A NOVEL CONNECTIONIST FRAMEWORK FOR COMPUTATION OF AN APPROXIMATE CONVEX-HULL OF A SET OF PLANAR POINTS, CIRCLES AND ELLIPSES

2006 ◽  
Vol 16 (01) ◽  
pp. 15-28 ◽  
Author(s):  
SRIMANTA PAL ◽  
SABYASACHI BHATTACHARYA ◽  
NIKHIL R. PAL
Keyword(s):  
Neural Network ◽  
Convex Hull ◽  
Rubber Band ◽  
Parameter Vector ◽  
Current Position ◽  
Direction Of Movement ◽  
Set Of Points ◽  
The Given ◽  
As If

We propose a two layer neural network for computation of an approximate convex-hull of a set of points or a set of circles/ellipses of different sizes. The algorithm is based on a very elegant concept — shrinking of a rubber band surrounding the set of planar objects. Logically, a set of neurons is placed on a circle (rubber band) surrounding the objects. Each neuron has a parameter vector associated with it. This may be viewed as the current position of the neuron. The given set of points/objects exerts a force of attraction on every neuron, which determines how its current position will be updated (as if, the force determines the direction of movement of the neuron lying on the rubber band). As the network evolves, the neurons (parameter vectors) approximate the convex-hull more and more accurately. The scheme can be applied to find the convex-hull of a planar set of circles or ellipses or a mixture of the two. Some properties related to the evolution of the algorithm are also presented.

scholarly journals Angle Bisector Algorithm and Modified Dynamic Programming Algorithm for Dubins Traveling Salesman Problem

2021 ◽  
Author(s):  
Eswara Venkata Kumar Dhulipala
Keyword(s):  
Euclidean Distance ◽  
Travelling Salesman Problem ◽  
Dynamic Programming Algorithm ◽  
Constant Factor ◽  
Programming Algorithm ◽  
Worst Case ◽  
Angle Bisector ◽  
Set Of Points ◽  
The Given ◽  
Tour Length

A Dubin's Travelling Salesman Problem (DTSP) of finding a minimum length tour through a given set of points is considered. DTSP has a Dubins vehicle, which is capable of moving only forward with constant speed. In this paper, first, a worst case upper bound is obtained on DTSP tour length by assuming DTSP tour sequence same as Euclidean Travelling Salesman Problem (ETSP) tour sequence. It is noted that, in the worst case, \emph{any algorithm that uses of ETSP tour sequence} is a constant factor approximation algorithm for DTSP. Next, two new algorithms are introduced, viz., Angle Bisector Algorithm (ABA) and Modified Dynamic Programming Algorithm (MDPA). In ABA, ETSP tour sequence is used as DTSP tour sequence and orientation angle at each point $i_k$ are calculated by using angle bisector of the relative angle formed between the rays $i_{k}i_{k-1}$ and $i_ki_{k+1}$. In MDPA, tour sequence and orientation angles are computed in an integrated manner. It is shown that the ABA and MDPA are constant factor approximation algorithms and ABA provides an improved upper bound as compared to Alternating Algorithm (AA) \cite{savla2008traveling}. Through numerical simulations, we show that ABA provides an improved tour length compared to AA, Single Vehicle Algorithm (SVA) \cite{rathinam2007resource} and Optimized Heading Algorithm (OHA) \cite{babel2020new,manyam2018tightly} when the Euclidean distance between any two points in the given set of points is at least $4\rho$ where $\rho$ is the minimum turning radius. The time complexity of ABA is comparable with AA and SVA and is better than OHA. Also we show that MDPA provides an improved tour length compared to AA and SVA and is comparable with OHA when there is no constraint on Euclidean distance between the points. In particular, ABA gives a tour length which is at most $4\%$ more than the ETSP tour length when the Euclidean distance between any two points in the given set of points is at least $4\rho$.

scholarly journals Educational Content of Today The Understanding of Architecture as a Collective Art

2019 ◽  
pp. 100-103
Author(s):  
Gro Lauvland
Keyword(s):  
Martin Heidegger ◽  
Market Economy ◽  
Human Beings ◽  
Educational Content ◽  
Nature And Culture ◽  
Production Processes ◽  
The World ◽  
The Given ◽  
As If ◽  
At Home

Our understanding of the world is manifested in what we make and produce. Through the last 250 years there has been a change in the understanding of man´s place in the world. Our way of building is characterized by market economy and controlled production processes — as if we can control everything through our consciousness. Both the given nature and what is transferred to us through history, are regarded as resources made for us. Today our understanding of the world makes the cities more and more similar. This understanding of nature and culture challenges our human conditions. As human beings, we are embedded in the place, according to both Martin Heidegger and Maurice Merleau-Ponty. In line with their understanding the Norwegian architect and theorist Christian Norberg-Schulz argued, for instance in Stedskunst (1995), that it is the qualities of the place we identify with, and which makes it possible for us to feel at home.

Digital Modeling and Movement Resolution of Rubber Band Analogy for 2D Packing Problem

2012 ◽  
Vol 220-223 ◽  
pp. 2466-2470 ◽  
Author(s):  
Jun Yan Ma ◽  
Xiao Ping Liao ◽  
Juan Lu ◽  
Hong Yao
Keyword(s):  
Convex Hull ◽  
Extreme Points ◽  
Packing Problem ◽  
Rubber Band ◽  
Scanning Method ◽  
Resultant Vector ◽  
Digital Modeling ◽  
Volume Decrease ◽  
Modeling Algorithm

Packing problem is how to arrange the components in available spaces to make the layout compact. This paper adopts a digital modeling algorithm to establish a novel rubber band convex hull model to solve this problem. A ray scanning method analogy QuickHull algorithm is presented to get extreme points of rubber band convex hull. A plural vector expression approach is adopted to movement resolution,which calculate the resultant vector to translate, rotate and slide the subbody to make the volume decrease. An experiment proved this digital modeling algorithm effective.

MOVEMENT AND MEMORY FUNCTION IN BIOLOGICAL NEURAL NETWORKS

1995 ◽  
Vol 04 (04) ◽  
pp. 489-500 ◽  
Author(s):  
NAOHIRO ISHII ◽  
KEN-ICHI NAKA
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Spatial Information ◽  
Memory Function ◽  
Amacrine Cells ◽  
Linear Analysis ◽  
Non Linear ◽  
Asymmetric Networks ◽  
Direction Of Movement ◽  
The Difference

Asymmetrical neural networks are shown in the biological neural network as the catfish retina. Horizontal and bipolar cell responses are linearly related to the input modulation of light, while amacrine cells work linearly and nonlinearly in their responses. These cells make asymmetrical neural networks in the retina. Several mechanisms have been proposed for the detection of motion in biological system. To make clear the difference among asymmetrical networks, we applied non-linear analysis developed by N. Wiener. Then, we can derive α-equation of movement, which shows the direction of movement. During the movement, we also can derive the movement equation, which implies that the movement holds regardless of the parameter α. By analyzing the biological asymmetric neural networks, it is shown that the asymmetric networks are excellent in the ability of spatial information processing on the retinal level. Then, the symmetric network was discussed by applying the non-linear analysis. In the symmetric neural network, it was suggested that memory function is needed to perceive the movement.

Inflectional Convex Space Curves

1984 ◽  
Vol 36 (3) ◽  
pp. 537-549 ◽  
Author(s):  
Tibor Bisztriczky
Keyword(s):  
Convex Hull ◽  
Convex Space ◽  
Intersection Point ◽  
List Type ◽  
Multiple Points ◽  
Space Curves ◽  
Euclidean Three Space ◽  
Set Of Points ◽  
Three Space ◽  
Regular Closed

Let Φ be a regular closed C2 curve on a sphere S in Euclidean three-space. Let H(S)[H(Φ) ] denote the convex hull of S[Φ]. For any point p ∈ H(S), let O(p) be the set of points of Φ whose osculating plane at each of these points passes through p.1. THEOREM ([8]). If Φ has no multiple points and p ∈ H(Φ), then |0(p) | ≧ 3[4] when p is [is not] a vertex of Φ.2. THEOREM ( [9]). a) If the only self intersection point of Φ is a doublepoint and p ∈ H(Φ) is not a vertex of Φ, then |O(p)| ≧ 2.b) Let Φ possess exactly n vertices. Then(1)|O(p)| ≦ nforp ∈ H(S) and(2)if the osculating plane at each vertex of Φ meets Φ at exactly one point, |O(p)| = n if and only if p ∈ H(Φ) is not vertex.

Modeling The Tower Of Hanoi Using Neural Network

1993 ◽  
pp. 47-56
Author(s):  
Mohamed Othman ◽  
Mohd. Hassan Selamat ◽  
Zaiton Muda ◽  
Lili Norliya Abdullah
Keyword(s):  
Neural Network ◽  
Knowledge Representation ◽  
Network Architecture ◽  
Learning Algorithm ◽  
Learning Rule ◽  
Neural System ◽  
Neural Systems ◽  
Tower Of Hanoi ◽  
Artificial Neural ◽  
The Given

This paper discusses the modeling of Tower of Hanoi using the concepts of neural network. The basis idea of backpropagation learning algorithm in Artificial Neural Systems is then described. While similar in some ways, Artificial Neural System learning deviates from tradition in its dependence on the modification of individual weights to bring about changes in a knowledge representation distributed across connection in a network. This unique form of learning is analyzed from two aspects: the selection of an appropriate network architecture for representing the problem, and the choice of a suitable learning rule capable qf reproducing the desired function within the given network. Key words: Tower of Hanoi; Backpropagation Algorithm; Knowledge Representation;

Spanning Properties of Yao and 𝜃-Graphs in the Presence of Constraints

2019 ◽  
Vol 29 (02) ◽  
pp. 95-120 ◽  
Author(s):  
Prosenjit Bose ◽  
André van Renssen
Keyword(s):  
Line Segment ◽  
Large Family ◽  
Upper Bounds ◽  
The Other ◽  
Additional Property ◽  
Graph Partitions ◽  
Set Of Points ◽  
The Given

We present improved upper bounds on the spanning ratio of constrained [Formula: see text]-graphs with at least 6 cones and constrained Yao-graphs with 5 or at least 7 cones. Given a set of points in the plane, a Yao-graph partitions the plane around each vertex into [Formula: see text] disjoint cones, each having aperture [Formula: see text], and adds an edge to the closest vertex in each cone. Constrained Yao-graphs have the additional property that no edge properly intersects any of the given line segment constraints. Constrained [Formula: see text]-graphs are similar to constrained Yao-graphs, but use a different method to determine the closest vertex. We present tight bounds on the spanning ratio of a large family of constrained [Formula: see text]-graphs. We show that constrained [Formula: see text]-graphs with [Formula: see text] ([Formula: see text] and integer) cones have a tight spanning ratio of [Formula: see text], where [Formula: see text] is [Formula: see text]. We also present improved upper bounds on the spanning ratio of the other families of constrained [Formula: see text]-graphs. These bounds match the current upper bounds in the unconstrained setting. We also show that constrained Yao-graphs with an even number of cones ([Formula: see text]) have spanning ratio at most [Formula: see text] and constrained Yao-graphs with an odd number of cones ([Formula: see text]) have spanning ratio at most [Formula: see text]. As is the case with constrained [Formula: see text]-graphs, these bounds match the current upper bounds in the unconstrained setting, which implies that like in the unconstrained setting using more cones can make the spanning ratio worse.

scholarly journals Design Space Exploration for YOLO Neural Network Accelerator

Electronics ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 1921
Author(s):  
Hongmin Huang ◽  
Zihao Liu ◽  
Taosheng Chen ◽  
Xianghong Hu ◽  
Qiming Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Design Space Exploration ◽  
Design Space ◽  
Space Exploration ◽  
Computation Time ◽  
Memory Bandwidth ◽  
Block Transmission ◽  
Transmission Strategy ◽  
The Neural Network ◽  
The Given

The You Only Look Once (YOLO) neural network has great advantages and extensive applications in computer vision. The convolutional layers are the most important part of the neural network and take up most of the computation time. Improving the efficiency of the convolution operations can greatly increase the speed of the neural network. Field programmable gate arrays (FPGAs) have been widely used in accelerators for convolutional neural networks (CNNs) thanks to their configurability and parallel computing. This paper proposes a design space exploration for the YOLO neural network based on FPGA. A data block transmission strategy is proposed and a multiply and accumulate (MAC) design, which consists of two 14 × 14 processing element (PE) matrices, is designed. The PE matrices are configurable for different CNNs according to the given required functions. In order to take full advantage of the limited logical resources and the memory bandwidth on the given FPGA device and to simultaneously achieve the best performance, an improved roofline model is used to evaluate the hardware design to balance the computing throughput and the memory bandwidth requirement. The accelerator achieves 41.99 giga operations per second (GOPS) and consumes 7.50 W running at the frequency of 100 MHz on the Xilinx ZC706 board.

SENTENCE ALIGNMENT USING FEED FORWARD NEURAL NETWORK

2006 ◽  
Vol 16 (06) ◽  
pp. 423-434 ◽  
Author(s):  
MOHAMED ABDEL FATTAH ◽  
FUJI REN ◽  
SHINGO KUROIWA
Keyword(s):  
Neural Network ◽  
Language Processing ◽  
Training Data ◽  
Parameter Vector ◽  
Feed Forward Neural Network ◽  
New Approach ◽  
Feed Forward ◽  
Parallel Corpora ◽  
Feature Parameter ◽  
Essential Resource

Parallel corpora have become an essential resource for work in multi lingual natural language processing. However, sentence aligned parallel corpora are more efficient than non-aligned parallel corpora for cross language information retrieval and machine translation applications. In this paper, we present a new approach to align sentences in bilingual parallel corpora based on feed forward neural network classifier. A feature parameter vector is extracted from the text pair under consideration. This vector contains text features such as length, punctuate score, and cognate score values. A set of manually prepared training data has been assigned to train the feed forward neural network. Another set of data was used for testing. Using this new approach, we could achieve an error reduction of 60% over length based approach when applied on English–Arabic parallel documents. Moreover this new approach is valid for any language pair and it is quite flexible approach since the feature parameter vector may contain more/less or different features than that we used in our system such as lexical match feature.

A SIMPLIFIED TECHNIQUE FOR HIDDEN-LINE ELIMINATION IN TERRAINS

1993 ◽  
Vol 03 (02) ◽  
pp. 167-181 ◽  
Author(s):  
FRANCO P. PREPARATA ◽  
JEFFREY SCOTT VITTER
Keyword(s):  
Data Structure ◽  
Convex Hull ◽  
Full Advantage ◽  
Implicit Representation ◽  
Geometrical Properties ◽  
Asymptotic Speed ◽  
Hidden Line ◽  
The Cost ◽  
Set Of Points

In this paper we give a practical and efficient output-sensitive algorithm for constructing the display of a polyhedral terrain. It runs in O((d+n) log 2 n) time and uses O(nα(n)) space, where d is the size of the final display, and α(n) is a (very slowly growing) functional inverse of Ackermann’s function. Our implementation is especially simple and practical, because we try to take full advantage of the specific geometrical properties of the terrain. The asymptotic speed of our algorithm has been improved upon theoretically by other authors, but at the cost of higher space usage and/or high overhead and complicated code. Our main data structure maintains an implicit representation of the convex hull of a set of points that can be dynamically updated in O( log 2 n) time. It is especially simple and fast in our application since there are no rebalancing operations required in the tree.

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