Small Matrix Research Articles

PathSum: A C++ and Fortran suite of fully quantum mechanical real-time path integral methods for (multi-)system + bath dynamics.

This paper reports the release of PathSum, a new software suite of state-of-the-art path integral methods for studying the dynamics of single or extended systems coupled to harmonic environments. The package includes two modules, suitable for system-bath problems and extended systems comprising many coupled system-bath units, and is offered in C++ and Fortran implementations. The system-bath module offers the recently developed small matrix path integral (SMatPI) and the well-established iterative quasi-adiabatic propagator path integral (i-QuAPI) method for iteration of the reduced density matrix of the system. In the SMatPI module, the dynamics within the entanglement interval can be computed using QuAPI, the blip sum, time evolving matrix product operators, or the quantum-classical path integral method. These methods have distinct convergence characteristics and their combination allows a user to access a variety of regimes. The extended system module provides the user with two algorithms of the modular path integral method, applicable to quantum spin chains or excitonic molecular aggregates. An overview of the methods and code structure is provided, along with guidance on method selection and representative examples.

Cd113 β -decay spectrum and gA quenching using spectral moments

We present an alternative analysis of the $^{113}\mathrm{Cd}\phantom{\rule{4pt}{0ex}}\ensuremath{\beta}$-decay electron energy spectrum in terms of spectral moments ${\ensuremath{\mu}}_{n}$, corresponding to the averaged values of $n\mathrm{th}$ powers of the $\ensuremath{\beta}$ particle energy. The zeroth moment ${\ensuremath{\mu}}_{0}$ is related to the decay rate, while higher moments ${\ensuremath{\mu}}_{n}$ are related to the spectrum shape. The here advocated spectral-moment method (SMM) allows for a complementary understanding of previous results, obtained using the so-called spectrum-shape method (SSM) and its revised version, in terms of two free parameters: $r={g}_{\mathrm{A}}/{g}_{\mathrm{V}}$ (the ratio of axial-vector to vector couplings) and $s$ (the small vectorlike relativistic nuclear matrix element, $s$-NME). We present numerical results for three different nuclear models with the conserved vector current hypothesis (CVC) assumption of ${g}_{\mathrm{V}}=1$. We show that most of the spectral information can be captured by the first few moments, which are simple quadratic forms (conic sections) in the $(r,\phantom{\rule{0.16em}{0ex}}s)$ plane: An ellipse for $n=0$ and hyperbolas for $n\ensuremath{\ge}1$, all being nearly degenerate as a result of cancellations among nuclear matrix elements. The intersections of these curves, as obtained by equating theoretical and experimental values of ${\ensuremath{\mu}}_{n}$, identify the favored values of $(r,\phantom{\rule{0.16em}{0ex}}s)$ at a glance, without performing detailed fits. In particular, we find that values around $r\ensuremath{\approx}1$ and $s\ensuremath{\approx}1.6$ are consistently favored in each nuclear model, confirming the evidence for ${g}_{\mathrm{A}}$ quenching in $^{113}\mathrm{Cd}$, and shedding light on the role of the $s$-NME. We briefly discuss future applications of the SMM to other forbidden $\ensuremath{\beta}$-decay spectra sensitive to ${g}_{\mathrm{A}}$.

Efficient segment-update block LMS-Newton algorithm for active control of road noise

For active control of road noise inside a vehicle, many reference signals are required in adaptive control systems, resulting in slow convergence speeds and heavy computational loads. In this paper, a means of reducing the computational complexity of adaptive control algorithms is investigated based on the fast-converging least-mean-squares Newton (LMS-Newton) algorithm. By analyzing the autocorrelation matrix of reference signals filtered by secondary paths, it is found that the dimensions of the autocorrelation matrix of filtered reference signals do not necessarily have to equal the dimensions of the adaptive control filters, and instead the dimensions can be determined from the correlation between reference signals filtered by secondary paths. Then a computationally efficient segment-update block algorithm is proposed that splits adaptive control filters into several segments and the coefficients of each segment are updated independently. Theoretical analysis shows that the proposed segment-update block algorithm has similar convergence speed and noise-reduction performance as the traditional LMS-Newton algorithm when a segment of appropriate length is chosen, but the computational complexity is reduced dramatically because the inverse autocorrelation matrix is replaced by a smaller matrix. The performance of the proposed algorithm is verified through simulation experiments with different recorded road noises and secondary paths, and the results are compared with those of some typical algorithms. The simulation results showed that the proposed algorithm achieved a similar noise-reduction performance with an approximately 8.9-times reduction of computational complexity compared with the traditional LMS-Newton algorithm.

Evaluation of the efficiency of implementation of asynchronous computing algorithms using coroutines and threads in С++

Modern multi-core systems are most effective when used in large server centers and for cloud computing. However, despite the known complexity of software implemen-tation, parallel computing on multiprocessors is increasingly used in computer model-ling. Advanced mechanisms of synchronous and multithreaded programming are in-creasingly used to improve the productivity of numerical studies, reducing the time of computer models implementation. One such mechanism is coroutines, a convenient tool for managing asynchronous operations introduced in the C++20 standard. A special feature of coroutines is the ability to suspend a function at a certain stage, saving its state, and after some time resume its execution from the previous stop. The aim of this research is to improve the performance of computer modelling by using coroutines and data threads. As a result of the work, a test algorithm for multiplying a matrix by a vector and its modified asynchronous version using the coroutine mechanism and splitting into two data threads was developed, which allowed to achieve 1.94 times increase in the com-puting speed when the matrix dimension is 15000 (2.25×106 elements). It has been found that at a small matrix dimension, the developed asynchronous algorithm using coroutines and splitting into two threads is less efficient than the single thread algo-rithm. This is due to the fact that the compiler needs some time to create threads and start execution simultaneously. With a large dimensionality, the performance of the asynchronous algorithm increases significantly. With a matrix dimension of more than 1200, the use of an asynchronous algorithm divided into two threads is guaranteed to be more efficient than a single-threaded. The data obtained are consistent with the results of similar studies of the problem of increasing the efficiency of computer modelling using alternative software and hard-ware. The new method of solving the problems of asynchronous programming provides a more efficient and simple mechanism for managing asynchronous operations.

Generalized Data–Driven Predictive Control: Merging Subspace and Hankel Predictors

Data–driven predictive control (DPC) is becoming an attractive alternative to model predictive control as it requires less system knowledge for implementation and reliable data is increasingly available in smart engineering systems. Two main approaches exist within DPC: the subspace approach, which estimates prediction matrices (unbiased for large data) and the behavioral, data-enabled approach, which uses Hankel data matrices for prediction (allows for optimizing the bias/variance trade–off). In this paper we develop a novel, generalized DPC (GDPC) algorithm by merging subspace and Hankel predictors. The predicted input sequence is defined as the sum of a known, baseline input sequence, and an optimized input sequence. The corresponding baseline output sequence is computed using an unbiased, subspace predictor, while the optimized predicted output sequence is computed using a Hankel matrix predictor. By combining these two types of predictors, GDPC can achieve high performance for noisy data even when using a small Hankel matrix, which is computationally more efficient. Simulation results for a benchmark example from the literature show that GDPC with a reduced size Hankel matrix can match the performance of data–enabled predictive control with a larger Hankel matrix in the presence of noisy data.

NSGA-II/SDR-OLS: A Novel Large-Scale Many-Objective Optimization Method Using Opposition-Based Learning and Local Search

Recently, many-objective optimization problems (MaOPs) have become a hot issue of interest in academia and industry, and many more many-objective evolutionary algorithms (MaOEAs) have been proposed. NSGA-II/SDR (NSGA-II with a strengthened dominance relation) is an improved NSGA-II, created by replacing the traditional Pareto dominance relation with a new dominance relation, termed SDR, which is better than the original algorithm in solving small-scale MaOPs with few decision variables, but performs poorly in large-scale MaOPs. To address these problems, we added the following improvements to the NSGA-II/SDR to obtain NSGA-II/SDR-OLS, which enables it to better achieve a balance between population convergence and diversity when solving large-scale MaOPs: (1) The opposition-based learning (OBL) strategy is introduced in the initial population initialization stage, and the final initial population is formed by the initial population and the opposition-based population, which optimizes the quality and convergence of the population; (2) the local search (LS) strategy is introduced to expand the diversity of populations by finding neighborhood solutions, in order to avoid solutions falling into local optima too early. NSGA-II/SDR-OLS is compared with the original algorithm on nine benchmark problems to verify the effectiveness of its improvement. Then, we compare our algorithm with six existing algorithms, which are promising region-based multi-objective evolutionary algorithms (PREA), a scalable small subpopulation-based covariance matrix adaptation evolution strategy (S3-CMA-ES), a decomposition-based multi-objective evolutionary algorithm guided by growing neural gas (DEA-GNG), a reference vector-guided evolutionary algorithm (RVEA), NSGA-II with conflict-based partitioning strategy (NSGA-II-conflict), and a genetic algorithm using reference-point-based non-dominated sorting (NSGA-III).The proposed algorithm has achieved the best results in the vast majority of test cases, indicating that our algorithm has strong competitiveness.

Coherence Maps and Flow of Excitation Energy in the Bacterial Light Harvesting Complex 2.

We present and analyze coherence maps [ J. Phys. Chem. B 2022, 126, 9361-9375] to investigate the quantum coherences that are created, sustained, and damped by vibrational modes during the transfer of excitation energy from the B800 (outer) to the B850 (inner) ring of the light harvesting complex 2 (LH2) of purple bacteria with a variety of initial conditions. The reduced density matrix of the 24-pigment complex, where the ground and excited electronic states of each bacteriochlorophyll are explicitly coupled to 50 intramolecular vibrations at room temperature, is obtained from fully quantum-mechanical small matrix path integral (SMatPI) calculations. The coherence maps show a very rapid localization within the outer ring, accompanied by the formation of inter-ring quantum superpositions that evolve to a partial quantum delocalization at equilibrium, and quantify in state-to-state detail the flow of energy within the complex.

The integration of the small‐island effect and nestedness pattern

AbstractAimThe small‐island effect (SIE) and nestedness are two important patterns in the fields of island biogeography and community ecology. However, to date, no study has tried to integrate the SIE and nestedness pattern. Therefore, the aim of this study was to integrate these two biogeographical patterns by proposing a new integrative hypothesis. The integrative hypothesis posits that the degree of nestedness of the large island matrix will be larger than that of the small island matrix split by the threshold of the SIE.LocationGlobal.TaxonPlants, invertebrates and vertebrates.MethodsWe compiled 219 global datasets with both the presence‐absence matrices and the variables of area and species richness. We also collected six island characteristics influencing the SIE and nestedness patterns, that is island type, taxonomic group, area range, the number of islands, species range and matrix fill. We applied breakpoint regressions to detect SIEs and used the metric NODF (Nestedness metric based on Overlap and Decreasing Fill) to quantify nestedness. We then employed logistic regressions and an information‐theoretic approach to determine which combination of island characteristics was important in determining whether the integrative hypothesis was supported.ResultsAmong the 92 datasets in which SIEs were unambiguously detected, nestedness analyses showed that in 64 cases (69.6%) the values of NODFc (nestedness among sites) for the large island matrices were larger than those of the small island matrices. Matrix fill and area range were substantially important in determining whether the integrative hypothesis was supported. By contrast, island type, taxonomic group, the number of islands and species range received considerably less support.Main ConclusionsOur study was the first to integrate the SIE and nestedness pattern. Overall, we found prevalent support for our integrative hypothesis. The integration of the SIE and nestedness provides new and interesting insights into these two biogeographical patterns.

A Wave Equation-Based Hybridizable Discontinuous Galerkin–Robin Transmission Condition Algorithm for Electromagnetic Problems Analyzing

In this work, a wave-equation-based discontinuous Galerkin (DG) method hybridized with the Robin transmission condition (DG-RTC) is developed to solve the frequency-domain electromagnetic (EM) problems. The proposed DG method directly discretizes the vector electric field wave equation in each subdomain, and subsequently, a term named numerical flux is introduced at the subdomain interfaces to connect the solutions between neighboring subdomains. However, the numerical flux depends not only on the electric field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {E}$ </tex-math></inline-formula> but also on the magnetic field <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {H}$ </tex-math></inline-formula> residing over the interface. Thereby, another equation is essential for solving <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {E}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {H}$ </tex-math></inline-formula> simultaneously. Realizing that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {H}$ </tex-math></inline-formula> only situates at the interface of adjacent subdomains, it is thus desired that the auxiliary equation also merely involves <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {H}$ </tex-math></inline-formula> at the interfaces. To reach this aim, at the subdomain interfaces, a Robin transmission condition (RTC) based on the tangential continuity of EM fields across the interface is introduced as the second equation. With this proposed DG-RTC algorithm, only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {E}$ </tex-math></inline-formula> is a volume variable, while <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {H}$ </tex-math></inline-formula> is a two-dimensional (2-D) one, and the degrees of freedom (DoFs) are thus greatly reduced compared with the traditional DG method. On the other hand, in the frequency domain, the established subdomain matrix equations are implicitly coupled with each other, resulting in a global matrix system. Directly solving it is not yet cheap. To alleviate the computational cost, a finite-element tearing and interconnecting (FETI)-like approach resorts. With the block-diagonal preconditioner and a restriction operator, the global matrix is decomposed into a surface matrix equation and several local matrix equations pertinent to each subdomain. In this way, a direct solver can be applied to solve these small matrix equations efficiently. To validate the proposed DG method in solving various EM problems, several representative examples are presented.

Fast low-rank-matrix-based connection center evolution for large hyperspectral image clustering

Clustering is a common data processing technique and has been increasingly applied in remote sensing processing. In recent years, a novel clustering algorithm called connection center evolution (CCE) has been proposed. To a certain extent, CCE solves the parameter sensitivity problem, which generally exists in traditional clustering algorithms. However, CCE is not feasible for handling large hyperspectral images (HSI) due to its computational bottlenecks. That is, when the size of HSI to be processed is large, the construction of the similarity matrix and the calculation of its power have very high space complexity and time complexity, respectively. To solve this problem, we propose a novel approach for large HSI datasets, named fast low-rank-matrix-based connectivity center evolution (LMCCE). The proposed LMCCE algorithm first introduces the KNN graph into CCE to construct a sparse similarity matrix, effectively reducing its space complexity. Then, symmetric non-negative matrix factorization (SymNMF) is used for the similarity matrix, which can maintain most of the information while reducing the redundancy and noise in similarity matrix. Furthermore, by performing SymNMF on the similarity matrix, the problem of calculating the power of the similarity matrix is transformed into the problem of calculating the power of a small matrix, which significantly reduces the time complexity. Experimental results on several synthetic and real HSI datasets demonstrate that the proposed LMCCE algorithm is faster than CCE, and can handle large HSI while achieving superior performance compared to state-of-the-art clustering methods.

Biomechanical comparison of porcine mitral leaflets with porcine small intestinal submucosa extracellular matrix.

Porcine small intestinal submucosa extracellular matrix (SIS-ECM) used for cardiac valve repair has shown conflicting clinical outcomes with respect to calcification and failure. This may be related to differences in biomechanical properties of the material compared with the host site. The aim of this study was to compare the biomechanical properties of porcine mitral valve leaflets with SIS-ECM. Fresh porcine anterior and posterior mitral leaflet samples were cut radially and circumferentially. Similarly, 2- and 4-layered SIS-ECM were cut in orthogonal directions: length and width. Samples were subjected to a uniaxial tensile test or a dynamic mechanical analysis. Results show that the load of the porcine anterior circumferential leaflet was 39.5 N (2.4-48.5 N), which was significantly higher compared with the 2-layered length SIS-ECM which was 7.5 N (7-7.9 N), and the 4- layered length SIS-ECM which was 7.5 N (7.1-8.1 N) (p < 0.001). The load of the posterior circumferential leaflet was 9.7 N (8.3-10.7 N), which is still significantly higher when compared with the two versions of SIS-ECM. The degree of anisotropy (i.e. the ratio between circumferential-radial and width-length properties) was higher for the anterior- (ratio: 19) and posterior leaflet (ratio: 6) than the 2-layered (ratio: 5.1) and 4-layered SIS-ECM (ratio: 1.9). Especially 2-layered SIS-ECM more closely resembles the posterior mitral leaflet than the anterior mitral leaflet tissue and would be more suitable as a repair material in this position. Additionally, the anisotropic properties of mitral leaflets and SIS-ECM underscore the importance of correct orientation of the implant to ensure optimal reconstruction.

Acellular biomaterial modulates myocardial inflammation and promotes endogenous mechanisms of postinfarct cardiac repair.

After myocardial infarction, we previously showed that epicardial implantation of porcine small intestinal submucosal extracellular matrix (SIS-ECM) improves postinfarct cardiac function through fibroblast-mediated angiogenic and antifibrotic pathways. Herein, we characterize how SIS-ECM also coordinates a reparative cardiac inflammatory response. RNA sequencing and multiplex characterized modulation of fibroblast transcriptional and paracrine activity by SIS-ECM. Inhibitors of fibroblast growth factor 2 and toll-like receptor 9 elucidated mechanism. Mice received coronary ligation (infarction) and either SIS-ECM implantation (treatment) or sham surgery (control). Flow cytometry of SIS-ECM and the murine myocardium quantified monocytes, neutrophils, and proangiogenic subtypes. Microscopy tracked fibroblasts and immune cells, and characterized myocardial angiogenesis. SIS-ECM increased fibroblast transcription of inflammatory pathways and production of angiogenic vascular endothelial growth factor and inflammatory cytokines via fibroblast growth factor 2 and toll-like receptor 9-dependent pathways. Two-photon microscopy showed that SIS-ECM became engrafted by native fibroblasts and leukocytes, subsequently increasing release of inflammatory cytokines and angiogenic vascular endothelial growth factor. On flow cytometry, SIS-ECM implantation increased day-7 myocardial counts of neutrophils, inflammatory monocytes, and proangiogenic vascular endothelial growth factor recptor 1 subtypes. SIS-ECM has a higher proportion of proangiogenic leukocytes compared with the myocardium. Resonant confocal microscopy showed neovascularization near SIS-ECM. SIS-ECM promotes engraftment by native fibroblasts and leukocytes, and modulates fibroblast activity via fibroblast growth factor 2 and toll-like receptor 9 to potentiate a proangiogenic inflammatory response. Subsequently, the material increases myocardial counts of reparative proangiogenic leukocytes that can induce neovascularization. This reparative inflammatory response may explain previously reported functional improvements. Fibroblast growth factor 2 and toll-like receptor 9 mechanisms can be leveraged to design next-generation materials for postinfarct cardiac repair.

Numerical simulation of fluid flow with a fast Boundary‐Domain Integral Method

AbstractFor the simulation of fluid flow the velocity‐vorticity formulation of the Navier‐Stokes equations can be used. Approximating the first order time derivative in these equations by finite differences, essentially, the Yukawa equation for the velocity has to be solved with an inhomogeneity governed by the vorticity. Applying the Boundary Element Method to such problems is not straightforward. However, the Boundary‐Domain Integral Method (BDIM) can be used, which requires to solve beside the boundary integrals as well a domain integral due to the inhomogeneity. Classical BEM formulations have a quadratic complexity with respect to the unknowns on the boundary and, for the BDIM additionally, for the unknowns in the domain. This prevents the BDIM from being applied to real‐world problems.To reduce the quadratic complexity in BEM, approximation methods like the fast multipole method, ℋ‐matrices in combination with the adaptive cross approximation or the ℋ2 ‐matrix technique can be used. All these methods reduce the complexity to an almost linear order. Here, the ℋ2 ‐matrix technique is applied to reduce storage and computing time for the right hand side, i.e., for the matrix of the domain integrals. Based on interpolatory kernel expansions and an heuristic criterium for too small matrix entries an almost linear complexity can be achieved. The numerical studies focus on a lid‐driven cavity. The complexity reduction is demonstrated.

Correlating variables with different scale types: A new framework based on matrix comparisons

AbstractEcological variables may be expressed on four basic measurement scales (nominal, ordinal, interval or ratio), whereas circular variables and those combining a nominal state with other scale types are also common. However, existing methods are not suited to calculate correlations between all pairwise combinations of such variables, preventing the application of standard multivariate techniques.The essence of the new approach is to derive a so‐called difference semimatrix for all pairs of observations for each variable, and then to calculate the matrix correlation based on two such semimatrices. The advantage of this function, termedd‐correlation, is that comparisons are made on the same logical basis regardless of the measurement scale, allowing for the use of principal components analysis to visualize interrelationships among many variables simultaneously. Further advantages are that missing values in the data are tolerated and that the Gower index of dissimilarity between objects may also be computed.The use of the method is demonstrated on a small toy matrix, an artificial plant trait matrix and a large dataset summarizing ecological features of all vascular plant species of Sardinia, Italy. The source code in R and FORTRAN, and applications for three different operation systems, are provided for computations with results serving as input for other statistical software.The new computational framework will allow the comparison of any types of ecological traits in a mathematically meaningful manner. This option was not available earlier in the field of multivariate statistics, and the method is expected to receive applications in other subject areas as well in which many objects are described in terms of variables expressed on different measurement scales.

Role of small intestinal submucosa extracellular matrix in advanced regenerative wound therapy.

Advanced regenerative therapies using cellular and tissue-based products (CTPs) can play an important role in effective management of hard-to-heal wounds. CTPs derived from allogenic or xenogenic tissues use an extracellular matrix (ECM) to provide a therapeutic ECM scaffold in the wound bed to facilitate tissue regeneration. One such example is OASIS Extracellular Matrix (Cook Biotech Incorporated), a porcine small intestinal submucosa extracellular matrix (SIS-ECM) that preclinical and clinical data have shown to be tolerable and effective in promoting tissue regeneration in hard-to-heal wounds.

Controlling Morphology and Voltage Loss with Ternary Strategy Triggers Efficient All-Small-Molecule Organic Solar Cells

Herein, an emerging acceptor L8-BO as the third component was combined with the B1:BO-4Cl system for constructing efficient ternary all-small-molecule organic solar cells (ASM-OSCs). Theoretical, morphological, and crystallographic studies reveal that L8-BO and BO-4Cl possess good compatibility, resulting in alloy-like state formation of two acceptors in ternary blends. The synergistic effect of two acceptors is conducive to forming favorable phase separation and molecular stacking for promoting charge splitting and extraction, which contributes to simultaneously boosting short-circuit current density and fill factor. Furthermore, the alloy-like state of two acceptors and the higher lowest unoccupied molecular orbital energy level of L8-BO assist ternary ASM-OSCs in achieving lower voltage loss with respect to the binary devices. The optimal ternary ASM-OSCs with 20 wt % L8-BO deliver a top-level efficiency of 17.10%. This work demonstrates that not only the morphology but also the voltage loss of the small molecular matrix can be well-manipulated by employing the ternary strategy.

Improving the Effective Spatial Resolution in 1H-MRSI of the Prostate with Three-Dimensional Overdiscretized Reconstructions.

In in vivo 1H-MRSI of the prostate, small matrix sizes can cause voxel bleeding extending to regions far from a voxel, dispersing a signal of interest outside that voxel and mixing extra-prostatic residual lipid signals into the prostate. To resolve this problem, we developed a three-dimensional overdiscretized reconstruction method. Without increasing the acquisition time from current 3D MRSI acquisition methods, this method is aimed to improve the localization of metabolite signals in the prostate without compromising on SNR. The proposed method consists of a 3D spatial overdiscretization of the MRSI grid, followed by noise decorrelation with small random spectral shifts and weighted spatial averaging to reach a final target spatial resolution. We successfully applied the three-dimensional overdiscretized reconstruction method to 3D prostate 1H-MRSI data at 3T. Both in phantom and in vivo, the method proved to be superior to conventional weighted sampling with Hamming filtering of k-space. Compared with the latter, the overdiscretized reconstructed data with smaller voxel size showed up to 10% less voxel bleed while maintaining higher SNR by a factor of 1.87 and 1.45 in phantom measurements. For in vivo measurements, within the same acquisition time and without loss of SNR compared with weighted k-space sampling and Hamming filtering, we achieved increased spatial resolution and improved localization in metabolite maps.

Simultaneous Decorrelation of Matrix Time Series

ABSTRACT We propose a contemporaneous bilinear transformation for a p × q matrix time series to alleviate the difficulties in modeling and forecasting matrix time series when p and/or q are large. The resulting transformed matrix assumes a block structure consisting of several small matrices, and those small matrix series are uncorrelated across all times. Hence, an overall parsimonious model is achieved by modeling each of those small matrix series separately without the loss of information on the linear dynamics. Such a parsimonious model often has better forecasting performance, even when the underlying true dynamics deviates from the assumed uncorrelated block structure after transformation. The uniform convergence rates of the estimated transformation are derived, which vindicate an important virtue of the proposed bilinear transformation, that is, it is technically equivalent to the decorrelation of a vector time series of dimension max(p, q) instead of p × q. The proposed method is illustrated numerically via both simulated and real data examples. Supplementary materials for this article are available online.

Role of small intestinal submucosa extracellular matrix in advanced regenerative wound therapy.

Advanced regenerative therapies using cellular and tissue-based products (CTPs) can play an important role in effective management of hard-to-heal wounds. CTPs derived from allogenic or xenogenic tissues use an extracellular matrix (ECM) to provide a therapeutic ECM scaffold in the wound bed to facilitate tissue regeneration. One such example is OASIS Extracellular Matrix (Cook Biotech Incorporated), a porcine small intestinal submucosa extracellular matrix (SIS-ECM) that preclinical and clinical data have shown to be tolerable and effective in promoting tissue regeneration in hard-to-heal wounds.

Clinical benefits of small intestinal submucosa extracellular matrix and review of the evidence.

There is a clear scientific rationale for using cellular, acellular and matrix-like products (CAMPs), such as small intestinal submucosa extracellular matrix (SIS-ECM), in hard-to-heal wounds, such as diabetic foot ulcers (DFUs), venous leg ulcers (VLUs), pressure ulcers and arterial leg ulcers. The clinical evidence supporting the use of SIS-ECM has grown over the past several decades. This evidence base now encompasses a wide range of hard-to-heal wound indications, including DFUs and VLUs, as well as increasingly complex acute wound indications, such as delayed postoperative wounds, traumatic wounds and burns. The aim of this article is to review the steadily amassed body of evidence that describes the clinical outcomes associated with treatment with SIS-ECM and its potential implications for the overall costs of treatment.