Affine Transformation Research Articles

Optimal transport-based machine learning to match specific patterns: application to the detection of molecular regulation patterns in omics data

Abstract We present several algorithms designed to learn a pattern of correspondence between 2 data sets in situations where it is desirable to match elements that exhibit a relationship belonging to a known parametric model. In the motivating case study, the challenge is to better understand micro-RNA regulation in the striatum of Huntington’s disease model mice. The algorithms unfold in 2 stages. First, an optimal transport plan P and an optimal affine transformation are learned, using the Sinkhorn–Knopp algorithm and a mini-batch gradient descent. Second, P is exploited to derive either several co-clusters or several sets of matched elements. A simulation study illustrates how the algorithms work and perform. The real data application further illustrates their applicability and interest.

Cauchy-Stieltjes Kernel families: Some properties

In the setting of the theory of Cauchy-Stieltjes Kernel (CSK) families, we present in this article some properties related to the Marchenko–Pastur and Semicircle laws. Let K+(μ)={Qmμ(dx);m∈(m1μ,m+μ)} be the CSK family generated by a non degenerate probability measure μ with support bounded from above. Firstly, for 0<t≠1 such that Qmμ⊞t is well defined, we prove that if Qmμ⊞t∈K+(μ) then the measure μ is a scale transformation of the Marchenko–Pastur law. Secondly, consider Tβ:x⟼x+β, for β∈R∖{0}. We prove that if Tβ(Qmμ)∈K+(μ), then the measure μ is an affine transformation of the Semicircle law.

Efficiency of Various Tiling Strategies for the Zuker Algorithm Optimization

This paper focuses on optimizing the Zuker RNA folding algorithm, a bioinformatics task with non-serial polyadic dynamic programming and non-uniform loop dependencies. The intricate dependence pattern is represented using affine formulas, enabling the automatic application of tiling strategies via the polyhedral method. Three source-to-source compilers—PLUTO, TRACO, and DAPT—are employed, utilizing techniques such as affine transformations, the transitive closure of dependence relation graphs, and space–time tiling to generate cache-efficient codes, respectively. A dedicated transpose code technique for non-serial polyadic dynamic programming codes is also examined. The study evaluates the performance of these optimized codes for speed-up and scalability on multi-core machines and explores energy efficiency using RAPL. The paper provides insights into related approaches and outlines future research directions within the context of bioinformatics algorithm optimization.

A unified immersed finite element error analysis for one-dimensional interface problems

It has been known that the traditional scaling argument cannot be directly applied to the error analysis of immersed finite elements (IFE) because, in general, the spaces on the reference element associated with the IFE spaces on different interface elements via the standard affine mapping are not the same. By analyzing a mapping from the involved Sobolev space to the IFE space, this article is able to extend the scaling argument framework to the error estimation for the approximation capability of a class of IFE spaces in one spatial dimension. As demonstrations of the versatility of this unified error analysis framework, the manuscript applies the proposed scaling argument to obtain optimal IFE error estimates for a typical first-order linear hyperbolic interface problem, a second-order elliptic interface problem, and the fourth-order Euler-Bernoulli beam interface problem, respectively.

Achieving widely distributed feature matches using flattened-affine-SIFT algorithm for fisheye images.

Performing correction first is the most common methods to address feature matching issues for fisheye images, but corrections often result in significant loss of scene details or stretching of images, leaving peripheral regions without matches. In this paper, we propose a novel approach, named flattened-affine-SIFT, to find widely distributed feature matches between stereo fisheye images. Firstly, we establish a new imaging model that integrates a scalable model and a hemisphere model. Utilizing the extensibility of the imaging model, we design a flattened array model to reduce the distortion of fisheye images. Additionally, the affine transformation is performed on the flattened simulation images, which are computed using the differential expansion and the optimal rigidity transformation. Then feature matches are extracted and matched from the simulated images. Experiments on indoor and outdoor fisheye images show that the proposed algorithm can find a large number of reliable feature matches. Moreover, these matches tend to be dispersed over the entire effective image, including peripheral regions with dramatic distortion.

Deformable 3D/3D CT-to-digital-tomosynthesis image registration in image-guided bronchoscopy interventions

Traditional navigational bronchoscopy procedures rely on preprocedural computed tomography (CT) and intraoperative chest radiography and cone-beam CT (CBCT) to biopsy peripheral lung lesions. This navigational approach is challenging due to the projective nature of radiography, and the high radiation dose, long imaging time, and large footprints of CBCT. Digital tomosynthesis (DTS) is considered an attractive alternative combining the advantages of radiography and CBCT. Only the depth resolution cannot match a full CBCT image due to the limited angle acquisition. To address this issue, preoperative CT is a good auxiliary in guiding bronchoscopy interventions. Nevertheless, CT-to-body divergence caused by anatomic changes and respiratory motion, hinders the effective use of CT imaging. To mitigate CT-to-body divergence, we propose a novel deformable 3D/3D CT-to-DTS registration algorithm employing a multistage, multiresolution approach and using affine and elastic B-spline transformation models with bone and lung mask images. A multiresolution strategy with a Gaussian image pyramid and a multigrid strategy within the B-spline model are applied. The normalized correlation coefficient is included in the cost function for the affine model and a multimetric weighted cost function is used for the B-spline model, with weights determined heuristically. Tested on simulated and real patient bronchoscopy data, the algorithm yields promising results. Assessed qualitatively by visual inspection and quantitatively by computing the Dice coefficient (DC) and the average symmetric surface distance (ASSD), the algorithm achieves mean DC of 0.82±0.05 and 0.74±0.05, and mean ASSD of 0.65±0.29mm and 0.93±0.43mm for simulated and real data, respectively. This algorithm lays the groundwork for CT-aided intraoperative DTS imaging in image-guided bronchoscopy interventions with future studies focusing on automated metric weight setting.

Determining dense velocity fields for fluid images based on affine motion.

In this article, we address the problem of estimating fluid flows between two adjacent images containing fluid and non-fluid objects. Typically, traditional optical flow estimation methods lack accuracy, because of the highly deformable nature of fluid, the lack of definitive features, and the motion differences between fluid and non-fluid objects. Our approach captures fluid motions using an affine motion model for each small patch of an image. To obtain robust patch matches, we propose a best-buddies similarity-based method to address the lack of definitive features but many similar features in fluid phenomena. A dense set of affine motion models was then obtained by performing nearest-neighbor interpolation. Finally, dense fluid flow was recovered by applying the affine transformation to each patch and was improved by minimizing a variational energy function. Our method was validated using different types of fluid images. Experimental results show that the proposed method achieves the best performance.

Comparing lateral plantar process trabecular structure to other regions of the human calcaneus.

Investigating skeletal adaptations to bipedalism informs our understanding of form-function relationships. The calcaneus is an important skeletal element to study because it is a weight-bearing bone with a critical locomotor role. Although other calcaneal regions have been well studied, we lack a clear understanding of the functional role of the lateral plantar process (LPP). The LPP is a bony protuberance on the inferolateral portion of the calcaneus thought to aid the tuberosity in transmission of ground reaction forces during heel-strike. Here, we analyze LPP internal trabecular structure relative to other calcaneal regions to investigate its potential functional affinities. Human calcanei (n = 20) were micro-CT scanned, and weighted spherical harmonic analysis outputs were used to position 251 volumes of interest (VOI) within each bone. Trabecular thickness (Tb.Th), spacing (Tb.Sp), degree of anisotropy (DA), and bone volume fraction (BV/TV) were calculated for each VOI. Similarities in BV/TV and DA (p = 0.2741) between the LPP and inferior tuberosity support suggestions that the LPP is a weight-bearing structure that may transmit forces in a similar direction. The LPP significantly differs from the inferior tuberosity in Tb.Th and Tb.Sp (p < 0.05). Relatively thinner, more closely spaced trabeculae in the LPP may serve to increase internal surface area to compensate for its relatively small size compared to the tuberosity. Significant differences in all parameters between LPP and joint articular surfaces indicate that trabecular morphology is differently adapted for the transmission of forces associated with body mass through joints.

Adaptive locating foveated ghost imaging based on affine transformation

Ghost imaging (GI) has been widely used in the applications including spectral imaging, 3D imaging, and other fields due to its advantages of broad spectrum and anti-interference. Nevertheless, the restricted sampling efficiency of ghost imaging has impeded its extensive application. In this work, we propose a novel foveated pattern affine transformer method based on deep learning for efficient GI. This method enables adaptive selection of the region of interest (ROI) by combining the proposed retina affine transformer (RAT) network with minimal computational and parametric quantities with the foveated speckle pattern. For single-target and multi-target scenarios, we propose RAT and RNN-RAT (recurrent neural network), respectively. The RAT network enables an adaptive alteration of the fovea of the variable foveated patterns spot to different sizes and positions of the target by predicting the affine matrix with a minor number of parameters for efficient GI. In addition, we integrate a recurrent neural network into the proposed RAT to form an RNN-RAT model, which is capable of performing multi-target ROI detection. Simulations and experimental results show that the method can achieve ROI localization and pattern generation in 0.358 ms, which is a 1 × 105 efficiency improvement compared with the previous methods and improving the image quality of ROI by more than 4 dB. This approach not only improves its overall applicability but also enhances the reconstruction quality of ROI. This creates additional opportunities for real-time GI.

Conservation of Affinity Rather Than Sequence Underlies a Dynamic Evolution of the Motif-Mediated p53/MDM2 Interaction in Ray-Finned Fishes.

The transcription factor and cell cycle regulator p53 is marked for degradation by the ubiquitin ligase MDM2. The interaction between these 2 proteins is mediated by a conserved binding motif in the disordered p53 transactivation domain (p53TAD) and the folded SWIB domain in MDM2. The conserved motif in p53TAD from zebrafish displays a 20-fold weaker interaction with MDM2, compared to the interaction in human and chicken. To investigate this apparent difference, we tracked the molecular evolution of the p53TAD/MDM2 interaction among ray-finned fishes (Actinopterygii), the largest vertebrate clade. Intriguingly, phylogenetic analyses, ancestral sequence reconstructions, and binding experiments showed that different loss-of-affinity changes in the canonical binding motif within p53TAD have occurred repeatedly and convergently in different fish lineages, resulting in relatively low extant affinities (KD = 0.5 to 5 μM). However, for 11 different fish p53TAD/MDM2 interactions, nonconserved regions flanking the canonical motif increased the affinity 4- to 73-fold to be on par with the human interaction. Our findings suggest that compensating changes at conserved and nonconserved positions within the motif, as well as in flanking regions of low conservation, underlie a stabilizing selection of "functional affinity" in the p53TAD/MDM2 interaction. Such interplay complicates bioinformatic prediction of binding and calls for experimental validation. Motif-mediated protein-protein interactions involving short binding motifs and folded interaction domains are very common across multicellular life. It is likely that the evolution of affinity in motif-mediated interactions often involves an interplay between specific interactions made by conserved motif residues and nonspecific interactions by nonconserved disordered regions.

Underapproximate Reachability Analysis for a Class of Linear Systems With Inputs

Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear systems typically assume the ability to compute transition matrices and their integrals exactly, which is not feasible in general, and/or suffer from high computational costs. In this note, we attempt to overcome these drawbacks for a class of linear time-invariant (LTI) systems, where we propose a novel method to under-approximate finite-time forward reachable sets and tubes, utilizing approximations of the matrix exponential and its integral. In particular, we consider the class of continuous-time LTI systems with an identity input matrix and initial and input values belonging to full dimensional sets that are affine transformations of closed unit balls. The proposed method yields computationally efficient under-approximations of reachable sets and tubes, when implemented using zonotopes, with first-order convergence guarantees in the sense of the Hausdorff distance. To illustrate its performance, we implement our approach in three numerical examples, where linear systems of dimensions ranging between 2 and 200 are considered.

Tracial oscillation zero and stable rank one

Abstract Let A be a separable (not necessarily unital) simple $C^*$ -algebra with strict comparison. We show that if A has tracial approximate oscillation zero, then A has stable rank one and the canonical map $\Gamma $ from the Cuntz semigroup of A to the corresponding lower-semicontinuous affine function space is surjective. The converse also holds. As a by-product, we find that a separable simple $C^*$ -algebra which has almost stable rank one must have stable rank one, provided it has strict comparison and the canonical map $\Gamma $ is surjective.

Development of a New Affinity Gold Polymer Membrane with Immobilized Protein A.

New and highly selective stationary phases for affinity membrane chromatography have the potential to significantly enhance the efficiency and specificity of therapeutic protein purification by reduced mass transfer limitations. This work developed and compared different immobilization strategies for recombinant Protein A ligands to a gold-sputtered polymer membrane for antibody separation in terms of functionalization and immobilization success, protein load, and stability. Successful, functionalization was validated via X-ray photoelectron spectroscopy (XPS). Here, a recombinant Protein A ligand was coupled by N-hydroxysuccinimide (NHS)/N-(3-dimethylaminopropyl)-N'-ethylcarbodiimide (EDC) chemistry to carboxy-functionalized, gold-sputtered membranes. We achieved a binding capacity of up to 104 ± 17 mg of the protein ligand per gram of the gold-sputtered membrane. The developed membranes were able to successfully capture and release the monoclonal antibody (mAb) Trastuzumab, as well as antibodies from fresh frozen human blood plasma in both static and dynamic setups. Therefore, they demonstrated successful functionalization and immobilization strategies. The antibody load was tested using bicinchoninic acid (BCA), ultraviolet-visible spectroscopy (UV-vis) measurements, and sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE). The outcome is a fully functional affinity membrane that can be implemented in a variety of different antibody purification processes, eliminating the need for creating individualized strategies for modifying the surface to suit different substrates or conditions.

Trajectory tracking with integral action of switched periodic affine systems

This paper deals with integral control of a class of switched affine systems characterised by time-varying differential equations that, along with the discontinuities caused by the switching, also depend periodically on an exogenous parameter, which is an affine function of time. The goal is to design a state-dependent switching function with integral action that ensures global asymptotic tracking of a trajectory of interest. The integral action is responsible for providing robustness to the system against uncertainties and load variations, whenever the discrepancy between the model and the real system is sufficiently bounded. Due to the integrator, all the convex combinations of the dynamic matrices are non-Hurwitz. In this case, the main difficulty is to guarantee that the time derivative of the Lyapunov function is strictly negative definite, which is done by means of LMIs and conditions on the affine terms. To the best of our knowledge, this is the first Lyapunov-based switching rule with integral action able to ensure global asymptotic tracking of a pre-specified profile. When applied to AC circuits the advantage is to design the switching rule based on the original system, without resorting to averaged models. The theory is illustrated by the control of a three-phase AC-DC converter.

Human brain mapping of homotopic functional affinity

Human brain mapping of homotopic functional affinity

Gini-stable Lorenz curves and their relation to the generalised Pareto distribution

We introduce an iterative discrete information production process where we can extend ordered normalised vectors by new elements based on a simple affine transformation, while preserving the predefined level of inequality, G, as measured by the Gini index.Then, we derive the family of empirical Lorenz curves of the corresponding vectors and prove that it is stochastically ordered with respect to both the sample size and G which plays the role of the uncertainty parameter. We prove that asymptotically, we obtain all, and only, Lorenz curves generated by a new, intuitive parametrisation of the finite-mean Pickands' Generalised Pareto Distribution (GPD) that unifies three other families, namely: the Pareto Type II, exponential, and scaled beta distributions. The family is not only totally ordered with respect to the parameter G, but also, thanks to our derivations, has a nice underlying interpretation. Our result may thus shed a new light on the genesis of this family of distributions.Our model fits bibliometric, informetric, socioeconomic, and environmental data reasonably well. It is quite user-friendly for it only depends on the sample size and its Gini index.

A continuous-time neurodynamic approach in matrix form for rank minimization

This article proposes a continuous-time neurodynamic approach for solving the rank minimization under affine constraints. As opposed to the traditional neurodynamic approach, the proposed neurodynamic approach extends the form of the variables from the vector form to the matrix form. First, a continuous-time neurodynamic approach with variables in matrix form is developed by combining the optimal rank r projection and the gradient. Then, the optimality of the proposed neurodynamic approach is rigorously analyzed by demonstrating that the objective function satisfies the functional property which is called as (2r,4r)-restricted strong convexity and smoothness ((2r,4r)-RSCS). Furthermore, the convergence and stability analysis of the proposed neurodynamic approach is rigorously conducted by establishing appropriate Lyapunov functions and considering the relevant restricted isometry property (RIP) condition associated with the affine transformation. Finally, through experiments involving low-rank matrix recovery under affine transformations and the completion of low-rank real image, the effectiveness of this approach has been demonstrated, along with its superiority compared to the vector-based approach.

An analytic approach for the moment-of-fluid interface reconstruction method on tetrahedral meshes

This article presents an original fast and robust approach for solving the moment-of-fluid interface reconstruction problem on tetrahedral meshes. We establish an explicit parametrization of the locus of the centroids under volume constrains using the spherical coordinates on a reference tetrahedron. This parametrization allows to write the moment-of-fluid objective function and its gradient by means of analytic formulas. Then, we show that the minimization problem on arbitrary tetrahedra can be effectively solved on the reference tetrahedron by using an affine transformation. Based on this transformation, we propose a improved technique for obtaining an initial condition for the minimization algorithm. We then describe the Gauss-Newton and the BFGS minimization algorithms, both combined with a trust-region method, to solve this reconstruction problem. Finally, we perform a verification and validation process on a series of increasingly complex test cases. These tests show that the proposed analytic method, paired with the Gauss-Newton algorithm, outperforms the other methods that were tested.

On the Construction of 3D Fibonacci Spirals

The paper aims to extend the classical two-dimensional (2D) Fibonacci spiral into three-dimensional (3D) space by using geometric constructions starting from cubic Fibonacci identities and relying on affine maps and parametrizations of the curves. We have already performed a comprehensive survey of cubic Fibonacci identities, which, to our surprise, uncovered only a handful of homogenous cubic identities. Obviously, the goal here is to show how one could use a particular homogenous cubic Fibonacci identity for generating 3D geometric designs similar in spirit to the way the classical Fibonacci spiral is built in 2D starting from a quadratic Fibonacci identity. This made us realize that for any cubic identity there are many different ways of packing cuboids, while only an insignificant fraction of those possible tilings might allow a smooth spiral-like curve to be drawn through them. After reviewing the state of the art, we present accurate details on ways to construct such 3D spirals using affine maps. We go on to prove the continuity and smoothness of such 3D spirals by giving a parametrization of the intersection of the surfaces that define the curves. Throughout the paper, we visualize the resulting 3D spirals by generating geometrically correct stereoscopic views. Finally, it is to be mentioned that the recursive 3D packing of cuboids tends to lead to fractal structures, which will need further investigations.

Robust registration of multi-modal remote sensing images based on multi-dimensional oriented self-similarity features

Registration of multi-modal remote sensing images (MRSI) is crucial for unlocking the full potential of heterogeneous remote sensing imagery. However, achieving accurate registration among MRSI is challenging due to the trade-off between geometric invariance and matching accuracy, caused by differences in signal-to-noise ratio and nonlinear radiometric distortion (NRD) arising from varying imaging mechanisms. To tackle the challenge, this paper proposes a lightweight and hybrid feature-guided registration algorithm for MRSI called the hybrid registration algorithm based on multi-dimensional oriented self-similarity features (MOSS). MOSS leverages the advantages of multi-dimensional oriented self-similarity features to progressively enhance registration performance. In the hybrid feature coarse matching stage, oriented self-similarity features are extracted from MRSI, and their directional information is utilized for feature description to estimate the initial affine transformation. The fine matching under multi-dimensional oriented self-similarity features stage takes the outputs of the coarse matching stage to perform a template-like matching process. To evaluate the performance of MOSS, comprehensive experiments are conducted using six different combinations of MRSI, and seven state-of-the-art registration algorithms are selected for comparison. The experimental results demonstrate that MOSS outperforms the compared methods, with the number of correct matches being at least about 1.6 times higher than the comparison methods. Moreover, MOSS exhibits the lowest root mean square error across all experiments, with an average RMSE of 1.86 pixels, achieving an RMSE within 2 pixels. This highlights its effectiveness in achieving precise alignment and robust registration of MRSI.