Block-diagonal Research Articles

ABOUT SOME PROBLEMS OF WATERFLOODING IN CARBONATE RESERVOIRS

The features of waterflooding of carbonate (fractured-porous) rocks, caused by the interaction of the system of fractures with the matrix (blocks) of the rock, are considered. It is shown that the slower propagation of the pressure pulse in the rock matrix in comparison with the propagation of this pulse along the fracture system of the formation leads to compression of the rock blocks in the near-wellbore zone of the injection well, as a result of which stress concentration occurs at the ends of vertical fractures, which increases the likelihood of these fractures growing into the roof of the productive formation. It is shown that in order to prevent the development of this process, the growth rate of water injection pressure should be limited in accordance with the time of liquid pressure equalization in the pore space of the rock matrix and in the fracture system. When developing production wells drilled in fractured porous media, in order to prevent the development of the process of closing fractures in the bottomhole zones of these wells, the drawdown reduction rate must also be limited in a similar way. It is noted that when applying technologies for non-stationary flooding of productive reservoirs, the main factor determining their effectiveness is the change in the direction of filtration flows in the reservoir. This leads to the activation of filtration processes in the stagnant zones of the formation and the intensification of the processes of capillary impregnation of low-permeability interlayers with water from more flooded highpermeability interlayers.At the same time, it is important to take into account that when changing the direction of filtration flows at a late stage of development of carbonate reservoirs, in order to prevent reimpregnation of hydrophobic rock blocks with oil, it is more expedient to change the operating modes of production rather than injection wells. It is shown that water flooding of hydrophobic carbonate reservoirs results in incomplete water displacement of oil as a wetting phase from rock blocks. To reduce the residual oil saturation of rock blocks, it is advisable to increase the displacement pressure gradient in the reservoir in combination with a change in the direction of filtration flows in it.

Scaled ILU smoothers for Navier–Stokes pressure projection

AbstractIncomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) ‐cycle for reducing high‐frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill‐level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong‐scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu‐Wind and PeleLM pressure solvers. For large problem sizes, GMRESAMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

Exact solutions for two dimensional [formula omitted] Toda equation

For the two dimensional Toda equation corresponding to the Kac–Moody algebra Dn(1), the Darboux transformation is constructed. The coefficient matrices of the Lax pair of this equation are of even order. Comparing with the scalars in the Darboux matrices for the two dimensional A2n(2) , Cn(1) and Dn+1(2) Toda equations, the structure of the 2 × 2 blocks in the Darboux matrix for this equation is much more complicated. In the construction of Darboux matrices, it is demanded that the solutions of the Lax pair are in Lag(ℂ2n). With the help of a dense subset of Lag(ℂ2n), the nontrivial blocks of the Darboux matrices are represented by elements of O(n,ℂ). Quite a few algebraic techniques are used to simplify the Darboux matrices and to show that the form of the Darboux matrices only depends on the parity of n.

AN ORDER-P TENSOR MULTIPLICATION WITH CIRCULANT STRUCTURE

Research on mathematical operations involving multidimensional arrays or tensors has increased along with the growing applications involving multidimensional data analysis. The -product of order- tensor is one of tensor multiplications. The -product is defined using two operations that transform the multiplication of two tensors into the multiplication of two block matrices, then the result is a block matrix which is further transformed back into a tensor. The composition of both operations used in the definition of -product can transform a tensor into a block circulant matrix. This research discusses the -product of tensors based on their circulant structure. First, we present a theorem of the -product of tensors involving circulant matrices. Second, we use the definition of identity, transpose, and inverse tensors under -product operation and investigate their relationship with circulant matrices. Third, we manifest the computation of the -product involving circulant matrices. The results of the discussion show that the -product of tensors fundamentally involves circulant matrix multiplication, which means that the operation at its core relies on multiplying circulant matrices. This implies the -product operation of tensors having properties analogous to standard matrix multiplication. Furthermore, since the -product of tensors fundamentally involves circulant matrix multiplication, its computation can be simplified by diagonalizing the circulant matrix first using the discrete Fourier transform matrix. Finally, based on the obtained results, an algorithm is constructed in MATLAB to calculate the -product.

Diagonal and off-diagonal blocks of positive definite partitioned matrices

We obtain new relations for the blocks of a positive semidefinite matrix [AXX⁎B] partitioned into four blocks in Mn. A consequence is(0.1)|X+X⁎|≤A+B+14V(A+B)V⁎ for some unitary V∈Mn. Here, for n≥2, the constant 1/4 cannot be replaced by any smaller one. Several eigenvalue inequalities for general matrices follow from our result. We can also derive from (0.1) some triangle type inequalities, for instance for three contractions,(0.2)|S+T+R|≤34I+|S|+|T|+|R| where I stands for the identity. We conjecture that the constant 3/4 is optimal.

Decomposition of kth Order Slant Toeplitz Operators

In this paper, we establish the block matrix decomposition of kth order slant Toeplitz operators. We also establish some relations between the compressions of kth order slant Toeplitz and kth order slant Hankel operators on H2. In the last section, we introduce the notion of kth order slant Toeplitz graphs.

Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries

We study the Hilbert space of the Class 5 model described in arXiv:1904.12005. Despite being integrable, neither its transfer matrix nor its Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz does not provide the full Hilbert space. Instead, we make use of the symmetries of the model to construct the Jordan blocks of the transfer matrix. We also show that the Hamiltonian and the transfer matrix, despite commuting, do not have the same Jordan block structure.

Enumeration of spanning trees in prisms of some graphs

In graph theory, a prism over a graph G is the cartesian product of the graph G with P₂. The purpose of this work is to investigate the complexity of the prisms of some path and cycle-related graphs. In particular, we obtain simpler and more explicit formulas for the complexity of a special class of prisms of path-related graphs: fan graph, ladder graph, the composition Pn[P₂] graph, and book graph. Moreover, we obtain straightforward formulas for the complexity of a special class of prisms of cycle-related graphs: wheel graph, gear graph, prism graph, n−crossed prism graph, mirror graph M(Cn) of even cycle Cn, twisted prism, total graph T(Cn) of the cycle Cn, the friendship graph, the flower graph, and planner sunflower graph. These closed formulas are deduced using some basic properties of block matrix, recurrence relation, eigenvalues of circulant matrices, and orthogonal polynomials.

A nested generalized sidelobe canceller for source counting, localization, and signal separation in reverberant fields

This paper proposes a nested generalized sidelobe canceller (NGSC) for typical array signal processing tasks, including source counting, localization, and signal separation. Multiple blocking matrices are arranged in a nested structure to successively eliminate dominant sources until the remaining signal is predominantly incoherent noise. The microphone signals are dereverberated using a multichannel weighted prediction error algorithm. In source counting, the number of sound sources is determined by tracking the average power of the blocked signal. In source localization, the direction-of-arrival (DOA) is estimated via cosine similarity in conjunction with the golden section search. In signal separation, the estimated DOA enables speech separation in a linearly constrained minimum variance beamformer with postfiltering (LCMV-PF). Monte Carlo simulations are performed to compare the proposed NGSC approach with four baselines, minimum description length, second order statistic of the eigenvalue, multistage Wiener filtering, and multiple signal classification. The results show that NGSC achieves at least 28.80% higher source counting accuracy with a 1.04° lower root mean square degree error than the baselines. The signal-to-distortion ratio achieved by LCMV-PF is 1.52 dB higher than that achieved by the linearly constrained minimum power beamformer and the multichannel Wiener filter.

Large-Scale Meta-Heuristic Feature Selection Based on BPSO Assisted Rough Hypercuboid Approach.

The selection of prominent features for building more compact and efficient models is an important data preprocessing task in the field of data mining. The rough hypercuboid approach is an emerging technique that can be applied to eliminate irrelevant and redundant features, especially for the inexactness problem in approximate numerical classification. By integrating the meta-heuristic-based evolutionary search technique, a novel global search method for numerical feature selection is proposed in this article based on the hybridization of the rough hypercuboid approach and binary particle swarm optimization (BPSO) algorithm, namely RH-BPSO. To further alleviate the issue of high computational cost when processing large-scale datasets, parallelization approaches for calculating the hybrid feature evaluation criteria are presented by decomposing and recombining hypercuboid equivalence partition matrix via horizontal data partitioning. A distributed meta-heuristic optimized rough hypercuboid feature selection (DiRH-BPSO) algorithm is thus developed and embedded in the Apache Spark cloud computing model. Extensive experimental results indicate that RH-BPSO is promising and can significantly outperform the other representative feature selection algorithms in terms of classification accuracy, the cardinality of the selected feature subset, and execution efficiency. Moreover, experiments on distributed-memory multicore clusters show that DiRH-BPSO is significantly faster than its sequential counterpart and is perfectly capable of completing large-scale feature selection tasks that fail on a single node due to memory constraints. Parallel scalability and extensibility analysis also demonstrate that DiRH-BPSO could scale out and extend well with the growth of computational nodes and the volume of data.

Hydroxyurea Improves Intelligence Quotient Scores in Children with Sickle Cell Anemia and Elevated Transcranial Doppler Velocity

Introduction: Structural brain abnormalities resulting from sickle cell disease because of strokes, silent cerebral infarcts (SCI) and other biophysical characteristics of parenchymal damage from repeated sickling affect cognitive functioning. Hydroxyurea therapy reduces transcranial Doppler (TCD) velocities and improves SCI and other neurological outcomes in children with sickle cell anaemia. Hence the objectives of EXpanding Treatment for Existing Neurological Disease (EXTEND, NCT02556099), a phase 2 clinical trial, was to determine whether hydroxyurea titrated to maximum tolerated dose was effective in lowering transcranial Doppler (TCD) velocities and improving cognitive function in Jamaican children with sickle cell anemia (SCA) with increased stroke risk. Methods: Full-Scale Intelligence Quotient (FSIQ), verbal and nonverbal IQ were measured with the Wechsler Abbreviated Scale of Intelligence (WASI-II) at baseline and after 18 months of hydroxyurea treatment in 30 of the 43 enrolled children. Verbal Comprehension Index (VCI) was assessed using the Vocabulary and Similarities subtests. Perceptual Reasoning Index (PRI) was scored with the Block Design and Matrix Reasoning subtests. Members of the team conducting the tests were trained and test results were verified by an experienced member of the Epidemiology Research Unit, Caribbean Institute for Health Research. Participants were enrolled in the EXTEND trial based on a pre-treatment conditional or abnormal TCD velocity. They were assigned to one of three risk categories according to treatment status and stroke history at study enrollment: Group 1 (low stroke risk: no previous stroke, on hydroxyurea treatment n= 12), Group 2 (medium stroke risk: no previous stroke, no hydroxyurea, n=10) and Group 3 (High stroke risk: previous stroke, no hydroxyurea n=8). Anthropometric variables, including height and weight, were recorded as well as oxygen saturation and hematological variables. Differences in post treatment outcome were modelled using mixed linear regression. A p-value of <0.05 was considered statistically significant. Results: There was no difference in mean anthropometric values or gender distribution at baseline by stroke risk category groups (Table 1). The mean(sd) age in years of participants in Group 1 was 8.2(1.7), while for Group 2 the average age was 7.7(2.1) and for Group 3 it was 10.5(2.8). The mean age of Group 3 was significantly greater than Group 1. After 18 months of hydroxyurea treatment, participants were taking an average dose of 25 mg/kg/d, range 13.7 to 34.9 mg/kg/d. On treatment TCD velocities decreased by mean(sd) of 29.5 cm/sec (31.5). Hemoglobin (Hb) concentration was lowest in Group 3 but all groups showed increases during treatment with the rate of increase in Groups 2 and 3 being greater than Group 1 (p<0.001). Absolute neutrophil counts and absolute reticulocyte counts were not different by group, and both decreased significantly post treatment (p<0.001) (Table 1). At both time points, the VCI, PRI and FSIQ mean scores in Group 3 were low [Overall means(sd); 71(11.7), 71(12.6),69(11.6), respectively] and were significantly lower compared with Group 1 (p<0.001) (Table 1). While there was no significant effect of treatment on VCI and PRI scores, the mean FSIQ score increased on average by 2.9 units (95%CI 0.3, 5.4) post treatment among participants. Adjusting for age at enrollment had no effect on the improvement on FSIQ, however adjusting for changes in hemoglobin resulted in an increase in FSIQ by 3.3 units (95%CI -0.4, 7.0) which approached statistical significance (p=0.079). Conclusion: Participants treated with hydroxyurea at maximum tolerated dose for 18 months with or without a previous stroke had significant improvement in hematological variables and neuropsychological scores. Children with sickle cell anemia with high risk of stroke may benefit from routine neuropsychological testing, hydroxyurea treatment in addition to educational interventions.

3-D induction log modelling with integral equation method and domain decomposition pre-conditioning

SUMMARY The deployment of electromagnetic (EM) induction tools while drilling is one of the standard routines for assisting the geosteering decision-making process. The conductivity distribution obtained through the inversion of the EM induction log can provide important information about the geological structure around the borehole. To image the 3-D geological structure in the subsurface, 3-D inversion of the EM induction log is required. Because the inversion process is mainly dependent on forward modelling, the use of a fast and accurate forward modelling tool is essential. In this paper, we present an improved version of the integral equation (IE) based modelling technique for general anisotropic media with domain decomposition pre-conditioning. The discretized IE after domain decomposition equals a fixed-point equation that is solved iteratively with either the block Gauss–Seidel or Jacobi pre-conditioning. Within each iteration, the inverse of the block matrix is computed using a Krylov subspace method instead of a direct solver. An additional reduction in computational time is obtained by using an adaptive relative residual stopping criterion in the iterative solver. Using this domain decomposition scheme, numerical experiments show computation time reductions by factors of 1.97–2.84 compared to solving the full-domain IE with a GMRES solver and a contraction IE pre-conditioner. Additionally, the reduction of memory requirement for covering a large area of the induction tool sensitivity enables acceleration with limited GPU memory. Hence, we conclude that the domain decomposition method is improving the efficiency of the IE method by reducing the computation time and memory requirement.

New lower bounds on crossing numbers of Km,n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{m,n}$$\\end{document} from semidefinite programming

In this paper, we use semidefinite programming and representation theory to compute new lower bounds on the crossing number of the complete bipartite graph Km,n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{m,n}$$\\end{document}, extending a method from de Klerk et al. (SIAM J Discrete Math 20:189–202, 2006) and the subsequent reduction by De Klerk, Pasechnik and Schrijver (Math Prog Ser A and B 109:613–624, 2007). We exploit the full symmetry of the problem using a novel decomposition technique. This results in a full block-diagonalization of the underlying matrix algebra, which we use to improve bounds on several concrete instances. Our results imply that cr(K10,n)≥4.87057n2-10n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathop {\ extrm{cr}}\\limits (K_{10,n}) \\ge 4.87057 n^2 - 10n$$\\end{document}, cr(K11,n)≥5.99939n2-12.5n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathop {\ extrm{cr}}\\limits (K_{11,n}) \\ge 5.99939 n^2-12.5n$$\\end{document}, cr(K12,n)≥7.25579n2-15n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathop {\ extrm{cr}}\\limits (K_{12,n}) \\ge 7.25579 n^2 - 15n$$\\end{document}, cr(K13,n)≥8.65675n2-18n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathop {\ extrm{cr}}\\limits (K_{13,n}) \\ge 8.65675 n^2-18n$$\\end{document} for all n. The latter three bounds are computed using a new and well-performing relaxation of the original semidefinite programming bound. This new relaxation is obtained by only requiring one small matrix block to be positive semidefinite.

Block Diagonalization in the 5G SA Network

In this paper, we did programming regarding the Block diagonalization technology in the 5G standalone SA network, in this program, we have created a 5G site with 16 antennas(minimum of Massive MIMO) and 4 active users equipped of 4 antennas, this system is called Multi Users Massive MIMO system, the link that was chosen is the downlink,we have calculated the maximum throughput in the 5G downlink where we have obained a value of 1673864 b/ms, this value is divided by the number of Massive MIMO layers which worth 16 to get a transport block size of 104616 b/ms (no Cyclic redundancy check CRC). The Block Error rate BLER is null (no detection of errors in reception) because we are in the case of no crc and no channel coding (uncoded transmission), the signal of each user among 4 to be transmitted consists of 4 vectors, each vector has a length of 52308 that corresponds to the number of symbols which are the outputs of Quadrature Phase Shift Keying QPSK Mapping Operation. The received signal at each user equipment UE has a form which can be represented by the multiplication of preconding matrix of this UE with the channel matrix between this UE and the 5G site plus the noise received at the antennas of this UE. the results show that the product of channel gain between UE and the 5G site(known in emission) with the precoding matrix of the other UE gives a matrix which composes of imaginary elements each of which has a real part and imaginary part which both tend to zero(the inter users interferences IUI is canceled). The results show also that when the Signal to Noise Ratio SNR increases(several transmissions) the Bit Error Rate decreases.

The universal envelope of a polarized anti-Jordan triple system of block matrices

We investigate the universal associative envelope [Formula: see text] of the simple polarized anti-Jordan triple system [Formula: see text] of [Formula: see text] [Formula: see text] block matrices: [Formula: see text] with the triple product [Formula: see text] over an algebraically closed field [Formula: see text] of characteristic 0. We prove that [Formula: see text], where [Formula: see text] is the ordinary associative algebra of all [Formula: see text] matrices over [Formula: see text]. From this result we classify up to equivalence all finite-dimensional irreducible representations of the anti-Jordan triple system [Formula: see text]. We conclude the paper with an open problem for further research.

Upper bounds of spectral radius of symmetric matrices and graphs

The spectral radius ρ(A) is the maximum absolute value of the eigenvalues of a matrix A. In this paper, we establish some relationship between the spectral radius of a symmetric matrix and its principal submatrices, i.e., if A is partitioned as a 2×2 block matrix A=(0A12A21A22), then ρ(A)2≤ρ22+θ⁎, where θ⁎ is the largest root of the equation μ2=(x−ν)2(ρ22+x) and ρ2=ρ(A22), μ=ρ(A12A22A21), ν=ρ(A12A21). Furthermore, the results are used to obtain several upper bounds of the spectral radius of graphs, which strengthen or improve some known results.

Revisiting thread configuration of SpMV kernels on GPU: A machine learning based approach

Sparse matrix-vector multiplication (SpMV) optimization on GPUs has been challenging due to irregular memory accesses and unbalanced workloads. The majority of existing solutions assign a fixed number of threads to one or more rows of sparse matrices according to empirical formulas. However, this method does not give the optimal thread configuration and results in a significant performance loss. This paper proposes a new machine learning-based thread assignment strategy for SpMV on GPU, predicting the near-optimal thread configuration for matrices. Further, we partition irregular sparse matrices into blocks according to the distribution of non-zero elements and predict the optimal thread configuration for each block. A new SpMV kernel is designed to accelerate the execution of different blocks. Experimental results show that our machine learning-based approach can select the near-optimal thread configuration for most matrices. The efficiency of SpMV for irregular matrices is also improved by matrix partitioning and blockwise prediction. Finally, we dive into the trained model to find out the connection between the features of a sparse matrix and its optimal thread configuration.

Covariance matrix estimation method of FDA-MIMO radar with low snapshot size

Frequency diverse array and multi-input and multi-output (FDA-MIMO) radar have been applied to many fields due to its angle-range-dependent beampattern. A part of the related array processing algorithms can be successfully used on the basis of the known covariance matrix (CM). The estimation accuracy of the CM directly influences the algorithm performance. In particular, the estimation performance of the sample covariance matrix (SCM) will be degraded shapely once the sample size is less than the channel number. Aiming to improve the estimation accuracy of the SCM with FDA-MIMO radar, we propose a novel shrinkage-to-tapering (ST)-based method combined with the block Toeplitz rectification (STT). Firstly, each block matrix in the CM is processed by using the Toeplitz rectification method, and then, three different estimation matrix structures based on the ST method are proposed. Next, by plugging the unbiased estimators into the optimal shrinkage coefficient and normalized mean square error (MSE), their closed forms of their estimators can be given. The numerical simulation results demonstrate that the proposed three different STT approaches are superior to a number of existing methods in terms of CM estimation performance, and the estimation performance is related with the choice of tapering matrix.

Simulation of SMA-based engineering applications considering large displacement and rotation, thermomechanical coupling and partial phase transformation

Shape memory alloys (SMAs) undergo large recoverable deformation due to their inherent diffusionless martensitic phase transformation. Two factors need to be taken into account to incisively emulate the behaviour of SMA based structures: (i) consideration of large displacement and rotation (LDR) effect, and (ii) capturing the consequence of transformation induced material level coupling. In this study, both these effects are apprehended by extending the infinitesimal strain-based constitutive model of SMA as proposed by Lagoudas et al. (2012), assuming small elastic strain but with finite inelastic strain. To preclude any spurious stress generation out of large rotation, the Jaumann stress rate is used, and incremental objectivity for finite rotation between two successive time instants is conserved by rotating the strain increment and spin tensor to the rotation-independent mid-point configuration following Hughes–Winget (Hughes and Winget, 1980) algorithm. In addition, the contribution of thermoelastic and latent heat evolved during transformation is taken into consideration in the thermal equilibrium equation. Moreover, the effect of partial phase transformation yielding minor hysteresis loop has also been captured. The equilibrium equation is expressed in the current configuration following the Updated Lagrangian formulation. The mechanical and thermal equilibrium equations are solved concurrently in block matrix form using the Newton–Raphson (NR) iterative technique, considering the coupling terms resulting from the phase transformation. The efficacy and robustness of the developed finite element model are corroborated through various practical applications of SMA-based members, e.g., SMA ring, SMA-actuated beam, morphing of corrugated airfoil, orthodontic palatal expander, compliant gripper, undergoing LDR while subjected to different thermomechanical loading conditions. The combined effects of LDR along with thermomechanical coupling yield a stiffening behaviour during loading and sluggish response at the time of thermal recovery.

Autologous tooth bone graft block compared with advanced platelet-rich fibrin in alveolar ridge preservation: A clinico-radiographic study.

To determine the clinico-radiographic efficiency of partially demineralized dentin matrix block (PDDM block), a mixture of PDDM with advanced-platelet-rich fibrin+ (A-PRF+) and injectable platelet-rich fibrin versus A-PRF+ alone in alveolar socket preservation. Sixteen molar teeth indicated for extraction were randomly assigned into two groups. For the test group, sockets were packed with PDDM block and control group, with A-PRF+ plug alone. Clinical and radiographic cone-beam computed tomography methods were used to assess the horizontal and vertical ridge dimensional changes at baseline and 4 months. Clinically, the mid buccal and palatal crestal height (10.25 ± 0.86 and 9.75 ± 0.28 mm) and alveolar ridge width (11.37 ± 0.25 mm) were significantly higher in the test group as compared to the control group, 4 months after tooth extraction (P < 0.01). Radiographically, there was improved apposition and nonsignificant resorption for the test group in ridge height and width, whereas statistically significant higher resorption was seen in the control group at 4 months. The application of the PDDM block demonstrated efficacy in maintaining the dimensions of the extraction socket when compared to A-PRF+ alone. This autologous and immune-free regenerative biomaterial is widely obtainable, offering a glimpse into the potential of next-generation biofuels for regeneration.