A geometric framework for specifying spatiotemporal objects

2003 ◽  
Author(s):  
J. Chomicki ◽  
P.Z. Revesz
Keyword(s):  
Geometric Framework

A geometric framework for rigid body attitude estimation

Automatica ◽  
2021 ◽  
Vol 128 ◽  
pp. 109494
Author(s):  
Yujendra Bharathi Mitikiri ◽  
Kamran Mohseni
Keyword(s):  
Rigid Body ◽  
Attitude Estimation ◽  
Geometric Framework ◽  
Body Attitude

scholarly journals Finite cell method for functionally graded materials based on V-models and homogenized microstructures

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Benjamin Wassermann ◽  
Nina Korshunova ◽  
Stefan Kollmannsberger ◽  
Ernst Rank ◽  
Gershon Elber
Keyword(s):  
Functionally Graded Materials ◽  
Large Scale ◽  
Functionally Graded ◽  
Material Behavior ◽  
Modeling Framework ◽  
Finite Cell Method ◽  
Geometric Framework ◽  
Graded Materials ◽  
Cell Method ◽  
Finite Cell

AbstractThis paper proposes an extension of the finite cell method (FCM) to V-rep models, a novel geometric framework for volumetric representations. This combination of an embedded domain approach (FCM) and a new modeling framework (V-rep) forms the basis for an efficient and accurate simulation of mechanical artifacts, which are not only characterized by complex shapes but also by their non-standard interior structure. These types of objects gain more and more interest in the context of the new design opportunities opened by additive manufacturing, in particular when graded or micro-structured material is applied. Two different types of functionally graded materials (FGM) are considered: The first one, multi-material FGM is described using the inherent property of V-rep models to assign different properties throughout the interior of a domain. The second, single-material FGM—which is heterogeneously micro-structured—characterizes the effective material behavior of representative volume elements by homogenization and performs large-scale simulations using the embedded domain approach.

scholarly journals RMPflow: A Geometric Framework for Generation of Multitask Motion Policies

2021 ◽  
pp. 1-20
Author(s):  
Ching-An Cheng ◽  
Mustafa Mukadam ◽  
Jan Issac ◽  
Stan Birchfield ◽  
Dieter Fox ◽  
...  
Keyword(s):  
Geometric Framework

scholarly journals The Invariant Set Postulate: a new geometric framework for the foundations of quantum theory and the role played by gravity

2009 ◽  
Vol 465 (2110) ◽  
pp. 3165-3185 ◽  
Author(s):  
T. N. Palmer
Keyword(s):  
Quantum Theory ◽  
Science Fiction ◽  
State Space ◽  
Fractal Geometry ◽  
Quantum Physics ◽  
Nonlinear Dynamical Systems ◽  
Physical Reality ◽  
Invariant Set ◽  
Geometric Framework

A new law of physics is proposed, defined on the cosmological scale but with significant implications for the microscale. Motivated by nonlinear dynamical systems theory and black-hole thermodynamics, the Invariant Set Postulate proposes that cosmological states of physical reality belong to a non-computable fractal state-space geometry I , invariant under the action of some subordinate deterministic causal dynamics D I . An exploratory analysis is made of a possible causal realistic framework for quantum physics based on key properties of I . For example, sparseness is used to relate generic counterfactual states to points p ∉ I of unreality, thus providing a geometric basis for the essential contextuality of quantum physics and the role of the abstract Hilbert Space in quantum theory. Also, self-similarity, described in a symbolic setting, provides a possible realistic perspective on the essential role of complex numbers and quaternions in quantum theory. A new interpretation is given to the standard ‘mysteries’ of quantum theory: superposition, measurement, non-locality, emergence of classicality and so on. It is proposed that heterogeneities in the fractal geometry of I are manifestations of the phenomenon of gravity. Since quantum theory is inherently blind to the existence of such state-space geometries, the analysis here suggests that attempts to formulate unified theories of physics within a conventional quantum-theoretic framework are misguided, and that a successful quantum theory of gravity should unify the causal non-Euclidean geometry of space–time with the atemporal fractal geometry of state space. The task is not to make sense of the quantum axioms by heaping more structure, more definitions, more science fiction imagery on top of them, but to throw them away wholesale and start afresh. We should be relentless in asking ourselves: From what deep physical principles might we derive this exquisite structure? These principles should be crisp, they should be compelling. They should stir the soul. Chris Fuchs ( Gilder 2008 , p. 335)

Maternal Dietary Fatty Acid Composition and Newborn Epigenetic Aging—A Geometric Framework Approach

2021 ◽  
Author(s):  
Nicholas A Koemel ◽  
Alistair M Senior ◽  
Hasthi U Dissanayake ◽  
Jason Ross ◽  
Rowena L McMullan ◽  
...  
Keyword(s):  
Newborn Infants ◽  
Intima Media Thickness ◽  
Response Surfaces ◽  
Geometric Framework ◽  
Body Fatness ◽  
Epigenetic Aging ◽  
Epigenetic Age ◽  
Framework Approach ◽  
Epigenetic Age Acceleration ◽  
Aortic Intima

Abstract Background Maternal nutrition is associated with epigenetic and cardiometabolic risk factors in offspring. Research in humans has primarily focused on assessing the impact of individual nutrients. Objective We sought to assess the collective impact of maternal dietary monounsaturated (MUFA), polyunsaturated (PUFA), and saturated fat (SFA) on epigenetic aging and cardiometabolic risk markers in healthy newborn infants using a geometric framework approach. Design Body fatness (n = 162), aortic intima-media thickness (n = 131), heart rate variability (n = 118), and epigenetic age acceleration (n = 124) were assessed in newborn infants. Maternal dietary intake was cross-sectionally assessed in the immediate postpartum period via a validated 80-item self-administered food-frequency questionnaire. Generalized additive models were used to explore interactive associations of nutrient intake, with results visualized as response surfaces. Results After adjustment for total energy intake, maternal age, gestational age, and sex there was a 3-way interactive association of MUFA, PUFA, and SFA (P = 0.001) with newborn epigenetic aging. This suggests that the nature of each fat class association depends upon one another. Response surfaces revealed MUFA was positively associated with newborn epigenetic age acceleration only at proportionately lower intakes of SFA or PUFA. We also demonstrate a potential beneficial association of omega-3 PUFA with newborn epigenetic age acceleration (P = 0.008). There was no significant association of fat class with newborn aortic intima-media thickness, heart rate variability, or body fatness. Conclusions In this study, we demonstrate an association between maternal dietary fat class composition and epigenetic aging in newborns. Future research should consider other characteristics such as the source of maternal dietary fatty acids.

scholarly journals Fast Feature-Preserving Approach to Carpal Bone Surface Denoising

Sensors ◽  
2018 ◽  
Vol 18 (7) ◽  
pp. 2379
Author(s):  
Ibrahim Salim ◽  
A. Hamza
Keyword(s):  
Objective Function ◽  
Linear Equations ◽  
Noise Model ◽  
Carpal Bone ◽  
Geometric Framework ◽  
Sparse System ◽  
Adaptive Kernel ◽  
Feature Preserving ◽  
Data Adaptive ◽  
Matrix Balancing

We present a geometric framework for surface denoising using graph signal processing, which is an emerging field that aims to develop new tools for processing and analyzing graph-structured data. The proposed approach is formulated as a constrained optimization problem whose objective function consists of a fidelity term specified by a noise model and a regularization term associated with prior data. Both terms are weighted by a normalized mesh Laplacian, which is defined in terms of a data-adaptive kernel similarity matrix in conjunction with matrix balancing. Minimizing the objective function reduces it to iteratively solve a sparse system of linear equations via the conjugate gradient method. Extensive experiments on noisy carpal bone surfaces demonstrate the effectiveness of our approach in comparison with existing methods. We perform both qualitative and quantitative comparisons using various evaluation metrics.

scholarly journals A Geometric Framework for Understanding Dynamic Information Integration in Context-Dependent Computation

2021 ◽  
Author(s):  
Xiaohan Zhang ◽  
Shenquan Liu ◽  
Zhe Sage Chen
Keyword(s):  
Decision Making ◽  
Prefrontal Cortex ◽  
Information Integration ◽  
Principal Component ◽  
Population Coding ◽  
Geometric Framework ◽  
Context Dependent ◽  
Activity State ◽  
Low Dimensional ◽  
Context Cues

AbstractPrefrontal cortex plays a prominent role in performing flexible cognitive functions and working memory, yet the underlying computational principle remains poorly understood. Here we trained a rate-based recurrent neural network (RNN) to explore how the context rules are encoded, maintained across seconds-long mnemonic delay, and subsequently used in a context-dependent decision-making task. The trained networks emerged key experimentally observed features in the prefrontal cortex (PFC) of rodent and monkey experiments, such as mixed-selectivity, sparse representations, neuronal sequential activity and rotation dynamics. To uncover the high-dimensional neural dynamical system, we further proposed a geometric framework to quantify and visualize population coding and sensory integration in a temporally-defined manner. We employed dynamic epoch-wise principal component analysis (PCA) to define multiple task-specific subspaces and task-related axes, and computed the angles between task-related axes and these subspaces. In low-dimensional neural representations, the trained RNN first encoded the context cues in a cue-specific subspace, and then maintained the cue information with a stable low-activity state persisting during the delay epoch, and further formed line attractors for sensor integration through low-dimensional neural trajectories to guide decision making. We demonstrated via intensive computer simulations that the geometric manifolds encoding the context information were robust to varying degrees of weight perturbation in both space and time. Overall, our analysis framework provides clear geometric interpretations and quantification of information coding, maintenance and integration, yielding new insight into the computational mechanisms of context-dependent computation.

scholarly journals A geometric framework for modeling dynamic decisions among arbitrarily many alternatives

2018 ◽  
Author(s):  
Peter D. Kvam
Keyword(s):  
Context Effects ◽  
Geometric Approach ◽  
Stopping Rules ◽  
Decision Space ◽  
Geometric Framework ◽  
Continuous Response ◽  
Similarity Relations ◽  
Preferential Choice ◽  
Dynamic Decisions ◽  
Choice Set

Multiple-choice and continuous-response tasks pose a number of challenges for models of the decision process, from empirical challenges like context effects to computational demands imposed by choice sets with a large number of outcomes. This paper develops a general framework for constructing models of the cognitive processes underlying both inferential and preferential choice among any arbitrarily large number of alternatives. This geometric approach represents the alternatives in a choice set along with a decision maker's beliefs or preferences in a ``decision space,'' simultaneously capturing the support for different alternatives along with the similarity relations between the alternatives in the choice set. Support for the alternatives (represented as vectors) shifts over time according to the dynamics of the belief / preference state (represented as a point) until a stopping rule is met (state crosses a hyperplane) and the corresponding selection is made. I review stopping rules that guarantee optimality in multi-alternative inferential choice, minimizing response time for a desired level of accuracy, as well as methods for constructing the decision space, which can result in context effects when applied to preferential choice.

Sign in / Sign up

Export Citation Format

Share Document