A survey of flooding, gossip routing, and related schemes for wireless multi- hop networks

Flooding is an essential and critical service in computer networks that is used by many routing protocols to send packets from a source to all nodes in the network. As the packets are forwarded once by each receiving node, many copies of the same packet traverse the network which leads to high redundancy and unnecessary usage of the sparse capacity of the transmission medium. Gossip routing is a well-known approach to improve the flooding in wireless multi-hop networks. Each node has a forwarding probability p that is either statically per-configured or determined by information that is available at runtime, e.g, the node degree. When a packet is received, the node selects a random number r. If the number r is below p, the packet is forwarded and otherwise, in the most simple gossip routing protocol, dropped. With this approach the redundancy can be reduced while at the same time the reachability is preserved if the value of the parameter p (and others) is chosen with consideration of the network topology. This technical report gives an overview of the relevant publications in the research domain of gossip routing and gives an insight in the improvements that can be achieved. We discuss the simulation setups and results of gossip routing protocols as well as further improved flooding schemes. The three most important metrics in this application domain are elaborated: reachability, redundancy, and management overhead. The published studies used simulation environments for their research and thus the assumptions, models, and parameters of the simulations are discussed and the feasibility of an application for real world wireless networks are highlighted. Wireless mesh networks based on IEEE 802.11 are the focus of this survey but publications about other network types and technologies are also included. As percolation theory, epidemiological models, and delay tolerant networks are often referred as foundation, inspiration, or application of gossip routing in wireless networks, a brief introduction to each research domain is included and the applicability of the particular models for the gossip routing is discussed

Preliminary specification and design documentation for software components to achieve catallaxy in computational systems

This Report is about the preliminary specifications and design documentation for software components to achieve Catallaxy in computational systems. -- Die Arbeit beschreibt die Spezifikation und das Design von Softwarekomponenten, um das Konzept der Katallaxie in Grid Systemen umzusetzen. Eine Einführung ordnet das Konzept der Katallaxie in bestehende Grid Taxonomien ein und stellt grundlegende Komponenten vor. Anschließend werden diese Komponenten auf ihre Anwendbarkeit in bestehenden Application Layer Netzwerken untersucht.Grid Computing

Data-Adaptive Wavelets and Multi-Scale Singular Spectrum Analysis

Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the construction of the lag-covariance matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M <= W <= N. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive wavelets; successive eigenvectors of C_M correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signal's covariance matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic and geophysical time series. A real application is to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 4 and 3 years supports the Devil's staircase scenario for the El Nino/Southern Oscillation phenomenon.Comment: 24 pages, 19 figure

기계 학습 방법론을 통한 상전이 연구

학위논문 (박사) -- 서울대학교 대학원 : 자연과학대학 물리학과, 2021. 2. 강병남.본 연구는 양자 접촉 모형의 양자 상전이를 인공신경망에 대한 기반 기계 학습 방법론을 통해 분석하였고 열린 양자계의 새로운 보편성을 가지는 임계현상이 있음을 밝혀내었다. 또한 기계 학습 방법론으로 구라모토 모형의 동기화 상전이의 임계현상을 분석하고 동역학 거동을 예측하므로써 동기화 현상에 대한 기계 학습을 대안적인 수치 분석의 틀거리로 활용할 수 있음을 보였다. 제1장은 임계 현상에 대한 상전이 이론과 기계 학습 방법론에 대한 일반적인 개념들을 개괄한다. 전통적인 상전이 이론은 통계물리학을 기반으로 전개되며 임계점 근방에서 발현하는 임계 현상과 그 보편성을 다룬다. 기계 학습 방법론은 기계 학습의 주요 요소들을 정의하고 모형의 형태와 모형의 최적화 과정에 대한 수학적인 기술을 제공한다. 더불어서 기계 학습 방법론 가운데서 유망한 인공신경망을 구현하는 방법을 소개하였다. 제2장은 양자 접촉 과정의 양자 상전이에 대한 기계 학습 방법론을 다룬다. 우리는 양자 도약 몬테 카를로를 이용하여 양자 접촉 과정을 따르는 1차원 스핀 사슬을 시뮬레이션하였고 관측된 활성 밀도에 따라 시스템이 활성 상태인지 흡수 상태인지를 판단할 수 있도록 합성곱 신경망과 완전결합 신경망과 같은 인공신경망을 지도 학습시켰다. 유한 크기 축적법만을 이용해서는 찾기 어려웠던 양자 상전이의 임계점을 인공신경망의 학습 결과에 외삽법을 적용하여 정교하게 측정할 수 있었다. 기계 학습을 통해서 얻어진 임계점에서 관측되는 임계 동역학을 유한 크기 축척법을 적용하여 1차원에서 양자 접촉 과정의 임계지수들을 구할 수 있었다. 1차원 양자 접촉 과정의 임계지수들 가운데서 스핀 체인의 활성 밀도에 관한 임계지수가 고전적인 단방향 스미기 모형에서 얻어지는 임계지수와 다르다는 것을 확인하였고 양자 상전이가 새로운 보편성을 보임을 밝혀내었다. 제3장은 쿠라모토 모형의 동기화 상전이에 대한 기계 학습 방법론을 다룬다. 구라모토 모형을 따라 움직이는 진동자들의 위상 거동을 관측하고 진동자들 간의 상호작용의 세기인 결합 상수를 예측할 수 있도록 순환 신경망과 전방향 신경망과 같은 인공신경망에 지도 학습시켰다. 학습된 인공신경망은 동기화된 상태의 진동자들의 상호작용의 세기를 측정할 수 있었을 뿐만 아니라 기존의 구라모토의 질서맺음 매개변수로는 추정할 수 없었던 비동기 상태에 놓여진 진동자들의 상호작용의 세기도 측정할 수 있었다. 이 결과는 인공신경망이 동기 상태에 대한 순서 매개변수와 비동기 상태에 대한 잠복 매개변수를 포착한다는 것을 나타낸다. 또한 우리는 진동자들의 위상 조합을 보고 시스템이 동기화 상태에 있는지 비동기 상태에 있는지를 판단할 수 있도록 합성곱 신경망과 완전결합 신경망과 같은 인공신경망을 지도 학습 시켰다. 데이터 중첩법으로 측정되지 않았던 진동자 간의 상호작용의 거리에 관한 임계지수를 인공신경망으로 측정한 결과를 외삽법으로 얻어냈다. 기계 학습 방법론이 동기화 상전이의 임계점과 임계지수를 분석하기 위한 수치적인 틀거리로 데이터 중첩법을 포함한 유한 크기 축척법에 대한 대안이 될 수 있다. 더 나아가 진동자들의 시간에 따른 위상 변화를 저수지 컴퓨터와 순환 신경망에 학습시켜 구라모토 모형의 동역학을 재현하거나 진동자들 간의 상호작용하는 연결망을 추적하기도 하였다. 제4장에서 본 연구의 결과에 의의를 정리해보았다. 양자 접촉 모형은 열린 양자계의 대표적인 모형으로 본 연구는 기계 학습 방법론이 고전적인 물리계와 닫힌 양자계를 넘어서 열린 양자계에도 적용될 수 있음을 보여준다. 또한 본 연구는 동기화 상전이를 보이는 대표적인 비선형 동역학 모형으로 쿠라모토 모형을 다루었지만 혼돈계의 거동을 예측하고 동기화 현상을 규명하기 위한 후속 연구에서 인공신경망 기법이 중요한 역할을 할 것으로 기대된다.This study analyzed the quantum phase transition in a quantum contact process through machine learning approaches based on the artificial neural network and discovered an open quantum system's critical phenomenon different from a classical system. Also, we analyzed the critical phenomena of the synchronization transition of the Kuramoto model with machine learning approaches and predicted the dynamic behavior of the model. It showed that the machine learning approached is an alternative framework for numerical analysis for synchronization phenomena. Chapter 1 outlines the conventional phase transition theory for critical phenomena and the general concepts of the machine learning approaches. The phase transition theory covers the critical phenomena and their universality near the critical point. Machine learning approaches define machine learning's essential elements and explain the model's type and model optimization as mathematical descriptions. Furthermore, we introduce artificial neural networks, which is a promising machine learning method. Chapter 2 includes the machine learning approaches for quantum phase transition of the quantum contact process. Using the quantum jump Monte Carlo method, we simulate a one-dimensional spin chain following a quantum contact process. We train the artificial neural networks such as convolutional neural networks and fully-connected neural networks with supervised learning to detect whether the system is in an active state or absorbing states depending on the observed density of active sites. It is hard to estimate the critical point of the quantum phase transition using only the finite-size scaling, but we measure the critical point precisely by extrapolating the well-train the artificial neural networks' results. We employ the finite-size scaling for critical dynamics at the critical point estimated by machine learning and measure the one-dimensional quantum contact process's critical exponents. As a result, we discover that the critical exponent related to the active site density in a homogeneous initial state different from the classical directed percolation model and find that quantum phase transition exhibits new universality. Chapter 3 includes the machine learning approaches for the synchronization transition of the Kuramoto model. We train the artificial neural networks such as recurrent neural networks and feed-forward networks with supervised learning to estimate the coupling constant, the strength of the interaction between oscillators from the dynamic behavior of oscillators governed by the Kuramoto model. Though the Kuramoto model's conventional order parameter can only estimate the coupling strength only in the synchronized state, the well-trained artificial neural networks measure the coupling strength among the oscillators in the synchronized asynchronous state. This result implicates that the artificial neural networks capture the order parameter for the synchronous state and the latent parameter for the asynchronous state. Also, we train the artificial neural networks such as convolutional neural networks and fully-connected neural networks with supervised learning to detect whether the system is in a synchronous state or asynchronous state according to the configuration of the oscillators' phase. Using extrapolation of the trained artificial neural network's outputs, we could estimate the critical exponent related to a correlation length between oscillators, which was not measured by the data collapse method. The machine learning approach can be an alternative to finite-size scaling methods, including the data collapse method, as a numerical framework for measuring the critical point and critical exponents of synchronization phenomena. Furthermore, as applications, we propose a reservoir computer and a recurrent neural network reproducing the Kuramoto model's dynamics or tracking the network of the interaction between oscillators. Chapter 4 remarks on the results and the meaning of this study. As the quantum contact process is a typical model of the open quantum system, this study shows that the machine learning approach can be applied to the open quantum system beyond the classical and closed quantum systems. Though this study focuses on the Kuramoto model as a typical nonlinear dynamics model exhibiting synchronization transition, we expect that the artificial neural networks will be a significant breakthrough in follow-up studies to predict the dynamical behavior of the chaotic system and to illuminate synchronization phenomena.1 Introduction 1 1.1 Theory of phase transitions 5 1.2 Machine learning 18 1.2.1 Data-driven optimization of multivariate functional 21 1.2.2 Artificial neural networks 41 2 Machine learning approach for open quantum systems 56 2.1 Quantum contact process 58 2.2 Finding the quantum phase transition 61 2.3 Finite-size scaling on quantum jump Monte Carlo 64 2.3.1 The pure quantum limit 64 2.3.2 The classcial limit 67 2.4 Discussion and Summary 69 3 Machine learning approach for non-linear dynamics systems 73 3.1 The Kuramoto model 74 3.2 Finding the coupling strength 76 3.3 Finding the synchronized state 78 3.4 Prediction of the phase dynamics 80 3.5 Reconstructing the network structure 83 3.6 Summary 85 4 Conclusion 87 Appendices 89 Appendix A Feed-forward neural networks 90 A.1 Forwarding propagation 90 A.2 Backpropagation 91 Appendix B Recurrent neural networks 95 B.1 Reservoir computer 95 Appendix C Techniques for deep learning 97 C.1 Data management 97 C.2 Advanced optimization 99 Appendix D Kasteleyn-Fortuin formalism 107 Bibliography 114 Abstract in Korean 129Docto