Closest Pair Algorithms in 2D space,a commentary on complexity and reductions

One of the most challenging problems in computational geometry is closest pair of points given n points. Brute force algorithms[1] and Divide and conquer[1] have been verified and the lowest complexity of attributed to latter class of algorithms, with worst case being for the former being . We propose a method of partitioning the set of n-points based on the least area rectangle that can circumscribe these points

A modified gravity model coupled to a Dirac field in 2D space–times with quadratic nonmetricity and curvature

After summarizing the basic concepts for the exterior algebra, we first discuss the gauge structure of the bundle over base manifold for deciding the form of the gravitational sector of the total Lagrangian in any dimensions. Then we couple minimally a Dirac spinor field to our gravitational Lagrangian 2-form which is quadratic in the nonmetricity and both linear and quadratic in the curvature in two dimensions. Subsequently, we obtain field equations by varying the total Lagrangian with respect to the independent variables. Finally, we find some classes of solutions of the vacuum theory and then a solution of the Dirac equation in a specific background and analyze them.

Finite Difference Method in Fluid Potential Function and Velocity Calculation

There is no deterministic solution for many fluid problems but by applying analytical solutions many of them are approximated. In this study an implicit finite difference method presented which solves the potential function and further expanded to drive out the velocity components in 2D-space by applying a point-by-point swiping approach. The results showed the rotational behavior of both potential function as well as velocity components while encountering central obstacle.

Crack detection using tap-testing and machine learning techniques to prevent potential rockfall incidents

Rockfalls are a hazard for the safety of infrastructure as well as people. Identifying loose rocks by inspection of slopes adjacent to roadways and other infrastructure and removing them in advance can be an effective way to prevent unexpected rockfall incidents. This paper proposes a system towards an automated inspection for potential rockfalls. A robot is used to repeatedly strike or tap on the rock surface. The sound from the tapping is collected by the robot and subsequently classified with the intent of identifying rocks that are broken and prone to fall. Principal Component Analysis (PCA) of the collected acoustic data is used to recognize patterns associated with rocks of various conditions, including intact as well as rock with different types and locations of cracks. The PCA classification was first demonstrated simulating sounds of different characteristics that were automatically trained and tested. Secondly, a laboratory test was conducted tapping rock specimens with three different levels of discontinuity in depth and shape. A real microphone mounted on the robot recorded the sound and the data were classified in three clusters within 2D space. A model was created using the training data to classify the reminder of the data (the test data). The performance of the method is evaluated with a confusion matrix.

Physics-informed deep learning characterizes morphodynamics of Asian soybean rust disease

Medicines and agricultural biocides are often discovered using large phenotypic screens across hundreds of compounds, where visible effects of whole organisms are compared to gauge efficacy and possible modes of action. However, such analysis is often limited to human-defined and static features. Here, we introduce a novel framework that can characterize shape changes (morphodynamics) for cell-drug interactions directly from images, and use it to interpret perturbed development of Phakopsora pachyrhizi, the Asian soybean rust crop pathogen. We describe population development over a 2D space of shapes (morphospace) using two models with condition-dependent parameters: a top-down Fokker-Planck model of diffusive development over Waddington-type landscapes, and a bottom-up model of tip growth. We discover a variety of landscapes, describing phenotype transitions during growth, and identify possible perturbations in the tip growth machinery that cause this variation. This demonstrates a widely-applicable integration of unsupervised learning and biophysical modeling.

Errors in visuospatial working memory across space and time

Visuospatial working memory (VSWM) involves cortical regions along the dorsal visual pathway, which are topographically organized with respect to the visual space. However, it remains unclear how such functional organization may constrain VSWM behavior across space and time. Here, we systematically mapped VSWM performance across the 2-dimensional (2D) space in various retention intervals in human subjects using the memory-guided and visually guided saccade tasks in two experiments. Relative to visually guided saccades, memory-guided saccades showed significant increases in unsystematic errors, or response variability, with increasing target eccentricity (3°–13° of visual angle). Unsystematic errors also increased with increasing delay (1.5–3 s, Experiment 1; 0.5–5 s, Experiment 2), while there was little or no interaction between delay and eccentricity. Continuous bump attractor modeling suggested neurophysiological and functional organization factors in the increasing unsystematic errors in VSWM across space and time. These findings indicate that: (1) VSWM representation may be limited by the functional topology of the visual pathway for the 2D space; (2) Unsystematic errors may reflect accumulated noise from memory maintenance while systematic errors may originate from non-mnemonic processes such as noisy sensorimotor transformation; (3) There may be independent mechanisms supporting the spatial and temporal processing of VSWM.