Transition Matrix Research Articles

Complementary to Multiple Labels: A Correlation-Aware Correction Approach.

Complementary label learning (CLL) requires annotators to give irrelevant labels instead of relevant labels for instances. Currently, CLL has shown its promising performance on multi-class data by estimating a transition matrix. However, current multi-class CLL techniques cannot work well on multi-labeled data since they assume each instance is associated with one label while each multi-labeled instance is relevant to multiple labels. Here, we show theoretically how the estimated transition matrix in multi-class CLL could be distorted in multi-labeled cases as they ignore co-existing relevant labels. Moreover, theoretical findings reveal that calculating a transition matrix from label correlations in multi-labeled CLL (ML-CLL) needs multi-labeled data, while this is unavailable for ML-CLL. To solve this issue, we propose a two-step method to estimate the transition matrix from candidate labels. Specifically, we first estimate an initial transition matrix by decomposing the multi-label problem into a series of binary classification problems, then the initial transition matrix is corrected by label correlations to enforce the addition of relationships among labels. We further show that the proposal is classifier-consistent, and additionally introduce an MSE-based regularizer to alleviate the tendency of BCE loss overfitting to noises. Experimental results have demonstrated the effectiveness of the proposed method.

Integrating complexity in population modelling: From matrix to dynamic models

Matrix models are widely used in population ecology studies and are valuable for analysing population dynamics, although they are limited in the use of time-varying parameters. This limitation can be overcome by dynamic models. In this study, we revisit a previously published study on a matrix model of a population of the box jellyfish Carybdea marsupialis (L. 1758) in the Western Mediterranean. A dynamic model integrating the transition matrix of the original model is developed in STELLA Architect with the following improvements: (1) Sensitivity study of the reliability of the methodology for calculating the transition matrix and estimation of the errors of the fitting parameters; (2) Closure of the jellyfish life cycle by adding the polyp stage. This will make it possible to simulate scenarios of ecological interest over several years such as a decline in food supply, jellyfish removal strategies, changes in drift currents and changes in substrate availability for planulae to settle. (3) The inclusion of more biological reality. In particular, a temporal pattern of strobilation is added, which improves the fit of the model to the field data.

CC4S: Encouraging Certainty and Consistency in Scribble-Supervised Semantic Segmentation.

Deep learning-based solutions have achieved impressive performance in semantic segmentation but often require large amounts of training data with fine-grained annotations. To alleviate such requisition, a variety of weakly supervised annotation strategies have been proposed, among which scribble supervision is emerging as a popular one due to its user-friendly annotation way. However, the sparsity and diversity of scribble annotations make it nontrivial to train a network to produce deterministic and consistent predictions directly. To address these issues, in this paper we propose holistic solutions involving the design of network structure, loss and training procedure, named CC4S to improve Certainty and Consistency for Scribble-Supervised Semantic Segmentation. Specifically, to reduce uncertainty, CC4S embeds a random walk module into the network structure to make neural representations uniformly distributed within similar semantic regions, which works together with a soft entropy loss function to force the network to produce deterministic predictions. To encourage consistency, CC4S adopts self-supervision training and imposes the consistency loss on the eigenspace of the probability transition matrix in the random walk module (we named neural eigenspace). Such self-supervision inherits the category-level discriminability from the neural eigenspace and meanwhile helps the network focus on producing consistent predictions for the salient parts and neglect semantically heterogeneous backgrounds. Finally, to further improve the performance, CC4S uses the network predictions as pseudo-labels and retrains the network with an extra color constraint regularizer. From comprehensive experiments, CC4S achieves comparable performance to those from fully supervised methods and shows promising robustness under extreme supervision cases.

Toward explainable deep learning in healthcare through transition matrix and user-friendly features

Modern artificial intelligence (AI) solutions often face challenges due to the “black box” nature of deep learning (DL) models, which limits their transparency and trustworthiness in critical medical applications. In this study, we propose and evaluate a scalable approach based on a transition matrix to enhance the interpretability of DL models in medical signal and image processing by translating complex model decisions into user-friendly and justifiable features for healthcare professionals. The criteria for choosing interpretable features were clearly defined, incorporating clinical guidelines and expert rules to align model outputs with established medical standards. The proposed approach was tested on two medical datasets: electrocardiography (ECG) for arrhythmia detection and magnetic resonance imaging (MRI) for heart disease classification. The performance of the DL models was compared with expert annotations using Cohen’s Kappa coefficient to assess agreement, achieving coefficients of 0.89 for the ECG dataset and 0.80 for the MRI dataset. These results demonstrate strong agreement, underscoring the reliability of the approach in providing accurate, understandable, and justifiable explanations of DL model decisions. The scalability of the approach suggests its potential applicability across various medical domains, enhancing the generalizability and utility of DL models in healthcare while addressing practical challenges and ethical considerations.

How to measure the probability of uracil chain tautomers as nucleotide bases in RNA?

The current research focuses on exploring tautomerism in uracil. 47 tautomers were found that varied in significance in RNA and stability. To discover these molecules, diverse potential energy levels were explored, and corresponding transition states were found in these pathways. But the imperative thing that was taken note in this investigation is that for the first time, a method was detailed for the probability of forming distinctive molecules relative to each other. In this method, the conversion of uracil and its tautomers, which together turn into 47 molecules, was composed as a Markov chain. Then, the transition matrix was explained using its support, whose components are the probability of creating molecules from each step. At last, by multiplying this matrix by n times, the probability of forming different molecules was obtained. Moreover, by solving this matrix at different times, it is conceivable to appear which molecules can be converted to uracil sooner. It was appeared that a few tautomers act as transitory absorption point or temporary terminal states and other molecules, to begin with convert to these molecules before turning into uracil.

Using land surface phenology and information theory to assess and map complex landscape dynamics

Abstract Context Characterizing landscape ecological complexity and change requires integrated description of spatial and temporal landscape organization and dynamics, as suggested by the shifting mosaic concept. Remotely sensed land surface phenology allows the detection of even small differences among landscape patches and through time, allowing for the analysis of landscapes as shifting mosaics. Objectives We sought to quantify aspects of the complex landscape behaviors that are implied by spatiotemporal variation in land surface phenology. We adapted an information-theoretic (IT) framework from ecosystem ecology to capture landscape-level spatiotemporal complexity and organization and map these properties across large areas. Methods Phenology data were derived from remotely sensed, pixel-level time series of a vegetation greenness index, across a large portion of North America. We summarized multi-year, multi-pixel dynamics in transition matrices, calculated IT metrics from the matrices, and used matrix projection to quantify disequilibrium dynamics and long-term trajectories of the metrics. Results Mapping the IT metrics and their disequilibria revealed gradients in the spatiotemporal complexity and organization of multi-year land surface phenology dynamics at continental to local scales. These gradients suggest influences of biophysical and biogeographic setting, ecological development and disturbances, land use, and other drivers of landscape ecological dynamics. The spatiotemporal IT metrics were influenced by both year-to-year dynamics and spatial landscape heterogeneity, but correlations with spatial and temporal complexity measures varied among the IT metrics. Landscapes showing the strongest disequilibrium dynamics were mostly in the western part of the continent and appeared to be associated with large-scale disturbances including severe fire, forest pathogens, climate variability, and land use change—important subjects for further study. Conclusions This approach reveals novel features of the shifting landscape mosaic, with implications for understanding landscape resilience and sustainability. Resulting spatial data products describing long-term landscape dynamics have potential applications in broad-scale ecological modeling, monitoring, assessment, and prediction.

Efficient Implementation of Monte Carlo Algorithms on Graphical Processing Units for Simulation of Adsorption in Porous Materials.

We present enhancements in Monte Carlo simulation speed and functionality within an open-source code, gRASPA, which uses graphical processing units (GPUs) to achieve significant performance improvements compared to serial, CPU implementations of Monte Carlo. The code supports a wide range of Monte Carlo simulations, including canonical ensemble (NVT), grand canonical, NVT Gibbs, Widom test particle insertions, and continuous-fractional component Monte Carlo. Implementation of grand canonical transition matrix Monte Carlo (GC-TMMC) and a novel feature to allow different moves for the different components of metal-organic framework (MOF) structures exemplify the capabilities of gRASPA for precise free energy calculations and enhanced adsorption studies, respectively. The introduction of a High-Throughput Computing (HTC) mode permits many Monte Carlo simulations on a single GPU device for accelerated materials discovery. The code can incorporate machine learning (ML) potentials, and this is illustrated with grand canonical Monte Carlo simulations of CO2 adsorption in Mg-MOF-74 that show much better agreement with experiment than simulations using a traditional force field. The open-source nature of gRASPA promotes reproducibility and openness in science, and users may add features to the code and optimize it for their own purposes. The code is written in CUDA/C++ and SYCL/C++ to support different GPU vendors. The gRASPA code is publicly available at https://github.com/snurr-group/gRASPA.

Mapping the Trade Direction of Indian Rice with Markov Chain Analysis

Agriculture is a cornerstone of India’s economy, with rice being a critical crop that ranks second globally, feeding over half of the world’s population and serving as a staple in Southeast Asia. This study explores the direction of India’s rice trade using Markov Chain Analysis, following an examination of the compound annual growth rate (CAGR) in rice exports to various global regions. Results reveal a 2.26 per cent CAGR in rice production, while export values surged by 16.8 per cent annually. Specifically, the CAGR for rice exports to Iraq and Iran reached 58.6 per cent and 46.47 per cent, respectively. In quantity, India’s rice exports grew by 10.82 per cent, with Iraq and Iran at 44 per cent and 34 per cent. The Transitional Probability Matrix for 2001-2022 indicates strong regional retention, with Africa maintaining 78 per cent of trade value and Asia 93.7 per cent, and similar trends in quantity, where Asia retained 92.6 per cent and Africa 89.1 per cent. These findings highlight India’s potential to diversify rice exports and strengthen its global competitive edge, urging a focus on enhancing processing, transportation, and quality standards for wider market appeal.

Pseudoentropy sum rule by analytical continuation of the superposition parameter

In this paper, we establish a sum rule that connects the pseudoentropy and entanglement entropy of the superposition state. Through analytical continuation of the superposition parameter, we demonstrate that the transition matrix and density matrix of the superposition state can be treated in a unified manner. Within this framework, we naturally derive sum rules for the (reduced) transition matrix, pseudo-Rényi entropy, and pseudoentropy. Furthermore, we demonstrate the close relationship between the sum rule for pseudoentropy and the singularity structure of the entropy function for the superposition state after analytical continuation. We also explore potential applications of the sum rule, including its relevance to understanding the gravity dual of non-Hermitian transition matrices and establishing upper bounds for the absolute value of pseudoentropy.

Useless Math – The Complex Untold Story

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations. The current classical discrete 3D+t space PDE, in which time is an external controller and not integrated into the 3D geometric space, cannot be integrated digitally. This space is logically incomplete and misleading in the production of definitions and hypotheses as well as in the resolution itself of time- dependent PDEs. No wonder these definitions/assumptions are ugly and result in weak or intractable mathematics, leading to all kinds of misunderstandings, from horrible notations to undisciplined length of theorems containing a considerable amount of black magic and ending with a gray nature of the mathematical result obtained. In this article we present some of the most catastrophic inaccurate assumptions existing in current classical mathematics, resulting from the use of 3D+t manifold space to specify initial conditions, boundary conditions and the source/sink term. Fortunately, these inaccurate assumptions that start with an ugly space for boundary conditions, initial conditions and source/sink term can be spotted and analyzed via 4D unitary numerical statistical theory called Cairo techniques in the format of transition chains of matrix B to complete what is missing. In other words, we present how to spot some of the ugliest mathematical conclusions of classical 3D geometry plus t as an external control numerical space, and then show how to correct them via the 4D unit space of statistical transition matrix chains. By complex and untold history, we mean that useless and misleading mathematics dominated scientific research and education throughout the 20th century, so much so that the accumulated legacy of misconceptions became a huge, complex mountain, almost impossible to eliminate. Fortunately, the numerical theory of Cairo techniques and the Laplacian theorem constitute an advanced and exhaustive form of the energy continuity equation and thus can create new logical mathematics. This is also the case of the famous Schrödinger time- dependent PDE.  The Laplacian theorem is one of the most important products created by the numerical statistical theory called Cairo techniques. In previous articles we introduced and briefly explained the so-called Laplacian theorem in the 4D x-t unit space, while in this article we highlight its importance and how it can generate new mathematics in more detail. The Laplacian partial differential equation that interests us is the one having a well-defined exclusive form and living in an isolated sample spatial control volume surrounded by a closed surface (A) and subject to Dirichlet boundary conditions. This very particular case of Laplacian PDE is always treated mathematically in a classical D^4 variety which is lazy and misleading. Finally, this article collects, studies, identifies and analyzes the dozen most common current useless mathematical events and presents an effective and adequate alternative.

Ab Initio Molecular Dynamics Study of Trivalent Rare Earth Rich Borate Glasses: Structural Insights and Formation Mechanisms.

In this work, trivalent rare earth (RE)-rich borate glasses (30 La2O3-70 B2O3, 50 La2O3-50 B2O3, 60 La2O3-40 B2O3, and 50 Y2O3-50 B2O3) were modeled using ab initio molecular dynamics (AIMD) simulations through the melt-quenching route. It was found that the AIMD-derived structures reproduced the experimental structure factors and 11B solid-state nuclear magnetic resonance data. Isolated borate units (monomers, dimers, and trimers) terminated with nonbridging oxygen were found in the structures. Polymer units containing four or more boron atoms were identified with and without three-membered boron rings (3-rings). Increasing the proportion of La2O3 in La2O3-B2O3 glasses resulted in an increased number of isolated units, indicating that La3+ acts as a network modifier, breaking the borate glass network. The formation of these units via the melt-quenching process was detected by labeling boron species at each AIMD step from 1500 to 300 K. Representation with transition matrices clarified the specific reaction routes, leading to the formation of isolated boron units in solid glass. A key finding is the stabilization of polymer units involving 3-ring formation. The formation of isolated units is achieved through the reaction of polymers without 3-rings. The RE coordination structure was thoroughly analyzed from the perspective of shape and symmetry. Reference structures derived from the solution of the Thomson problem were compared to the AIMD-derived coordination structures and crystalline LaBO3 and YBO3. The results highlight the specificity of the Y coordination structure with 3-rings in YBO3, which is not observed in RE borate glasses. The analytical approaches and interpretations used in this study provide insights into the diverse coordination structures of glasses containing heavy elements other than REs.

Analysis of the Wangping Brownfield Using a Two-Step Urban Brownfield Redevelopment Model

With societal progress, urban brownfields have become restrictive, and redevelopment studies have become an important part of urban renewal. In this work, we developed a two-step model for urban brownfield redevelopment, while considering the Wangping brownfield as the study area. Site suitability evaluation models for brownfield parks, agricultural picking gardens, and creative industrial centers were developed based on the elevation, slope, and surface runoff, and the evaluation results were categorized into five levels. The redevelopment plan was formulated based on these evaluation results. To study the effect of the plan, a transition matrix of land use was assessed using satellite images and the cellular automata (CA)–Markov model; based on the analysis, we predicted the land use situation of the Wangping brownfield, with respect to natural development, for 2030. A comparison of the redevelopment planning with the forecasted results revealed that the proportions of grassland, construction, and unused land decreased by 25.68, 3.12, and 2.38% and those of plowland and forest land increased by 6.61 and 24.57%. This confirms the advantages of redevelopment planning for restoring plowland and increasing biological carbon sinks. Notably, our two-step urban brownfield redevelopment model can enrich the current research on urban brownfields and guide similar urban renewal projects.

Using Visual Basic for Applications to Implement Markov Analysis in Market Share Forecasting

Objective: This paper is an examination of the use of Markov analysis in market share prediction, and the use of Visual Basic for Applications (VBA) to increase the speed and precision of the computation and model. Theoretical Framework: The Markov analysis, used to predict future states from current transitions, sheds light on the consumer behavior and brand loyalty dynamics With VBA, the data processing can be automated, and transition matrices built that are dynamic, so that forecasts can be updated in real time. Method: Markov analysis is based on transition matrices, which define the probabilities of transitioning from one state to another. These matrices are then used to predict long term probabilities by raising the transition matrix to some power that is equal to the number of future steps being studied. Results and Discussion: By utilizing Visual Basic for Applications (VBA), the study facilitates the swift creation of transition matrices and enables real-time modifications in response to new data. This implies that with the use of VBA and Markov analysis, not only is the forecasting process made easier, but also more accurate predictions are made, and for that reason VBA should be one of the tools that any firm looking to maximize its market share strategies should employ. Research Implications: This capability results in a more flexible and responsive forecasting instrument, enhancing the overall adaptability of market share predictions. Originality/Value: The originality of this research is found in its innovative methodological framework that builds upon conventional Markov analysis.

An MPC-DCM Control Method for a Forward-Bending Biped Robot Based on Force and Moment Control

For a forward-bending biped robot with 10 degrees of freedom on its legs, a new control framework of MPC-DCM based on force and moment is proposed in this paper. Specifically, the Diverging Component of Motion (DCM) is a stability criterion for biped robots based on linear inverted pendulum, and Model Predictive Control (MPC) is an optimization solution strategy using rolling optimization. In this paper, DCM theory is applied to the state transition matrix of the system, combined with simplified rigid body dynamics, the mathematical description of the biped robot system is established, the classical MPC method is used to optimize the control input, and DCM constraints are added to the constraints of MPC, making the real-time DCM approximate to a straight line in the walking single gait. At the same time, the linear angle and friction cone constraints are considered to enhance the stability of the robot during walking. In this paper, MATLAB/Simulink is used to simulate the robot. Under the control of this algorithm, the robot can reach a walking speed of 0.75 m/s and has a certain anti-disturbance ability and ground adaptability. In this paper, the Model-H16 robot is used to deploy the physical algorithm, and the linear walking and obstacle walking of the physical robot are realized.

A Study on the Growth Model of Natural Forests in Southern China Under Climate Change: Application of Transition Matrix Model

This study establishes a climate-sensitive transition matrix growth model and predicts forest growth under different carbon emission scenarios (representative concentration pathways RCP2.6, RCP4.5, and RCP8.5) over the next 40 years. Data from the Eighth (2013) and Ninth (2019) National Forest Resource Inventories in Chongqing and climate data from Climate AP are utilized. The model is used to predict forest growth and compare the number of trees, basal area, and stock volume under different climate scenarios. The results show that the climate-sensitive transition matrix growth model has high accuracy. The relationships between the variables and forest growth, mortality, and recruitment correspond to natural succession and growth. Although the number of trees, basal area, and stock volume do not differ significantly for different climate scenarios, the forest has sufficient seedling regeneration and large-diameter trees. The growth process aligns with succession, with pioneer species being replaced by climax species. The proposed climate-sensitive transition matrix growth model fills the gap in growth models for natural secondary forests in Chongqing and is an accurate method for predicting forest growth. The model can be used for long-term prediction of forest stands to understand future forest growth trends and provide reliable references for forest management. Forest growth can be predicted for different harvesting intensities to determine the optimal intensity to guide natural forest management in Chongqing City. The results of this study can help formulate targeted forest management policies to deal more effectively with climate change and promote sustainable forest health.

Sustainable Development of Production–Living–Ecological Spaces: Insights from a 30-Year Remote Sensing Analysis

The rapid pace of urbanization and industrialization has reshaped land use patterns globally, particularly within the interconnected domains of ‘production, living, and ecological spaces’ (PLES). Understanding the spatiotemporal evolution of these spaces is crucial for guiding sustainable development. Although a number of previous studies have explored aspects of their dynamics and driving factors, further investigation is needed to fully understand their long-term spatiotemporal evolution and the broader influences of socio-economic and environmental forces. This study aims to fill that important gap by leveraging advanced remote sensing techniques to analyze PLES transformations over a 30-year period. Using Henan Province, China, as a testbed, this study applies high-resolution Landsat data, land use transition matrices, dynamic degree analysis, Principal Component Analysis (PCA), and multiple linear regressions to uncover trends and underlying drivers. The results reveal a substantial reduction in production spaces by 3394.62 km² steady growth in living spaces by 4459.41 km² and complex, non-linear changes in ecological spaces, which decreased by 1067.43 km². Key driving forces, such as economic growth, urbanization, and fiscal policies are identified and discussed. These insights provide a robust framework for sustainable land use planning, with broader implications for rapidly urbanizing regions worldwide.

Correlations and Fractality in Sentence-Level Sentiment Analysis Based on VADER for Literary Texts

We perform a sentence-level sentiment analysis study of different literary texts in English language. Each text is converted into a series in which the data points are the sentiment value of each sentence obtained using the sentiment analysis tool (VADER). By applying the Detrended Fluctuation Analysis (DFA) and the Higuchi Fractal Dimension (HFD) methods to these sentiment series, we find that they are monofractal with long-term correlations, which can be explained by the fact that the writing process has memory by construction, with a sentiment evolution that is self-similar. Furthermore, we discretize these series by applying a classification approach which transforms the series into a one on which each data point has only three possible values, corresponding to positive, neutral or negative sentiments. We map these three-states series to a Markov chain and investigate the transitions of sentiment from one sentence to the next, obtaining a state transition matrix for each book that provides information on the probability of transitioning between sentiments from one sentence to the next. This approach shows that there are biases towards increasing the probability of switching to neutral or positive sentences. The two approaches supplement each other, since the long-term correlation approach allows a global assessment of the sentiment of the book, while the state transition matrix approach provides local information about the sentiment evolution along the text.

Modeling of the leader-follower satellite formation for long baseline

Abstract Interferometric Synthetic Aperture Radar (InSAR) represents a crucial component of synthetic aperture radar technologies, with the accuracy of measurements significantly improving as the baseline length increases. In comparison with the traditional Hill-Clohessy-Wiltshire (HCW) equations, the application of curvilinear coordinate systems for modeling satellite formations in circular orbits has demonstrated enhanced precision, especially when the formations span larger distances. However, these improvements were initially limited to circular orbits. Addressing this limitation, this study introduces a novel approach by incorporating elliptical orbits into the model, thereby refining the state transition matrix through the incorporation of eccentricity factors and maintaining the direct correlation with the temporal dynamics of satellite motion in three dimensions. Through rigorous numerical simulations, it has been established that this refined model substantially improves accuracy in leader-follower satellite formations.

Age-related differences of the time-varying features in the brain functional connectivity and cognitive aging.

Brain functional modular organization changes with age. Considering the brain as a dynamic system, recent studies have suggested that time-varying connectivity provides more information on brain functions. However, the spontaneous reconfiguration of modular brain structures over time during aging remains poorly understood. In this study, we investigated the age-related dynamic modular reconfiguration using resting-state functional MRI data (615 participants, aged 18-88 years) from Cam-CAN. We employed a graph-based modularity analysis to investigate modular variability and the transition of nodes from one module to another in modular brain networks across the adult lifespan. Results showed that modular structure exhibits both linear and nonlinear age-related trends. The modular variability is higher in early and late adulthood, with higher modular variability in the association networks and lower modular variability in the primary networks. In addition, the whole-brain transition matrix showed that the times of transition from other networks to the dorsal attention network were the largest. Furthermore, the modular structure was closely related to the number of cognitive components and memory-related cognitive performance, suggesting a potential contribution to flexibility cognitive function. Our findings highlighted the notable dynamic characteristics in large-scale brain networks across the adult lifespan, which enhanced our understanding of the neural substrate in various cognitions during aging. These findings also provided further evidence that dedifferentiation and compensation are the outcomes of functional brain interactions.

Guidance Strategy and Fast Robustness Analysis for Space Debris Flyby

Envisioning the scenario of space debris inspection by orbital flyby, this paper investigates the guidance strategy and fast robustness analysis method considering the relative state constraints. First, the corrected state transition matrix is derived to predict and correct the perturbed relative state at the flyby moment. Based on the state transition matrix, a free-flight corridor model is established to characterize the maximum allowed magnitude of the deviation, which can quickly estimate the robustness of the trajectory under uncertainties and circumvent intensive numerical sampling. The corresponding optimization, with four norm-extreme constraints, can be solved by a proposed double-layer algorithm with proven convergence. Numerical simulations demonstrate that the guidance algorithm is effective, and the free-flight corridor can accurately and efficiently reflect the robustness of the nominal trajectory.