scholarly journals Multiobjective Maximization of Monotone Submodular Functions with Cardinality Constraint

2020 ◽  
pp. ijoo.2019.0041
Author(s):  
Rajan Udwani
Keyword(s):  
Asymptotic Formula ◽  
Fast Algorithm ◽  
Asymptotic Approximation ◽  
Constant Factor ◽  
The Other ◽  
Submodular Functions ◽  
Cardinality Constraint ◽  
Greedy Methods ◽  
Deterministic Formula ◽  
Single Objective

We consider the problem of multiobjective maximization of monotone submodular functions subject to cardinality constraint, often formulated as [Formula: see text]. Although it is widely known that greedy methods work well for a single objective, the problem becomes much harder with multiple objectives. In fact, it is known that when the number of objectives m grows as the cardinality k, that is, [Formula: see text], the problem is inapproximable (unless P = NP). On the other hand, when m is constant, there exists a a randomized [Formula: see text] approximation with runtime (number of queries to function oracle) the scales as [Formula: see text]. We focus on finding a fast algorithm that has (asymptotic) approximation guarantees even when m is super constant. First, through a continuous greedy based algorithm we give a [Formula: see text] approximation for [Formula: see text]. This demonstrates a steep transition from constant factor approximability to inapproximability around [Formula: see text]. Then using multiplicative-weight-updates (MWUs), we find a much faster [Formula: see text] time asymptotic [Formula: see text] approximation. Although these results are all randomized, we also give a simple deterministic [Formula: see text] approximation with runtime [Formula: see text]. Finally, we run synthetic experiments using Kronecker graphs and find that our MWU inspired heuristic outperforms existing heuristics.

scholarly journals Variation of MODIS reflectance and vegetation indices with viewing geometry and soybean development

2012 ◽  
Vol 84 (2) ◽  
pp. 263-274 ◽  
Author(s):  
Fábio M. Breunig ◽  
Lênio S. Galvão ◽  
Antônio R. Formaggio ◽  
José C.N. Epiphanio
Keyword(s):  
Vegetation Index ◽  
Normalized Difference Vegetation Index ◽  
Vegetation Indices ◽  
Constant Factor ◽  
The Other ◽  
Large Field ◽  
Phenological Stages ◽  
Water Index ◽  
Growing Seasons ◽  
Moderate Resolution Imaging Spectroradiometer

Directional effects introduce a variability in reflectance and vegetation index determination, especially when large field-of-view sensors are used (e.g., Moderate Resolution Imaging Spectroradiometer - MODIS). In this study, we evaluated directional effects on MODIS reflectance and four vegetation indices (Normalized Difference Vegetation Index - NDVI; Enhanced Vegetation Index - EVI; Normalized Difference Water Index - NDWI1640 and NDWI2120) with the soybean development in two growing seasons (2004-2005 and 2005-2006). To keep the reproductive stage for a given cultivar as a constant factor while varying viewing geometry, pairs of images obtained in close dates and opposite view angles were analyzed. By using a non-parametric statistics with bootstrapping and by normalizing these indices for angular differences among viewing directions, their sensitivities to directional effects were studied. Results showed that the variation in MODIS reflectance between consecutive phenological stages was generally smaller than that resultant from viewing geometry for closed canopies. The contrary was observed for incomplete canopies. The reflectance of the first seven MODIS bands was higher in the backscattering. Except for the EVI, the other vegetation indices had larger values in the forward scattering direction. Directional effects decreased with canopy closure. The NDVI was lesser affected by directional effects than the other indices, presenting the smallest differences between viewing directions for fixed phenological stages.

scholarly journals The principal magnetic susceptibilities of neodymium sulphate octahydrate at low temperatures

1939 ◽  
Vol 170 (941) ◽  
pp. 266-271 ◽  
Keyword(s):  
Low Temperatures ◽  
Room Temperature ◽  
Energy Levels ◽  
Constant Factor ◽  
The Other ◽  
Crystalline Field ◽  
Cubic Symmetry ◽  
The Subject ◽  
The Difference ◽  
The One

The magnetic and other related properties of neodymium sulphate have been the subject of numerous investigations in recent years, but there is still a remarkable conflict of evidence on all the essential points. The two available determinations of the susceptibility of the powdered salt at low temperatures, those of Gorter and de Haas (1931) from 290 to 14° K and of Selwood (1933) from 343 to 83° K both fit the expression X ( T + 45) = constant over the range of temperature common to both, but the constants are not the same and the susceptibilities at room temperature differ by 11%. The fact that the two sets of results can be converted the one into the other by multiplying throughout by a constant factor suggested that the difference in the observed susceptibilities was due to some error of calibration. It could, however, also be due to the different purity of the samples examined though the explanation of the occurrence of the constant factor is then by no means obvious. From their analysis of the absorption spectrum of crystals of neodymium sulphate octahydrate Spedding and others (1937) conclude that the crystalline field around the Nd+++ ion is predominantly cubic in character since they find three energy levels at 0, 77 and 260 cm. -1 .* Calculations of the susceptibility from these levels reproduce Selwood’s value at room temperature but give no agreement with the observations-at other temperatures. On the other hand, Penney and Schlapp (1932) have shown that Gorter and de Haas’s results fit well on the curve calculated for a crystalline field of cubic symmetry and such a strength that the resultant three levels lie at 0, 238 and 834 cm. -1 , an overall spacing almost three times as great as Spedding’s.

THE DIMENSION OF CENTRALISERS OF MATRICES OF ORDER

2016 ◽  
Vol 94 (3) ◽  
pp. 353-361
Author(s):  
DONG ZHANG ◽  
HANCONG ZHAO
Keyword(s):  
Asymptotic Formula ◽  
Fast Algorithm ◽  
Recurrence Formula ◽  
Combinatorial Interpretation ◽  
Integer Sequence

In this paper, we study the integer sequence$(E_{n})_{n\geq 1}$, where$E_{n}$counts the number of possible dimensions for centralisers of$n\times n$matrices. We give an example to show another combinatorial interpretation of$E_{n}$and present an implicit recurrence formula for$E_{n}$, which may provide a fast algorithm for computing$E_{n}$. Based on the recurrence, we obtain the asymptotic formula$E_{n}=\frac{1}{2}n^{2}-\frac{2}{3}\sqrt{2}n^{3/2}+O(n^{5/4})$.

scholarly journals TSCDA: A novel greedy approach for community discovery in networks

2021 ◽  
Author(s):  
Arman Ferdowsi ◽  
Alireza Khanteymoori ◽  
Maryam Dehghan Chenary
Keyword(s):  
Detection Method ◽  
State Of The Art ◽  
The Other ◽  
Community Discovery ◽  
New Approach ◽  
Influential Node ◽  
New Community ◽  
Greedy Methods ◽  
Two Stages ◽  
The Impact

In this paper, we introduce a new approach for detecting community structures in networks. The approach is subject to modifying one of the connectivity-based community quality functions based on considering the impact that each community's most influential node has on the other vertices. Utilizing the proposed quality measure, we devise an algorithm that aims to detect high-quality communities of a given network based on two stages: finding a promising initial solution using greedy methods and then refining the solutions in a local search manner. The performance of our algorithm has been evaluated on some standard real-world networks as well as on some artificial networks. The experimental results of the algorithm are reported and compared with several state-of-the-art algorithms. The experiments show that our approach is competitive with the other well-known techniques in the literature and even outperforms them. This approach can be used as a new community detection method in network analysis.

scholarly journals Bootstrap Percolation in High Dimensions

2010 ◽  
Vol 19 (5-6) ◽  
pp. 643-692 ◽  
Author(s):  
JÓZSEF BALOGH ◽  
BÉLA BOLLOBÁS ◽  
ROBERT MORRIS
Keyword(s):  
Positive Root ◽  
Constant Factor ◽  
The Other ◽  
Bootstrap Percolation ◽  
Main Question ◽  
Critical Probability ◽  
High Dimensions ◽  
Critical Window ◽  
Fixed Constant ◽  
Image Position

In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A ⊂ V(G) is chosen independently at random, with density p, and new vertices are subsequently infected if they have at least r infected neighbours. The set A is said to percolate if eventually all vertices are infected. Our aim is to understand this process on the grid, [n]d, for arbitrary functions n = n(t), d = d(t) and r = r(t), as t → ∞. The main question is to determine the critical probability pc([n]d, r) at which percolation becomes likely, and to give bounds on the size of the critical window. In this paper we study this problem when r = 2, for all functions n and d satisfying d ≫ log n.The bootstrap process has been extensively studied on [n]d when d is a fixed constant and 2 ⩽ r ⩽ d, and in these cases pc([n]d, r) has recently been determined up to a factor of 1 + o(1) as n → ∞. At the other end of the scale, Balogh and Bollobás determined pc([2]d, 2) up to a constant factor, and Balogh, Bollobás and Morris determined pc([n]d, d) asymptotically if d ≥ (log log n)2+ϵ, and gave much sharper bounds for the hypercube.Here we prove the following result. Let λ be the smallest positive root of the equation so λ ≈ 1.166. Then if d is sufficiently large, and moreover as d → ∞, for every function n = n(d) with d ≫ log n.

scholarly journals On the two-dimensional steady flow of a viscous fluid behind a solid body.―I

1933 ◽  
Vol 142 (847) ◽  
pp. 545-562 ◽  
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Velocity Distribution ◽  
Asymptotic Approximation ◽  
Constant Velocity ◽  
Boundary Layer Theory ◽  
The Other ◽  
Main Stream ◽  
Two Dimensional ◽  
Prandtl Equations

1.1. The purpose of this paper is to exhibit, for reasons given below, calculations of the velocity distribution some distance downstream behind any symmetrical obstacle in a stream of viscous fluid, but particularly behind an infinitely thin plate parallel to the stream, the motion being two-dimensional. For a slightly viscous fluid, Blasius worked out the velocity distribution in the boundary layer from the front to the downstream end of the plate; and in a previous paper, I calculated the velocity in the wake for a distance varying from 0.3645 to 0.5 of the length of the plate from its downstream end (according to distance from its plane). In these calculations the fluid was supposed unlimited, and the undisturbed velocity in front of the plate was taken as constant. The viscosity being assumed small, the work was carried out on the basis of Pranstl's boundary layer theory, with zero pressure gradient in the direction of the stream. The velocity is then constant everywhere expect within a thin layer near the plate, and in a wake which must gradually broaden out downstream. (The broadening of the wake just behind the plate is so gradual that it could not be shown by calculations of the accuracy obtained in I). Pressure variations in a direction at right angles to the stream are negligible, and so is the velocity in that direction. Later, Tollmien attcked the problem from the other end, and found a first asymptotic approximation for the velocity distribution in the wake at a considerable distance downstream. He simplified the Prandtl equations by assuming that the departure from the constant velocity, U 0 , of the main stream is small, and neglecting terms quadratic in this departure. In other words, he applied the notion of the Oseen approximation to the Prandtl equations. His result for the velocity is U = U 0 {1 - a X -½ exp (-U 0 Y 2 /4νX)}.

Monotone submodular maximization over the bounded integer lattice with cardinality constraints

2019 ◽  
Vol 11 (06) ◽  
pp. 1950075
Author(s):  
Lei Lai ◽  
Qiufen Ni ◽  
Changhong Lu ◽  
Chuanhe Huang ◽  
Weili Wu
Keyword(s):  
Approximation Algorithm ◽  
Greedy Algorithm ◽  
Deterministic Algorithm ◽  
Submodular Function ◽  
Integer Lattice ◽  
Cardinality Constraint ◽  
Cardinality Constraints ◽  
Definition Of ◽  
Deterministic Formula ◽  
Submodular Maximization

We consider the problem of maximizing monotone submodular function over the bounded integer lattice with a cardinality constraint. Function [Formula: see text] is submodular over integer lattice if [Formula: see text], [Formula: see text], where ∨ and ∧ represent elementwise maximum and minimum, respectively. Let [Formula: see text], and [Formula: see text], we study the problem of maximizing submodular function [Formula: see text] with constraints [Formula: see text] and [Formula: see text]. A random greedy [Formula: see text]-approximation algorithm and a deterministic [Formula: see text]-approximation algorithm are proposed in this paper. Both algorithms work in value oracle model. In the random greedy algorithm, we assume the monotone submodular function satisfies diminishing return property, which is not an equivalent definition of submodularity on integer lattice. Additionally, our random greedy algorithm makes [Formula: see text] value oracle queries and deterministic algorithm makes [Formula: see text] value oracle queries.

scholarly journals XXIX. On the analytical theory of the conic

1862 ◽  
Vol 152 ◽  
pp. 639-662
Keyword(s):  
Linear Function ◽  
Constant Factor ◽  
Analytical Theory ◽  
The Other ◽  
Analytical Basis ◽  
Linear Factor

The decomposition into its linear factors of a decomposable quadric function cannot be effected in a symmetrical manner otherwise than by formulæ containing supernumerary arbitrary quantities; thus, for a binary quadric (which of course is always decomposable) we have ( a, b, c )( x, y ) 2 = 1/( a, b, c )( x 1 , y 1 ) 2 Prod. {( a, b, c )( x, y )( x 1 , y 1 ) ± √ ac - b 2 ( xy 1 - x 1 y )}; or the expression for a linear factor is 1/√( a, b, c )( x 1 , y 1 ) 2 {( a , b , a, b, c )( x, y )( x 1 , y 1 ) ± √ ac - b 2 ( xy 1 - x 1 y )}, which involves the arbitrary quantities ( x 1 , y 1 ). And this appears to be the reason why, in the analytical theory of the conic, the questions which involve the decomposition of a decomposable ternary quadric have been little or scarcely at all considered: thus, for instance, the expressions for the coordinates of the points of intersection of a conic by a line (or say the line-equations of the two ineunts), and the equations for the tangents (separate each from the other) drawn from a given point not on the conic, do not appear to have been obtained. These questions depend on the decomposition of a decom­posable ternary quadric, which decomposition itself depends on that for the simplest case, when the quadric is a perfect square. Or we may say that in the first instance they depend on the transformation of a given quadric function U = (*)( x, y, z ) 2 into the form W 2 + V, where W is a linear function, given save as to a constant factor (that is, W = 0 is the equation of a given line), and V is a decomposable quadric function, which is ultimately decomposed into its linear factors, = QR, so that we have U = W 2 + QR. The formula for this purpose, which is exhibited in the eight different forms I, II, III, IV, I(bis), Il(bis), Ill(bis), IV(bis), is the analytical basis of the whole theory; and the greater part of the memoir relates to the establishment of these forms. The solution of the geometrical questions above referred to is (as shown in the memoir) involved in and given immediately by these forms. It is also shown that the formulæ are greatly simplified in the case e. g. of tangents drawn to a conic from a point in a conic having double contact with the first-mentioned conic, and that in this case they lead to the linear Automorphic Transformation of the ternary quadric. The memoir concludes with some formulæ relating to the case of two conics, which however is treated of in only a cursory manner.

A Fast Algorithm Detection for Barcode Inclination Defect

2014 ◽  
Vol 644-650 ◽  
pp. 1172-1175
Author(s):  
Ya Li Qi ◽  
Ye Li Li ◽  
Cui Wang ◽  
Li Kun Lu
Keyword(s):  
Real Time ◽  
Fast Algorithm ◽  
The Other ◽  
Detection Methods ◽  
Detection Accuracy ◽  
Time System ◽  
Real Time System ◽  
The Real ◽  
Online System ◽  
Real Time Detection

Barcode detection has many applications and detection methods. Most applications have their own requirements for detection accuracy and speed. This paper has its requirement for speed in the real time system to detection inclination defect of barcode. It predominantly researches on two algorithms and their applications on 1-dimentional barcode scanning. One is location and the other is angle of inclination. The algorithms are particularly useful for real time detection of barcodes in online system with image vision devices.

scholarly journals An Approach for Solving Multi-Objective Linear Fractional Programming Problem with fully Rough Interval Coefficients

2021 ◽  
Vol 23 (07) ◽  
pp. 94-109
Author(s):  
Mohamed Solomon ◽  
◽  
Hegazy Zaher ◽  
Naglaa Ragaa ◽  
◽  
...  
Keyword(s):  
Fractional Programming ◽  
Efficient Solution ◽  
The Other ◽  
Regular Simplex ◽  
Linear Fractional Programming ◽  
Multi Objective ◽  
Interval Coefficients ◽  
Rough Interval ◽  
Single Objective ◽  
Linear Fractional Programming Problem

In this paper, a multi-objective linear fractional programming (MOLFP) problem is considered where all of its coefficients in the objective function and constraints are rough intervals (RIs). At first, to solve this problem, we will construct two MOLFP problems with interval coefficients. One of these problems is a MOLFP where all of its coefficients are upper approximations of RIs and the other is a MOLFP where all of its coefficients are lower approximations of RIs. Second, the MOLFP problems are transformed into a single objective linear programming (LP) problem using a proposal given by Nuran Guzel. Finally, the single objective LP problem is solved by a regular simplex method which yields an efficient solution of the original MOLFP problem. A numerical example is given to demonstrate the results.

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