Search results for "algebra"
showing 10 items of 4129 documents
A New Embedded Coprocessor for Clifford Algebra based Software Intensive Systems
2011
Computer graphics applications require efficient tools to model geometric objects and their transformations. Clifford algebra (also known as geometric algebra) is receiving a growing attention in many research fields, such as computer graphics, machine vision and robotics, as a new, interesting computational paradigm that offers a natural and intuitive way to perform geometric calculations. At the same time, compute-intensive graphics algorithms require the execution of million Clifford operations. Clifford algebra based software intensive systems need therefore the support of specialized hardware architectures capable of accelerating Clifford operations execution. In this paper the archite…
GAPPCO: An Easy to Configure Geometric Algebra Coprocessor Based on GAPP Programs
2017
Because of the high numeric complexity of Geometric Algebra, its use in engineering applications relies heavily on tools and devices for efficient implementations. In this article, we present a novel hardware design for a Geometric Algebra coprocessor, called GAPPCO, which is based on Geometric Algebra Parallelism Programs (GAPP). GAPPCO is a design for a coprocessor combining the advantages of optimizing software with a configurable hardware able to implement arbitrary Geometric Algebra algorithms. The idea is to have a fixed hardware easily and fast to be configured for different algorithms. We describe the new hardware design together with the complete tool chain for its configuration.
Clifford Rotors for Conceptual Representation in Chatbots
2013
In this abstract we introduce an unsupervised sub-symbolic natural language sentences encoding procedure aimed at catching and representing into a Chatbot Knowledge Base (KB) the concepts expressed by an user interacting with a robot. The chatbot KB is coded in a conceptual space induced from the application of the Latent Semantic Analysis (LSA) paradigm on a corpus of documents. LSA has the effect of decomposing the original relationships between elements into linearly-independent vectors. Each basis vector can be considered therefore as a "conceptual coordinate", which can be tagged by the words which better characterize it. This tagging is obtained by performing a (TF-IDF)-like weighting…
A genetic approach to the maximum common subgraph problem
2019
Finding the maximum common subgraph of a pair of given graphs is a well-known task in theoretical computer science and with considerable practical applications, for example, in the fields of bioinformatics, medicine, chemistry, electronic design and computer vision. This problem is particularly complex and therefore fast heuristics are required to calculate approximate solutions. This article deals with a simple yet effective genetic algorithm that finds quickly a solution, subject to possible geometric constraints.
A Family of Embedded Coprocessors with Native Geometric Algebra Support
2015
Clifford Algebra or Geometric Algebra (GA) is a simple and intuitive way to model geometric objects and their transformations. Operating in high-dimensional vector spaces with significant computational costs, the practical use of GA requires, however, dedicated software and/or hardware architectures to directly support Clifford data types and operators. In this paper, a family of embedded coprocessors for the native execution of GA operations is presented. The paper shows the evolution of the coprocessor family focusing on the latest two architectures that offer direct hardware support to up to five-dimensional Clifford operations. The proposed coprocessors exploit hardware-oriented represe…
Springs-based Simulation for Image Retargeting
2011
In this paper an efficient method for image retargeting is pro- posed. It relies onto a mechanical model based on springs network. Each pixel displacement (compression or expan- sion) is given by the network response, according to the springs stiffness. The properties of the springs are deter- mined as function of the visual relevance of the pixels. Such model does not require any optimization, since its so- lution is obtained simply from a linear system of equations, allowing real-time application even for large images. The approach is fully automatic, though can be improved by interactively providing cues such as geometric constraints and/or manual relevant object labeling. The results pr…
Geometric Algebra Rotors for Sub-Symbolic Coding of Natural Language Sentences
2007
A sub-symbolic encoding methodology for natural language sentences is presented. The procedure is based on the creation of an LSA-inspired semantic space and associates rotation operators derived from Geometric Algebra to word bigrams of the sentence. The operators are subsequently applied to an orthonormal standard basis of the created semantic space according to the order in which words appear in the sentence. The final rotated basis is then coded as a vector and its orthogonal part constitutes the sub-symbolic coding of the sentence. Preliminary experimental results for a classification task, compared with the traditional LSA methodology, show the effectiveness of the approach.
Real-Time Object Detection in Embedded Video Surveillance Systems
2008
In this paper we report a new method to detect both moving objects and new stationary objects in video sequences. On the basis of temporal consideration we classify pixels into three classes: background, midground and foreground to distinguish between long-term, medium-term and short-term changes. The algorithm has been implemented on a hardware platform with limited resources and it could be used in a wider system like a wireless sensor networks. Particular care has been put in realizing the algorithm so that the limited available resources are used in an efficient way. Experiments have been conducted on publicly available datasets and performance measures are reported.
Sentence Induced Transformations in Conceptual Spaces
2008
The proposed work illustrates how "primitive concepts" can be automatically induced from a text corpus. The primitive concepts are identified by the orthonormal axis of a "conceptual" space induced by a methodology inspired to the latent semantic analysis approach. The methodology represents a natural language sentence by means of a set of rotations of an orthonormal basis in the "conceptual"space. The rotations, triggered by the sequence of words composing the sentence and realized by means of geometric algebra rotors, allow to highlight "conceptual" relations that can arise among the primitive concepts.
The electron and Occam's razor
2017
This paper introduces a Zitterbewegung (ZBW) model of the electron by applying the principle of Occam’s razor to Maxwell’s equations and by introducing a scalar component in the electromagnetic field. The aim is to explain, by using simple and intuitive concepts, the origin of the electric charge and the electromagnetic nature of mass and inertia. A ZBW model of the electron is also proposed as the best suited theoretical framework to study the structure of Ultra-Dense Deuterium (UDD), the origin of anomalous heat in metal–hydrogen systems and the possibility of existence of “super-chemical” aggregates at Compton scale.