Extensions of D-optimal Minimal Designs for Symmetric Mixture Models.

The purpose of mixture experiments is to explore the optimum blends of mixture components, which will provide desirable response characteristics in finished products. D-optimal minimal designs have been considered for a variety of mixture models, including Scheffé\u27s linear, quadratic, and cubic models. Usually, these D-optimal designs are minimally supported since they have just as many design points as the number of parameters. Thus, they lack the degrees of freedom to perform the Lack of Fit tests. Also, the majority of the design points in D-optimal minimal designs are on the boundary: vertices, edges, or faces of the design simplex. IN THIS PAPER EXTENSIONS OF THE D-OPTIMAL MINIMAL DESIGNS ARE DEVELOPED FOR A GENERAL MIXTURE MODEL TO ALLOW ADDITIONAL INTERIOR POINTS IN THE DESIGN SPACE TO ENABLE PREDICTION OF THE ENTIRE RESPONSE SURFACE: Also a new strategy for adding multiple interior points for symmetric mixture models is proposed. We compare the proposed designs with Cornell (1986) two ten-point designs for the Lack of Fit test by simulations

Universal optimality of Patterson's crossover designs

We show that the balanced crossover designs given by Patterson [Biometrika 39 (1952) 32--48] are (a) universally optimal (UO) for the joint estimation of direct and residual effects when the competing class is the class of connected binary designs and (b) UO for the estimation of direct (residual) effects when the competing class of designs is the class of connected designs (which includes the connected binary designs) in which no treatment is given to the same subject in consecutive periods. In both results, the formulation of UO is as given by Shah and Sinha [Unpublished manuscript (2002)]. Further, we introduce a functional of practical interest, involving both direct and residual effects, and establish (c) optimality of Patterson's designs with respect to this functional when the class of competing designs is as in (b) above.Comment: Published at http://dx.doi.org/10.1214/009053605000000723 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Hermitian unitary matrices with modular permutation symmetry

We study Hermitian unitary matrices $\mathcal{S}\in\mathbb{C}^{n,n}$ with the following property: There exist $r\geq0$ and $t>0$ such that the entries of $\mathcal{S}$ satisfy $|\mathcal{S}_{jj}|=r$ and $|\mathcal{S}_{jk}|=t$ for all $j,k=1,\ldots,n$, $j\neq k$. We derive necessary conditions on the ratio $d:=r/t$ and show that these conditions are very restrictive except for the case when $n$ is even and the sum of the diagonal elements of $\S$ is zero. Examples of families of matrices $\mathcal{S}$ are constructed for $d$ belonging to certain intervals. The case of real matrices $\mathcal{S}$ is examined in more detail. It is demonstrated that a real $\mathcal{S}$ can exist only for $d=\frac{n}{2}-1$, or for $n$ even and $\frac{n}{2}+d\equiv1\pmod 2$. We provide a detailed description of the structure of real $\mathcal{S}$ with $d\geq\frac{n}{4}-\frac{3}{2}$, and derive a sufficient and necessary condition of their existence in terms of the existence of certain symmetric $(v,k,\lambda)$-designs. We prove that there exist no real $\mathcal{S}$ with $d\in\left(\frac{n}{6}-1,\frac{n}{4}-\frac{3}{2}\right)$. A parametrization of Hermitian unitary matrices is also proposed, and its generalization to general unitary matrices is given. At the end of the paper, the role of the studied matrices in quantum mechanics on graphs is briefly explained.Comment: revised version, 21 page

Extended Generalized Right-Angular Designs

8 pages, 1 article*Extended Generalized Right-Angular Designs* (Raghavarao, Damaraju) 8 page

Characterization of BIB Designs for Constructing Minimal Fractional Combinatorial Treatment Designs

8 pages, 1 article*Characterization of BIB Designs for Constructing Minimal Fractional Combinatorial Treatment Designs* (Raghavarao, Damaraju; Federer, Walter T.) 8 page

Gold Nanoparticles Based Enzyme Biosensor for the Detection of Chloramphenicol

Chronic use of chloramphenicol (CAM) antibiotic leads to anaemia and bone marrow suppression resulting in 40 – 50% mortality. Hence, there is a need to develop an economical, fast and convenient method to detect CAM in milk, honey, shrimp and other aquaculture products. In the current method, coenzyme A was used to indirectly quantify CAM (since it is the cofactor product of the acetylation reaction of CAM). Coenzyme A (CoASH) was used to stabilize gold nanoparticles which were characterized by studying their extinction spectra. The reductant concentration and synthesis time were optimized. With optimized parameters the proposed system could detect CoASH up to 0.1 nM in buffer, with a linear range of detection from 0.1 μM to 1 mM

Statistical Characteristics of Repeated Block Designs

9 pages, 1 article*Statistical Characteristics of Repeated Block Designs* (Raghavarao, D.; Federer, W. T.; Seiden, E.; Lee, F.-C. H.) 9 page

Lipase production by solid-state fermentation of olive pomace in tray-type and pressurized bioreactors

Background: Bioreactor type, sterilization and specific operational conditions are key factors for the scale-up of solid-state fermentation (SSF). This work deals with the lipase production by SSF of olive pomace (OP) at a traditional tray-type and pressurized bioreactors. Important aspects for SSF at bioreactors were studied, such as the need of sterilization and moisture content (MC) control. RESULTS At larger scale, there was no significant difference in lipase production between sterilized and unsterilized substrates, but MC control had significant impact. The production of lipase in a pressurized bioreactor, under air absolute pressure of 200 kPa and 400 kPa, was two-fold higher than in tray-type bioreactor using the same amount of substrate (500 g) and the same bed height. The protein content of substrate increased from 10 to 18% (w/w) after SSF and the fermented solid presented an antioxidant activity of 10 mmol Trolox kg-1. CONCLUSIONS SSF in pressurized bioreactor allowed to efficiently produce lipase with higher substrate bed height in contrast to that in tray-type bioreactor. The improvement of nutritional value of substrate by SSF indicates its potential applicability in animal feed.Felisbela Oliveira acknowledges the financial support from the Portuguese Foundation for Science and Technology (FCT) through grant SFRH/BD/87953/2012. José Manuel Salgado was supported by grant CEB/N2020 – INV/01/2016 from Project “BIOTECNORTE - Underpinning Biotechnology to foster the north of Portugal bioeconomy” (NORTE-01-0145-FEDER-000004). This study was supported by the Portuguese Foundation for Science and Technology (FCT) under the scope of the strategic funding of UID/BIO/04469/2013 unit and COMPETE 2020 (POCI-01-0145-FEDER-006684) and BioTec-Norte operation (NORTE-01-0145-FEDER-000004) funded by the European Regional Development Fund under the scope of Norte2020 ProgramaOperacionalRegionaldoNorte. Noelia Pérez-Rodríguez acknowledges the financial support of FPU from Spanish Ministry of Education, Culture and Sports. The authors thank the Spanish Ministry of Science and Innovation for the financial support of this work (projectCTQ2011-28967), which has partial financial support from the FEDER funds of the European Union.info:eu-repo/semantics/publishedVersio