Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

中枢神経系疾患の治療は正常細胞（ニューロン）の機能維持を目的とするが，脳血管障害のように機能障害の原因が細胞の死滅に基づくことは多い．一方，脳腫瘍の治療においては薬物療法や放射線療法といった腫瘍細胞の死滅を目標とするものが大きな位置を占める．いずれの場合にも，細胞死の機序を理解することは各種病態や治療法の理解のうえで重要である．現在のところ最も研究の進んでいる細胞死の型はアポトーシスである．そのなかで重要な位置を占めるミトコンドリアにおける反応および抗アポトーシス因子について概要を紹介する．

Neuroscience 細胞死：最近の知見

where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

This text presents a modern theory of analysis, control, and optimization for dynamic networks. Mathematical techniques of Lyapunov drift and Lyapunov optimization are developed and shown to enable constrained optimization of time averages in general stochastic systems. The focus is on communication and queueing systems, including wireless networks with time-varying channels, mobility, and randomly arriving traffic. A simple drift-plus-penalty framework is used to optimize time averages such as throughput, throughput-utility, power, and distortion. Explicit performance-delay tradeoffs are provided to illustrate the cost of approaching optimality. This theory is also applicable to problems in operations research and economics, where energy-efficient and profit-maximizing decisions must be made without knowing the future. Topics in the text include the following: - Queue stability theory - Backpressure, max-weight, and virtual queue methods - Primal-dual methods for non-convex stochastic utility maximization - Universal scheduling theory for arbitrary sample paths - Approximate and randomized scheduling theory - Optimization of renewal systems and Markov decision systems Detailed examples and numerous problem set questions are provided to reinforce the main concepts. Table of Contents: Introduction / Introduction to Queues / Dynamic Scheduling Example / Optimizing Time Averages / Optimizing Functions of Time Averages / Approximate Scheduling / Optimization of Renewal Systems / Conclusions

Stochastic Network Optimization with Application to Communication and Queueing Systems

Cloud data centers host diverse applications, mixing workloads that require small predictable latency with others requiring large sustained throughput. In this environment, today's state-of-the-art TCP protocol falls short. We present measurements of a 6000 server production cluster and reveal impairments that lead to high application latencies, rooted in TCP's demands on the limited buffer space available in data center switches. For example, bandwidth hungry "background" flows build up queues at the switches, and thus impact the performance of latency sensitive "foreground" traffic.To address these problems, we propose DCTCP, a TCP-like protocol for data center networks. DCTCP leverages Explicit Congestion Notification (ECN) in the network to provide multi-bit feedback to the end hosts. We evaluate DCTCP at 1 and 10Gbps speeds using commodity, shallow buffered switches. We find DCTCP delivers the same or better throughput than TCP, while using 90% less buffer space. Unlike TCP, DCTCP also provides high burst tolerance and low latency for short flows. In handling workloads derived from operational measurements, we found DCTCP enables the applications to handle 10X the current background traffic, without impacting foreground traffic. Further, a 10X increase in foreground traffic does not cause any timeouts, thus largely eliminating incast problems.

/pdf/data-center-tcp-dctcp-4d3pj8xdal.pdf

Data center TCP (DCTCP)

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

1. The Single Server Queue

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 need to understand the interaction between these effects. This paper reviews the buffer-sizing theory in G. Raina and D. Wischik (2005) and extends it to cope with bursty TCP traffic. This enables us to explain an observation about TCP pacing made in A. Aggarwal et al. (2000)

Buffer sizing theory for bursty TCP flows

The modelling of small-scale processes is a major source of error in climate models, hindering the accuracy of low-cost models which must approximate such processes through parameterization. Red noise is essential to many operational parameterization schemes, helping model temporal correlations. We show how to build on the successes of red noise by combining the known benefits of stochasticity with machine learning. This is done using a physically-informed recurrent neural network within a probabilistic framework. Our model is competitive and often superior to both a bespoke baseline and an existing probabilistic machine learning approach (GAN) when applied to the Lorenz 96 atmospheric simulation. This is due to its superior ability to model temporal patterns compared to standard first-order autoregressive schemes. It also generalises to unseen scenarios. We evaluate across a number of metrics from the literature, and also discuss the benefits of using the probabilistic metric of hold-out likelihood.

Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 model

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 means for treating AD. We have developed cell-free and cellular models and transgenic mice that model tauopathy and demonstrate the molecular basis for achieving pharmacological selectivity of TAIs. Methylthioninium chloride, the first selective TAI identified, has demonstrated efficacy in a phase 2 trial of AD on both clinical and functional molecular neuroimaging end points. This supports the potential for use of TAIs both for prevention and for treatment of the disease. Leucomethylthioninium is now in phase 3 trials of AD and behavioral-variant frontotemporal degeneration in order to confirm the concept of TAI therapy for these tauopathies.

Inhibition of Tau Aggregation as a Basis for Treatment and Prevention of Alzheimer's Disease

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 explicitly avoid interference at the receivers by allowing at most one of the transmitters in its range to transmit. This improvement in performance is realized by means of a medium access algorithm with: (a) polynomial computational complexity per timeslot, (b) polynomially bounded expected queue-length at the transmitters, and (c) a throughput region that is at least a poly-logarithmic fraction of the largest possible throughput-region under any algorithm operating using that treats interference as noise. Thus, the hardness of low-delay network scheduling (a result by Shah, Tse and Tsitsiklis [1]) is an artifact of explicitly avoiding interference, or treating it as noise and can be overcome by a rather simple medium access algorithm that does not require information theoretic “block codes.”

/pdf/interference-is-not-noise-4mb3191g8i.pdf

Damon Wischik

Papers

1. The Single Server Queue

Buffer sizing theory for bursty TCP flows

Using Probabilistic Machine Learning to Better Model Temporal Patterns in Parameterizations: a case study with the Lorenz 96 model

Inhibition of Tau Aggregation as a Basis for Treatment and Prevention of Alzheimer's Disease

Interference is not noise