D-optimal designs for binary and weighted linear regression models: one design variable

D-optimality is a well-known concept in experimental design that seeks to select an optimal set of design points to estimate the unknown parameters of a statistical model with a minimum variance. In this paper, we focus on proving a conjecture made by Ford, Torsney and Wu regarding the existence of a class of D-optimal designs for binary and weighted linear regression models. Our concentration is on models with one design variable. The conjecture states that, for any given level of precision, there exists a two-level factorial design that is D-optimal for these models. To prove this conjecture, we use an intuitive approach that explores various link functions in the generalised linear model context to establish the veracity of the conjecture. We also present explicit and clear plots of various functions wherever deemed necessary and appropriate to further strengthen the proofs. Our results establish the existence of D-optimal designs for binary and weighted linear regression models with one design variable, which have important implications for the efficient design of experiments in various fields. These findings contribute to the development of optimal experimental designs for studying binary and weighted linear regression models and provide a foundation for future research in this area

Efficient algorithms for constructing D- and I-optimal exact designs for linear and non-linear models in mixture experiments

The problem of finding optimal exact designs is more challenging than that of approximate optimal designs. In the present paper, we develop two efficient algorithms to numerically construct exact designs for mixture experiments. The first is a novel approach to the well-known multiplicative algorithm based on sets of permutation points, while the second uses genetic algorithms. Using (i) linear and non-linear models, (ii) D/- and I-optimality criteria, and (iii) constraints on the ingredients, both approaches are explored through several practical problems arising in the chemical, pharmaceutical and oil industry

Neuronal circuitry for pain processing in the dorsal horn

Neurons in the spinal dorsal horn process sensory information, which is then transmitted to several brain regions, including those responsible for pain perception. The dorsal horn provides numerous potential targets for the development of novel analgesics and is thought to undergo changes that contribute to the exaggerated pain felt after nerve injury and inflammation. Despite its obvious importance, we still know little about the neuronal circuits that process sensory information, mainly because of the heterogeneity of the various neuronal components that make up these circuits. Recent studies have begun to shed light on the neuronal organization and circuitry of this complex region

The beauty in a beast: Minimising the effects of diverse recording quality on vowel formant measurements in sociophonetic real-time studies

Sociophonetic real-time studies of vowel variation and change rely on acoustic analyses of sound recordings made at different times, often using different equipment and data collection procedures. The circumstances of a recording are known to affect formant tracking and may therefore compromise the validity of conclusions about sound changes made on the basis of real-time data. In this paper, a traditional F1/F2-analysis using linear predictive coding (LPC) was applied to the vowels /i u a/ extracted from spontaneous speech corpora of Glaswegian vernacular, that were recorded in the 1970s and 2000s. We assessed the technical quality of each recording, concentrating on the average levels of noise and the properties of spectral balance, and showed that the corpus comprised of mixed quality data. A series of acoustic vowel analyses subsequently unveiled that formant measurements using LPC were sensitive to the technical specification of a recording, with variable magnitudes of the effects for vowels of different qualities. We evaluated the performance of three commonly used formant normalisation procedures (Lobanov, Nearey and Watt-Fabricius) as well as normalisations by a distance ratio metric and statistical estimation, and compared these results to raw Bark-scaled formant data, showing that some of the approaches could ameliorate the impact of technical issues better than the others. We discuss the implications of these results for sociophonetic research that aims to minimise extraneous influences on recorded speech data while unveiling gradual, potentially small-scale sound changes across decades

Efficient algorithms for constructing D- and I-optimal exact designs for linear and non-linear models in mixture experiments

The problem of finding optimal exact designs is more challenging than that of approximate optimal designs. In the present paper, we develop two efficient algorithms to numerically construct exact designs for mixture experiments. The first is a novel approach to the well-known multiplicative algorithm based on sets of permutation points, while the second uses genetic algorithms. Using (i) linear and non-linear models, (ii) D/- and I-optimality criteria, and (iii) constraints on the ingredients, both approaches are explored through several practical problems arising in the chemical, pharmaceutical and oil industry

Transcriptional activation of endoglin and transforming growth factor-? signaling components by cooperative interaction between Sp1 and KLF6: their potential role in the response to vascular injury

Endoglin is an endothelial membrane glycoprotein involved in cardiovascular morphogenesis and vascular remodeling. It associates with transforming growth factor-? (TGF-?) signaling receptors to bind TGF-? family members, forming a functional receptor complex. Arterial injury leads to up-regulation of endoglin, but the underlying regulatory events are unknown. The transcription factor KLF6, an immediate-early response gene induced in endothelial cells during vascular injury, transactivates TGF-?, TGF-? signaling receptors, and TGF-?-stimulated genes. KLF6 and, subsequently, endoglin were colocalized to vascular endothelium (ie, expressed in the same cell type) following carotid balloon injury in rats. After endothelial denudation, KLF6 was induced and translocated to the nucleus; this was followed 6 hours later by increased endoglin expression. Transient overexpression of KLF6, but not Egr-1, stimulated endogenous endoglin mRNA and transactivated the endoglin promoter. This transactivation was dependent on a GC-rich tract required for basal activity of the endoglin promoter driven by the related GC box binding protein, Sp1. In cells lacking Sp1 and KLF6, transfected KLF6 and Sp1 cooperatively transactivated the endoglin promoter and those of collagen alpha1(I), urokinase-type plasminogen activator, TGF-?1, and TGF-? receptor type 1. Direct physical interaction between Sp1 and KLF6 was documented by coimmunoprecipitation, pull-down experiments, and the GAL4 one-hybrid system, mapping the KLF6 interaction to the C-terminal domain of Sp1. These data provide evidence that injury-induced KLF6 and preexisting Sp1 may cooperate in regulating the expression of endoglin and related members of the TGF-? signaling complex in vascular repair