scholarly journals Asymptotic Expansions and Strategies in the Online Increasing Subsequence Problem

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
Amirlan Seksenbayev
Keyword(s):  
Dynamic Programming ◽  
Asymptotic Expansions ◽  
Dual Problem ◽  
Infinite Length ◽  
Expected Time ◽  
Selection Strategies ◽  
Dynamic Programming Equation ◽  
Optimal Values ◽  
Design Selection ◽  
Selection Of

AbstractWe study two closely related problems in the online selection of increasing subsequence. In the first problem, introduced by Samuels and Steele (Ann. Probab. 9(6):937–947, 1981), the objective is to maximise the length of a subsequence selected by a nonanticipating strategy from a random sample of given size $n$ n . In the dual problem, recently studied by Arlotto et al. (Random Struct. Algorithms 49:235–252, 2016), the objective is to minimise the expected time needed to choose an increasing subsequence of given length $k$ k from a sequence of infinite length. Developing a method based on the monotonicity of the dynamic programming equation, we derive the two-term asymptotic expansions for the optimal values, with $O(1)$ O ( 1 ) remainder in the first problem and $O(k)$ O ( k ) in the second. Settling a conjecture in Arlotto et al. (Random Struct. Algorithms 52:41–53, 2018), we also design selection strategies to achieve optimality within these bounds, that are, in a sense, best possible.

MODEL OF SOCIAL POTENTIAL OF CHILDHOOD IN THE RUSSIAN REGIONS: THE RESULTS OF EXPERIMENTS

2019 ◽  
pp. 152-162
Author(s):  
A.G. Filipova ◽  
A.V. Vysotskaya
Keyword(s):  
Third Wave ◽  
Russian Regions ◽  
The Third ◽  
Control Factors ◽  
Social Potential ◽  
System Input ◽  
Optimal Values ◽  
Fixed Ideal ◽  
And Control ◽  
Selection Of

The article presents the results of mathematical experiments with the system «Social potential of childhood in the Russian regions». In the structure of system divided into three subsystems – the «Reproduction of children in the region», «Children’s health» and «Education of children», for each defined its target factor (output parameter). The groups of infrastructure factors (education, health, culture and sport, transport), socio-economic, territorial-settlement, demographic and en-vironmental factors are designated as the factors that control the system (input parameters). The aim of the study is to build a model îf «Social potential of childhood in the Russian regions», as well as to conduct experiments to find the optimal ratio of the values of target and control factors. Three waves of experiments were conducted. The first wave is related to the analysis of the dynam-ics of indicators for 6 years. The second – with the selection of optimal values of control factors at fixed ideal values of target factors. The third wave allowed us to calculate the values of the target factors based on the selected optimal values of the control factors of the previous wave.

scholarly journals Mooring Design Selection of Aquaculture Cage for Indonesian Ocean

2018 ◽  
Vol 135 ◽  
pp. 012022
Author(s):  
Y Mulyadi ◽  
N Syahroni ◽  
K Sambodho ◽  
M Zikra ◽  
Wahyudi ◽  
...  
Keyword(s):  
Design Selection ◽  
Selection Of

Dynamic programming and gambling models

1974 ◽  
Vol 6 (03) ◽  
pp. 593-606 ◽  
Author(s):  
Sheldon M. Ross
Keyword(s):  
Dynamic Programming ◽  
Additional Structure ◽  
Expected Time ◽  
Playing Time

Dynamic programming is used to solve some simple gambling models. In particular we consider the situation where an individual may bet any integral amount not greater than his fortune and he will win this amount with probability p or lose it with probability 1 — p. It is shown that if p ≧ ½ then the timid strategy (always bet one dollar) both maximizes the probability of ever reaching any preassigned fortune, and also stochastically maximizes the time until the bettor becomes broke. Also, if p ≦ ½ then the timid strategy while not stochastically maximizing the playing time does maximize the expected playing time. We also consider the same model but with the additional structure that the bettor need not gamble but may instead elect to work for some period of time. His goal is to minimize the expected time until his fortune reaches some preassigned goal. We show that if p ≦ ½ then (i) always working is optimal, and (ii) among those strategies that only allow working when the bettor is broke it is the bold strategy that is optimal

scholarly journals Selection strategies of segregant soybean populations for resistance to Asian rust

2009 ◽  
Vol 44 (11) ◽  
pp. 1452-1459 ◽  
Author(s):  
Aliny Simony Ribeiro ◽  
José Francisco Ferraz de Toledo ◽  
Magno Antonio Patto Ramalho
Keyword(s):  
Genetic Variance ◽  
Additive Genetic Variance ◽  
Infected Leaf ◽  
Good Resistance ◽  
Narrow Sense Heritability ◽  
Growing Seasons ◽  
Selection Strategies ◽  
Line Selection ◽  
Soybean Resistance ◽  
Selection Of

The objective of this work was to identify the best selection strategies for the more promising parental combinations to obtain lines with good resistance to soybean Asian rust (Phakopsora pachyrhizi). Two experiments were carried out in the field during the 2006/2007 and 2007/2008 growing seasons, to determine the percentage of infected leaf area of individual plants of five parents and their segregant F2 and F3 populations. The data obtained indicates that additive genetic variance predominates in the control of soybean resistance to Asian rust, and that the year and time of assessment do not significantly influence the estimates of the genetic parameters obtained. The narrow-sense heritability (h²r) ranged from 23.12 to 55.83%, and indicates the possibility of successful selection of resistant individuals in the early generations of the breeding program. All the procedures used to select the most promising populations to generate superior inbred lines for resistance to P. pachyrhizi presented similar results and identified the BR01-18437 x BRS 232 population as the best for inbred line selection.

A distributional theory for asymptotic expansions

1990 ◽  
Vol 428 (1875) ◽  
pp. 399-430 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Asymptotic Series ◽  
Generalized Functions ◽  
The Moment ◽  
The One ◽  
Topological Tensor Products ◽  
Multidimensional Integrals ◽  
Vector Valued ◽  
Selection Of ◽  
Mathematics And Physics

We present various techniques for the asymptotic expansions of generalized functions. We show that the moment asymptotic expansions hold for a very wide variety of kernels such as generalized functions of rapid decay and rapid oscillations. We do not use Mellin transform techniques as done by previous authors in the field. Instead, we introduce a direct approach that not only solves the one-dimensional problems but also applies to various multidimensional integrals and oscillatory kernels as well. This approach also helps in the development of various asymptotic series arising in diverse fields of mathematics and physics. We find that the asymptotic expansions of generalized functions depend on the selection of suitable spaces of test functions. Accordingly, we have exercised special care in classifying the spaces and the distributions defined on them. Furthermore, we use the theory of topological tensor products to obtain the expansions of vector-valued distributions. We present several examples to illustrate that many classical results follow in a simple manner. For instance, we derive from our results the asymptotic expansions of certain series considered by Ramanujan.

scholarly journals Analysis of the inheritance of pericarp color and other characters in the rice hybrid Kuboyar × Gagat

2020 ◽  
Vol 200 (9) ◽  
pp. 32-41
Author(s):  
Pavel Kostylev ◽  
E. Krasnova ◽  
A. Aksenov ◽  
E. Balyukova
Keyword(s):  
Second Generation ◽  
Source Material ◽  
Black Rice ◽  
Pericarp Color ◽  
Optimal Values ◽  
White Grain ◽  
First And Second Generation ◽  
Black Color ◽  
Dominant Genes ◽  
Selection Of

Abstract. Rice can form not only white, but also red, brown and black grains. In black rice, pericarp grains contain anthocyanins, which have antioxidant activity and are beneficial to human health. The purpose of the work is to study the inheritance of the black color of the pericarp and other qualitative traits in the intersubspecific hybrid of rice Kuboyar × Gagat, the selection of the best recombinant forms combining early ripeness, a compact erect panicle and black grain, the creation of the source material for practical selection. Methods The studies were carried out on hybrids of the first and second generation from crossing a white-grain variety of rice Kuboyar with black-grained Gagat in 2018–2019 in the Separate Division “Proletarskoye” of the Rostov Region. Results. A genetic analysis of the inheritance of the duration of the growing season, qualitative signs of coloring of flower scales and rice grains, and spinousness was carried out. In the second generation, 54 photosensitive non-flowering plants and 128 normal ones broke out, which indicates the interaction of four dominant genes in the genotype. The splitting according to the color of the pericarp was carried out according to the trihybrid scheme according to the type of com-plementarity in the ratio of 27 black: 21 brown: 16 white. The black color of the pericarp was formed when three dominant genes Kala1, 3, and 4 were present in the genotype, brown was determined by the Kala4 gene, and white by the remaining combinations of genes. According to the color of flowering scales, the cleavage occurred according to the digrid pattern: 9 black: 3 yellow with black apiculus: 4 straw yellow. Although the parental varieties were boneless, 39 spinous forms appeared in F2 with three complementary dominant genes An-a, An-b, An-c and inhibitor I, the remaining 89 plants were boneless. The best recombinant forms were selected, combining the optimal values of plants and panicles and black grain, the source material for practical selection was created.

scholarly journals Selection strategies in agronomic characters in progenies F3:4 of transgenic soy RR

2021 ◽  
Vol 45 ◽  
Author(s):  
Anna Regina Tiago Carneiro ◽  
Osvaldo Toshiyuki Hamawaki ◽  
Ana Paula Oliveira Nogueira ◽  
Arthur Felipe Eustáquio e Silva ◽  
Raphael Lemes Hamawaki ◽  
...  
Keyword(s):  
Agronomic Traits ◽  
Indirect Selection ◽  
Direct Selection ◽  
Selection Strategies ◽  
Aggregate Information ◽  
Genetic Potential ◽  
Superior Genotypes ◽  
Selection Indexes ◽  
Total Gain ◽  
Selection Of

ABSTRACT The selection indexes aggregate information to multiple characters and, with this, they are able to carry out the selection of a set of variables simultaneously. The objective was to verify the genetic potential of agronomic traits and to select soybean F3:4 progenies based on different selection strategies. 123 progenies and the parents were sown in randomized blocks with two replications. The gains of direct selection by the indexes, the sum of “ranks” and the genotype-ideotype were lower for all characters when compared to the gains of direct and indirect selection. The rank sum index stood out for achieving the highest total gain with 37.11%. The index of the genotype-ideotype obtained a lower gain (-0.48%) for the character number of days for flowering compared to the sum index of “ranks” (-0.54%) and reached a negative gain for the attribute insertion height of the first pod with -1.82%. The genetic potential of the F3:4 population is high and allows different selection strategies to be applied to reach superior genotypes. The progenies UFU 72, UFU 116, UFU 86, UFU 45, UFU 117, UFU 56, UFU 5, UFU 106, UFU 6, UFU 4, UFU 73, UFU 101, UFU 96, UFU 90, UFU 123, UFU 116, UFU 88, UFU 65, UFU 70, UFU 3, UFU 69 and UFU 37 were selected by both selection indexes. The UFU 72, UFU 90, UFU 88 and UFU 69 progenies are agronomically superior both in direct and indirect selection, as in Mulamba and Mock (1978) sum of “ranks” selections and genotype-ideotype.

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