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SummaryGlobal biodiversity is declining at rates faster than at any other point in human history. Experimental manipulations of biodiversity at small spatial scales have demonstrated that communities with fewer species consistently produce less biomass than higher diversity communities. However, understanding how the global extinction crisis is likely to impact global ecosystem functioning will require applying these local and largely experimental findings to natural systems at substantially larger spatial and temporal scales. Here we propose that we can use two simple macroecological patterns – the species area curve and the biomass-area curve – to upscale the species richness-biomass relationship. We demonstrate that at local spatial scales, each additional species will contribute more to biomass production with increasing area sampled because the species-area curve saturates and the biomass-area curve increases monotonically. We use species-area and biomass-area curves from a Minnesota grassland and a Panamanian tropical dry forest to examine the species richness – biomass relationship at three and ten sampling extents, respectively. In both datasets, the observed relationship between biodiversity and biomass production at every sampling extent was predicted from simple species-area and biomass-area relationships. These findings suggest that macroecological patterns like the species-area curve underpin the scaling of biodiversity-ecosystem functioning research and can be used to predict these relationships at the global scales where they are relevant for species loss.

Global biodiversity is declining at rates faster than at any other point in human history. Experimental manipulations at small spatial scales have demonstrated that communities with fewer species consistently produce less biomass than higher diversity communities. Understanding the consequences of the global extinction crisis for ecosystem functioning requires understanding how local experimental results are likely to change with increasing spatial and temporal scales and from experiments to naturally assembled systems. Scaling across time and space in a changing world requires baseline predictions. Here, we provide a graphical null model for area scaling of biodiversity–ecosystem functioning relationships using observed macroecological patterns: the species–area curve and the biomass–area curve. We use species–area and biomass–area curves to predict how species richness–biomass relationships are likely to change with increasing sampling extent. We then validate these predictions with data from two naturally assembled ecosystems: a Minnesota savanna and a Panamanian tropical dry forest. Our graphical null model predicts that biodiversity–ecosystem functioning relationships are scale-dependent. However, we note two important caveats. First, our results indicate an apparent contradiction between predictions based on measurements in biodiversity–ecosystem functioning experiments and from scaling theory. When ecosystem functioning is measured as per unit area (e.g. biomass per m2), as is common in biodiversity–ecosystem functioning experiments, the slope of the biodiversity ecosystem functioning relationship should decrease with increasing scale. Alternatively, when ecosystem functioning is not measured per unit area (e.g. summed total biomass), as is common in scaling studies, the slope of the biodiversity–ecosystem functioning relationship should increase with increasing spatial scale. Second, the underlying macroecological patterns of biodiversity experiments are predictably different from some naturally assembled systems. These differences between the underlying patterns of experiments and naturally assembled systems may enable us to better understand when patterns from biodiversity–ecosystem functioning experiments will be valid in naturally assembled systems. Synthesis. This paper provides a simple graphical null model that can be extended to any relationship between biodiversity and any ecosystem functioning across space or time. Furthermore, these predictions provide crucial insights into how and when we may be able to extend results from small-scale biodiversity experiments to naturally assembled regional and global ecosystems where biodiversity is changing.

The complexity of immune responses limits the usefulness of univariate methods in answering complex immunology questions. To demonstrate the utility of a multivariate approach, we employ such approach to compare T cells of African green monkeys (AGMs) and rhesus macaques (RMs). Among the most prominent distinguishing features we found were lower CD3 and higher CD28 surface expression in AGMs compared to RMs. After in vitro stimulation, a larger proportion of AGM T cells secreted cytokines, especially those producing more than one cytokine (i.e. multifunctional cells). To find out whether multifunctional responses associate with protection in other species, we compared T cells of cynomolgus macaques (CMs) infected with wild-type Simian Immunodeficiency Virus (SIV) to those of CMs infected (vaccinated) with a replication-defective virus. Wild-type SIV infection in macaques leads to simian Acquired Immunodeficiency Syndrome (AIDS), which does not happen in animals previously vaccinated with a replication-defective virus. Interestingly, after in vitro stimulation, multifunctional cells were more abundant among T cells of vaccinated CMs. Our results propose T-cell multifunctionality as a potentially useful marker of immunity, although additional verification is needed. Finally, we hope our multivariate model and its associated validation methods will inform future studies in the field of immunology.

(2006). Another Step Further… On a Problem of the 1988 IMO. Mathematics Magazine: Vol. 79, No. 1, pp. 45-53.

We consider the problem of finding the optimal, robust stabilization of linear systems within a family of nonlinear feedback laws. Investigation of the efficiency of full-state based and partial-state based so-called NPID feedback schemes proposed for the stabilization of systems in robotic applications has provided the motivation for our work. We prove that, for a given quadratic Lyapunov function and a given family of nonlinear feedback laws, there exist optimal piecewise linear feedbacks that make the generalized Lyapunov derivative of the closed-loop system minimal. The result provides improved stabilization over the nonlinear stabilizing feedback law proposed in Ref. 1 as demonstrated in simulations of the Sarcos Dextrous Manipulator.

A command and control (C/sup 2/) problem for military air operations is addressed. Specifically, we consider C/sup 2/ problems for air vehicles against ground-based targets and defensive systems. The problem is viewed as a stochastic game. We restrict our attention to the C/sup 2/ level where the problem may consist of a few unmanned combat air vehicles (UCAVs) or aircraft (or possibly teams of vehicles), less than say, a half-dozen enemy surface-to-air missile air defense units (SAMs), a few enemy assets (viewed as targets from our standpoint), and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some targets are mapped out and possible SAM sites that are unavoidably part of the situation are known. One may then employ a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged (if any), and by what series of air vehicle operations. We provide analysis, numerical implementation, and simulation for full state-feedback and measurement feedback control within this C/sup 2/ context. Sensitivity to parameter uncertainty is discussed. Some insight into the structure of optimal and near-optimal strategies for C/sup 2/ is obtained. The analysis is extended to the case of observations which may be affected by adversarial inputs. A heuristic based on risk-sensitive control is applied, and it is found that this produces improved results over more standard approaches.

Embryo transfer (ET) is the final component of the in vitro fertilization process, and the limiting component to its success rate. The procedure is characterized by considerable technical variations in clinical practice and the effects of these different variations on the overall outcome is little understood. In this article we simulate the embryo transfer procedure based on a 2-dimensional fluid dynamics model and, in a large computational effort, we investigate the sensitivity of embryo placement on an array of procedural parameters. The results support the consensus among practitioners in what is the best choice of procedural factors. Based on the study we propose a set of optimal parameters with which to perform the ET procedure; in addition we suggest a novel technique of volume replacement prior to the catheter withdrawal.

It is well known that the solvability of the regulator problem, for finite dimensional systems, is related to the system zeros, or in other words, to the system zero dynamics. We demonstrate the existence of the zero dynamics for a class of SISO distributed parameter systems and provide a result relating the eigenvalues of the zero dynamics and the system transmission zeros.

For certain single input single output (SISO) distributed parameter systems we provide a useful solvability criteria for the regulator problem in terms of the eigenvalues of the exo-system and the transmission zeros. Namely, we show that the regulator problem is solvable provided that the eigenvalues of the exo-system do not coincide with the systems' transmission zeros. One very appealing consequence of the proof of this result is that it also provides an easily implementable procedure for solving the regulator problem.

In this paper we state our recent solvability result for the state feedback regulator problem for distributed parameter systems and present two examples in set point control using this methodology for a one dimensional heat equation. In addition, we discuss some computational issues associated with the explicit implementation of the feedback design strategies.

The Command and Control (C2) problem for Military Air Operations is addressed. The problem is viewed as a stochastic game. Due to the large size of the problem, several techniques are used to decompose the problem into manageable pieces. At the outermost level, hierarchical techniques are used to solve progressively larger problems where the distributions of outcomes at one level become the dynamics of the problem at the next higher level. At the lowest level, the problem may consist of a few aircraft (or possibly packages), less than say a half-dozen, enemy SAMs, a few enemy assets (viewed as targets from our standpoint), and some enemy decoys (assumed to mimic SAM radar signatures). At this low level, some minimal cost (to our aircraft) routes to the eventual targets are mapped out, and these are used to determine SAM sites (possibly decoys) that are unavoidable. One then employs a discrete stochastic game problem formulation to determine which of these SAMs should optimally be engaged, and by what series of aircraft operations. Since this in a game model, the optimal opponent strategy is also determined. The problem of imperfect information is addressed. The technique also allows the evaluation of various approaches in terms of expected cost and the variance of cost. One may plot these as functions of various parameters to determine when the situation is at a point where the optimal strategies may jump out suddenly.