Separation of Albumin from Bovine Serum Applying Ionic-Liquid-Based Aqueous Biphasic Systems

In this work, the extraction and separation of bovine serum albumin (BSA) from its original matrix, i.e., bovine serum, was performed using a novel ionic-liquid-based aqueous biphasic system (IL-based ABS). To this end, imidazolium-, phosphonium-, and ammonium-based ILs, combined with the anions’ acetate, arginate and derived from Good Buffers, were synthesized, characterized, and applied in the development of ABS with K2HPO4/KH2PO4 buffer aqueous solutions at pH 7. Initial studies with commercial BSA revealed a preferential migration of the protein to the IL-rich phase, with extraction efficiencies of 100% obtained in a single-step. BSA recovery yields ranging between 64.0% and 84.9% were achieved, with the system comprising the IL tetrabutylammonium acetate leading to the maximum recovery yield. With this IL, BSA was directly extracted and separated from bovine serum using the respective ABS. Different serum dilutions were further investigated to improve the separation performance. Under the best identified conditions, BSA can be extracted from bovine serum with a recovery yield of 85.6% and a purity of 61.2%. Moreover, it is shown that the BSA secondary structure is maintained in the extraction process, i.e., after being extracted to the IL-rich phase. Overall, the new ABS herein proposed may be used as an alternative platform for the purification of BSA from serum samples and can be applied to other added-value proteins.

Can One Hear a Matrix? Recovering a Real Symmetric Matrix from Its Spectral Data

The spectrum of a real and symmetric $$N\times N$$ N × N matrix determines the matrix up to unitary equivalence. More spectral data is needed together with some sign indicators to remove the unitary ambiguities. In the first part of this work, we specify the spectral and sign information required for a unique reconstruction of general matrices. More specifically, the spectral information consists of the spectra of the N nested main minors of the original matrix of the sizes $$1,2,\ldots ,N$$ 1 , 2 , … , N . However, due to the complicated nature of the required sign data, improvements are needed in order to make the reconstruction procedure feasible. With this in mind, the second part is restricted to banded matrices where the amount of spectral data exceeds the number of the unknown matrix entries. It is shown that one can take advantage of this redundancy to guarantee unique reconstruction of generic matrices; in other words, this subset of matrices is open, dense and of full measure in the set of real, symmetric and banded matrices. It is shown that one can optimize the ratio between redundancy and genericity by using the freedom of choice of the spectral information input. We demonstrate our constructions in detail for pentadiagonal matrices.

Finding normal modes of a loaded string with the method of Lagrange multipliers

We consider the normal mode problem of a vibrating string loaded with n identical beads of equal spacing, which involves an eigenvalue problem. Unlike the conventional approach to solving this problem by considering the difference equation for the components of the eigenvector, we modify the eigenvalue equation by introducing matrix-valued Lagrange undetermined multipliers, which regularize the secular equation and make the eigenvalue equation non-singular. Then, the eigenvector can be obtained from the regularized eigenvalue equation by multiplying the indeterminate eigenvalue equation by the inverse matrix. We find that the inverse matrix is nothing but the adjugate matrix of the original matrix in the secular determinant up to the determinant of the regularized matrix in the limit that the constraint equation vanishes. The components of the adjugate matrix can be represented in simple factorized forms. Finally, one can directly read off the eigenvector from the adjugate matrix. We expect this new method to be applicable to other eigenvalue problems involving more general forms of the tridiagonal matrices that appear in classical mechanics or quantum physics.

Determinan Matriks Sirkulan Dengan Metode Kondensasi Dodgson

One of the important topics in mathematics is matrix theory. There are various types of matrix, one of which is a circulant matrix. Circulant matrix generally fulfill the same operating axioms as square matrix, except that there are some specific properties for the circulant matrix. Every square matrix has a determinant. The concept of determinants is very useful in the development of mathematics and across disciplines. One method of determining the determinant is condensation. The condensation method is classified as a method that is not widely known. The condensation matrix method in determining the determinant was proposed by several scientists, one of which was Charles Lutwidge Dodgson with the Dodgson condensation method. This paper will discuss the Dodgson condensation method in determining the determinant of the circulant matrix. The result of the condensation of the matrix will affect the size of the original matrix as well as new matrix entries. Changes in the circulant matrix after Dodgson's conduction load the Toeplitz matrix, in certain cases, the determinant of the circulant matrix can also be determined by simple mental computation.

Support for the Development of Technological Innovations at an R&D Organisation

Effective development of technological innovations requires efficient management at the stages of their generation, realisation, and their implementation. For this aim, concepts such as foresight, technology assessment, and organisational capabilities assessment can be applied; however, so far they have been used mainly individually or sometimes combined but to a very limited extent. Moreover, they are not used comprehensively, but only selectively, e.g., at some stages of the innovation processes. The research problem undertaken in the paper concerns the effectiveness of the integration of these concepts: future research (mainly foresight), technology assessment, and organisational capabilities assessment for the needs of supporting innovation processes. The paper is aimed at presenting an original approach assuming the integration of the aforementioned triad. The proposed approach has been developed individually by the paper’s author on the basis of (1) state of the art analysis comprising both theoretical approaches and practical examples of individual and combined application of the concepts analysed, and (2) the author’s practical experience resulting from research projects conducted collectively. The research result comprises an original matrix approach where the individual concepts of the triad are applied in a way enabling their mutual complementation at all successive stages of the innovation process. The approach proposed comprises modules referring to the succeeding stages of the innovation process, namely generation, realisation and application of technological innovations. The areas of the approach application and possible directions of its further development are presented.

On the minimal residual methods for solving diffusion-convection SLAEs

The objective of this research is to develop and to study iterative methods in the Krylov subspaces for solving systems of linear algebraic equations (SLAEs) with non-symmetric sparse matrices of high orders arising in the approximation of multi-dimensional boundary value problems on the unstructured grids. These methods are also relevant in many applications, including diffusion-convection equations. The considered algorithms are based on constructing ATA — orthogonal direction vectors calculated using short recursions and providing global minimization of a residual at each iteration. Methods based on the Lanczos orthogonalization, AT — preconditioned conjugate residuals algorithm, as well as the left Gauss transform for the original SLAEs are implemented. In addition, the efficiency of these iterative processes is investigated when solving algebraic preconditioned systems using an approximate factorization of the original matrix in the Eisenstat modification. The results of a set of computational experiments for various grids and values of convective coefficients are presented, which demonstrate a sufficiently high efficiency of the approaches under consideration.

Secure Outsourcing of Matrix Determinant Computation under the Malicious Cloud

Computing the determinant of large matrix is a time-consuming task, which is appearing more and more widely in science and engineering problems in the era of big data. Fortunately, cloud computing can provide large storage and computation resources, and thus, act as an ideal platform to complete computation outsourced from resource-constrained devices. However, cloud computing also causes security issues. For example, the curious cloud may spy on user privacy through outsourced data. The malicious cloud violating computing scripts, as well as cloud hardware failure, will lead to incorrect results. Therefore, we propose a secure outsourcing algorithm to compute the determinant of large matrix under the malicious cloud mode in this paper. The algorithm protects the privacy of the original matrix by applying row/column permutation and other transformations to the matrix. To resist malicious cheating on the computation tasks, a new verification method is utilized in our algorithm. Unlike previous algorithms that require multiple rounds of verification, our verification requires only one round without trading off the cheating detectability, which greatly reduces the local computation burden. Both theoretical and experimental analysis demonstrate that our algorithm achieves a better efficiency on local users than previous ones on various dimensions of matrices, without sacrificing the security requirements in terms of privacy protection and cheating detectability.

Numerical Simulation of Multiphase Multicomponent Flow in Porous Media: Efficiency Analysis of Newton-Based Method

Newton’s method has been widely used in simulation multiphase, multicomponent flow in porous media. In addition, to solve systems of linear equations in such problems, the generalized minimal residual method (GMRES) is often used. This paper analyzed the one-dimensional problem of multicomponent fluid flow in a porous medium and solved the system of the algebraic equation with the Newton-GMRES method. We calculated the linear equations with the GMRES, the GMRES with restarts after every m steps—GMRES (m) and preconditioned with Incomplete Lower-Upper factorization, where the factors L and U have the same sparsity pattern as the original matrix—the ILU(0)-GMRES algorithms, respectively, and compared the computation time and convergence. In the course of the research, the influence of the preconditioner and restarts of the GMRES (m) algorithm on the computation time was revealed; in particular, they were able to speed up the program.

A hybrid recommender system based on data enrichment on the ontology modelling

Background: A recommender system captures the user preferences and behaviour to provide a relevant recommendation to the user. In a hybrid model-based recommender system, it requires a pre-trained data model to generate recommendations for a user. Ontology helps to represent the semantic information and relationships to model the expressivity and linkage among the data. Methods: We enhanced the matrix factorization model accuracy by utilizing ontology to enrich the information of the user-item matrix by integrating the item-based and user-based collaborative filtering techniques. In particular, the combination of enriched data, which consists of semantic similarity together with rating pattern, will help to reduce the cold start problem in the model-based recommender system. When the new user or item first coming into the system, we have the user demographic or item profile that linked to our ontology. Thus, semantic similarity can be calculated during the item-based and user-based collaborating filtering process. The item-based and user-based filtering process are used to predict the unknown rating of the original matrix. Results: Experimental evaluations have been carried out on the MovieLens 100k dataset to demonstrate the accuracy rate of our proposed approach as compared to the baseline method using (i) Singular Value Decomposition (SVD) and (ii) combination of item-based collaborative filtering technique with SVD. Experimental results demonstrated that our proposed method has reduced the data sparsity from 0.9542% to 0.8435%. In addition, it also indicated that our proposed method has achieved better accuracy with Root Mean Square Error (RMSE) of 0.9298, as compared to the baseline method (RMSE: 0.9642) and the existing method (RMSE: 0.9492). Conclusions: Our proposed method enhanced the dataset information by integrating user-based and item-based collaborative filtering techniques. The experiment results shows that our system has reduced the data sparsity and has better accuracy as compared to baseline method and existing method.

Similarity Measure Algorithm for Text Document Clustering, Using Singular Value Decomposition

We examined a similarity measure between text documents clustering. Data mining is a challenging field with more research and application areas. Text document clustering, which is a subset of data mining helps groups and organizes a large quantity of unstructured text documents into a small number of meaningful clusters. An algorithm which works better by calculating the degree of closeness of documents using their document matrix was used to query the terms/words in each document. We also determined whether a given set of text documents are similar/different to the other when these terms are queried. We found that, the ability to rank and approximate documents using matrix allows the use of Singular Value Decomposition (SVD) as an enhanced text data mining algorithm. Also, applying SVD to a matrix of a high dimension results in matrix of a lower dimension, to expose the relationships in the original matrix by ordering it from the most variant to the lowest.