Hierarchical Recursion Research Articles

Hierarchical cumulative network for unsupervised medical image registration

Unsupervised deep learning techniques have gained increasing popularity in deformable medical image registration However, existing methods usually overlook the optimal similarity position between moving and fixed images To tackle this issue, we propose a novel hierarchical cumulative network (HCN), which explicitly considers the optimal similarity position with an effective Bidirectional Asymmetric Registration Module (BARM). The BARM simultaneously learns two asymmetric displacement vector fields (DVFs) to optimally warp both moving images and fixed images to their optimal similar shape along the geodesic path. Furthermore, we incorporate the BARM into a Laplacian pyramid network with hierarchical recursion, in which the moving image at the lowest level of the pyramid is warped successively for aligning to the fixed image at the lowest level of the pyramid to capture multiple DVFs. We then accumulate these DVFs and up-sample them to warp the moving images at higher levels of the pyramid to align to the fixed image of the top level. The entire system is end-to-end and jointly trained in an unsupervised manner. Extensive experiments were conducted on two public 3D Brain MRI datasets to demonstrate that our HCN outperforms both the traditional and state-of-the-art registration methods. To further evaluate the performance of our HCN, we tested it on the validation set of the MICCAI Learn2Reg 2021 challenge. Additionally, a cross-dataset evaluation was conducted to assess the generalization of our HCN. Experimental results showed that our HCN is an effective deformable registration method and achieves excellent generalization performance.

Inclusive Multiple Models (IMM) for predicting groundwater levels and treating heterogeneity

An explicit model management framework is introduced for predictive Groundwater Levels (GWL), particularly suitable to Observation Wells (OWs) with sparse and possibly heterogeneous data. The framework implements Multiple Models (MM) under the architecture of organising them at levels, as follows: (i) Level 0: treat heterogeneity in the data, e.g. Self-Organised Mapping (SOM) to classify the OWs; and decide on model structure, e.g. formulate a grey box model to predict GWLs. (ii) Level 1: construct MMs, e.g. two Fuzzy Logic (FL) and one Neurofuzzy (NF) models. (iii) Level 2: formulate strategies to combine the MM at Level 1, for which the paper uses Artificial Neural Networks (Strategy 1) and simple averaging (Strategy 2). Whilst the above model management strategy is novel, a critical view is presented, according to which modelling practices are: Inclusive Multiple Modelling (IMM) practices contrasted with existing practices, branded by the paper as Exclusionary Multiple Modelling (EMM). Scientific thinking over IMMs is captured as a framework with four dimensions: Model Reuse (MR), Hierarchical Recursion (HR), Elastic Learning Environment (ELE) and Goal Orientation (GO) and these together make the acronym of RHEO. Therefore, IMM-RHEO is piloted in the aquifer of Tabriz Plain with sparse and possibly heterogeneous data. The results provide some evidence that (i) IMM at two levels improves on the accuracy of individual models; and (ii) model combinations in IMM practices bring ‘model-learning’ into fashion for learning with the goal to explain baseline conditions and impacts of subsequent management changes.

Micro-scale Flood Hazard Assessment Based on Catastrophe Theory and an Integrated 2-D Hydraulic Model: A Case Study of Gongshuangcha Detention Basin in Dongting Lake Area, China

Assessments of urban flood hazards are crucial for planning and early warning flood system design. Moreover, hazard risk assessment is useful for emergency planning and insurance. There are two common methods for conducting flood hazard risk assessments (FHRA): those based on physical models and those based on parameters. Although physical models are able to simulate flood propagation processes accurately, they also have obvious shortcomings. Parameter-based FHRAs are more comprehensive because they emphasize the analysis of hazard factors. However, this approach also has various flaws, including its qualitative, macro-scale and high subjective nature. In this study, the strengths of both methods were combined to develop a new micro-scale FHRA. Taking the FHRA of the flood storage and detention area of Dongting Lake as an example, this study used high-precision digital elevation model (DEM) data generated from an airborne light detection and ranging (LiDAR) point cloud to construct a two-dimensional (2-D) flood propagation model. Micro-scale FHRAs were then performed using eight selected FHR indicators based on catastrophe theory. By automatically calculating the FHR value of each assessment unit based on hierarchical recursion, the catastrophe theory and catastrophe progression method effectively avoided uncertainty in weight assignment, which is an issue commonly faced by parameter-based methods. The FHRA results obtained under 144 different sequences of assessment indicators also show that the proposed method has a low sensitivity to the ranking of FHR indicators, as well as a high fault tolerance for different assessment results arising from subjective rankings by humans.

Hierarchical Recursive Organization and the Free Energy Principle: From Biological Self-Organization to the Psychoanalytic Mind.

The present paper argues that a systems theory epistemology (and particularly the notion of hierarchical recursive organization) provides the critical theoretical context within which the significance of Friston's (2010a) Free Energy Principle (FEP) for both evolution and psychoanalysis is best understood. Within this perspective, the FEP occupies a particular level of the hierarchical organization of the organism, which is the level of biological self-organization. This form of biological self-organization is in turn understood as foundational and pervasive to the higher levels of organization of the human organism that are of interest to both neuroscience as well as psychoanalysis. Consequently, central psychoanalytic claims should be restated, in order to be located in their proper place within a hierarchical recursive organization of the (situated) organism. In light of the FEP the realization of the psychoanalytic mind by the brain should be seen in terms of the evolution of different levels of systematic organization where the concepts of psychoanalysis describe a level of hierarchical recursive organization superordinate to that of biological self-organization and the FEP. The implication of this formulation is that while “psychoanalytic” mental processes are fundamentally subject to the FEP, they nonetheless also add their own principles of process over and above that of the FEP. A model found in Grobbelaar (1989) offers a recursive bottom-up description of the self-organization of the psychoanalytic ego as dependent on the organization of language (and affect), which is itself founded upon the tendency toward autopoiesis (self-making) within the organism, which is in turn described as formally similar to the FEP. Meaningful consilience between Grobbelaar's model and the hierarchical recursive description available in Friston's (2010a) theory is described. The paper concludes that the valuable contribution of the FEP to psychoanalysis underscores the necessity of reengagement with the core concepts of psychoanalytic theory, and the usefulness that a systems theory epistemology—particularly hierarchical recursive description—can have for this goal.

Renormalization group approach to interacting crumpled surfaces: The hierarchical recursion

We study the scaling limit of a model of a tethered crumpled D-dimensionalrandom surface interacting through an exclusion condition with a fixed impurity in d-dimensional euclidean space by the methods of Wilson's renormalization group. In this paper we consider a hierarchical version of the model and we prove rigorously the existence of the scaling limit and convergence to a non-gaussian fixed point for 1 ⩽ D < 2 and ϵ > 0 sufficiently small, where ϵ = D − 1 2 (2−D)d .

A Hierarchical Recursive Method for Substantially Improving Trending of Small Area Load Forecasts

A Hierarchical Recursive Method for Substantially Improving Trending of Small Area Load Forecasts

A Hierarchical Recursive Method for Substantially Improving Trending of Small Area Load Forecasts

A spatially recursive technique for structuring the trending of a small area load forecast is described. The method employs trending of more than just the individual small area loads. Computer implementation of the technique is simple and straightforward, and requires only slightly more computer time and memory than previous trending methods, while maintaining the low data requirements and ease of use common to such techniques. Forecasts obtained using the new method have only from one half to one fourth of the error of forecasts obtained from other trending methods.