Damon Wischik

University of Cambridge | Cam · Computer Laboratory

There is an unavoidable tension between prediction and explanation: between the idea that predictive accuracy is what matters, and the requirement for explanation. In the law, Holmes drew a distinction between explanation as articulated in a judicial decision using the language of logic, and the real explanation that can be found by looking at the...

The output of a machine learning system is nothing more than statements of the following form: “such and such a new case is likely to behave similarly to other similar cases that belong to the training dataset that was used to train this machine.” It has been described as “just curve fitting”, in the sense of drawing a curve through the datapoints...

To the legal formalist, the law consists in applying rules to facts using logic, similar to working out a mathematical proof. It is a common view of computers that they should be thought of in the same way: that they run algorithms, which should be described using rules of logic. This view of computing is appealing to formalist lawyers, who see the...

Holmes’s famous epigram, that “prophecies of what the courts will do” is what constitutes the law, applies equally well to machine learning. In machine learning, prediction is the be-all and end-all. Machine learning requires that its tasks be formulated as prediction problems—not just forecasting, but prediction in the broader sense of “give an an...

Holmes saw juries as a conduit into the courtroom of popular feelings and prejudices, ensuring that the law is kept in accord with the will of the community. Thus juries are analogous to the training dataset: they provide the givens, the ground truth. A judge who is faced with an intractable question about which she would rather not make a decision...

Machine learning gives rise to concerns about “algorithmic bias,” arising from bias in the training dataset. A dataset necessarily reflects a past state of affairs, but we may anticipate that the future will be different, or desire it to be so. Law has struggled with an analogous problem: how to deal with “bad evidence” and prejudice. Holmes’s broa...

Holmes thought that the law is drawn from much wider sources than legal formalists of the day maintained: not just the law codes, but experience at large. “The life of the law has not been logic; it has been experience.” The algorithmists, analogous to legal formalists, see the source code as what matters. In machine learning there is still source...

Holmes’s enduring interest was in the development of the law, as indicated by the title The Path of the Law. He drew on the philosophy of science and the role of induction in forming scientific theories, and he added a new ingredient: social induction. Social induction has two parts. First, the law develops through the accumulation of cases, which...

Holmes, in tune with the “scientism” prevalent in his time, speculated that science might reveal rules about society and human relations, and that these rules might come to replace the legal system—that society might be regulated using a rules-based algorithmic formalism. He had a long standing interest in statistics (“the man of the future is the...

Legal thinkers can be typecast as conservative and skeptical, compared to the technologist who embraces disruption and innovation. There has nonetheless been a revolution in thinking about the law, a revolution which began in the late nineteenth century, driven by a turn toward inductive reasoning. It mirrors the revolution of machine learning, und...

Background: Hydromethylthionine is a potent inhibitor of pathological aggregation of tau and TDP-43 proteins. Objective: To compare hydromethylthionine treatment effects at two doses and to determine how drug exposure is related to treatment response in bvFTD. Methods: We undertook a 52-week Phase III study in 220 bvFTD patients randomized to...

This open access book explores machine learning and its impact on how we make sense of the world. It does so by bringing together two ‘revolutions’ in a surprising analogy: the revolution of machine learning, which has placed computing on the path to artificial intelligence, and the revolution in thinking about the law that was spurred by Oliver We...

Following our discovery of a fragment from the repeat domain of tau protein as a structural constituent of the PHF-core in Alzheimer's disease (AD), we developed an assay that captured several key features of the aggregation process. Tau-tau binding through the core tau fragment could be blocked by the same diaminophenothiazines found to dissolve p...

Background: LMTM is being developed as a treatment for AD based on inhibition of tau aggregation. Objectives: To examine the efficacy of LMTM as monotherapy in non-randomized cohort analyses as modified primary outcomes in an 18-month Phase III trial in mild AD. Methods: Mild AD patients (n = 800) were randomly assigned to 100 mg twice a day o...

Tau pathology in Alzheimer’s disease (AD) initiates early, before clinical symptoms are observed and before accumulation of extracellular amyloid-β. Tau aggregation is an autocatalytic process that does not depend on its phosphorylation and is highly correlated with clinical dementia. Tau aggregation inhibitors (TAIs) could provide the therapeutic...

Background: Leuco-methylthioninium bis(hydromethanesulfonate; LMTM), a stable reduced form of the methylthioninium moiety, acts as a selective inhibitor of tau protein aggregation both in vitro and in transgenic mouse models. Methylthioninium chloride has previously shown potential efficacy as monotherapy in patients with Alzheimer's disease. We a...

Background: As tau aggregation pathology correlates with clinical dementia in Alzheimer's disease (AD), a tau aggregation inhibitor (TAI) could have therapeutic utility. Methylthioninium (MT) acts as a selective TAI in vitro and reduces tau pathology in transgenic mouse models. Objective: To determine the minimum safe and effective dose of MT re...

This paper looks at the problem of designing medium access algorithm for wireless networks with the objective of providing high throughput and low delay performance to the users, while requiring only a modest computational effort at the transmitters and receivers. Additive inter-user interference at the receivers is an important physical layer char...

This paper looks at the problem of designing medium access algorithm for wireless networks with the objective of providing high throughput and low delay performance to the users, while requiring only a modest computational effort at the transmitters and receivers. Additive inter-user interference at the receivers is an important physical layer char...

We consider switched queueing networks in which there are constraints on which queues may be served simultaneously. The scheduling policy for such a network specifies which queues to serve at any point in time. We introduce and study a variant of the popular maximum weight or backpressure policy which chooses the collection of queues to serve that...

This paper describes Steptacular, an online interactive incentive system for encouraging people to walk more. A trial offering Steptacular to the employees of Accenture-USA was conducted over a 6 month period. Over 5,000 employees registered for the program and close to 3,000 participants wore USB-enabled pedometers; from time to time they plugged...

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The latest large-scale data centers offer higher aggregate bandwidth and robustness by creating multiple paths in the core of the net- work. To utilize this bandwidth requires different flows take different paths, which poses a challenge. In short, a single-path transport seems ill-suited to such networks. We propose using Multipath TCP as a replac...

We consider a switched network (i.e. a queueing network in which there are constraints on which queues may be served simultaneously), in a state of overload. We analyse the behaviour of two scheduling algorithms for multihop switched networks: a generalized version of max-weight, and the α-fair policy. We show that queue sizes grow linearly with ti...

This paper looks at the problem of designing wireless medium access algorithms. Inter-user interference at the receivers is an important characteristic of wireless networks. We show that decoding (or canceling) this interference results in significant improvement in the system performance over protocols that either treat interference as noise, or e...

Multipath TCP, as proposed by the IETF working group mptcp, allows a single data stream to be split across multiple paths. This has obvious benefits for reliability, and it can also lead to more efficient use of networked resources. We describe the design of a multipath congestion control algorithm, we implement it in Linux, and we evaluate it for...

To ensure the timely publication of articles, Communications created the Virtual Extension (VE) to expand the page limitations of the print edition by bringing readers the same high-quality articles in an online-only format. VE articles undergo the same ...

We consider a queueing network in which there are constraints on which queues may be served simultaneously; such networks may be used to model input-queued switches and wireless networks. The scheduling policy for such a network specifies which queues to serve at any point in time. We consider a family of scheduling policies, related to the maximum...

Recently new data center topologies have been proposed that offer higher aggregate bandwidth and location independence by creating multiple paths in the core of the network. To effectively use this bandwidth requires ensuring different flows take different paths, which poses a challenge. Plainly put, there is a mismatch between single-path transpor...

By simultaneously using multiple paths through the Internet, multipath transport protocols have the potential to greatly improve performance, resilience and flexibility. Further, by linking the congestion behavior of the subflows of a connec-tion, it is possible to move traffic away from congested paths, allowing network capacity to be pooled and b...

Alzheimer's disease is an irreversible, neurodegenerative disorder characterized by the progressive loss of memory and thinking skills. A close correlate of this cognitive decline is the aggregation of tau protein, of which neurofibrillary tangles are composed. The process of tau aggregation follows a stereotypical pattern of spread throughout the...

There are moves in the Internet architecture community to add multipath capabilities to TCP, so that end-systems will be able to shift their traffic away from congested parts of the network. We study two problems relating to the design of multipath TCP. (i) We investigate stochastic packet-level behaviour of some proposed multipath congestion contr...

We consider a queueing network in which there are constraints on which queues may be served simultaneously. Such networks, called ldquoswitched networksrdquo [3] can be used to model input-queued switches, wireless networks, or bandwidth sharing in the Internet. The scheduling algorithm for such a network specifies which queues to serve at any poin...

Since the ARPAnet, network designers have built localized mechanisms for statistical multiplexing, load balancing, and failure resilience, often without understanding the broader implications. These mechanisms are all types of resource pooling, which means making a collection of resources behave like a single pooled resource. We believe that the na...

This paper has three purposes. The first one is to explain to a general audience what is involved in retrieving a web page or performing some other complex network transaction, and what can make it slow, and why the problem of slowness is likely to get worse as networked applications become more complex. The second is to describe, to those who prog...

Introduction In this chapter we argue that future high-speed switches should have buffers that are much smaller than those used today. We present recent work in queueing theory that will be needed for the design of such switches. There are two main benefits of small buffers. First, small buffers means very little queueing delay or jitter, which mea...

The input-queued switch architecture is widely used in Internet routers, due to its ability to run at very high line speeds. A central problem in designing an input-queued switch is choosing the scheduling algorithm, i.e. deciding which packets to transfer from ingress ports to egress ports in a given timeslot. Important metrics for evaluating a sc...

This note is a reply to some of the points about buffer sizing raised by Dhamdhere and Dovrolis [1]. I'll use a simple mathematical model to make stark some of the tradeoffs that need to be weighed when deciding on buffer size.

In a router serving many TCP flows, queues will build up from time to time. The manner in which queues build up depends on the buffer space available and on the burstiness of the TCP traffic. Conversely, the traffic generated by a TCP flow depends on the congestion it sees at queues along its route. In order to decide how big buffers should be, we...

As the Internet grows, it is becoming increasingly difficult to collect performance measurements, to monitor its state, and to perform simulations efficiently. This is because the size and the heterogeneity of the Internet makes it time-consuming and difficult to devise traffic models and analytic tools which would allow us to work with summary sta...

A core Internet router can typically buffer 250 ms worth of data (1.25 GByte at 40 Gb/s). This would be challenging for an all-optical router. Happily, recent theory suggests that the optimal buffer size is around 30 kByte.

In this article we describe recent work on buffer sizing for core Internet routers. This work suggests that the widely-used rule of thumb leads to buffers which are much larger than they need to be. For example, the buffer in a backbone router could be reduced from 1,000,000 packets to 10,000 without loss in performance. It could be reduced even fu...

Internet users are increasingly mobile. Their hosts are often only intermittently connected to the Internet, due to using multiple access networks, gaps in wireless coverage or explicit user choice. When such hosts communicate using the current Internet ...

This article describes how control theory has been used to address the question of how to size the buffers in core Internet routers. Control theory aims to predict whether the is stable, i.e. whether TCP flows are desynchronized. If flows are desynchronized then small buffers are sufficient [14 ]; the theory here shows that small buffers actually p...

In large multiplexers with many TCP flows, the aggregate traffic flow behaves predictably; this is a basis for the fluid model of Misra, Gong and Towsley V. Misra et al., (2000) and for a growing literature on fluid models of congestion control. In this paper we argue that different fluid models arise from different buffer-sizing regimes. We consid...

This article describes how control theory has been used to address the question of how to size the buffers in core Internet routers. Control theory aims to predict whether the is stable, i.e. whether TCP flows are desynchronized. If flows are desynchronized then small buffers are sufficient [14 ]; the theory here shows that small buffers actually p...

As the Internet grows, it is becoming increasingly difficult to collect performance measurements of a network or a web-server farm, to monitor its state, and to perform simulations efficiently. Besides, the heterogeneity of the Internet makes it time-consuming and difficult to devise traffic models and analytic tools which would allow us to work wi...

In networks and in Web server farms, it is useful to collect performance measurements, to monitor the state of the system, and to perform simulations. However, the sheer volume of traffic in large high-speed network systems makes it hard to monitor their performance or to simulate them efficiently. And the heterogeneity of the Internet means it is...

Traffic flows with long-range dependence satisfy a certain type of scal-ing relationship, and it is this scaling relationship which governs the scal-ing behaviour of a queueing network fed by such flows. In this paper we present a mathematical technique for reasoning about scaling behaviour in queueing systems, based on large deviations theory. Our...

4.1 Topology and Metric Spaces 4.2 Definition of LDP 4.3 The Contraction Principle 4.4 Other Useful LDP Results

Contents. 2.1 Some Examples 2.2 Principle of the Largest Term 2.3 Large Deviations Principle 2.4 Cumulant Generating Functions 2.5 Convex Duality 2.6 Cramér’s Theorem 2.7 Sanov’s Theorem for Finite Alphabets 2.8 A Generalisation of Cramér’s Theorem

9.1 Motivation 9.2 Traffic Processes 9.3 Queue Scalings 9.4 Shared Buffers 9.5 Mixed Limits

Contents. 6.1 The Space of Input Processes 6.2 Large Deviations for Partial Sums Processes 6.3 Linear Geodesics 6.4 Queues with Infinite Buffers 6.5 Queues with Finite Buffers 6.6 Queueing Delay 6.7 Departure Process 6.8 Mean Rate of Departures 6.9 Quasi-Reversibility 6.10 Scaling Properties of Networks 6.11 Statistical Inference for the Tail-Behav...

8.1 What Is Long Range Dependence? 8.2 Implications for Queues 8.3 Sample Path LDP for Fractional Brownian Motion 8.4 Scaling Properties 8.5 How Does Long Range Dependence Arise? 8.6 Philosophical Difficulties with LRD Modelling

Contents. 5.1 Introduction 5.2 An Example: Queues with Large Buffers 5.3 The Continuous Mapping Approach 5.4 Continuous Functions 5.5 Some Convenient Notation 5.6 Queues with Infinite Buffers 5.7 Queues with Finite Buffers 5.8 Queueing Delay 5.9 Priority Queues 5.10 Processor Sharing 5.11 Departures from a Queue 5.12 Conclusion

1.1 The Single-Server Queueing Model 1.2 One-Dimensional Large Deviations 1.3 Application to Queues with Large Buffers 1.4 Application to Queues with Many Sources

7.1 Traffic Scaling 7.2 Topology for Sample Paths 7.3 The Sample Path LDP 7.4 Example Sample Path LDPs 7.5 Applying the Contraction Principle 7.6 Queues with Infinite Buffers 7.7 Queues with Finite Buffers 7.8 Overflow and Underflow 7.9 Paths to Overflow 7.10 Priority Queues 7.11 Departures from a Queue

3.1 Queues with Correlated Inputs 3.2 Queues with Many Sources and Power-Law Scalings 3.3 Queues with Large Buffers and Power-Law Scalings

10.1 Effective Bandwidths 10.1.1 Effective Bandwidths for the Large-Buffer Scaling 10.1.2 Effective Bandwidths for the Many-Flows Scaling 10.2 Numerical Estimates 10.2.1 From Limits to Estimates 10.2.2 Common Form of Estimates 10.2.3 Refined Estimates 10.2.4 Numerical Comparison 10.3 A Global Approximation 10.4 Scaling Laws 10.5 Types of Traffic 10...

In networks and in web-server farms, it is useful to collect performance measurements, to monitor the state of the system, and to perform simulations. However, the sheer volume of traffic in large high-speed network systems makes it hard to monitor their performance or to simulate them efficiently. And the heterogeneity of the Internet means it is...

As the Internet grows, so do the complexity and computational requirements of network simulations. This leads either to unrealistic, or to prohibitely expensive simulation experiments.We explore a way to side-step this problem, by combining simulation with sampling and analysis. Our hypothesis is this: if we take a sample of the traffic, and feed i...

The relationship between timing parameters in a WR-OBS network architecture is analyzed with respect to packet loss, delay constraints, and network scalability. A novel burst-aggregation scheme provides low latencies even for high traffic loads.

As the Internet grows, so do the complexity and computational requirements of network simulations. This leads either to unrealistic, or to prohibitely expensive simulation experiments. We explore a way to side-step this problem, by combining simulation with sampling and analysis. Our hypothesis is this: if we take a sample of the traffic, and feed...

The relationship of three timing parameters in the WR-OBS network architecture has been identified and investigated, to quantify the limits on the operation of a dynamic network. An adaptive burst assembler at the network edge provides an accurate estimation of the maximum edge delay whilst preventing buffer overflow, depending only on the mean and...

This paper presents a large deviations principle for the average of real-valued processes indexed by the positive integers, one which is particularly suited to queueing systems with many traffic flows. Examples are given of how it may be applied to standard queues with finite and infinite buffers, to priority queues and to finding most likely paths...

Contents Preface iii 1 Introduction 1 1.1 Internet Congestion . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Large deviations . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Large deviations and Internet congestion . . . . . . . . . . . . . . 3 1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Traffi...

Consider a switch which queues traffic from many independent input flows. We show that in the large deviations limiting regime in which the number of inputs increases and the service rate and buffer size are increased in proportion, the statistical characteristics of a flow are essentially unchanged by passage through the switch. This significantly...

A network router that marks packets to signal congestion should do so fairly. We propose a definition of fairness, using ideas from effective bandwidth theory and economics. Our definition measures both the level of congestion at a router and the contribution of each flow to that congestion, taking into account the flow's burstiness. We then use la...

Calls that make large, persistent demands for network resources will be denied consistent service, unless the network employs adequate control mechanisms. Calls of this type include video conferences. Although overprovisioning network capacity would increase the likelihood of accepting these calls, it is a very expensive option to apply uniformly i...

Hyperphosphorylated tau protein which can be isolated on the basis of insolubility in 1% sarkosyl (A68-tau fraction) is thought to represent a precursor pool for PHF assembly, associated histologically with neuritic pathology, which feeds into a more resistant tangle-associated PHF pool via cross-linking and proteolysis. We examined these predictio...

Moderate deviations theory concerns a collection of scales between large deviations theory and the central limit theorem. When applied to queueing problems, moderate deviations theory combines the simplicity of large deviations techniques with the parsimony of heavy traffic approxima- tions. This leads to some very simple heuristics for traffic eng...

In this report we describe a selection of probabilistic limit theorems, and discuss which are relevant for modelling OBS networks. This report accompanies "Mathematical modelling of Optical Burst-Switched (OBS) Networks" (7).

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