Search results for " Algebra"
showing 10 items of 2082 documents
An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm
2022
Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, ar…
Implementation and evaluation of medical imaging techniques based on conformal geometric algebra
2020
Medical imaging tasks, such as segmentation, 3D modeling, and registration of medical images, involve complex geometric problems, usually solved by standard linear algebra and matrix calculations. In the last few decades, conformal geometric algebra (CGA) has emerged as a new approach to geometric computing that offers a simple and efficient representation of geometric objects and transformations. However, the practical use of CGA-based methods for big data image processing in medical imaging requires fast and efficient implementations of CGA operations to meet both real-time processing constraints and accuracy requirements. The purpose of this study is to present a novel implementation of …
Ģeogrāfiskās informācijas sistēmas izmantošana brīvas izvēles pārgājienu maršrutu plānošanā
2016
Bakalaura darbs ir veltīts zemāko izmaksu metodes izmantošanas iespējām tūrisma pārgājienu maršrutu izveidē. Došanās pārgājienos brīvā dabā kļūst arvien populārāka dažāda gadagājuma cilvēku vidū. Pārgājienu maršrutu izveide pamatā tiek balstīta uz jau eksistējošiem ceļiem un takām, kas palīdz radīt vieglas sarežģītības pakāpes maršrutus un atvieglo organizatoru darbu, taču tajā pašā laikā nesniedz iespēju nokļūt vietās, kas nav sasniedzamas ar ceļu tīklu. Pētījumā piedāvāts risinājums ar ģeogrāfiskās informācijas sistēmas palīdzību optimizēt un atvieglot pārgājienu maršrutu izveidi, pamatā neizmantojot jau esošos ceļus un kustoties brīvā telpā. Pētījuma mērķis ir izstrādāt metodiku izmaksu …
Teachers' procedures when introducing algebraic expression in two Norwegian grade 8 classrooms
2015
International audience; We investigate similarities and differences in two teachers’ way of introducing algebraic expressions by designed examples. One teacher moves from the specific to the general, and the other moves from the general to the specific. They both mediate the passage from the students’ real world and the school mathematics they know, to algebra.
Semigenerated Carnot algebras and applications to sub-Riemannian perimeter
2021
This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic: such a phenomenon happens if and only if the semigroup generated by each horizontal half-space is a vertical half-space. We call semigenerated those Carnot groups with this property. For Carnot groups of nilpotency step 3 we provide a complete characterization of semigeneration in terms of whether such groups do not have any Engel-type quotients. Engel-type groups, which are introduced here, are the minimal (in terms of quotients) counterexamples. In add…
On Variational Measures Related to Some Bases
2000
Abstract We extend, to a certain class of differentiation bases, some results on the variational measure and the δ-variation obtained earlier for the full interval basis. In particular the theorem stating that the variational measure generated by an interval function is σ-finite whenever it is absolutely continuous with respect to the Lebesgue measure is extended to any Busemann–Feller basis.
Discrete cortical representations and their stability in the presence of synaptic turnover
2015
Population imaging in mouse auditory cortex revealed clustering of neural responses to brief complex sounds: the activity of a local population typically falls close to one out of a small number of observed states [1]. These clusters appear to group sets of auditory stimuli into a discrete set of activity patterns and could thereby form the basis for representations of sound categories. However, to be useful for the brain, such representations should be robust against fluctuations in the underlying circuitry, which are significant even in the absences of any explicit learning paradigm [2]. Here we introduce a novel firing rate based circuit model of mouse auditory cortex to study the emerge…
On the spatial spread of a pattern
1980
A simple process is considered for the spread of a pattern in a spatially distributed population. Expressions are given for the stochastic means, variances and covariances. Central limit theorems are obtained for the number of individuals that have the pattern, and the time needed for the pattern to reach the n-th subpopulation.
A Neuro-Ethological Approach for the TSP: Changing Metaphors in Connectionist Models.
1994
Biological systems often offer solutions to difficult problems which are not only original but also efficient. Connectionist models have been inspired by neural systems and successfully applied to the formulation of algorithms for solving complex problems such as the travelling salesman problem. In this paper we extend the connectionist metaphor to include an ethological account of how problems similar to the travelling salesman problem are solved by real living systems. A model is presented in which a population of neural networks with simple sensory-motor systems evolve genetically in simulated environments which represent the problem instances to be solved. Preliminary results are discu…
Comparison of non-Markovianity criteria in a qubit system under random external fields
2013
We give the map representing the evolution of a qubit under the action of non-dissipative random external fields. From this map we construct the corresponding master equation that in turn allows us to phenomenologically introduce population damping of the qubit system. We then compare, in this system, the time-regions when non-Markovianity is present on the basis of different criteria both for the non-dissipative and dissipative case. We show that the adopted criteria agree both in the non-dissipative case and in the presence of population damping.