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Towards automatic troubleshooting for user-level performance degradation in cellular services
Network monitoring systems are a key building block in today's networks. They all follow a common framework where measurement data from network elements is aggregated at a central collector for network-wide visibility. When designing network monitoring systems, two key properties have to be taken into account: (1) efficiency, to minimize the communication overhead from network elements to the collector; (2) high-fidelity, to faithfully represent the network status. However, in presence of network dynamics, tracking the right operating point to ensure both high fidelity and efficiency is hard and we observe that prior monitoring approaches trade off one for the other.
In this paper, we show that it is possible to satisfy both these properties with NetGSR, a new deep learning based solution we introduce that reconstructs the fine-grained behavior of network status at the collector while requiring low resolution measurement data from network elements. This is achieved through a combination of a new custom-tailored conditional deep generative model (DistilGAN), and a new feedback mechanism (Xaminer) based on model uncertainty estimation and denoising that allows the collector to adjust the sampling rate for measurement data from network elements, at run-time. We extensively evaluate NetGSR using three different network scenarios with corresponding real-world network monitoring datasets as well as two downstream use cases. We show that NetGSR can faithfully reconstruct fine-grained network status with 25x greater measurement efficiency than prior approaches while requiring only few ms of inference time at the collector.
Recent years have witnessed fast growth in outdoor location-based services. While GPS is considered a ubiquitous localization system, it is not supported by low-end phones, requires direct line of sight to the satellites, and can drain the phone battery quickly.
In this paper, we propose DeepLoc: a deep learning-based outdoor localization system that obtains GPS-like localization accuracy without its limitations. In particular, DeepLoc leverages the ubiquitous cellular signals received from the different cell towers heard by the mobile device as hints to localize it. To do that, crowd-sensed geo-tagged received signal strength information coming from different cell towers is used to train a deep model that is used to infer the user's position. As part of DeepLoc design, we introduce modules to address a number of practical challenges including scaling the data collection to large areas, handling the inherent noise in the cellular signal and geo-tagged data, as well as providing enough data that is required for deep learning models with low-overhead.
We implemented DeepLoc on different Android devices. Evaluation results in realistic urban and rural environments show that DeepLoc can achieve a median localization accuracy within 18.8m in urban areas and within 15.7m in rural areas. This accuracy outperforms the state-of-the-art cellular-based systems by more than 470% and comes with 330% savings in power compared to the GPS. This highlights the promise of DeepLoc as a ubiquitous accurate and low-overhead localization system.
Timely accurate traffic forecast is crucial for urban traffic control and guidance. Due to the high nonlinearity and complexity of traffic flow, traditional methods cannot satisfy the requirements of mid-and-long term prediction tasks and often neglect spatial and temporal dependencies. In this paper, we propose a novel deep learning framework, Spatio-Temporal Graph Convolutional Networks (STGCN), to tackle the time series prediction problem in traffic domain. Instead of applying regular convolutional and recurrent units, we formulate the problem on graphs and build the model with complete convolutional structures, which enable much faster training speed with fewer parameters. Experiments show that our model STGCN effectively captures comprehensive spatio-temporal correlations through modeling multi-scale traffic networks and consistently outperforms state-of-the-art baselines on various real-world traffic datasets.
Machine learning on graphs is an important and ubiquitous task with applications ranging from drug design to friendship recommendation in social networks. The primary challenge in this domain is finding a way to represent, or encode, graph structure so that it can be easily exploited by machine learning models. Traditionally, machine learning approaches relied on user-defined heuristics to extract features encoding structural information about a graph (e.g., degree statistics or kernel functions). However, recent years have seen a surge in approaches that automatically learn to encode graph structure into low-dimensional embeddings, using techniques based on deep learning and nonlinear dimensionality reduction. Here we provide a conceptual review of key advancements in this area of representation learning on graphs, including matrix factorization-based methods, random-walk based algorithms, and graph convolutional networks. We review methods to embed individual nodes as well as approaches to embed entire (sub)graphs. In doing so, we develop a unified framework to describe these recent approaches, and we highlight a number of important applications and directions for future work.
Supervised learning techniques construct predictive models by learning from a large number of training examples, where each training example has a label indicating its ground-truth output. Though current techniques have achieved great success, it is noteworthy that in many tasks it is difficult to get strong supervision information like fully ground-truth labels due to the high cost of data labeling process. Thus, it is desired for machine learning techniques to work with weak supervision. This article reviews some research progress of weakly supervised learning, focusing on three typical types of weak supervision: incomplete supervision where only a subset of training data are given with labels; inexact supervision where the training data are given with only coarse-grained labels; inaccurate supervision where the given labels are not always ground-truth.
Telecommunications operators (telcos) traditional sources of income, voice
and SMS, are shrinking due to customers using over-the-top (OTT) applications
such as WhatsApp or Viber. In this challenging environment it is critical for
telcos to maintain or grow their market share, by providing users with as good
an experience as possible on their network.
But the task of extracting customer insights from the vast amounts of data
collected by telcos is growing in complexity and scale everey day. How can we
measure and predict the quality of a user's experience on a telco network in
real-time? That is the problem that we address in this paper.
We present an approach to capture, in (near) real-time, the mobile customer
experience in order to assess which conditions lead the user to place a call to
a telco's customer care center. To this end, we follow a supervised learning
approach for prediction and train our 'Restricted Random Forest' model using,
as a proxy for bad experience, the observed customer transactions in the telco
data feed before the user places a call to a customer care center.
We evaluate our approach using a rich dataset provided by a major African
telecommunication's company and a novel big data architecture for both the
training and scoring of predictive models. Our empirical study shows our
solution to be effective at predicting user experience by inferring if a
customer will place a call based on his current context.
These promising results open new possibilities for improved customer service,
which will help telcos to reduce churn rates and improve customer experience,
both factors that directly impact their revenue growth.
Recent studies on cellular network measurement have provided the evidence that significant geospatial correlations, in terms of traffic volume and application access, exist in cellular network usage. Such geospatial correlation patterns provide local optimization opportunities to cellular network operators for handling the explosive growth in the traffic volume observed in recent years. To the best of our knowledge, in this paper, we provide the first fine-grained characterization of the geospatial dynamics of application usage in a 3G cellular data network. Our analysis is based on two simultaneously collected traces from the radio access network (containing location records) and the core network (containing traffic records) of a tier-1 cellular network in the United States. To better understand the application usage in our data, we first cluster cell locations based on their application distributions and then study the geospatial dynamics of application usage across different geographical regions. The results of our measurement study present cellular network operators with fine-grained insights that can be leveraged to tune network parameter settings.
Effective management of large-scale cellular data networks is critical to meet customer demands and expectations. Customer calls for technical support provide direct indication as to the problems customers encounter. In this paper, we study the customer tickets - free-text recordings and classifications by customer support agents - collected at a large cellular network provider, with two inter-related goals: i) to characterize and understand the major factors which lead to customers to call and seek support; and ii) to utilize such customer tickets to help identify potential network problems. For this purpose, we develop a novel statistical approach to model customer call rates which account for customer-side factors (e.g., user tenure and handset types) and geo-locations. We show that most calls are due to customer-side factors and can be well captured by the model. Furthermore, we also demonstrate that location-specific deviations from the model provide a good indicator of potential network-side issues.
Frequent patterns provide solutions to datasets that do not have well-structured feature vectors. However, frequent pat- tern mining is non-trivial since the number of unique pat- terns is exponential but many are non-discriminative and correlated. Currently, frequent pattern mining is performed in two sequential steps: enumerating a set of frequent pat- terns, followed by feature selection. Although many meth- ods have been proposed in the past few years on how to perform each separate step efficiently, there is still limited success in eventually finding highly compact and discrimi- native patterns. The culprit is due to the inherent nature of this widely adopted two-step approach. This paper discusses these problems and proposes a new and different method. It builds a decision tree that partitions the data onto different nodes. Then at each node, it directly discovers a discrimi- native pattern to further divide its examples into purer sub- sets. Since the number of examples towards leaf level is relatively small, the new approach is able to examine pat- terns with extremely low global support that could not be enumerated on the whole dataset by the two-step method. The discovered feature vectors are more accurate on some of the most difficult graph as well as frequent itemset problems than most recently proposed algorithms but the total size is typically 50% or more smaller. Importantly, the minimum support of some discriminative patterns can be extremely low (e.g. 0.03%). In order to enumerate these low support patterns, state-of-the-art frequent pattern algorithm either cannot finish due to huge memory consumption or have to enumerate 101 to 103 times more patterns before they can even be found. Software and datasets are available by con- tacting the author.
Detecting anomalous traffic is a crucial part of managing IP networks. In recent years, network-wide anomaly de- tection based on Principal Component Analysis (PCA) has emerged as a powerful method for detecting a wide vari- ety of anomalies. We show that tuning PCA to operate effectively in practice is difficult and requires more robust techniques than have been presented thus far. We analyze a week of network-wide traffic measurements from two IP backbones (Abilene and Geant) across three different traffic aggregations (ingress routers, OD flows, and input links), and conduct a detailed inspection of the feature time se- ries for each suspected anomaly. Our study identifies and evaluates four main challenges of using PCA to detect traf- fic anomalies: (i) the false positive rate is very sensitive to small differences in the number of principal components in the normal subspace, (ii) the effectiveness of PCA is sensi- tive to the level of aggregation of the traffic measurements, (iii) a large anomaly may inadvertently pollute the normal subspace, (iv) correctly identifying which flow triggered the anomaly detector is an inherently challenging problem.
Traditional DSL troubleshooting solutions are reactive, relying mainly on customers to report problems, and tend to be labor-intensive, time consuming, prone to incorrect resolutions and overall can contribute to increased customer dissatisfaction. In this paper, we propose a proactive approach to facilitate troubleshooting customer edge problems and reducing customer tickets. Our system consists of: i) a ticket predictor which predicts future customer tickets; and ii) a trouble locator which helps technicians accelerate the troubleshooting process during field dispatches. Both components infer future tickets and trouble locations based on existing sparse line measurements, and the inference models are constructed automatically using supervised machine learning techniques. We propose several novel techniques to address the operational constraints in DSL networks and to enhance the accuracy of NEVERMIND. Extensive evaluations using an entire year worth of customer tickets and measurement data from a large network show that our method can predict thousands of future customer tickets per week with high accuracy and signifcantly reduce the time and effort for diagnosing these tickets. This is benefcial as it has the effect of both reducing the number of customer care calls and improving customer satisfaction.
Function approximation is viewed from the perspective of numerical optimization in function space, rather than parameter space. A connection is made between stagewise additive expansions and steepest--descent minimization. A general gradient--descent "boosting" paradigm is developed for additive expansions based on any fitting criterion. Specific algorithms are presented for least--squares, least--absolute--deviation, and Huber--M loss functions for regression, and multi--class logistic likelihood for classification. Special enhancements are derived for the particular case where the individual additive components are decision trees, and tools for interpreting such "TreeBoost" models are presented. Gradient boosting of decision trees produces competitive, highly robust, interpretable procedures for regression and classification, especially appropriate for mining less than clean data. Connections between this approach and the boosting methods of Freund and Shapire 1996, and Fr...
With the widespread use of artificial intelligence (AI) systems and applications in our everyday lives, accounting for fairness has gained significant importance in designing and engineering of such systems. AI systems can be used in many sensitive environments to make important and life-changing decisions; thus, it is crucial to ensure that these decisions do not reflect discriminatory behavior toward certain groups or populations. More recently some work has been developed in traditional machine learning and deep learning that address such challenges in different subdomains. With the commercialization of these systems, researchers are becoming more aware of the biases that these applications can contain and are attempting to address them. In this survey, we investigated different real-world applications that have shown biases in various ways, and we listed different sources of biases that can affect AI applications. We then created a taxonomy for fairness definitions that machine learning researchers have defined to avoid the existing bias in AI systems. In addition to that, we examined different domains and subdomains in AI showing what researchers have observed with regard to unfair outcomes in the state-of-the-art methods and ways they have tried to address them. There are still many future directions and solutions that can be taken to mitigate the problem of bias in AI systems. We are hoping that this survey will motivate researchers to tackle these issues in the near future by observing existing work in their respective fields.
Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications, where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on the existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this article, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art GNNs into four categories, namely, recurrent GNNs, convolutional GNNs, graph autoencoders, and spatial-temporal GNNs. We further discuss the applications of GNNs across various domains and summarize the open-source codes, benchmark data sets, and model evaluation of GNNs. Finally, we propose potential research directions in this rapidly growing field.
An essential step in the customer care routine of cellular service carriers is determining whether an individual user is impacted by on-going service issues. This is traditionally done by monitoring the network and the services. However, user feedback data, generated when users call customer care agents with problems, is a complementary source of data for this purpose. User feedback data is particularly valuable as it provides the user perspective of the service issues. However, this data is extremely noisy, due to range of issues that users have and the diversity of the language used by care agents. In this paper, we present LOTUS, a system that identifies users impacted by a common root cause (such as a network outage) from user feedback. LOTUS is based on novel algorithmic framework that tightly couples co-training and spatial scan statistics. To model the text in the user feedback, LOTUS also incorporates custom-built language models using deep sequence learning. Through experimental analysis on synthetic and live data, we demonstrate the accuracy of LOTUS. LOTUS has been deployed for several months, and has identified the impact over 200 events.
In an increasingly mobile connected world, our user experience of mobile applications more and more depends on the performance of cellular radio access networks (RAN). To achieve high quality of experience for the user, it is imperative that operators identify and diagnose performance problems quickly. In this paper, we describe our experience in understanding the challenges in automating the diagnosis of RAN performance problems. Working with a major cellular network operator on a part of their RAN that services more than 2 million users, we demonstrate that fine-grained modeling and analysis could be the key towards this goal. We describe our methodology in analyzing RAN problems, and highlight a few of our findings, some previously unknown. We also discuss lessons from our attempt at building automated diagnosis solutions.
With the advent of cellular network technologies, mobile Internet access becomes the norm in everyday life. In the meantime, the complaints made by subscribers about unsatisfactory cellular network access also become increasingly frequent. From a network operator's perspective, achieving accurate and timely cellular network diagnosis about the causes of the complaints is critical for both improving subscriber-perceived experience and maintaining network robustness. We present the Intelligent Customer Care Assistant (ICCA), a distributed fault classification system that exploits a data-driven approach to perform large-scale cellular network diagnosis. ICCA takes massive network data as input, and realizes both offline model training and online feature computation to distinguish between user and network faults in real time. ICCA is currently deployed in a metropolitan LTE network in China that is serving around 50 million subscribers. We show via evaluation that ICCA achieves high classification accuracy (85.3%) and fast query response time (less than 2.3 seconds). We also report our experiences learned from the deployment.
Understanding mobile traffic patterns of large scale cellular towers in urban environment is extremely valuable for Internet service providers, mobile users, and government managers of modern metropolis. This paper aims at extracting and modeling the traffic patterns of large scale towers deployed in a metropolitan city. To achieve this goal, we need to address several challenges, including lack of appropriate tools for processing large scale traffic measurement data, unknown traffic patterns, as well as handling complicated factors of urban ecology and human behaviors that affect traffic patterns. Our core contribution is a powerful model which combines three dimensional information (time, locations of towers, and traffic frequency spectrum) to extract and model the traffic patterns of thousands of cellular towers. Our empirical analysis reveals the following important observations. First, only five basic time-domain traffic patterns exist among the 9600 cellular towers. Second, each of the extracted traffic pattern maps to one type of geographical locations related to urban ecology, including residential area, business district, transport, entertainment, and comprehensive area. Third, our frequency-domain traffic spectrum analysis suggests that the traffic of any tower among 9600 can be constructed using a linear combination of four primary components corresponding to human activity behaviors. We believe that the proposed traffic patterns extraction and modeling methodology, combined with the empirical analysis on the mobile traffic, pave the way toward a deep understanding of the traffic patterns of large scale cellular towers in modern metropolis.
We introduce Adam, an algorithm for first-order gradient-based optimization
of stochastic objective functions. The method is straightforward to implement
and is based an adaptive estimates of lower-order moments of the gradients. The
method is computationally efficient, has little memory requirements and is well
suited for problems that are large in terms of data and/or parameters. The
method is also ap- propriate for non-stationary objectives and problems with
very noisy and/or sparse gradients. The method exhibits invariance to diagonal
rescaling of the gradients by adapting to the geometry of the objective
function. The hyper-parameters have intuitive interpretations and typically
require little tuning. Some connections to related algorithms, on which Adam
was inspired, are discussed. We also analyze the theoretical convergence
properties of the algorithm and provide a regret bound on the convergence rate
that is comparable to the best known results under the online convex
optimization framework. We demonstrate that Adam works well in practice when
experimentally compared to other stochastic optimization methods.
This paper presents NetSieve, a system that aims to do automated problem inference from network trouble tickets. Network trouble tickets are diaries comprising fixed fields and free-form text written by operators to document the steps while troubleshooting a problem. Unfortunately, while tickets carry valuable information for network management, analyzing them to do problem inference is extremely difficult--fixed fields are often inaccurate or incomplete, and the free-form text is mostly written in natural language. This paper takes a practical step towards automatically analyzing natural language text in network tickets to infer the problem symptoms, troubleshooting activities and resolution actions. Our system, NetSieve, combines statistical natural language processing (NLP), knowledge representation, and ontology modeling to achieve these goals. To cope with ambiguity in free-form text, NetSieve leverages learning from human guidance to improve its inference accuracy. We evaluate NetSieve on 10K+ tickets from a large cloud provider, and compare its accuracy using (a) an expert review, (b) a study with operators, and (c) vendor data that tracks device replacement and repairs. Our results show that NetSieve achieves 89%-100% accuracy and its inference output is useful to learn global problem trends. We have used NetSieve in several key network operations: analyzing device failure trends, understanding why network redundancy fails, and identifying device problem symptoms.
Customer care calls serve as a direct channel for a service provider to learn feedbacks from their customers. They reveal details about the nature and impact of major events and problems observed by customers. By analyzing the customer care calls, a service provider can detect important events to speed up problem resolution. However, automating event detection based on customer care calls poses several significant challenges. First, the relationship between customers' calls and network events is blurred because customers respond to an event in different ways. Second, customer care calls can be labeled inconsistently across agents and across call centers, and a given event naturally give rise to calls spanning a number of categories. Third, many important events cannot be detected by looking at calls in one category. How to aggregate calls from different categories for event detection is important but challenging. Lastly, customer care call records have high dimensions (e.g., thousands of categories in our dataset). In this paper, we propose a systematic method for detecting events in a major cellular network using customer care call data. It consists of three main components: (i) using a regression approach that exploits temporal stability and low-rank properties to automatically learn the relationship between customer calls and major events, (ii) reducing the number of unknowns by clustering call categories and using L1 norm minimization to identify important categories, and (iii) employing multiple classifiers to enhance the robustness against noise and different response time. For the detected events, we leverage Twitter social media to summarize them and to locate the impacted regions. We show the effectiveness of our approach using data from a large cellular service provider in the US.
A major assumption in many machine learning and data mining algorithms is that the training and future data must be in the same feature space and have the same distribution. However, in many real-world applications, this assumption may not hold. For example, we sometimes have a classification task in one domain of interest, but we only have sufficient training data in another domain of interest, where the latter data may be in a different feature space or follow a different data distribution. In such cases, knowledge transfer, if done successfully, would greatly improve the performance of learning by avoiding much expensive data-labeling efforts. In recent years, transfer learning has emerged as a new learning framework to address this problem. This survey focuses on categorizing and reviewing the current progress on transfer learning for classification, regression, and clustering problems. In this survey, we discuss the relationship between transfer learning and other related machine learning techniques such as domain adaptation, multitask learning and sample selection bias, as well as covariate shift. We also explore some potential future issues in transfer learning research.
This work builds on the method of to create a prototype access control system, capable of handling variations in illumination and expression, as well as significant occlusion or disguise. Our demonstration will allow participants to interact with the algorithm, gaining a better understanding strengths and limitations of sparse representation as a tool for robust recognition.
We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by C
1
-minimization, we propose a general classification algorithm for (image-based) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly by exploiting the fact that these errors are often sparse with respect to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm and corroborate the above claims.
Network anomaly detection using dimensionality reduction techniques has received much recent attention in the liter- ature. For example, previous work has aggregated netflow records into origin-destination (OD) flows, yielding a much smaller set of dimensions which can then be mined to un- cover anomalies. However, this approach can only identify which OD flow is anomalous, not the particular IP flow(s) responsible for the anomaly. In this paper we show how one can use random aggregations of IP flows (i.e., sketches) to enable more precise identification of the underlying causes of anomalies. We show how to combine traffic sketches with a subspace method to (1) detect anomalies with high accu- racy and (2) identify the IP flows(s) that are responsible for the anomaly. Our method has detection rates comparable to previous methods and detects many more anomalies than prior work, taking us a step closer towards a robust on-line system for anomaly detection and identification.
Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IR
m
that maps a graph G and one of its nodes
n
into an
m
-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.
Sequential pattern mining is an important data mining problem with broad applications. It is challenging since one may need to examine a combinatorially explosive number of possible subsequence patterns. Most of the previously developed sequential pattern mining methods follow the methodology of which may substantially reduce the number of combinations to be examined. However, still encounters problems when a sequence database is large and/or when sequential patterns to be mined are numerous and/or long.
Language Modeling with Gated Convolutional Networks
- Angela Yann N Dauphin
- Michael Fan
- David Auli
- Grangier
- Dauphin Yann N
Ajay Mahimkar, Carlos Eduardo de Andrade, Rakesh Sinha, and Giritharan Rana. 2021. A Composition Framework for Change Management
- Ajay Mahimkar
- Carlos Eduardo De Andrade
- Rakesh Sinha
- Giritharan Rana
- Mahimkar Ajay
Xin Li, Fang Bian, Mark Crovella, Christophe Diot, Ramesh Govindan, Gianluca Iannaccone, and Anukool Lakhina. 2006. Detection and Identification of Network Anomalies Using Sketch Subspaces
- Xin Li
- Fang Bian
- Mark Crovella
- Christophe Diot
- Ramesh Govindan
- Li Xin
A Social Network Under Social Distancing: {Risk-Driven} Backbone Management During {COVID-19} and Beyond
- Yiting Xia
- Ying Zhang
- Zhizhen Zhong
- Guanqing Yan
- Chiun Lin Lim
- Satyajeet Singh Ahuja
- Soshant Bali
- Alexander Nikolaidis
- Kimia Ghobadi
- Manya Ghobadi
- Xia Yiting
How Powerful Are Graph Neural Networks?
- Keyulu Xu
- Weihua Hu
- Jure Leskovec
- Stefanie Jegelka
- Xu Keyulu
Representation Learning on Graphs: Methods and Applications
- Hamilton William L