Goodness of Fit of Discriminant Functions from the Vector Space of Fixed Variates

Alternative proofs of some of KSHIRSAGAR's (1971) results on testing discriminant functions or canonical variables in the vector space of fixed variates are given. These results are derived in terms of the original variates unlike KSHIRSAGAR (1971) who derives the results by using random orthogonal transformations and triangular decompositions of the original matrix variates.     

Hierarchical Bayesian modeling of random and residual variance–covariance matrices in bivariate mixed effects models

Bivariate mixed effects models are often used to jointly infer upon covariance matrices for both random effects ( u ) and residuals ( e ) between two different phenotypes in order to investigate the architecture of their relationship. However, these (co)variances themselves may additionally depend upon covariates as well as additional sets of exchangeable random effects that facilitate borrowing of strength across a large number of clusters. We propose a hierarchical Bayesian extension of the classical bivariate mixed effects model by embedding additional levels of mixed effects modeling of reparameterizations of u‐ level and e ‐level (co)variances between two traits. These parameters are based upon a recently popularized square‐root‐free Cholesky decomposition and are readily interpretable, each conveniently facilitating a generalized linear model characterization. Using Markov Chain Monte Carlo methods, we validate our model based on a simulation study and apply it to a joint analysis of milk yield and calving interval phenotypes in Michigan dairy cows. This analysis indicates that the e ‐level relationship between the two traits is highly heterogeneous across herds and depends upon systematic herd management factors.     

Microbial carbon limitation: The need for integrating microorganisms into our understanding of ecosystem carbon cycling

Numerous studies have demonstrated that fertilization with nutrients such as nitrogen, phosphorus, and potassium increases plant productivity in both natural and managed ecosystems, demonstrating that primary productivity is nutrient limited in most terrestrial ecosystems. In contrast, it has been demonstrated that heterotrophic microbial communities in soil are primarily limited by organic carbon or energy. While this concept of contrasting limitations, that is, microbial carbon and plant nutrient limitation, is based on strong evidence that we review in this paper, it is often ignored in discussions of ecosystem response to global environment changes. The plant‐centric perspective has equated plant nutrient limitations with those of whole ecosystems, thereby ignoring the important role of the heterotrophs responsible for soil decomposition in driving ecosystem carbon storage. To truly integrate carbon and nutrient cycles in ecosystem science, we must account for the fact that while plant productivity may be nutrient limited, the secondary productivity by heterotrophic communities is inherently carbon limited. Ecosystem carbon cycling integrates the independent physiological responses of its individual components, as well as tightly coupled exchanges between autotrophs and heterotrophs. To the extent that the interacting autotrophic and heterotrophic processes are controlled by organisms that are limited by nutrient versus carbon accessibility, respectively, we propose that ecosystems by definition cannot be ‘limited’ by nutrients or carbon alone. Here, we outline how models aimed at predicting non‐steady state ecosystem responses over time can benefit from dissecting ecosystems into the organismal components and their inherent limitations to better represent plant–microbe interactions in coupled carbon and nutrient models.     

Modeling of dynamical systems through deep learning

This review presents a modern perspective on dynamical systems in the context of current goals and open challenges. In particular, our review focuses on the key challenges of discovering dynamics from data and finding data-driven representations that make nonlinear systems amenable to linear analysis. We explore various challenges in modern dynamical systems, along with emerging techniques in data science and machine learning to tackle them. The two chief challenges are (1) nonlinear dynamics and (2) unknown or partially known dynamics. Machine learning is providing new and powerful techniques for both challenges. Dimensionality reduction methods are used for projecting dynamical methods in reduced form, and these methods perform computational efficiency on real-world data. Data-driven models drive to discover the governing equations and give laws of physics. The identification of dynamical systems through deep learning techniques succeeds in inferring physical systems. Machine learning provides advanced new and powerful algorithms for nonlinear dynamics. Advanced deep learning methods like autoencoders, recurrent neural networks, convolutional neural networks, and reinforcement learning are used in modeling of dynamical systems.     

Meiofauna promotes litter decomposition in stream ecosystems depending on leaf species

Litter decomposition, a fundamental process of nutrient cycling and energy flow in freshwater ecosystems, is driven by a diverse array of decomposers. As an important component of the heterotrophic food web, meiofauna can provide a trophic link between leaf‐associated microbes (i.e., bacteria and fungi)/plant detritus and macroinvertebrates, though their contribution to litter decomposition is not well understood. To investigate the role of different decomposer communities in litter decomposition, especially meiofauna, we compared the litter decomposition of three leaf species with different lignin to nitrogen ratios in litter bags with different mesh sizes (0.05, 0.25, and 2 mm) in a forested stream, in China for 78 days. The meiofauna significantly enhanced the decomposition of leaves of high‐and medium‐ quality, while decreasing (negative effect) or increasing (positive effect) the fungal biomass and diversity. Macrofauna and meiofauna together contributed to the decomposition of low‐quality leaf species. The presence of meiofauna and macrofauna triggered different aspects of the microbial community, with their effects on litter decomposition varying as a function of leaf quality. This study reveals that the meiofauna increased the trophic complexity and modulated their interactions with microbes, highlighting the important yet underestimated role of meiofauna in detritus‐based ecosystems.     

Mass loss and nutrient release during the decomposition of sixteen types of plant litter with contrasting quality under three precipitation regimes

Mass loss and nutrient release during litter decomposition drive biogeochemical cycling in terrestrial ecosystems. However, the relationship between the litter decomposition process and the decomposition stage, precipitation, and litter quality has rarely been addressed, precluding our understanding of how litter decomposition regulates nutrient cycling in various ecosystems and their responses to climate change. In this study, we measured mass loss as well as carbon and nutrient releases during the decomposition of 16 types of leaf litter under three precipitation treatments over 12 months in a common garden experiment (i.e., using standardized soil and climatic conditions). Sixteen types of leaves were divided into three functional groups (evergreen, deciduous, and herbaceous). The objectives were to understand the effects of decomposition stages and precipitation regimes on litter decomposition and to examine the relationship between this effect and chemical properties. The mass loss and release of nitrogen and potassium were significantly higher in the 6‐ to 12‐month stage of decomposition (high temperature and humidity) than in the 0‐ to 6‐month stage. Phosphorus was relatively enriched in evergreen leaves after 6 months of decomposition. The rates of mass loss and nutrient release were significantly greater in herbaceous than in deciduous and evergreen leaves. Increasing precipitation from 400 to 800 mm accelerated mass loss and potassium release but decreased phosphorus release in the 0‐ to 6‐month stage of decomposition. These results highlighted the contribution to and complexity of litter chemical properties in litter decomposition.     

Empirical Mode Decomposition and Wavelet Transform Based ECG Data Compression Scheme

ObjectiveIn health-care systems, compression is an essential tool to solve the storage and transmission problems. In this regard, this paper reports a new electrocardiogram (ECG) data compression scheme which employs sifting function based empirical mode decomposition (EMD) and discrete wavelet transform.MethodEMD based on sifting function is utilized to get the first intrinsic mode function (IMF). After EMD, the first IMF and four significant sifting functions are combined together. This combination is free from many irrelevant components of the signal. Discrete wavelet transform (DWT) with mother wavelet ‘bior4.4’ is applied to this combination. The transform coefficients obtained after DWT are passed through dead-zone quantization. It discards small transform coefficients lying around zero. Further, integer conversion of coefficients and run-length encoding are utilized to achieve a compressed form of ECG data.ResultsCompression performance of the proposed scheme is evaluated using 48 ECG records of the MIT-BIH arrhythmia database. In the comparison of compression results, it is observed that the proposed method exhibits better performance than many recent ECG compressors. A mean opinion score test is also conducted to evaluate the true quality of the reconstructed ECG signals.ConclusionThe proposed scheme offers better compression performance with preserving the key features of the signal very well.     

Effect of environmental conditions on decomposition in eight woody species of a dry tropical forest

Litter decay is a significant part of carbon budget. Due to strong environmental control, the changes in the environment may drastically influence the litter decay rates. Litter decomposition of eight dry tropical woody species, viz. Shorea robusta, Buchanania lanzan, Diospyros melanoxylon, Lagerstroemia parviflora, Lannea coromandelica, Terminalia tomentosa, Holarrhena antidysenterica and Lantana camara was studied to document the effect of intra-annual changes in the environment. Litter decomposition was monitored at monthly intervals at five sites using litter bag technique over an annual cycle in a dry tropical deciduous forest of Vindhyan highland, India. Weight loss differed among species and through months, and ranged from 15.38% in L. camara at Kotwa site in January to 30.72% in T. tomentosa at Hathinala site in August. Peak weight loss occurred in August and averaged 46.2% across species and sites. Nitrogen and phosphorus mineralization rates also varied significantly from species to species. T. tomentosa having higher nitrogen content and lower C/N ratio than other species exhibited faster weight loss. Nitrogen and phosphorus contents of litter showed significant positive correlation with weight loss. C/N ratio was negatively related to decay constant, and the weight loss was positively related to the soil surface temperature as well as soil moisture content.     

Vegetation feedbacks of nutrient addition lead to a weaker carbon sink in an ombrotrophic bog

To study vegetation feedbacks of nutrient addition on carbon sequestration capacity, we investigated vegetation and ecosystem CO₂ exchange at Mer Bleue Bog, Canada in plots that had been fertilized with nitrogen (N) or with N plus phosphorus (P) and potassium (K) for 7–12 years. Gross photosynthesis, ecosystem respiration, and net CO₂ exchange were measured weekly during May–September 2011 using climate‐controlled chambers. A substrate‐induced respiration technique was used to determine the functional ability of the microbial community. The highest N and NPK additions were associated with 40% less net CO₂ uptake than the control. In the NPK additions, a diminished C sink potential was due to a 20–30% increase in ecosystem respiration, while gross photosynthesis rates did not change as greater vascular plant biomass compensated for the decrease in Sphagnum mosses. In the highest N‐only treatment, small reductions in gross photosynthesis and no change in ecosystem respiration led to the reduced C sink. Substrate‐induced microbial respiration was significantly higher in all levels of NPK additions compared with control. The temperature sensitivity of respiration in the plots was lower with increasing cumulative N load, suggesting more labile sources of respired CO₂. The weaker C sink potential could be explained by changes in nutrient availability, higher woody : foliar ratio, moss loss, and enhanced decomposition. Stronger responses to NPK fertilization than to N‐only fertilization for both shrub biomass production and decomposition suggest that the bog ecosystem is N‐P/K colimited rather than N‐limited. Negative effects of further N‐only deposition were indicated by delayed spring CO₂ uptake. In contrast to forests, increased wood formation and surface litter accumulation in bogs seem to reduce the C sink potential owing to the loss of peat‐forming Sphagnum.