L-optimal Design Research Articles

Intranasal bilosomes in thermosensitive hydrogel: advancing desvenlafaxine succinate delivery for depression management

Depression, the second biggest cause of disability worldwide, is widespread. Many antidepressant medications, including Desvenlafaxine Succinate (D.V.S.), function by elevating neurotransmitter levels at the synapse through the inhibition of reabsorption by neurons. However, the effectiveness of these treatments is often limited by their inability to reach the brain using conventional administration methods. Bilosome-stabilized nanovesicles containing bile salts have drawn much interest because of their adaptability and versatility in various applications. This study aimed to address this issue by formulating intranasal bilosomes incorporated into a mucoadhesive in situ gel to deliver D.V.S. directly to the brain for depression treatment. The desvenlafaxine-loaded bilosomes were developed using a thin film hydration method based on the l-optimal design. They were intended to provide a more convenient route of administration for antidepressants, enhancing bioavailability and brain targeting through intranasal delivery. The study assessed the optimized bilosomes for particle size (311.21 ± 0.42 nm), Zeta potential (–37.35 ± 0.43)and encapsulation efficiency (99.53 ± 0.41%) and further evaluated them in ex vivo and in vivo pharmacokinetics studies. Pharmacokinetic data reveal enhanced brain uptake compared to a free drug. A statistically optimized bilosome formulation was determined. The intranasal administration of mucoadhesive in situ gel containing desvenlafaxine succinate-loaded bilosomes facilitated direct nose-to-brain drug delivery, improving brain bioavailability.

Study of the Excess Property of the L-Optimal Design for the Label Model

Study of the Excess Property of the L-Optimal Design for the Label Model

L-Optimal Designs for a Trigonometric Fourier Regression Model with no Intercept

This paper is devoted to the problem of constructing L-optimal designs for a trigonometric Fourier regression model with no intercept. The paper considers diagonal matrices L with a combination of zeros and ones on the main diagonal. It is shown that in the case when L = I (i.e., when the identity matrix is chosen as the matrix L), the L-optimal design coincides with the D-optimal one. In the more general case (when some diagonal elements are zero), it is shown that the dimension of the problem can be reduced if the optimal design is symmetric. The results are illustrated by the example of the problem of constructing two L-optimal designs for the twelfth-order trigonometric model, which is reduced to the problem of constructing designs for third- and fourth-order models, correspondingly.

Study of the excess property of the L-optimal design for the Laible model

For a rational two-dimensional nonlinear in parameters Laible model used in analytical chemistry, the problem of constructing L-optimal designs is investigated. It is shown that there are two types of optimal designs for this model: saturated (i. e., designs with the number of support points equal to the number of model parameters) and excess (i. e., designs with the number of support points greater than the number of model parameters) and that with some homothetic transformations of the design space, locally L-optimal designs can change the type from saturated to excess and vice versa. An analytical solution to the problem of finding the dependence between the number of the optimal design support points and the values of the model parameters based on the application of a functional approach is proposed. The L-efficiency of D-optimal designs is investigated.

L-optimal designs for a trigonometric Fourier regression model with no intercept

This paper is devoted to the problem of constructing L-optimal designs for a trigonometric Fourier regression model with no intercept. The paper considers diagonal matrices L with a combination of zeros and ones on the main diagonal. It is shown that in the case when L = I (i. e., when the unit matrix is chosen as the matrix L), the L-optimal design coincides with the D-optimal one. In the more general case (when some diagonal elements are equal to zero), it is shown that the dimension of the problem can be reduced if the optimal design is symmetric. The obtained results are illustrated by the example of the problem of constructing two L-optimal designs for the trigonometric model of order 12, which is reduced to the problem of constructing designs for models of order 3 and 4 correspondingly.

Using SeDuMi to find various optimal designs for regression models.

We introduce a powerful and yet seldom used numerical approach in statistics for solving a broad class of optimization problems where the search space is discretized. This optimization tool is widely used in engineering for solving semidefinite programming (SDP) problems and is called SeDuMi (self-dual minimization). We focus on optimal design problems and demonstrate how to formulate A-, A s -, c-, I-, and L-optimal design problems as SDP problems and show how they can be effectively solved by SeDuMi in MATLAB. We also show the numerical approach is flexible by applying it to further find optimal designs based on the weighted least squares estimator or when there are constraints on the weight distribution of the sought optimal design. For approximate designs, the optimality of the SDP-generated designs can be verified using the Kiefer-Wolfowitz equivalence theorem. SDP also finds optimal designs for nonlinear regression models commonly used in social and biomedical research. Several examples are presented for linear and nonlinear models.

Optimal designs subject to cost constraints in simultaneous equations models

A procedure based on a multiplicative algorithm for computing optimal experimental designs subject to cost constraints in simultaneous equations models is presented. A convex criterion function based on a usual criterion function and an appropriate cost function is considered. A specific L-optimal design problem and a numerical example are taken from Conlisk (J Econ 11:63–76, 1979) to compare the procedure. The problem would need integer nonlinear programming to obtain exact designs. To avoid this, he solves a continuous nonlinear programming problem and then he rounds off the number of replicates of each experiment. The procedure provided in this paper reduces dramatically the computational efforts in computing optimal approximate designs. It is based on a specific formulation of the asymptotic covariance matrix of the full-information maximum likelihood estimators, which simplifies the calculations. The design obtained for estimating the structural parameters of the numerical example by this procedure is not only easier to compute, but also more efficient than the design provided by Conlisk.

Equivalence theorem for singular L-optimal designs

The present paper is devoted to studying the problem of checking whether a given singular design is L optimal. As a possible solution, a general version of the equivalence theorem for L-optimal designs is formulated. A method for finding coefficients of an extreme polynomial in the case where this polynomial cannot be unambiguously determined by the dispersion matrix of a design is proposed.

Optimal designs for trigonometric regression models

In the common Fourier regression model we investigate the optimal design problem for the estimation of linear combinations of the coefficients, where the explanatory variable varies in the interval [ − π , π ] . In a recent paper Dette et al. (2009) determined optimal designs for estimating certain pairs of the coefficients in the model. The optimal design problem corresponds to a linear optimality criterion for a specific matrix L. In the present paper these results are extended to more general matrices L. By our results the optimal design problem for a Fourier regression of large degree can be reduced to a design problem in a model of lower degree, which allows the determination of L-optimal designs in many important cases. The results are illustrated by several examples.

Solution of the problem of L-optimal experiment design with a skeleton algorithm

For the solution of the problem of L-optimal design of an experiment use is made of a skeleton algorithm [1]. This algorithm is modified for the solution of a multiparameter problem of linear programming, to which the initial problem reduces. The algorithm ensures the lack of almost degenerate iterations and does not require operations of the matrix inversion.

L-optimal designs in the trigonometric regression model on the full circle

Singular L-optimal designs minimizing the sum of the variances of the estimates for different pairs of coefficients in the trigonometric regression models on the full circle are found.

Control-relevant design of periodic test input signals for iterative open-loop identification of multivariable FIR systems

In this paper, the problem of control-relevant test input design for iterative system identification is considered. Two approaches are presented for the L-optimal input test signal design by Cooley and Lee (2001). which minimizes the a posteriori closed-loop error based on a priori information given by the data already collected from previous iterations. To simplify the computation, we limit our design to a period signal of period n, which is the number of FIR coefficients. The first approach is direct time-domain search for optimal test input values, which can be formulated as a nonconvex optimization or a concave Quadratic Program. The second approach considers frequency domain solution of the L-optimal design problem to obtain the optimal discrete spectra of the test signals, which is subsequently realized as a periodic signal.

Optimal Central Composite Designs in the Presence of Dispersion Effects

The central composite design (CCD) is often used to provide estimation of a second-order regression model. The CCD involves a possibly fractionated two-level factorial design, axial points, and replicated runs in the design center and is usually used with the assumption of homogeneous variance in the design region. However, when dispersion effects exist, standard CCD's may not be optimal. With a specified number of experimental runs available, the goal is to find the optimal allocation of the runs to the CCD locations. In this paper, several variance structures are considered in conjunction with several scaled degrees of heterogeneity expressed in terms of variance ratios. Optimality criteria based on the determinant of the variance-covariance matrix of coefficients (D-optimality) and on the integrated prediction variance (I-optimality) are used. Two, three, and four variable models are considered, and in each heterogeneous variance structure case, the run allocations that creates the D- and l-optimal designs are presented.

Tolerance-weighted L-optimal experiment design: a new approach to task-directed sensing

The choice of 'where to look next' is a special case of an optimal experiment design. This paper proposes the tolerance-optimal experiment design, which is a special instance of the well-known L-optimal design, that minimizes the weighted trace of the covariance matrix of the estimated state under Gaussian assumptions. The weighting matrix is chosen such that the design is invariant to transformations with non-singular Jacobians, and such that the emerging sensing sequence reflects the information needs of the task. This tolerance-optimal design does not require more calculations than existing optimal experiment designs. Existing optimal experiment designs do not reflect the information needs of the task. In addition, some of them physically do not make sense if the estimated state has inconsistent units.

Second order methods for solving extremum problems form optimal linar regression design

Extremum problems arising in optimal design for linear regression models lead to minimizing a convex function over a convex set, which is essentially given as the convex hull of a compact generator set. We assume that the generator is simple enough to allow easy minimization of linear functions. Gradient methods were considered by Gaffke & Mathar in [5]. In the present paper we establish second order methods, one of Newton- and the other of BFGS type. Applications are given firstly to optimal invariant designs for multiple cubic regression, and secondly to Bayes L-optimal design for a first order model which also appears as a dual problem to linear minimax estimation. The former is sketched only briefly, since it has been studied in greater detail in [2]

A graphical approach for the construction of constrained a and l-optimal designs using efficiency plots

In this paper, a graphical approach for computing constrained optimal designs in regression experiments is presented. The method is simple to implement and can be used in design problems where there are two optimality criteria, and these criteria are expressible as convex functionals of information matrices. The method is applied to seek constrained L and D-optimal designs in quadratic and cubic polynomial models. Several interesting features are noted, including (i) ifξ0 and ξ1 are optimal designs for two optimality criteria φ0 and φ1 and the two designs have the same support, the optimal design for a convex combination of φ0 and φ1 can have a different set of support points, and (ii) D-restricted extrapolation designs. are generally more efficient than A-restricted extrapolation designs for estimating the model parameters.

Optimal Designs for Estimating the Slope of a Polynomial Regression

Abstract The problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that (a) the variance of the least-square estimate of the slope at the fixed point is a minimum and (b) the average variance of the least-square estimate of the slope is a minimum is discussed in this paper. In general these designs can be obtained using Kiefer-Wolfowitz [5] characterization of c-optimal designs, Federov [2] characterization of L-optimal designs, and Studden's [10] generalization of the Elfving Theorem [1]. After presenting a brief review of these characterization theorems, specific illustrations for the quadratic and cubic regressions are presented in detail.