Typical delay determines waiting time on periodic-food schedules: Static and dynamic tests.

Pigeons and other animals soon learn to wait (pause) after food delivery on periodic-food schedules before resuming the food-rewarded response. Under most conditions the steady-state duration of the average waiting time, t, is a linear function of the typical interfood interval. We describe three experiments designed to explore the limits of this process. In all experiments, t was associated with one key color and the subsequent food delay, T, with another. In the first experiment, we compared the relation between t (waiting time) and T (food delay) under two conditions: when T was held constant, and when T was an inverse function of t. The pigeons could maximize the rate of food delivery under the first condition by setting t to a consistently short value; optimal behavior under the second condition required a linear relation with unit slope between t and T. Despite this difference in optimal policy, the pigeons in both cases showed the same linear relation, with slope less than one, between t and T. This result was confirmed in a second parametric experiment that added a third condition, in which T + t was held constant. Linear waiting appears to be an obligatory rule for pigeons. In a third experiment we arranged for a multiplicative relation between t and T (positive feedback), and produced either very short or very long waiting times as predicted by a quasi-dynamic model in which waiting time is strongly determined by the just-preceding food delay.

We Are the Ones We Have Been Waiting for: Pan-African Consciousness Raising and Organizing in the United States and Venezuela

We Are the Ones We Have Been Waiting for: Pan-African Consciousness Raising and Organizing in the United States and Venezuela, draws on fifteen months of field research accompanying organizers, participating in protests, planning/strategy meetings, state-run programs, academic conferences and everyday life in these two countries. Through comparative examination of the processes by which African Diaspora youth become radically politicized, this work deconstructs tendencies to deify political s/heroes of eras past by historicizing their ascent to political acclaim and centering the narratives of present youth leading movements for Black/African liberation across the Diaspora. I employ Manuel Callahan’s description of “encuentros”, “the disruption of despotic democracy and related white middle-class hegemony through the reconstruction of the collective subject”; “dialogue, insurgent learning, and convivial research that allows for a collective analysis and vision to emerge while affirming local struggles” to theorize the moments of encounter, specifically, the moments (in which) Black/African youth find themselves becoming politically radicalized and by what. I examine the ways in which Black/African youth organizing differs when responding to their perpetual victimization by neoliberal, genocidal state-politics in the US, and a Venezuelan state that has charged itself with the responsibility of radically improving the quality of life of all its citizens. Through comparative analysis, I suggest the vertical structures of “representative democracy” dominating the U.S. political climate remain unyielding to critical analyses of social stratification based on race, gender, and class as articulated by Black youth. Conversely, I contend that present Venezuelan attempts to construct and fortify more horizontal structures of “popular democracy” under what Hugo Chavez termed 21st Century Socialism, have resulted in social fissures, allowing for a more dynamic and hopeful negation between Afro-Venezuelan youth and the state.

An energy-efficient data delivery scheme for delay-sensitive traffic in wireless sensor networks

We propose a novel data-delivery method for delay-sensitive traffic that significantly reduces the energy consumption in wireless sensor networks without reducing the number of packets that meet end-to-end real-time deadlines. The proposed method, referred to as SensiQoS, leverages the spatial and temporal correlation between the data generated by events in a sensor network and realizes energy savings through application-specific in-network aggregation of the data. SensiQoS maximizes energy savings by adaptively waiting for packets from upstream nodes to perform in-network processing without missing the real-time deadline for the data packets. SensiQoS is a distributed packet scheduling scheme, where nodes make localized decisions on when to schedule a packet for transmission to meet its end-to-end real-time deadline and to which neighbor they should forward the packet to save energy. We also present a localized algorithm for nodes to adapt to network traffic to maximize energy savings in the network. Simulation results show that SensiQoS improves the energy savings in sensor networks where events are sensed by multiple nodes, and spatial and/or temporal correlation exists among the data packets. Energy savings due to SensiQoS increase with increase in the density of the sensor nodes and the size of the sensed events. © 2010 Harshavardhan Sabbineni and Krishnendu Chakrabarty.

Spike avalanches exhibit universal dynamics across the sleep-wake cycle.

BACKGROUND: Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and extinction. In theory, criticality provides many desirable features for the behaving brain, optimizing computational capabilities, information transmission, sensitivity to sensory stimuli and size of memory repertoires. However, a thorough characterization of neuronal avalanches in freely-behaving (FB) animals is still missing, thus raising doubts about their relevance for brain function. METHODOLOGY/PRINCIPAL FINDINGS: To address this issue, we employed chronically implanted multielectrode arrays (MEA) to record avalanches of action potentials (spikes) from the cerebral cortex and hippocampus of 14 rats, as they spontaneously traversed the wake-sleep cycle, explored novel objects or were subjected to anesthesia (AN). We then modeled spike avalanches to evaluate the impact of sparse MEA sampling on their statistics. We found that the size distribution of spike avalanches are well fit by lognormal distributions in FB animals, and by truncated power laws in the AN group. FB data surrogation markedly decreases the tail of the distribution, i.e. spike shuffling destroys the largest avalanches. The FB data are also characterized by multiple key features compatible with criticality in the temporal domain, such as 1/f spectra and long-term correlations as measured by detrended fluctuation analysis. These signatures are very stable across waking, slow-wave sleep and rapid-eye-movement sleep, but collapse during anesthesia. Likewise, waiting time distributions obey a single scaling function during all natural behavioral states, but not during anesthesia. Results are equivalent for neuronal ensembles recorded from visual and tactile areas of the cerebral cortex, as well as the hippocampus. CONCLUSIONS/SIGNIFICANCE: Altogether, the data provide a comprehensive link between behavior and brain criticality, revealing a unique scale-invariant regime of spike avalanches across all major behaviors.

The protective role of religious coping in adolescents' responses to poverty and sexual decision-making in rural Kenya.

In this study, we explored how adolescents in rural Kenya apply religious coping in sexual decision-making in the context of high rates of poverty and Human Immunodeficiency Virus (HIV). Semi-structured interviews were conducted with 34 adolescents. One-third (13) reported religious coping related to economic stress, HIV, or sexual decision-making; the majority (29) reported religious coping with these or other stressors. Adolescents reported praying for God to partner with them to engage in positive behaviors, praying for strength to resist unwanted behaviors, and passive strategies characterized by waiting for God to provide resources or protection from HIV. Adolescents in Sub-Saharan Africa may benefit from HIV prevention interventions that integrate and build upon their use of religious coping.

Bayesian Inference in Large-scale Problems

Many modern applications fall into the category of "large-scale" statistical problems, in which both the number of observations n and the number of features or parameters p may be large. Many existing methods focus on point estimation, despite the continued relevance of uncertainty quantification in the sciences, where the number of parameters to estimate often exceeds the sample size, despite huge increases in the value of n typically seen in many fields. Thus, the tendency in some areas of industry to dispense with traditional statistical analysis on the basis that "n=all" is of little relevance outside of certain narrow applications. The main result of the Big Data revolution in most fields has instead been to make computation much harder without reducing the importance of uncertainty quantification. Bayesian methods excel at uncertainty quantification, but often scale poorly relative to alternatives. This conflict between the statistical advantages of Bayesian procedures and their substantial computational disadvantages is perhaps the greatest challenge facing modern Bayesian statistics, and is the primary motivation for the work presented here.

Two general strategies for scaling Bayesian inference are considered. The first is the development of methods that lend themselves to faster computation, and the second is design and characterization of computational algorithms that scale better in n or p. In the first instance, the focus is on joint inference outside of the standard problem of multivariate continuous data that has been a major focus of previous theoretical work in this area. In the second area, we pursue strategies for improving the speed of Markov chain Monte Carlo algorithms, and characterizing their performance in large-scale settings. Throughout, the focus is on rigorous theoretical evaluation combined with empirical demonstrations of performance and concordance with the theory.

One topic we consider is modeling the joint distribution of multivariate categorical data, often summarized in a contingency table. Contingency table analysis routinely relies on log-linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a reduced rank tensor factorization of the probability mass function for multivariate categorical data, while log-linear models achieve dimensionality reduction through sparsity. Little is known about the relationship between these notions of dimensionality reduction in the two paradigms. In Chapter 2, we derive several results relating the support of a log-linear model to nonnegative ranks of the associated probability tensor. Motivated by these findings, we propose a new collapsed Tucker class of tensor decompositions, which bridge existing PARAFAC and Tucker decompositions, providing a more flexible framework for parsimoniously characterizing multivariate categorical data. Taking a Bayesian approach to inference, we illustrate empirical advantages of the new decompositions.

Latent class models for the joint distribution of multivariate categorical, such as the PARAFAC decomposition, data play an important role in the analysis of population structure. In this context, the number of latent classes is interpreted as the number of genetically distinct subpopulations of an organism, an important factor in the analysis of evolutionary processes and conservation status. Existing methods focus on point estimates of the number of subpopulations, and lack robust uncertainty quantification. Moreover, whether the number of latent classes in these models is even an identified parameter is an open question. In Chapter 3, we show that when the model is properly specified, the correct number of subpopulations can be recovered almost surely. We then propose an alternative method for estimating the number of latent subpopulations that provides good quantification of uncertainty, and provide a simple procedure for verifying that the proposed method is consistent for the number of subpopulations. The performance of the model in estimating the number of subpopulations and other common population structure inference problems is assessed in simulations and a real data application.

In contingency table analysis, sparse data is frequently encountered for even modest numbers of variables, resulting in non-existence of maximum likelihood estimates. A common solution is to obtain regularized estimates of the parameters of a log-linear model. Bayesian methods provide a coherent approach to regularization, but are often computationally intensive. Conjugate priors ease computational demands, but the conjugate Diaconis--Ylvisaker priors for the parameters of log-linear models do not give rise to closed form credible regions, complicating posterior inference. In Chapter 4 we derive the optimal Gaussian approximation to the posterior for log-linear models with Diaconis--Ylvisaker priors, and provide convergence rate and finite-sample bounds for the Kullback-Leibler divergence between the exact posterior and the optimal Gaussian approximation. We demonstrate empirically in simulations and a real data application that the approximation is highly accurate, even in relatively small samples. The proposed approximation provides a computationally scalable and principled approach to regularized estimation and approximate Bayesian inference for log-linear models.

Another challenging and somewhat non-standard joint modeling problem is inference on tail dependence in stochastic processes. In applications where extreme dependence is of interest, data are almost always time-indexed. Existing methods for inference and modeling in this setting often cluster extreme events or choose window sizes with the goal of preserving temporal information. In Chapter 5, we propose an alternative paradigm for inference on tail dependence in stochastic processes with arbitrary temporal dependence structure in the extremes, based on the idea that the information on strength of tail dependence and the temporal structure in this dependence are both encoded in waiting times between exceedances of high thresholds. We construct a class of time-indexed stochastic processes with tail dependence obtained by endowing the support points in de Haan's spectral representation of max-stable processes with velocities and lifetimes. We extend Smith's model to these max-stable velocity processes and obtain the distribution of waiting times between extreme events at multiple locations. Motivated by this result, a new definition of tail dependence is proposed that is a function of the distribution of waiting times between threshold exceedances, and an inferential framework is constructed for estimating the strength of extremal dependence and quantifying uncertainty in this paradigm. The method is applied to climatological, financial, and electrophysiology data.

The remainder of this thesis focuses on posterior computation by Markov chain Monte Carlo. The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It has long been common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention has been paid to convergence and estimation error in these approximating Markov Chains. In Chapter 6, we propose a framework for assessing when to use approximations in MCMC algorithms, and how much error in the transition kernel should be tolerated to obtain optimal estimation performance with respect to a specified loss function and computational budget. The results require only ergodicity of the exact kernel and control of the kernel approximation accuracy. The theoretical framework is applied to approximations based on random subsets of data, low-rank approximations of Gaussian processes, and a novel approximating Markov chain for discrete mixture models.

Data augmentation Gibbs samplers are arguably the most popular class of algorithm for approximately sampling from the posterior distribution for the parameters of generalized linear models. The truncated Normal and Polya-Gamma data augmentation samplers are standard examples for probit and logit links, respectively. Motivated by an important problem in quantitative advertising, in Chapter 7 we consider the application of these algorithms to modeling rare events. We show that when the sample size is large but the observed number of successes is small, these data augmentation samplers mix very slowly, with a spectral gap that converges to zero at a rate at least proportional to the reciprocal of the square root of the sample size up to a log factor. In simulation studies, moderate sample sizes result in high autocorrelations and small effective sample sizes. Similar empirical results are observed for related data augmentation samplers for multinomial logit and probit models. When applied to a real quantitative advertising dataset, the data augmentation samplers mix very poorly. Conversely, Hamiltonian Monte Carlo and a type of independence chain Metropolis algorithm show good mixing on the same dataset.

Mothers but not wives: The increasing lag between nonmarital births and marriage

This study analyzed trends in marital behavior for unwed mothers who gave birth between 1960 and 2004. With nationally representative data on 15,353 White and Black unmarried mothers, results indicated that mothers who gave birth after 1989 were waiting much longer to marry than were mothers giving birth before 1968. The most pronounced delays were found immediately after a birth. Over the study period, the cumulative proportion of women who married within three years of a birth decreased for Whites by 27% and for Blacks by 60%. Findings underscore the separation that has developed between first births and first marriages in the United States, and they highlight the older ages at which children are experiencing a transition to marriage. © National Council on Family Relations, 2011.