Bereichsspezifische Strategien im Stochastiksunterricht

2019 ◽  
pp. 149-168
Author(s):  
Stefan Götz
Keyword(s):  
Transition Probabilities ◽  
Directed Graphs ◽  
Random Processes ◽  
Mean Value ◽  
Absorption Probability ◽  
Specific Strategy ◽  
Domain Specific ◽  
Multi Stage ◽  
One Step ◽  
Multi Level

For multi-stage random experiments, probability trees are used for their description. Using the path rules, probabilities for the results of such multi-level experiments can be calculated from the probabilities that characterize the transitions from one step to the next. A natural next step is to look for sequences of random experiments, which can be represented by directed graphs. Analogous to the path rules, mean value rules serve to determine probabilities for an end of these random processes and their expected durations. Directed graphs and mean rules represent domain-specific strategies that take up and develop concepts of stochastic teaching at secondary level. Classification: D54, K64, N74, D29. Keywords: stochastics education, stochastically thinking, domain-specific strategy, MARKOV chains, directed graph, absorption probability, mean hitting time, transition probabilities, “Mittelwertsregeln”.

Towards Open Graphical Tool-Building Framework

2011 ◽  
Vol 43 (1) ◽  
pp. 80-87 ◽  
Author(s):  
Edgars Rencis ◽  
Janis Barzdins ◽  
Sergejs Kozlovics
Keyword(s):  
Deep Understanding ◽  
Easy Task ◽  
Domain Specific ◽  
Activity Diagrams ◽  
Graphical Tool ◽  
One Step ◽  
Uml Activity Diagrams ◽  
Definition Of ◽  
Tool Building

Towards Open Graphical Tool-Building Framework Nowadays, there are many frameworks for developing domain-specific tools. However, if we want to create a really sophisticated tool with specific functionality requirements, it is not always an easy task to do. Although tool-building platforms offer some means for extending the tool functionality and accessing it from external applications, it usually requires a deep understanding of various technical implementation details. In this paper we try to go one step closer to a really open graphical tool-building framework that would allow both to change the behavior of the tool and to access the tool from the outside easily. We start by defining a specialization of metamodels which is a great and powerful facility itself. Then we go on and show how this can be applied in the field of graphical domain-specific tool building. The approach is demonstrated on an example of a subset of UML activity diagrams. The benefits of the approach are also clearly indicated. These include a natural and intuitive definition of tools, a strict logic/presentation separation and the openness for extensions as well as for external applications.

scholarly journals Random Walks with Invariant Loop Probabilities: Stereographic Random Walks

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 729
Author(s):  
Miquel Montero
Keyword(s):  
Random Walks ◽  
Stereographic Projection ◽  
Transition Probabilities ◽  
Simple Random Walk ◽  
General Introduction ◽  
Elliptic Case ◽  
One Step ◽  
Underlying Geometry ◽  
Step Transition ◽  
Wide Family

Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.

scholarly journals A new multi-level algorithm for balanced partition problem on large scale directed graphs

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Xianyue Li ◽  
Yufei Pang ◽  
Chenxia Zhao ◽  
Yang Liu ◽  
Qingzhen Dong
Keyword(s):  
Large Scale ◽  
Directed Graphs ◽  
Vlsi Design ◽  
Graph Partition ◽  
Partition Problem ◽  
Multi Level ◽  
The Stability ◽  
Recursive Partition ◽  
Balanced Partition ◽  
Partition Method

AbstractGraph partition is a classical combinatorial optimization and graph theory problem, and it has a lot of applications, such as scientific computing, VLSI design and clustering etc. In this paper, we study the partition problem on large scale directed graphs under a new objective function, a new instance of graph partition problem. We firstly propose the modeling of this problem, then design an algorithm based on multi-level strategy and recursive partition method, and finally do a lot of simulation experiments. The experimental results verify the stability of our algorithm and show that our algorithm has the same good performance as METIS. In addition, our algorithm is better than METIS on unbalanced ratio.

scholarly journals Membrane Distillation for the Production of Pharmaceutical-Grade Water—Investigation into the Application of AGMD and VMD

2021 ◽  
Vol 18 (11) ◽  
pp. 6058
Author(s):  
Cornelius Nellessen ◽  
Thomas Klein ◽  
Hans-Jürgen Rapp ◽  
Frank Rögener
Keyword(s):  
Energy Demand ◽  
Tap Water ◽  
Membrane Distillation ◽  
Pharmaceutical Products ◽  
Optimum Process ◽  
The European Union ◽  
Pharmaceutical Ingredients ◽  
Multi Stage ◽  
One Step ◽  
Selection Of

The production of pharmaceutical ingredients, intermediates and final products strongly depends on the utilization of water. Water is also required for the purification and preparation of reagents. Each specific application determines the respective water quality. In the European Union, the European Pharmacopeia (Ph. Eur.) contains the official standards that assure quality control of pharmaceutical products during their life cycle. According to this, the production of water for pharmaceutical use is mainly based on multi-stage distillation and membrane processes, especially, reverse osmosis. Membrane distillation (MD) could be an alternative process to these classical methods. It offers advantages in terms of energy demand and a compact apparatus design. In the following study, the preparation of pharmaceutical-grade water from tap water in a one-step process using MD is presented. Special emphasis is placed on the performance of two different module designs and on the selection of optimum process parameters.

Optimal control of random walks, birth and death processes, and queues

1981 ◽  
Vol 13 (01) ◽  
pp. 61-83 ◽  
Author(s):  
Richard Serfozo
Keyword(s):  
Optimal Control ◽  
Random Walks ◽  
Queue Length ◽  
Transition Probabilities ◽  
Transition Rates ◽  
Average Reward ◽  
Birth And Death Processes ◽  
Optimal Policies ◽  
One Step ◽  
Increasing Functions

This is a study of simple random walks, birth and death processes, and M/M/s queues that have transition probabilities and rates that are sequentially controlled at jump times of the processes. Each control action yields a one-step reward depending on the chosen probabilities or transition rates and the state of the process. The aim is to find control policies that maximize the total discounted or average reward. Conditions are given for these processes to have certain natural monotone optimal policies. Under such a policy for the M/M/s queue, for example, the service and arrival rates are non-decreasing and non-increasing functions, respectively, of the queue length. Properties of these policies and a linear program for computing them are also discussed.

scholarly journals UAV Path Planning Based on Multi-Stage Constraint Optimization

Drones ◽  
2021 ◽  
Vol 5 (4) ◽  
pp. 144
Author(s):  
Yong Shen ◽  
Yunlou Zhu ◽  
Hongwei Kang ◽  
Xingping Sun ◽  
Qingyi Chen ◽  
...  
Keyword(s):  
Path Planning ◽  
Three Dimensional ◽  
Evolutionary Process ◽  
Constraint Processing ◽  
Multi Stage ◽  
Planning Ability ◽  
Path Constraints ◽  
Aerial Vehicle ◽  
Multi Level ◽  
Processing Mechanism

Evolutionary Algorithms (EAs) based Unmanned Aerial Vehicle (UAV) path planners have been extensively studied for their effectiveness and high concurrency. However, when there are many obstacles, the path can easily violate constraints during the evolutionary process. Even if a single waypoint causes a few constraint violations, the algorithm will discard these solutions. In this paper, path planning is constructed as a multi-objective optimization problem with constraints in a three-dimensional terrain scenario. To solve this problem in an effective way, this paper proposes an evolutionary algorithm based on multi-level constraint processing (ANSGA-III-PPS) to plan the shortest collision-free flight path of a gliding UAV. The proposed algorithm uses an adaptive constraint processing mechanism to improve different path constraints in a three-dimensional environment and uses an improved adaptive non-dominated sorting genetic algorithm (third edition—ANSGA-III) to enhance the algorithm’s path planning ability in a complex environment. The experimental results show that compared with the other four algorithms, ANSGA-III-PPS achieves the best solution performance. This not only validates the effect of the proposed algorithm, but also enriches and improves the research results of UAV path planning.

Single-shelf library-type Markov chains with infinitely many books

1977 ◽  
Vol 14 (02) ◽  
pp. 298-308 ◽  
Author(s):  
Peter R. Nelson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Transition Probabilities ◽  
Natural Order ◽  
Order Book ◽  
Exit Boundary ◽  
One Step ◽  
Step Transition ◽  
The Right ◽  
Positive Recurrent

In a single-shelf library having infinitely many books B 1 , B 2 , …, the probability of selecting each book is assumed known. Books are removed one at a time and replaced in position k prior to the next removal. Books are moved either to the right or the left as is necessary to vacate position k. Those arrangements of books where after some finite position all the books are in natural order (book i occupies position i) are considered as states in an infinite Markov chain. When k > 1, we show that the chain can never be positive recurrent. When k = 1, we find the limits of ratios of one-step transition probabilities; and when k = 1 and the chain is transient, we find the Martin exit boundary.

Perturbation theory for unbounded Markov reward processes with applications to queueing

1988 ◽  
Vol 20 (01) ◽  
pp. 99-111 ◽  
Author(s):  
Nico M. Van Dijk
Keyword(s):  
Transition Probabilities ◽  
Arrival Rate ◽  
Average Reward ◽  
Reward Function ◽  
One Step ◽  
Reward Process ◽  
Markov Reward ◽  
Step Transition ◽  
The One ◽  
Queueing Processes

Consider a perturbation in the one-step transition probabilities and rewards of a discrete-time Markov reward process with an unbounded one-step reward function. A perturbation estimate is derived for the finite horizon and average reward function. Results from [3] are hereby extended to the unbounded case. The analysis is illustrated for one- and two-dimensional queueing processes by an M/M/1-queue and an overflow queueing model with an error bound in the arrival rate.

A Domain Specific Strategy for Complex Dynamic Processes

2011 ◽  
pp. 1422-1446
Author(s):  
Semih Cetin ◽  
N. Ilker Altintas ◽  
Ozgur Tufekci
Keyword(s):  
Process Management ◽  
Business Processes ◽  
Dynamic Processes ◽  
Specific Strategy ◽  
Domain Specific ◽  
Complex Processes ◽  
Business Agility ◽  
Business Cases ◽  
Management Techniques ◽  
Traditional Process

This chapter identifies the issues that might create orthogonal complexities for process dynamism, and decouples the components implementing them in a “domain specific” way. Authors believe that traditional process management techniques for modeling and executing the processes still fall short to improve the dynamism of an enterprise. Some of the reasons are: using too “generic” techniques and tools for process management that are not scalable enough for typical business cases, having lack of architectural coverage to manage the tradeoffs between dynamism and other business quality issues, insufficient support for integrating legacy business processes, and unbalanced guidance between “primary” and “supportive” processes. In order to improve the business agility particularly with dynamic processes, effective abstraction and composition techniques are needed for the systematic design of primary and supportive processes in an organization. Authors bring in the “Domain Specific Kit” abstraction as a way to improve the dynamism of complex processes.

Dynamic fuzzy paths and cycles in multi-level directed graphs

2015 ◽  
Vol 37 ◽  
pp. 194-206 ◽  
Author(s):  
B. Petelin ◽  
I. Kononenko ◽  
V. Malačič ◽  
M. Kukar
Keyword(s):  
Directed Graphs ◽  
Multi Level
Sign in / Sign up

Export Citation Format

Share Document