We develop general theory for finding locally optimal designs in a class of single-covariate models under any differentiable optimality criterion. Yang and Stufken [Ann. Statist. 40 (2012) 1665–1681] and Dette and Schorning [Ann. Statist. 41 (2013) 1260–1267] gave complete class results for optimal designs under such models. Based on their results, saturated optimal designs exist; however, how to find such designs has not been addressed. We develop tools to find saturated optimal designs, and also prove their uniqueness under mild conditions.

This essay examines my work as expert witness in the case of U.S. v. Michigan, a Indigenous use-rights case. I was charged with parsing the intention of a specific article of the 1836 Treaty of Washington compelling land cession by Anishinaabe peoples and with writing a history of land use in the area from that date to the present for the Chippewa Ottawa Resource Authority (my employer). The challenges were not only methodological (how do you estimate use from ownership?) and epistemological (what constitutes proof that will satisfy both historians and lawyers?), but also sociological and psychological: what happens when an associate professor puts her progress toward full professor on hold for the sake of a court case?

Cancer cell invasion is a major component of metastasis and is responsible for extensive cell diffusion into and major destruction of tissues. Cells exhibit complex invasion modes, including a variety of collective behaviors. This phenomenon results in the structural heterogeneity of the extracellular matrix (ECM) in tissues. Here, we systematically investigated the environmental heterogeneity facilitating tumor cell invasion via a combination of in vitro cell migration experiments and computer simulations. Specifically, we constructed an ECM microenvironment in a microfabricated biochip and successfully created a three-dimensional (3D) funnel-like matrigel interface inside. Scanning electron microscopy demonstrated that the interface was at the interior defects of the nano-scale molecular anisotropic orientation and the localized structural density variations in the matrigel. Our results, particularly the correlation of the collective migration pattern with the geometric features of the funnel-like interface, indicate that this heterogeneous in vitro ECM structure strongly guides and promotes aggressive cell invasion in the rigid matrigel space. A cellular automaton model was proposed based on our experimental observations, and the associated quantitative analysis indicated that cell invasion was initiated and controlled by several mechanisms, including microenvironment heterogeneity, long-range cell-cell homotype and gradient-driven directional cellular migration. Our work shows the feasibility of constructing a complex and heterogeneous in vitro 3D ECM microenvironment that mimics the in vivo environment. Moreover, our results indicate that ECM heterogeneity is essential in controlling collective cell invasive behaviors and therefore determining metastasis efficiency.

We study the problem of controlling multiple 2-D directional sensors while maximizing an objective function based on the information gain corresponding to multiple target locations. We assume a joint prior Gaussian distribution for the target locations. A sensor generates a (noisy) measurement of a target only if the target lies within the field-of-view of the sensor, where the statistical properties of the measurement error depend on the location of the target with respect to the sensor and direction of the sensor. The measurements from the sensors are fused to form global estimates of target locations. This problem is combinatorial in nature-the computation time increases exponentially with the number of sensors. We develop heuristic methods to solve the problem approximately, and provide analytical results on performance guarantees. We then improve the performance of our heuristic approaches by applying an approximate dynamic programming approach called rollout. In addition, we address a variant of the above problem, where the goal is to map the sensors to the targets while maximizing the abovementioned objective function. This mapping problem also turns out to be combinatorial in nature, so we extend one of the above heuristics to solve this mapping problem approximately. We compare the performance of these heuristic approaches analytically and empirically.

We demonstrate transverse-magnetic (TM) dominant deep-ultraviolet (DUV) stimulated emission from photo-pumped AlGaN multiple-quantum-well lasers grown pseudomorphically on an AlN/sapphire template by means of photoluminescence at room temperature. The TM-dominant stimulated emission was observed at wavelengths of 239, 242, and 243 nm with low thresholds of 280, 250, and 290 kW/cm[superscript 2], respectively. In particular, the lasing wavelength of 239 nm is shorter compared to other reports for AlGaN lasers grown on foreign substrates including sapphire and SiC. The peak wavelength difference between the transverse-electric (TE)-polarized emission and TM-polarized emission was approximately zero for the lasers in this study, indicating the crossover of crystal-field split-off hole and heavy-hole valence bands. The rapid variation of polarization between TE- and TM-dominance versus the change in lasing wavelength from 243 to 249 nm can be attributed to a dramatic change in the TE-to-TM gain coefficient ratio for the sapphire-based DUV lasers in the vicinity of TE-TM switch.

This work presents a new mathematical model for the domestic transmission of Chagas disease, a parasitic disease affecting humans and other mammals throughout Central and South America. The model takes into account congenital transmission in both humans and domestic mammals as well as oral transmission in domestic mammals. The model has time-dependent coefficients to account for seasonality and consists of four nonlinear differential equations, one of which has a delay, for the populations of vectors, infected vectors, infected humans, and infected mammals in the domestic setting. Computer simulations show that congenital transmission has a modest effect on infection while oral transmission in domestic mammals substantially contributes to the spread of the disease. In particular, oral transmission provides an alternative to vector biting as an infection route for the domestic mammals, who are key to the infection cycle. This may lead to high infection rates in domestic mammals even when the vectors have a low preference for biting them, and ultimately results in high infection levels in humans.

In vitro rearing is an important and useful tool for honey bee (Apis mellifera L.) studies. However, it often results in intercastes between queens and workers, which are normally are not seen in hive-reared bees, except when larvae older than three days are grafted for queen rearing. Morphological classification (queen versus worker or intercastes) of bees produced by this method can be subjective and generally depends on size differences. Here, we propose an alternative method for caste classification of female honey bees reared in vitro, based on weight at emergence, ovariole number, spermatheca size and size and shape, and features of the head, mandible and basitarsus. Morphological measurements were made with both traditional morphometric and geometric morphometrics techniques. The classifications were performed by principal component analysis, using naturally developed queens and workers as controls. First, the analysis included all the characters. Subsequently, a new analysis was made without the information about ovariole number and spermatheca size. Geometric morphometrics was less dependent on ovariole number and spermatheca information for caste and intercaste identification. This is useful, since acquiring information concerning these reproductive structures requires time-consuming dissection and they are not accessible when abdomens have been removed for molecular assays or in dried specimens. Additionally, geometric morphometrics divided intercastes into more discrete phenotype subsets. We conclude that morphometric geometrics are superior to traditional morphometrics techniques for identification and classification of honey bee castes and intermediates.

The microtubule (MT) “plus end” constitutes the platform for the accumulation of a structurally and functionally diverse group of proteins, collectively called “MT plus-end tracking proteins” (+TIPs). +TIPs control MT dynamics and link MTs to diverse sub-cellular structures. Neurospora crassa MicroTubule Binding protein-3 (MTB-3) is the homolog of yeast EB1, a highly conserved +TIP. To address the function of MTB-3, we examined strains with mtb-3 deletions, and we tagged MTB-3 with GFP to assess its dynamic behavior. MTB-3-GFP was present as comet-like structures distributed more or less homogeneously within the hyphal cytoplasm, and moving mainly towards the apex at speeds up to 4× faster than the normal hyphal elongation rates. MTB-3-GFP comets were present in all developmental stages, but were most abundant in mature hyphae. MTB-3-GFP comets were observed moving in anterograde and retrograde direction along the hypha. Retrograde movement was also observed as originating from the apical dome. The integrity of the microtubular cytoskeleton affects the presence and dynamics of MTB-3-GFP comets, while actin does not seem to play a role. The size of MTB-3-GFP comets is affected by the absence of dynactin and conventional kinesin. We detected no obvious morphological phenotypes in Δmtb-3 mutants but there were fewer MTs in Δmtb-3, MTs were less bundled and less organized. Compared to WT, both MT polymerization and depolymerization rates were significantly decreased in Δmtb-3. In summary, the lack of MTB-3 affects overall growth and morphological phenotypes of N. crassa only slightly, but deletion of mtb-3 has strong effect on MT dynamics.

Non-alcoholic fatty liver disease (NAFLD) is a common liver disease; the histological spectrum of which ranges from steatosis to steatohepatitis. Nonalcoholic steatohepatitis (NASH) often leads to cirrhosis and development of hepatocellular carcinoma. To better understand pathogenesis of NAFLD, we performed the pathway of distinction analysis (PoDA) on a genome-wide association study dataset of 250 non-Hispanic white female adult patients with NAFLD, who were enrolled in the NASH Clinical Research Network (CRN) Database Study, to investigate whether biologic process variation measured through genomic variation of genes within these pathways was related to the development of steatohepatitis or cirrhosis. Pathways such as Recycling of eIF2:GDP, biosynthesis of steroids, Terpenoid biosynthesis and Cholesterol biosynthesis were found to be significantly associated with NASH. SNP variants in Terpenoid synthesis, Cholesterol biosynthesis and biosynthesis of steroids were associated with lobular inflammation and cytologic ballooning while those in Terpenoid synthesis were also associated with fibrosis and cirrhosis. These were also related to the NAFLD activity score (NAS) which is derived from the histological severity of steatosis, inflammation and ballooning degeneration. Eukaryotic protein translation and recycling of eIF2:GDP related SNP variants were associated with ballooning, steatohepatitis and cirrhosis. Il2 signaling events mediated by PI3K, Mitotic metaphase/anaphase transition, and Prostanoid ligand receptors were also significantly associated with cirrhosis. Taken together, the results provide evidence for additional ways, beyond the effects of single SNPs, by which genetic factors might contribute to the susceptibility to develop a particular phenotype of NAFLD and then progress to cirrhosis. Further studies are warranted to explain potential important genetic roles of these biological processes in NAFLD.