Affine Combination Research Articles

Equal loss under separatorization and egalitarian values

We characterize the equal division value, the equal surplus division value, and the class of their affine combinations for TU-games involving equal loss under separatorization. This axiom requires that, if a player becomes a dummifying player (Casajus and Huettner, 2014), then any two other players are equally affected.

Modeling of Mechanosensing Mechanisms Reveals Distinct Cell Migration Modes to Emerge From Combinations of Substrate Stiffness and Adhesion Receptor-Ligand Affinity.

Mesenchymal cell migration is an integral process in development and healing. The process is regulated by both mechanical and biochemical properties. Mechanical properties of the environment are sensed through mechanosensing, which consists of molecular responses mediated by mechanical signals. We developed a computational model of a deformable 3D cell on a flat substrate using discrete element modeling. The cell is polarized in a single direction and thus moves along the long axis of the substrate. By modeling discrete focal adhesions and stress fibers, we implement two mechanosensing mechanisms: focal adhesion stabilization by force and stress fiber strengthening upon contraction stalling. Two substrate-associated properties, substrate (ligand) stiffness and adhesion receptor–ligand affinity (in the form of focal adhesion disassembly rate), were varied for different model setups in which the mechanosensing mechanisms are set as active or inactive. Cell displacement, focal adhesion number, and cellular traction were quantified and tracked in time. We found that varying substrate stiffness (a mechanical property) and adhesion receptor–ligand affinity (a biochemical property) simultaneously dictate the mode in which cells migrate; cells either move in a smooth manner reminiscent of keratocytes or in a cyclical manner reminiscent of epithelial cells. Mechanosensing mechanisms are responsible for the range of conditions in which a cell adopts a particular migration mode. Stress fiber strengthening, specifically, is responsible for cyclical migration due to build-up of enough force to elicit rupture of focal adhesions and retraction of the cellular rear. Together, both mechanisms explain bimodal dependence of cell migration on substrate stiffness observed in the literature.

Fluorescence Anion Chemosensor Array Based on Pyrenylboronic Acid.

A novel fluorescence chemosensor array composed of pyrenylboronic acid-based probes for multi- anion detection has been developed. The pyrenylboronic acid derivatives showed fluorescence quenching or enhancement due to photoinduced electron transfer originating from anion binding. The recognition ability was assessed by fluorescence titrations and electrospray ionization mass spectrometry. Because the array is constructed with cross-reactive probes, the combination of differential binding affinities for anions (i.e., fluoride, acetate, oxalate, malonate, citrate, dihydrogen phosphate, and pyrophosphate) and pattern recognitions, such as linear discriminant analysis, offered a successful simultaneous anion detection with a classification rate of 100%. Furthermore, the chemosensor array allowed for quantitative prediction of oxalate, malonate, and citrate in mixtures using a support vector machine. Importantly, the array system employs low-cost and commercially available reagents as probes. Thus, this study could lead to the development of user-friendly and high-throughput methods to detect a variety of analytes in complicated systems.

Non-rigid infrared and visible image registration by enhanced affine transformation

Image registration is a prerequisite for infrared (IR) and visible (VIS) image fusion. In practical application, most scenes are not planar and there is significant distinctness between IR and VIS cameras. Therefore, for non-rigid IR and VIS image registration, non-linear transformation is more applicable than affine transformation. Typically, non-linear transformation is modeled with point feature. However, this can degrade the generalization ability of transformation model and increase computational complexity. Aim at this problem, we propose an enhanced affine transformation (EAT) for non-rigid IR and VIS image registration. In this paper, image registration is transformed into point set registration and then the optimal EAT model constructed by global deformation is estimated from local feature. At first, a Gaussian-fields-based objective function is established and simplified by using the potential correspondence between an image pair. With the combination of affine and polynomial transformation, the EAT model is then proposed to describe the regular pattern of non-rigid and global deformation between an image pair. Finally, a coarse-to-fine strategy based on quasi-Newton method is designed and applied to determine the optimal transformation coefficients from edge point feature of IR and VIS images, in order to accomplish non-rigid image registration. The qualitative and quantitative comparisons on synthesized point sets and real images demonstrate that the proposed method is superior over the state-of-the-art methods in the accuracy and efficiency of image registration.

Comparison of optimal linear, affine and convex combinations of metamodels

In this article, five different formulations for establishing optimal ensembles of metamodels are presented and compared. The comparison is done by minimizing different norms of the residual vector of the leave-one-out cross-validation errors for linear, affine and convex combinations of 10 metamodels. The norms are taken to be the taxicab, the Euclidean and the infinity norm, respectively. The ensemble of metamodels consists of quadratic regression, Kriging with linear or quadratic bias, radial basis function networks with a-priori linear or quadratic bias, radial basis function networks with a-posteriori linear or quadratic bias, polynomial chaos expansion, support vector regression and least squares support vector regression. Eight benchmark functions are studied as ‘black-boxes’ using Halton and Hammersley samplings. The optimal ensembles are established for either one of the samplings and then the corresponding root mean square errors are established using the other sampling and vice versa. In total, 80 different test cases (5 formulations, 8 benchmarks and 2 samplings) are studied and presented. In addition, an established design optimization problem is solved using affine and convex combinations. It is concluded that minimization of the taxicab or Euclidean norm of the residual vector of the leave-one-out cross-validation errors for convex combinations of metamodels produces the best ensemble of metamodels.

High School Students’ Responses in Solving Linear Program Problems Based on SOLO Taxonomy Viewed from Mathematical Disposition

In mathematics learning, students need a cognitive domain that is supported by an equivalent affective domain. One of the factors students can master or like math is that they must have an interest and curiosity in learning mathematics. Interest of students can solve mathematics problems more efficiently. The combination of affinity and interest in learning mathematics will form a positive attitude which is often called a mathematical disposition. Mathematical disposition is students’ beliefs and attitudes about mathematics that support the tendency to see mathematics as reasonable and useful as well as the role he or she believes diligence plays in solving mathematical tasks. SOLO taxonomy can be classified into five levels ranging from simple to high levels, pre-structural, uni-structural, multi-structural, relational, and extended abstract. This study uses descriptive qualitative research that has the purpose of describing level response of students who have high, medium, and low mathematical disposition categories. The subjects in this study were senior high school students in the City of Kediri with a purposive sampling technique in a class of 35 students and obtained three subjects which represent every category of mathematical disposition. The results of this study are (1) Student with high mathematical disposition is at the extended abstract level, (2) Student with medium mathematical disposition is at the multi-structural level, (3) Student with low mathematical disposition is at the pre-structural level.

Parameter optimization of software reliability models using improved differential evolution algorithm

Differential evolution (DE) is known as a strong and simple optimization method able to work with non-differential, nonlinear, and multimodal functions. This paper proposes a modified differential evolution (MDE) algorithm for solving a high dimensional nonlinear optimization problem. The issue is finding maximum likelihood estimation (MLE) for the parameters of a non-homogeneous Poisson process (NHPP) software reliability model. We make two modifications to DE: a mutation scheme based on a new affine combination of three points for increasing the exploration power of the algorithm, and another is a uniform scaling crossover scheme to increase the exploitation ability of the algorithm. The performance of the proposed scheme is empirically validated using five software reliability models on three software failure datasets. Analysis of research findings indicates that the proposed scheme enhances the convergence speed of the DE algorithm, and preserves the quality of the solution. A comparison with two other peer algorithms is also shown the superiority of the proposed algorithm.

SCreg: a registration-based platform to compare unicondylar knee arthroplasty SPECT/CT scans

BackgroundA combination of conventional computed tomography and single photon emitted computed tomography (SPECT/CT) provides simultaneous data on the intensity and location of osteoblastic activity. Currently, since SPECT/CT scans are not spatially aligned, scans following knee arthroplasty are compared by extracting average and maximal values of osteoblastic activity intensity from large subregions of the structure of interest, which leads to a loss of resolution, and hence, information. Therefore, this paper describes the SPECT/CT registration platform (SCreg) based on the principle of image registration to spatially align SPECT/CT scans following unicondylar knee arthroplasty (UKA) and allow full resolution intra-subject and inter-subject comparisons.MethodsSPECT-CT scans of 20 patients were acquired before and 1 year after UKA. Firstly, scans were pre-processed to account for differences in voxel sizes and divided in volumes of interest. This was followed by optimization of registration parameters according to their volumetric agreement, and alignment using a combination of rigid, affine and non-rigid registration. Finally, radiotracer uptakes were normalized, and differences between pre-operative and post-operative activity were computed for each voxel. Wilcoxon signed rank sum test was performed to compare Dice similarity coefficients pre- and post-registration.ResultsQualitative and quantitative validation of the platform assessing the correct alignment of SPECT/CT scans resulted in Dice similarity coefficient values over 80% and distances between predefined anatomical landmarks below the fixed threshold of (2;2;0) voxels. Locations of increased and decreased osteoblastic activity obtained during comparisons of osteoblastic activity before and after UKA were mainly consistent with literature.ConclusionsThus, a full resolution comparison performed on the platform could assist surgeons and engineers in optimizing surgical parameters in view of bone remodeling, thereby improving UKA survivorship.

Efficient Solvers for Sparse Subspace Clustering

Sparse subspace clustering (SSC) clusters n points that lie near a union of low-dimensional subspaces. The SSC model expresses each point as a linear or affine combination of the other points, using either ℓ1 or ℓ0 regularization. Using ℓ1 regularization results in a convex problem but requires O(n2) storage, and is typically solved by the alternating direction method of multipliers which takes O(n3) flops. The ℓ0 model is non-convex but only needs memory linear in n, and is solved via orthogonal matching pursuit and cannot handle the case of affine subspaces. This paper shows that a proximal gradient framework can solve SSC, covering both ℓ1 and ℓ0 models, and both linear and affine constraints. For both ℓ1 and ℓ0, algorithms to compute the proximity operator in the presence of affine constraints have not been presented in the SSC literature, so we derive an exact and efficient algorithm that solves the ℓ1 case with just O(n2) flops. In the ℓ0 case, our algorithm retains the low-memory overhead, and is the first algorithm to solve the SSC-ℓ0 model with affine constraints. Experiments show our algorithms do not rely on sensitive regularization parameters, and they are less sensitive to sparsity misspecification and high noise.

Human Tyrosinase: Temperature-Dependent Kinetics of Oxidase Activity.

Human tyrosinase (Tyr) is involved in pigment biosynthesis, where mutations in its corresponding gene TYR have been linked to oculocutaneous albinism 1, an autosomal recessive disorder. Although the enzymatic capabilities of Tyr have been well-characterized, the thermodynamic driving forces underlying melanogenesis remain unknown. Here, we analyze protein binding using the diphenol oxidase behavior of Tyr and van ’t Hoff temperature-dependent analysis. Recombinant Tyr was expressed and purified using a combination of affinity and size-exclusion chromatography. Michaelis-Menten constants were measured spectrophotometrically from diphenol oxidase reactions of Tyr, using L-3,4-dihydroxyphenylalanine (L-DOPA) as a substrate, at temperatures: 25, 31, 37, and 43 °C. Under the same conditions, the Tyr structure and the L-DOPA binding activity were simulated using 3 ns molecular dynamics and docking. The thermal Michaelis-Menten kinetics data were subjected to the van ‘t Hoff analysis and fitted with the computational model. The temperature-dependent analysis suggests that the association of L-DOPA with Tyr is a spontaneous enthalpy-driven reaction, which becomes unfavorable at the final step of dopachrome formation.

Analysis of Multivalent IDP Interactions: Stoichiometry, Affinity, and Local Concentration Effect Measurements.

Nuclear magnetic resonance (NMR) titration and isothermal titration calorimetry can be combined to provide an assessment of how multivalent intrinsically disordered protein (IDP) interactions can involve enthalpy-entropy balance. Here, we describe the underlying technical details and additional methods, such as dynamic light scattering analysis, needed to assess these reactions. We apply this to a central interaction involving the disordered regions of phe-gly nucleoporins (FG-Nups) that contain multiple phenylalanine-glycine repeats which are of particular interest, as their interactions withnuclear transport factors (NTRs) underlie the paradoxically rapid yet also highly selective transport of macromolecules mediated by the nuclear pore complex (NPC). These analyses revealed that a combination of low per-FG motif affinity and the enthalpy-entropy balance prevents high-avidity interaction between FG-Nups and NTRs while the large number of FG motifs promotes frequent FG-NTRcontacts, resulting in enhanced selectivity.

Hybridising neural network and pattern matching under dynamic time warping for time series prediction

Pattern matching-based forecasting models are attractive due to their simplicity and the ability to predict complex nonlinear behaviours. Euclidean measure is the most commonly used metric for pattern matching in time series. However, its weakness is that it is sensitive to distortion in time axis; so, this can influence on forecasting results. The dynamic time warping (DTW) measure is introduced as a solution to the weakness of Euclidean distance metric. In addition, artificial neural networks (ANNs) have been widely used in the time series forecasting. They have been used to capture the complex relationships with a variety of patterns. In this work, we propose an improved hybrid method which is an affine combination of neural network model and DTW-based pattern matching model for time series prediction. This method can take full advantage of the individual strengths of the two models to create a more effective approach for time series prediction. Experimental results show that our proposed method outperforms neural network model and DTW-based pattern matching method used separately in time series prediction.

Compromising between the Proportional and Equal Division Values: Axiomatization, Consistency and Implementation

We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an alpha-mollified value, is obtained in two steps. First, a linear function with respect to the worths of all coalitions is defined which associates a real number to every TU-game. Second, the weight assigned by this function is used to weigh proportionality and equality principles in allocating the worth of the grand coalition. We provide an axiomatic characterization of this family, and show that this family contains the affine combinations of the equal division value and the equal surplus division value as the only linear values. Further, we identify the proportional division value and the affine combinations of the equal division value and the equal surplus division value as those members of this family, that satisfy projection consistency. Besides, we provide a procedural implementation of each single value in this family.

Affine Combination of Diffusion Strategies Over Networks

Diffusion adaptation is a powerful strategy for distributed estimation and learning over networks. Motivated by the concept of combining adaptive filters, this work proposes a combination framework that aggregates the operation of multiple diffusion strategies for enhanced performance. By assigning a combination coefficient to each node, and using an adaptation mechanism to minimize the network error, we obtain a combined diffusion strategy that benefits from the best characteristics of all component strategies simultaneously in terms of excess-mean-square error (EMSE). Analyses of the universality are provided to show the superior performance of affine combination scheme and to characterize its behavior in the mean and mean-square sense. Simulation results are presented to demonstrate the effectiveness of the proposed strategies, as well as the accuracy of theoretical findings.

Convex Combination of Diffusion Strategies Over Networks

Combining diffusion strategies with complementary properties enables enhanced performance when they can be run simultaneously. In this article, we first propose two schemes for the convex combination of two diffusion strategies, namely, the power-normalized scheme and the sign-regressor scheme. Then, we conduct theoretical analysis for one of the schemes, i.e., the power-normalized one. An analysis of universality shows that it cannot perform worse than any of its component strategies in terms of the excess mean-square-error (EMSE) at steady state, and sometimes even better. An analysis of stability also reveals that it is more stable than affine combination schemes already proposed by the authors in the literature. Next, several adjustments are proposed to further improve the performance of convex combination schemes. A discussion about the computational and communication complexity is provided, as well as a comparison between convex and affine combination schemes. Finally, simulation results are shown to demonstrate their effectiveness, the accuracy of the theoretical results, and the improved stability of the convex power-normalized scheme over the affine one.

Bioinspired Mineral–Organic Bone Adhesives for Stable Fracture Fixation and Accelerated Bone Regeneration

AbstractThe use of hydrogel‐based bone adhesives has the potential to revolutionize the clinical treatment of bone repairs. However, severe deficiencies remain in current products, including cytotoxicity concerns, inappropriate mechanical strength, and poor fixation performance in wet biological environments. Inspired by the unique roles of glue molecules in the robust mechanical strength and fracture resistance of bone, a design strategy is proposed using novel mineral–organic bone adhesives for strong water‐resistant fixation and guided bone tissue regeneration. The system leveraged tannic acid (TA) as a phenolic glue molecule to spontaneously co‐assemble with silk fibroin (SF) and hydroxyapatite (HA) in order to fabricate the inorganic–organic hybrid hydrogel (named SF@TA@HA). The combination of the strong affinity between SF and TA along with sacrificial coordination bonds between TA and HA significantly improves the toughness and adhesion strength of the hydrogel by increasing the amount of energy dissipation at the nanoscale. This in turn facilitated adequate and stable fixation of bone fracture in wet biological environments. Furthermore, SF@TA@HA promotes the regeneration of bone defects at an early stage in vivo. This work presents a type of bioinspired bone adhesive that is able to provide stable fracture fixation and accelerated bone regeneration during the bone remodeling process.

Polymer Blends for Improved CO2 Capture Membranes.

We investigated the possibility of improving the performance of polysulfone (PSf) membranes to be used in carbon dioxide capture devices by blending PSf with a commercial polyethylene imine, Lupasol G20, previously modified with benzoyl chloride (mG20). Additive amount ranged between 2 and 20 wt %. Membranes based on these blends were prepared by phase inversion precipitation and exhibited different morphologies with respect to neat PSf. Surface roughness, water contact angles, and water uptake increased with mG20 content. Mass transfer coefficient was also increased for both N2 and CO2; however, this effect was more evident for carbon dioxide. Carbon dioxide absorption performance of composite membranes was evaluated for potassium hydroxide solution in a flat sheet membrane contactor (FSMC) in cross flow module at different liquid flow rates. We found that, at the lowest flow rate, membranes exhibit a very similar behaviour to neat PSf; nevertheless, significant differences can be found at higher flow rates. In particular, the membranes with 2 and 5 wt % additive behave more efficiently than neat PSf. In contrast, 10 and 20 wt % additive content has an adverse effect on CO2 capture when compared with neat PSf. In the former case, a combination of additive chemical affinity to CO2 and membrane porosity can be claimed; in the latter case, the remarkably higher wettability and water uptake could determine membrane clogging and consequent loss of efficiency in the capture device.

Offset free data driven control: application to a process control trainer

This work presents a data driven control strategy able to track a set point without steady-state error. The control sequence is computed as an affine combination of past control signals, which belong to a set of trajectories stored in a process historian database. This affine combination is computed so that the variance of the tracking error is minimised. It is shown that offset free control, that is zero mean tracking error, is achieved under the assumption that the state is measurable, the underlying dynamics are linear and the trajectories of the database share the same error dynamics and are in turn offset free. The proposed strategy learns the underlying controller stored in the database while maintaining its offset free tracking capability in spite of differences in the reference, disturbances and operating conditions. No training phase is required and newly obtained process data can be easily taken into account. The proposed strategy, related to direct weight optimisation learning techniques, is tested on a process control trainer.

Frequency-wavenumber spectrum estimation using blended dominant mode rejection beamforming

Capon [Proc. IEEE (1969)] designed the minimum variance distortionless response (MVDR) beamformer to obtain spectral estimates with better resolution than the conventional averaged-periodogram estimator. The MVDR spectrum is a function of the inverse of the sample covariance matrix (SCM), which often must be regularized prior to inversion. To address conditioning problems, Abraham and Owsley [IEEE Oceans (1990)] developed a modified MVDR approach called dominant mode rejection (DMR). The DMR beamformer defines its weights using a structured covariance consisting of a low-rank interference subspace plus an orthogonal noise subspace. It assumes the rank of the interference is known. Recently, Buck and Singer [IEEE SAM (2018)] proposed the blended DMR beamformer that eliminates the need for rank estimation by defining a weight vector that is an affine combination of fixed-rank DMR beamformers. This talk investigates frequency-wavenumber estimation using blended DMR, focusing particularly on efficient implementations for large linear arrays. Adapting the approach described by Therrien [Prentice Hall (1992)] for MVDR, the blended DMR spectrum for an equally spaced array can be computed using fast Fourier transforms of the sample eigenvectors. Results will be illustrated using experimental data from underwater vertical arrays. [Work supported by ONR.]

Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of high-fidelity MRI data is realized by solving a non-convex minimization task for the linear decompression operator and affine combinations of landmark points which locally approximate the latent manifold geometry. An algorithm with guaranteed convergence to stationary solutions of the non-convex minimization task is also provided. The aforementioned framework exploits the underlying spatio-temporal patterns and geometry of the acquired data without any prior training on external data or information. Extensive numerical results on simulated as well as real cardiac-cine MRI data illustrate noteworthy improvements of the advocated machine-learning framework over state-of-the-art reconstruction techniques.