Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. In this paper, we develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMM's) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMM's are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMM's to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMM's, we develop novel algorithms for signal denoising, classification, and detection. Index Terms-Hidden Markov model, probabilistic graph, wavelets. 1053-587X/98$10.00 © 1998 IEEE Matthew S. Crouse (S'93) received the B.S.E.E. degree (magna cum laude) from Rice University, Houston, TX, in 1993. He received the M.S.E.E. degree from University of Illinois, Urbana, in 1995 and is presently a Ph.D. student in electrical and computer engineering at Rice University. His research interests include wavelets, fractals, and statistical signal and image processing. Robert D. Nowak (M'95) received the B.S. (with highest distinction), M.S., and Ph.D. degrees in electrical engineering from the University

In this paper, we develop a new multiscale modeling framework for characterizing positive-valued data with longrange-dependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing Npoint data sets. We study both the second-order and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variance-time plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.

Abstract-Many studies have indicated the importance of capturing scaling properties when modeling traffic loads; however, the influence of long-range dependence (LRD) and marginal statistics still remains on unsure footing. In this paper, we study these two issues by introducing a multiscale traffic model and a novel multiscale approach to queuing analysis. The multifractal wavelet model (MWM) is a multiplicative, wavelet-based model that captures the positivity, LRD, and "spikiness" of non-Gaussian traffic. Using a binary tree, the model synthesizes an N-point data set with only 0 (N) computations.Leveraging the tree structure of the model, we derive a multiscale queuing analysis that provides a simple closed form approximation to the tail queue probability, valid for any given buffer size. The analysis is applicable. not only to the MWM but to tree-based models in general, including fractional Gaussian noise. Simulated queuing experiments demonstrate the accuracy of the MWM for matching real data traces and the precision of our theoretical queuing formula. Thus, the MWM is useful not only for fast synthesis of data for simulation purposes but also for applications requiring accurate queuing formulas such as call admission control. Our results clearly indicate that the marginal distribution of traffic at different time-resolutions affects queuing and that a Gaussian assumption can lead to over-optimistic predictions of tail queue probability even when taking LRD into account.

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The focus of this review is maternal nutrition during the periconceptual period and offspring developmental outcomes in beef cattle, with an emphasis on the first 50 d of gestation, which represents the embryonic period. Animal agriculture in general, and specifically the beef cattle industry, currently faces immense challenges. The world needs to significantly increase its output of animal food products by 2050 and beyond to meet the food security and agricultural sustainability needs of the rapidly growing human population. Consequently, efficient and sustainable approaches to livestock production are essential. Maternal nutritional status is a major factor that leads to developmental programming of offspring outcomes. Developmental programming refers to the influence of pre-and postnatal factors, such as inappropriate maternal nutrition, that affect growth and development and result in long-term consequences for health and productivity of the offspring. In this review, we discuss recent studies in which we and others have addressed the questions, “Is development programmed periconceptually?” and, if so, “Does it matter practically to the offspring in production settings?” The reviewed studies have demonstrated that the periconceptual period is important not only for pregnancy establishment but also may be a critical period during which fetal, placental, and potentially postnatal development and function are programmed. The evidence for fetal and placental programming during the periconceptual period is strong and implies that research efforts to mitigate the negative and foster the positive benefits of developmental programming need to include robust investigative efforts during the periconceptual period to better understand the implications for life-long health and productivity.

Abstract We hypothesized that a moderate maternal nutrient restriction during the first 50 d of gestation in beef heifers would affect transcript abundance of genes associated with tissue metabolism, accretion, and function in fetal liver, muscle, and cerebrum. Angus-cross heifers were estrus synchronized and assigned at breeding to one of two dietary treatments (CON- 100% of nutrient requirements to gain 0.45 kg/d; RES- 60% of CON). At day 50 of gestation, 14 heifers were ovariohysterectomized, and fetal liver, muscle, and cerebrum were collected. Transcriptome analysis via RNA-seq was conducted on the Illumina HiSeq 2500 platform using 50-bp paired-end reads at a depth of 2 × 10.4M reads/sample. Bioinformatic analysis was performed using the Tuxedo Suite and ontological analysis with DAVID 6.8. For fetal liver, muscle, and cerebrum, a total of 548, 317, and 151 genes, respectively (P < 0.01) were differentially expressed, of which 201, 144, and 28 genes, respectively were false discovery rate protected (FDR; q < 0.10). Differentially expressed genes were screened for fit into functional categories of pathways or ontologies associated with known impacts on tissue metabolism, accretion, and function. In fetal liver, five functional categories of interest (n = 125 genes) were affected by nutritional treatment: metabolic pathways, protein kinase, nucleosome core, mRNA splicing, and complement/coagulation cascades, of which 105 genes were upregulated in RES. In fetal muscle, three functional categories of interest (n = 106 genes) were affected by nutritional treatment: skeletal muscle, embryogenesis, and signaling cascades, of which 64 genes were upregulated in RES. In fetal cerebrum, three functional categories of interest (n = 60 genes) were affected by nutritional treatment: hippocampus and neurogenesis, metal-binding, and cytoskeleton, of which 58 genes were upregulated in RES. These results demonstrate that a moderate maternal nutrient restriction during the first 50 d of gestation in beef heifers alters transcript abundance of genes potentially impacting tissue metabolism, accretion, and function in fetal liver, muscle, and cerebrum. Furthermore, these results indicate that affected categories are tissue-specific and moderate maternal nutrient restriction generally increases expression of genes in fetuses from RES fed dams. Finally, these data lay the foundation upon which further research that identifies phenotypic responses to changes in these pathways may be elucidated.

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