based on a comparison of the obtained semantic information with the 2D map. The localization result can be utilized in a navigation application and other applications

Дисульфідні зв’язки у структурно-функціональній організації протеїнів

Обговорюються сучасні уявлення про роль дисульфідного зв’язку в забезпеченні структурно-функціональних властивостей протеїнів плазми крові. Узагальнюються нові підходи до можливостей рефолдингу рекомбінантних і секреторних протеїнів. Розглянуто проблему окисного фолдингу та значення дисульфідного зв’язку для посттрансляційного «дозрівання» секреторних протеїнів у порожнині ендоплазматичного ретикулума з участю редуктазної системи ензимів.Обсуждаются современные представления о роли дисульфидной связи в обеспечении структурно-функциональних свойств протеинов плазмы крови. Обобщаются новые подходы к возможностям рефолдинга рекомбинантных и секреторных протеинов. Рассмотрены проблема окислительного фолдинга и значение дисульфидной связи для посттрансляционного «созревания» секреторных протеинов в эндоплазматическом ретикулуме с участием редуктазной системы энзимов.Modern vision about disulfide bonds role in light of providing the structural and functional properties of blood plasma proteins is proposed. New approaches concerning recombinant and secretory proteins refolding are generalized. A problem concerning oxidative folding and disulfide bonds significance for secretory protein posttranslation ripening inside of endoplasmic reticulum with reductase enzyme system participation is discussed

Enhanced Image Retrieval Under Scene Changes for Indoor Localization Using 3D Gaussian Splatting and Object Masking

We propose a method for image retrieval in indoor scenes that are subject to perceptual changes caused by the temporal replacement of common household objects. To address this challenge, we propose a method that masks out these dynamic regions in either the query or database images, allowing retrieval based on the static scene elements. Additionally, we augment the database by rendering images from unseen viewpoints using 3D Gaussian splatting, thereby making candidate matches more likely to be retrieved from an augmented database. Each design choice is supported by the corresponding supporting experiments. Through evaluation on a dataset collected in several indoor scenes under the changes, we show that our method, which augments the database and masks object regions, outperforms the baseline (without masking neither query nor database and without augmentation), especially at thresholds of (0.5 m, 15 ) and (2.0 m, 60 ), achieving a 3% improvement in precision

Research on interdisciplinary project-based geography fieldwork in education for sustainable development

The ability to solve real-world problems for a sustainable future has become a worldwide consensus, and interdisciplinary competencies and project-based learning (PBL) have become the focus of curriculum reform in China. This study investigates the effectiveness of interdisciplinary PBL fieldwork in geography education for sustainable development, focusing on the perceptions of students from a junior high school in Chongming, Shanghai, of the interdisciplinary effectiveness of PBL fieldwork. Over a one-month pilot program, the results suggest that the new fieldwork approach did not achieve the expected benefits. The significant gains of students can be grouped into four perspectives, namely, understanding of nature and classroom knowledge; problem-solving skills and environmental action; scientific spirit, environmental awareness, and interest in geography; and understanding of local needs and sustainable development issues, which increased their interest in learning. The students generally accepted the ability to collect information and data and the thinking ability of circular development. The influencing factors of activity effectiveness include the time and difficulty of the activity, cognitive and knowledge levels, learning habits of students, student participation, and teaching experience of teachers. The study offers valuable insights for improving fieldwork in other regions and for future research

Evaluating World-Locking Capabilities of an Immersive Environment

Systems and methods are proposed that measure and evaluate the world-locking capability of an immersive environment. World-locking refers to the ability to position a virtual reality object in a physical environment and have the object remain stable and reliably fixed at the same location without drifting when the user moves around. To evaluate the world-locking capability of an immersive environment, a device with a pair of eye proxy cameras is used to simulate a user’s experience of looking through an extended reality (XR) device such as a head-wearable device. A stationary target is then positioned at a specific location within the field of view of the XR device. A marker tracking application is used to generate and position a virtual reality object at the location of the stationary target. The XR device is then moved, and the positions of the stationary and virtual reality objects are identified and measured when the XR device moves to measure any differences between the location of the virtual reality object and the location of the stationary object. Any detected differences point to shortcomings in the ability of the virtual environment to world-lock virtual objects. The detected differences may be collected, analyzed and used to improve the systems

Visible-light-driven coproduction of diesel precursors and hydrogen from lignocellulose-derived methylfurans

Photocatalytic hydrogen production from biomass is a promising alternative to water splitting thanks to the oxidation half-reaction being more facile and its ability to simultaneously produce solar fuels and value-added chemicals. Here, we demonstrate the coproduction of H2 and diesel fuel precursors from lignocellulose-derived methylfurans via acceptorless dehydrogenative C 12C coupling, using a Ru-doped ZnIn2S4 catalyst and driven by visible light. With this chemistry, up to 1.04\u2009g\u2009gcatalyst 121\u2009h 121 of diesel fuel precursors (~41% of which are precursors of branched-chain alkanes) are produced with selectivity higher than 96%, together with 6.0\u2009mmol\u2009gcatalyst 121\u2009h 121 of H2. Subsequent hydrodeoxygenation reactions yield the desired diesel fuels comprising straight- and branched-chain alkanes. We suggest that Ru dopants, substituted in the position of indium ions in the ZnIn2S4 matrix, improve charge separation efficiency, thereby accelerating C 12H activation for the coproduction of H2 and diesel fuel precursors