Matrix Model Research Articles

Mechanical Properties of End-of-life Waste Tyres Steel Fibre Reinforced Concrete: RSM-Based Modelling and Optimisation

The influence of fibres on the compressive strength of concrete is complex and is determined by the type, quantity, and characteristics of the fibres utilized in designing and forming the concrete. Designing fibre reinforced concrete (FRC) constituents is challenging and affects the concrete's performance and practicality. This study utilized response surface methodology (RSM) to optimize the properties of concrete containing steel fibre extracted from end-of-life tyres (ELTs). Face-cantered central composite design (FC-CCD) of RSM was used in the design of experiments (DOE) with aspect ratio (10-70) and volume fraction (0.5 % - 1.2 %) as the input variables. Three levels of each variable were used in forming the design matrix. The resulting concretes were then tested for slump and compressive strength at 7 and 28 days of curing. As the aspect ratio and volume fraction increased, slump values decreased, and 7- and 28-day compressive strength increased up to an aspect ratio of 45 and 1.0% volume fraction. Beyond an aspect ratio of 45 and 1.0% volume fraction, a declining trend in compressive strength at all curing ages was observed. The Analysis of Variance (ANOVA) revealed that the variables volume fraction and aspect ratio significantly affect the variability in the FRC models, with all models being statistically significant at the 95% level across all factor levels. A numerical optimization method was used to determine the optimal mix proportions for ELTFRC. The optimum response values were achieved by combining a 1.01% volume fraction and a 33.86 aspect ratio, resulting in a desirability of 0.73.

Modeling of Metal Matrix Concentrated Solar Receivers for sCO2 Power Blocks

Abstract Supercritical CO2 power blocks for Concentrating Solar Power (CSP) with novel metal matrix solar receivers have the potential to reduce operating expenses while improving overall system efficiencies. These concentrated solar receivers integrated with a metal matrix-based phase change (PCM) thermal storage medium provide the compounding effect of an efficient heat exchanger while also integrating thermal storage within the receiver. Detailed numerical modeling of such devices with enthalpy-porosity-based formulation for phase change and turbulent convective heat transfer for the sCO2 microchannels is described in the current work. With sCO2 power blocks operating at temperatures and pressures beyond 800°C and 200 bar, different high-temperature PCMs are studied. A detailed steady charging followed by discharge and charging transients is simulated to analyze the thermal performance of these devices. In the current work, the energy storage density of PCMs is studied, followed by an analysis of the movement of the melt-pool interface over the streamwise length of a high corrugation wavy microchannel. A scaling analysis is carried out to estimate the heat transfer coefficients while compare them with the numerical model predictions. The results from the current work can be utilized for sizing and detailed design of integrated solar receivers for high-temperature sCO2 power block applications.

BCFT One-point Functions of Coulomb Branch Operators

We show that supersymmetry can be used to compute the BCFT one-point function coefficients for chiral primary operators, in 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs with 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS boundary conditions. The main ingredient is the hemisphere partition function, with the boundary condition on the equatorial S3. A supersymmetric Ward identity relates derivatives with respect to the chiral coupling constants to the insertion of the primaries at the pole of the hemisphere. Exact results for the one-point functions can be then obtained in terms of the localization matrix model. We discuss in detail the example of the super Maxwell theory in the bulk, interacting with 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs on the boundary. In particular we derive the action of the SL(2,ℤ) duality on the one-point functions.

Quantum Chaos and Coherence: Random Parametric Quantum Channels

The survival probability of an initial Coherent Gibbs State (CGS) is a natural extension of the Spectral Form Factor (SFF) to open quantum systems. To quantify the interplay between quantum chaos and decoherence away from the semi-classical limit, we investigate the relation of this generalized SFF with the corresponding l1-norm of coherence. As a working example, we introduce Parametric Quantum Channels (PQC), a discrete-time model of unitary evolution mixed with the effects of measurements or transient interactions with an environment. The Energy Dephasing (ED) dynamics arises as a specific case in the Markovian limit. We demonstrate our results in a series of random matrix models.

A study on the performance of super duplex stainless steel cladding over mild steel using a CMT welding

Low carbon steels can be cladded with super-duplex stainless steels to enhance the surface’s mechanical and wear properties. The current study examines the impact of process parameters on weld bead geometry and dilution % during cold metal transfer (CMT) cladding of super duplex stainless steel 2507 over low carbon steel. Response Surface Methodology (RSM) with a Central Composite Design matrix was used to optimize the process parameters (welding current, welding speed, and nozzle to workpiece distance (NTD)). The adequacy of the model was checked using an ANOVA analysis. The optimal bead width, height, penetration, and dilution values were 8.05 mm, 4.52 mm, 1.56 mm and 14.64%, respectively. The ideal input parameters were 200 A of welding current, 4.64 mm/s of welding speed, and 14 mm of NTD. The welding speed is the most dominant parameter, followed by the welding current and NTD. The cladding samples were prepared from the optimal parameters. The CMT-clad layer’s microstructure, microhardness, and wear properties were also evaluated. The results indicate a dense crack-free and non-porous clad surface was obtained under optimal conditions.

Optimized seismic hazard and structural vulnerability model considering macroseismic intensity measures

Macroseismic intensity measures are fundamental quantitative indicators for evaluating the vulnerability and resilience of regional building clusters. The vulnerability model of building portfolios established can provide a noteworthy reference for the development of large-scale regional earthquake risk distributions. However, there are differences in the quantitative scales of the macroseismic intensity standards used in multiple regions. The positive effects of instrument intensity and probabilistic seismic hazard theory on the vulnerability assessment of regional buildings are rarely considered, resulting in significant differences in their assessment results. This paper comprehensively considers the impact of instrument intensity and seismic hazard models on traditional macroseismic intensity. An updated macroseismic intensity measure (UCMS-20) is proposed for evaluating regional buildings, which is combined with the latest version of China's seismic intensity standards. The actual seismic damage sample dataset (31,649 buildings) of four types of building clusters in three typical earthquakes in China (Wenchuan 2008, Yushu 2010, and Jiuzhaigou 2017) has been expanded and updated. Using the UCMS-20, the European Macroseismic Scale (EMS-98), the Modified Mercalli intensity (MMI), and the Medvedev, Sponheuer, and Karnik Scale (MSK-64), vulnerability assessments are conducted on the extended empirical structural seismic damage dataset, and an empirical disaster matrix model considering updating damage states is established. A nonlinear vulnerability prediction model considering updated macrointensity measures is proposed, and the optimized model is validated and compared against the developed multiscale empirical structure dataset. The multiscale vulnerability index calculation model is improved, and novel optimization curves, point clouds, and matrix probability risk models are established, considering the expansion of empirical structural vulnerability databases.

Solute transport in stochastic discrete fracture-matrix systems: Impact of network structure

Obtaining a comprehensive understanding of solute transport in fractured rocks is crucial for various geoengineering applications, including waste disposal and construction of geo-energy infrastructure. It was realized that solute transport in fractured rocks is controlled by stochastic discrete fracture-matrix systems. However, the impacts and specific uncertainty caused by fracture network structures on solute transport in discrete fracture-matrix systems have yet not been fully understood. In this article, we aim to investigate the influence of fracture network structure on solute transport in stochastic discrete fracture-matrix systems. The fluid flow and solute transport are simulated using a three-dimensional discrete fracture matrix model with considering various values of fracture density and size (i.e., radius). The obtained results reveal that as the fracture density or minimum fracture radius increases, the corresponding fluid flow and solute transport channels increase, and the solute concentration distribution range expands in the matrix. This phenomenon, attributed to the enhanced connectivity of the fracture network, leads to a rise in the effluent solute concentration mean value from 0.422 to 0.704, or from 0.496 to 0.689. Furthermore, when solute transport reached a steady state, the coefficient of variation of effluent concentration decreases with the increasing fracture density or minimum fracture radius in different scenarios, indicating an improvement in the homogeneity of solute transport results. The presented analysis results of solute transport in stochastic discrete fracture-matrix systems can be helpful for uncertainty management in the geological disposal of high-level radioactive waste.

Modified Einstein equations from the 1-loop effective action of the IKKT model

Abstract We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor Cµν capturing the classical Yang-Mills-type action. The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat Friedmann–Lemaître–Robertson–Walker cosmological evolution governed by the classical action.

Reconfigurable directional selective tunneling of p-type phonons in polarized elastic wave systems

There have been many studies on the ground state of phononic crystals, but few studies on the nature of the excited state. In this paper, we introduce the asymmetric Klein tunneling method in phononic systems, which enables selective direction and control of elastic waves by inducing polarization through an external field in an artificial barrier. Using tight-binding theory, we systematically studied phononics in a super-honeycomb structure, demonstrating the anisotropic transition properties of excited state phonons through a matrix model involving the ground state’s s-type and the first excited state’s p-type wave functions. Additionally, we exploit the thermal sensitivity of epoxy to achieve localized thermal field-induced distortion of the bottom flat band, forming a tiled Dirac cone, and thereby creating a reconfigurable polarized artificial barrier in the elastic wave system. Elastic waves propagate in these systems with topological charge conservation. Combining this with the theoretical of excited-state phonons, we demonstrate asymmetric Klein tunneling with directional selectivity in the elastic wave carriers, and systematically investigate the performance of this tunneling. Furthermore, we design a four-port elastic waveguide based on the principle of asymmetric tunneling, which achieves exceptional directional selectivity of elastic wave signals by adjusting the polarization direction of barriers at the junctions. These studies not only extend the application of Klein tunneling in elastic wave systems but also open new research avenues for the study of elastic wave devices controlled by various external fields, showing direct application potential in elastic wave signal processing.

A Scaling Relation, Zm-Type Deconfinement Phases, and Imaginary Chemical Potentials in Finite Temperature Large-N Gauge Theories

Abstract We show that the effective potentials for the Polyakov loops in finite temperature SU$(N)$ gauge theories obey a certain scaling relation with respect to temperature in the large-N limit. This scaling relation strongly constrains the possible terms in the Polyakov loop effective potentials. Moreover, by using the effective potentials in the presence of imaginary chemical potentials or imaginary angular velocities in several models, we find that phase transitions to $Z_m$-type deconfinement phases ($Z_m$ phase) occur, where the eigenvalues of the Polyakov loop are distributed $Z_m$ symmetrically. Physical quantities in the $Z_m$ phase obey the scaling properties of the effective potential. The models include Yang–Mills (YM) theories, the bosonic BFSS matrix model, and ${\mathcal {N}}=4$ supersymmetric YM theory on $S^3$. Thus, the phase diagrams of large-N gauge theories with imaginary chemical potentials are very rich and the stable $Z_m$ phase would be ubiquitous. Monte-Carlo calculations also support this. As a related topic, we discuss the phase diagrams of large-N YM theories with real angular velocities in finite volume spaces.

Inclusion of fibrinoid necrosis increases the accuracy of synovial tissue assessment in predicting response to methotrexate: analysis of the UCLouvain Brussels ERA Cohort

ObjectiveRheumatoid Arthritis (RA) often exhibits suboptimal treatment response despite early diagnosis and treatment. This study aimed to analyze Early Rheumatoid Arthritis (ERA) synovial biopsies through histology and immunohistochemistry (IHC) to identify predictive factors for treatment response to Methotrexate (MTX).Methods140 ERA patients from the UCLouvain Arthritis Cohort underwent synovial biopsy and were monitored after initiating Disease-Modifying Antirheumatic Drug (DMARD) therapy. Histological features [Synovial Hyperplasia, Fibrinoid Necrosis (FN), Hypervascularization and Inflammatory Infiltrate] and IHC (CD3, CD20, CD138, CD68) were each semi-quantitatively assessed on a 0–3 scale with 7 levels.ResultsA strong association was observed between synovial CD68 and Fibrinoid Necrosis scores [r = 0.44 (0.27 − 0.56); p < 0.0001]. CD68 correlated with C-Reactive Protein (CRP), DAS28, SDAI and CDAI. Fibrinoid Necrosis score correlated with CRP and DAS28. Patients were then categorized as CD68NecrosisHIGH (CD68 + Necrosis ≥ 3) and CD68NecrosisLOW (CD68 + Necrosis < 3). CD68NecrosisHIGH exhibited higher pre-treatment disease activity [5.48 (1.6) versus 4.8 (1.7); p = 0.03] and a greater fall in DAS28 [1.99 (2.06) versus 1.1 (2.27), p = 0.03], SDAI [21.45 (IQR 23.3) versus 11.65 (IQR 17.5); p = 0.003] and CDAI [16 [14.9] versus 10.5 (20.1), p = 0.04]. CD68NecrosisHIGH patients had a higher EULAR Moderate/Good Response rate. CD68Necrosis score was incorporated into a probability matrix model together with clinical features (SJC44 and DAS28) to predict achieving a Moderate/Good EULAR Response Criteria at 3 months with a good performance (AUC 0.724).ConclusionFN and CD68 + in ERA synovial biopsies identify patients with higher disease activity and predict a better treatment response at three months. A model including synovial CD68 and fibrinoid necrosis with baseline clinical features predicts EULAR response at 3 months.

Rational Polynomial Coefficient Estimation via Adaptive Sparse PCA-Based Method

The Rational Function Model (RFM) is composed of numerous highly correlated Rational Polynomial Coefficients (RPCs), establishing a mathematical relationship between two-dimensional images and three-dimensional spatial coordinates. Due to the existence of ill-posedness and overparameterization, the estimated RPCs are sensitive to any slight perturbations in the observation data, particularly when handling a limited number of Ground Control Points (GCPs). Recently, Principal Component Analysis (PCA) has demonstrated significant performance improvements in the RFM optimization problem. In the PCA-based RFM, each Principal Component (PC) is a linear combination of all variables in the design matrix. However, some original variables are noise related and have very small or almost zero contributions to the construction of PCs, which leads to the overparameterization problem and makes the RPC estimation process ill posed. To address this problem, in this paper, we propose an Adaptive Sparse Principal Component Analysis-based RFM method (ASPCA-RFM) for RPC estimation. In this method, the Elastic Net sparsity constraint is introduced to ensure that each PC contains only a small number of original variables, which automatically eliminates unnecessary variables during PC computation. Since the optimal regularization parameters of the Elastic Net vary significantly in different scenarios, an adaptive regularization parameter approach is proposed to dynamically adjust the regularization parameters according to the explained variance of PCs and degrees of freedom. By adopting the proposed method, the noise and error in the design matrix can be reduced, and the ill-posedness and overparameterization of the RPC estimation can be significantly mitigated. Additionally, we conduct extensive experiments to validate the effectiveness of our method. Compared to existing state-of-the-art methods, the proposed method yields markedly improved or competitive performance.

A supersymmetric SYK model with a curious low energy behavior

We consider N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like S = S0 + (constant)Ta, where a ≠ 1. The large N equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.

Development of a Pedagogical Design Matrix for ICT-based Boundary Crossing in Dual VET

Research on networked learning is concerned with finding new and productive ways of connecting people and their practice across boundaries in different contexts. Particularly in dual Vocational Education and Training (VET), there is a need to focus continuously on learning in and between boundaries of domains, practices and the school-workplace contexts. Information and Communications Technologies (ICTs) have been proposed as artefacts that enable mediation and bridge the gap between different boundaries. In this paper, we present findings from a research project aimed at understanding Danish VET teachers’ use of ICT as boundary objects in relation to boundary crossing activities. In the first phase of the research project, interviewed VET teachers pointed to the need for new materials directed at the planning stage in their work with design for boundary crossing. As part of the research project a pedagogical design framework, including design principles and a design matrix that focuses on boundary crossing mediated by ICT-based boundary objects, was developed and tested. While the research project has been designed as a multiple case study, the development and testing of the design matrix has been inspired by Educational Design Research (McKenny &amp; Reeves, 2013). Theoretically, the research project is founded on a sociocultural perspective with research on boundary work, boundary crossing and boundary objects (Akkerman &amp; Bakker, 2012, 2011a, 2011b) and research on mediating artifacts (Henningsen &amp; Mogensen, 2013) as the backdrop. By way of combining four dialogical boundary crossing activities (identification, coordination, reflection and transformation) with four main affordances (documentation, simulation, construction and interaction) of the ICT-based boundary objects, the pedagogical design matrix was developed and tested in three iterations. Selected findings show that the participating Danish VET teachers do not fully realize the potentials of using ICT-based boundary objects in their boundary work. Our data show that the VET teachers designed ICT-mediated activities aimed at boundary crossing through identification, coordination and reflection, whereas data point to no activities directed towards transformation. In terms of ICT-based boundary objects, the VET teachers were mainly focused on ICTs that afford documentation with sparse focus on construction and interaction, and no explicit focus on simulation as boundary activity. In the final discussion we point to possible explanations as to why the VET teachers’ use of ICT in boundary work is relatively limited and we suggest further research.

Large N universality of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal index and AdS black holes

We study the large N limit of the matrix models associated with the superconformal indices of four-dimensional N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal field theories. We find that for a large class of N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal gauge theories, the superconformal indices in the large N limit of such theories are dominated by the ‘parallelogram’ saddle, providing O(N2) free energy for the generic value of chemical potentials. This saddle corresponds to BPS black holes in AdS5 whenever a holographic dual description is available. Our saddle applies to a large class of gauge theories, including ADE quiver gauge theories, and the theories with rank-2 tensor matters. Our analysis works for most N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 superconformal gauge theories that admit a suitable large N limit while keeping the flavor symmetry fixed. We also find ‘multi-cut’ saddle points, which correspond to the orbifolded Euclidean black holes in AdS5.

Utilizing neural networks and genetic algorithms in AI-assisted CFD for optimizing PCM-based thermal energy storage units with extended surfaces

Phase Change Materials (PCMs) offer significant benefits for applications such as electronic cooling and Thermal Energy Storage (TES) due to their high energy storage capacity and stability. However, their limited thermal conductivity restricts widespread utilization. To address this limitation, the use of fins has become a common technique to enhance heat transfer. Optimizing fin lengths and locations is challenging, as they affect natural convection. This study aims to develop a model using a feed-forward back-propagation network, trained on simulation data, for designing a TES unit. A design matrix, incorporating factors such as fin lengths and heights, is obtained through response surface methodology. Single- and multi-objective Genetic Algorithms (GAs) are employed to seek optimal solutions, considering Complete Melting Time (CMT) and total fin length. The results demonstrate the excellent performance of the network model, with an error of less than 2.98%. The single-objective GA yields a minimum CMT. In a finless enclosure, the CMT is 338.5% higher compared to the single-objective configuration. The multi-objective GA, using Euclidean distance specified from the Pareto front to balance weight and material costs, results in a CMT that is 192% higher compared to the single-objective optimization but with a total fin length that is 286% shorter. While these improvements are significant, it is important to note that fins can increase material and manufacturing costs, as well as the overall unit weight. This artificial intelligence-computational fluid dynamics method not only predicts TES unit performance but also reduces computational costs in designing an optimal TES unit.

Leslie Matrix Model For Euphorbia Hirta L Population

Invasive species management has developed into a highly specialized field utilizing a systems approach. It requires knowledge of their life history, growth requirements, and population dynamics that integrate their biology and control. The foundation of strategic planning for the management of invasive species is laid by demographic studies, which record the birth, growth, reproduction, and death of individuals within a population. The present study makes use of the Discrete Leslie Matrix Model to analyze the growth in the age-structured population of Euphorbia hirta, an invasive species in agrosystems, identify critical stages in the species' life cycle, and project the structure and size of future population.

Optimization of Alkali Treatment Conditions of Ramie Fabrics Using Box–Behnken Method

Ramie is a widely used plant fiber for making textiles and reinforcement in biodegradable composites. Pretreating cellulosic fibers with alkali before producing composites is increasingly used to enhance adhesion with polymeric resin. In this work, response surface methodology (RSM) based on the Box-Behnken technique was utilized to investigate the impact of independent variables on ramie fabric characteristics and determine the optimal treatment condition. The impact of alkali concentration, treatment time, and temperature on the breaking load and elongation at break of woven ramie fabrics were evaluated using Design-Expert software, which established the design matrix and analyzed the experimental data employing numerical and graphical optimization methods. Moreover, the impact of alkali treatment conditions on the surface morphology, structural change of ramie fabrics, and thermal properties was investigated. Based on the analysis of variance (ANOVA) results, the suggested quadratic models can adequately predict the breaking load and elongation at break of the ramie woven fabrics within the range of conditions applied in this investigation. The RSM revealed that an alkali concentration of 6.12%, a treatment time of 30 min, and a temperature of 39.13°C resulted in an optimum treatment condition with a breaking load of 518.28 N and elongation at break of 23.36%.

Evaluation of potential factors affecting the success of Cisco re-introduction and re-establishment in Lake Huron

Recent food web changes led to an opportunity to reintroduce (fingerling stocking) Cisco in central Lake Huron. We examined 9 factors affecting the ability of stocked Cisco fingerlings to survive, and reproduce and for their progeny to survive and reproduce. These values (obtained from the literature) were applied to a stochastic Leslie Matrix model and projected forward 30 years. The mean terminal eigenvalue (λ) of the final 10 years was used to indicate if the resulting wild population would continue to increase or decrease and thresholds for each variable. Recovery success was sensitive to survival rates especially in early life stages. Numbers stocked and the rate of homing by hatchery fish only affected the rate of recovery. Adult survival, if adjusted up, helped compensate for many of the earlier life stages lower survival rates. Simulations indicated the likelihood of successful establishment of ongoing natural reproduction if periodicity of boom years of reproduction were at least once every 5 years on average, but higher adult survival rates can relax this requirement allowing for an expanding population at less frequent periodicities.

Permutation invariant tensor models and partition algebras

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been shown to satisfy large N factorisation properties relevant to holography, while also having applications to the statistical analysis of ensembles of real-world matrices. Here, we develop 3-index tensor models in dimension D with a discrete symmetry of permutations in the symmetric group S_{D} . We construct the most general permutation invariant Gaussian tensor model using the representation theory of symmetric groups and associated partition algebras. We define a representation basis for the 3-index tensors, where the two-point function is diagonalised. Inverting the change of basis gives an explicit formula for the two-point function in the tensor basis for general D .