Abraham J. Wyner

A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable?

Predicting historic temperatures based on tree rings, ice cores, and other natural proxies is a difficult endeavor. The relationship between proxies and temperature is weak and the number of proxies is far larger than the number of target data points. Furthermore, the data contain complex spatial and temporal dependence structures which are not easily captured with simple models. In this paper, we assess the reliability of such reconstructions and their statistical significance against various null models. We find that the proxies do not predict temperature significantly better than random series generated independently of temperature. Furthermore, various model specifications that perform similarly at predicting temperature produce extremely different historical backcasts. Finally, the proxies seem unable to forecast the high levels of and sharp run-up in temperature in the 1990s either in-sample or from contiguous holdout blocks, thus casting doubt on their ability to predict such phenomena if in fact they occurred several hundred years ago. We propose our own reconstruction of Northern Hemisphere average annual land temperature over the last millennium, assess its reliability, and compare it to those from the climate science literature. Our model provides a similar reconstruction but has much wider standard errors, reflecting the weak signal and large uncertainty encountered in this setting.

On the role of pattern matching in information theory

In this paper, the role of pattern matching in information theory is motivated and discussed. We describe the relationship between a patterns recurrence time and its probability under the data-generating stochastic source. We show how this relationship has led to great advances in universal data compression. We then describe nonasymptotic uniform bounds on the performance of data-compression algorithms in cases where the size of the training data that is available to the encoder is not large enough so as to yield the asymptotic compression: the Shannon entropy. We then discuss applications of pattern matching and universal compression to universal prediction, classification, and entropy estimation.

Improved redundancy of a version of the Lempel-Ziv algorithm

The fixed-database Lempel-Ziv algorithm (FDLZ) closely resembles practical versions of the LZ algorithm that are widely in use. Bender and Wolf (1991) suggested a variant of LZ which empirically appears to perform well. We suggest a finite memory version of their scheme, and show that it has redundancy /spl rho//sub n/=O(1/log n) where n is the memory size. We are concerned with a data source which is a stationary, finite-memory random sequence that takes values in an alphabet of finite size A. The data source can be losslessly encoded using (H+/spl rho//sub n/) bits per source symbol, where n is a measure of the complexity of the code, and /spl rho//sub n//spl rarr/0, as n/spl rarr//spl infin/. The LZ algorithm is a universal procedure (which does not depend on the source statistics) for encoding the source at a rate close to the entropy. >

Characterization of the bout durations of sleep and wakefulness

STUDY OBJECTIVES (a) Develop a new statistical approach to describe the microarchitecture of wakefulness and sleep in mice; (b) evaluate differences among inbred strains in this microarchitecture; (c) compare results when data are scored in 4-s versus 10-s epochs. DESIGN Studies in male mice of four inbred strains: AJ, C57BL/6, DBA and PWD. EEG/EMG were recorded for 24h and scored independently in 4-s and 10-s epochs. MEASUREMENTS AND RESULTS Distribution of bout durations of wakefulness, NREM and REM sleep in mice has two distinct components, i.e., short and longer bouts. This is described as a spike (short bouts) and slab (longer bouts) distribution, a particular type of mixture model. The distribution in any state depends on the state the mouse is transitioning from and can be characterized by three parameters: the number of such bouts conditional on the previous state, the size of the spike, and the average length of the slab. While conventional statistics such as time spent in state, average bout duration, and number of bouts show some differences between inbred strains, this new statistical approach reveals more major differences. The major difference between strains is their ability to sustain long bouts of NREM sleep or wakefulness. Scoring mouse sleep/wake in 4-s epochs offered little new information when using conventional metrics but did when evaluating the microarchitecture based on this new approach. CONCLUSIONS Standard statistical approaches do not adequately characterize the microarchitecture of mouse behavioral state. Approaches based on a spike-and-slab provide a quantitative description.

Role of Homer Proteins in the Maintenance of Sleep-Wake States

Sleep is an evolutionarily conserved process that is linked to diurnal cycles and normal daytime wakefulness. Healthy sleep and wakefulness are integral to a healthy lifestyle; this occurs when an organism is able to maintain long bouts of both sleep and wake. Homer proteins, which function as adaptors for group 1 metabotropic glutamate receptors, have been implicated in genetic studies of sleep in both Drosophila and mouse. Drosophila express a single Homer gene product that is upregulated during sleep. By contrast, vertebrates express Homer as both constitutive and immediate early gene (H1a) forms, and H1a is up-regulated during wakefulness. Genetic deletion of Homer in Drosophila results in fragmented sleep and in failure to sustain long bouts of sleep, even under increased sleep drive. However, deletion of Homer1a in mouse results in failure to sustain long bouts of wakefulness. Further evidence for the role of Homer1a in the maintenance of wake comes from the CREB alpha delta mutant mouse, which displays a reduced wake phenotype similar to the Homer1a knockout and fails to up-regulate Homer1a upon sleep loss. Homer1a is a gene whose expression is induced by CREB. Sustained behaviors of the sleep/wake cycle are created by molecular pathways that are distinct from those for arousal or short bouts, and implicate an evolutionarily-conserved role for Homer in sustaining these behaviors.

DAF-16/FOXO regulates homeostasis of essential sleep-like behavior during larval transitions in C. elegans.

Sleep homeostasis, which refers to the maintenance of sleep amount or depth following sleep deprivation, indicates that sleep and sleep-like states serve fundamental functions that cannot be bypassed [1]. Homeostasis of sleep-like behavior is observed during C. elegans lethargus, a 2-3 hr behavioral quiescent period that occurs during larval state transitions [2]. Here, we report a role for DAF-16/FOXO, a transcription factor that is active under conditions of stress [3], in the response to deprivation of lethargus quiescence. Forced locomotion during lethargus results in nuclear translocation of DAF-16. The formation of dauer larvae, a developmental state promoted by daf-16, is increased in response to quiescence deprivation. daf-16 mutants show an impaired homeostatic response to deprivation of lethargus quiescence and are hypersensitive to the lethal effects of forced locomotion during lethargus. DAF-16 expression in muscle cells, but not in neurons, is sufficient to restore a homeostatic response to deprivation of quiescence, pointing to a role for muscle in sleep homeostasis. These findings are relevant to clinical observations of altered metabolic signaling in response to sleep deprivation and suggest that these signaling pathways may act in nonneuronal tissue to regulate sleep behaviors.

Universal codes for finite sequences of integers drawn from a monotone distribution

We offer two noiseless codes for blocks of integers X/sup n/ = (X/sub 1/, ..., X/sub n/). We provide explicit bounds on the relative redundancy that are valid for any distribution F in the class of memoryless sources with a possibly infinite alphabet whose marginal distribution is monotone. Specifically, we show that the expected code length L (X/sup n/) of our first universal code is dominated by a linear function of the entropy of X/sup n/. Further, we present a second universal code that is efficient in that its length is bounded by nH/sub F/ + o(nH/sub F/), where H/sub F/ is the entropy of F which is allowed to vary with n. Since these bounds hold for any n and any monotone F we are able to show that our codes are strongly minimax with respect to relative redundancy (as defined by Elias (1975)). Our proofs make use of the elegant inequality due to Aaron Wyner (1972).

Aging in mice reduces the ability to sustain sleep/wake states.

One of the most significant problems facing older individuals is difficulty staying asleep at night and awake during the day. Understanding the mechanisms by which the regulation of sleep/wake goes awry with age is a critical step in identifying novel therapeutic strategies to improve quality of life for the elderly. We measured wake, non-rapid eye movement (NREM) and rapid-eye movement (REM) sleep in young (2–4 months-old) and aged (22–24 months-old) C57BL6/NIA mice. We used both conventional measures (i.e., bout number and bout duration) and an innovative spike-and-slab statistical approach to characterize age-related fragmentation of sleep/wake. The short (spike) and long (slab) components of the spike-and-slab mixture model capture the distribution of bouts for each behavioral state in mice. Using this novel analytical approach, we found that aged animals are less able to sustain long episodes of wakefulness or NREM sleep. Additionally, spectral analysis of EEG recordings revealed that aging slows theta peak frequency, a correlate of arousal. These combined analyses provide a window into the mechanisms underlying the destabilization of long periods of sleep and wake and reduced vigilance that develop with aging.

Estimation of General Stationary Processes by Variable Length Markov Chains

We develop new results about a sieve methodology for the estimation of minimal state spaces and probability laws in the class of stationary processes defined on finite categorical spaces. Using a sieve approximation with variable length Markov chains of increasing order, we show that an adapted version of the Context algorithm yields asymptotically correct estimates for the minimal state space and for the underlying probability distribution. As a side product, the method of sieves yields a nice graphical tree representation for the potentially infinite dimensional minimal state space of the data generating process, which is very useful for exploration of the memory. Copyright 2003 Board of the Foundation of the Scandinavian Journal of Statistics..

Assessing REM Sleep in Mice Using Video Data

STUDY OBJECTIVES Assessment of sleep and its substages in mice currently requires implantation of chronic electrodes for measurement of electroencephalogram (EEG) and electromyogram (EMG). This is not ideal for high-throughput screening. To address this deficiency, we present a novel method based on digital video analysis. This methodology extends previous approaches that estimate sleep and wakefulness without EEG/EMG in order to now discriminate rapid eye movement (REM) from non-REM (NREM) sleep. DESIGN Studies were conducted in 8 male C57BL/6J mice. EEG/EMG were recorded for 24 hours and manually scored in 10-second epochs. Mouse behavior was continuously recorded by digital video at 10 frames/second. Six variables were extracted from the video for each 10-second epoch (i.e., intraepoch mean of velocity, aspect ratio, and area of the mouse and intraepoch standard deviation of the same variables) and used as inputs for our model. MEASUREMENTS AND RESULTS We focus on estimating features of REM (i.e., time spent in REM, number of bouts, and median bout length) as well as time spent in NREM and WAKE. We also consider the models epoch-by-epoch scoring performance relative to several alternative approaches. Our model provides good estimates of these features across the day both when averaged across mice and in individual mice, but the epoch-by-epoch agreement is not as good. CONCLUSIONS There are subtle changes in the area and shape (i.e., aspect ratio) of the mouse as it transitions from NREM to REM, likely due to the atonia of REM, thus allowing our methodology to discriminate these two states. Although REM is relatively rare, our methodology can detect it and assess the amount of REM sleep.