Recursive Representation Research Articles

RENA-Depth: toward recursion representation enhancement in neighborhood attention guided lightweight self-supervised monocular depth estimation

RENA-Depth: toward recursion representation enhancement in neighborhood attention guided lightweight self-supervised monocular depth estimation

Forecasting maximum formwork pressure for self-compacting concrete using ARX-Laguerre machine learning model

Forecasting the maximum pressure exerted by cast-in-place self-compacting concrete (SCC) is a major concern for formwork designers, researchers, and site engineers to accurately design the bearing capacity of the formwork and control the casting rate for safe and fast construction. This article aims to utilize the ARX-Laguerre model, which is a data-driven model to forecast the maximum form pressure. A laboratory instrumented setup was used to cast a 2-m column using SCC made with two different types of cement. A pressure system consisting of four sensors was used to document the pressure during casting. The data were sent to the cloud at every 1-min interval for real-time monitoring. The data were used to develop the model. The results demonstrated that forecasting with the ARX-Laguerre model is highly accurate. The model can forecast the maximum pressure exerted by SCC with less complexity. The model performance was also found to be consistent with insignificant differences between actual experimental results and predicted results. With a recursive and straightforward representation, the resulting model, known as the ARX-Laguerre model, ensures the parameter number reduction. Providing fast prediction of the maximum pressure. The model enables formwork designers to forecast the form pressure to design safe formwork and also helps to control the casting rate when SCC is used.

The deepest foundation of our democratic crisis

The deepest foundation of our democratic crisis is our increasing human interdependence. That interdependence creates increasing needs for ‘free-use goods’: goods that, once produced, anyone can use without paying (other names: “public goods,” “non-excludable goods”). Such goods produce the classic “free-rider” problems to which the most efficient solution in societies of strangers is usually government provision through taxes or regulation, both of which depend on a combination of voluntarism (based on duty and solidarity) and legitimate coercion. More interdependence creates more free-rider problems, which require more government intervention/coercion. Our eighteenth-century democratic mechanisms were not designed to legitimate the amount of state coercion we now need. To bolster legitimacy, we need to embrace the logic of free-use goods and replace one-way with recursive representation, the principle of distinction with more descriptive representation, corruption with clean institutions, and legislative-centric democracy with a full representative system approach, all drawing on our collective intelligence.

Advancing deliberative reform in a parliamentary system: prospects for recursive representation

AbstractRecent theories of democratic representation push beyond ‘minimalist’ notions that only rely on periodic elections to connect officials and constituents. For example, Jane Mansbridge (2019) calls for ‘recursive representation’, which seeks ongoing, two-way interaction between representatives and their constituents. Given the scale and complexity of modern representative democracies, how can such ambitious proposals be translated into practice? We analyze two Deliberative Town Halls (DTHs) convened with a Federal Member of Australian Parliament in 2020 to discuss a complex issue, mitochondrial donation, ahead of a parliamentary debate and conscience vote on this issue. Drawing on interviews with participants, we argue that democratic innovations such as DTHs can contribute to realizing recursive representation when three criteria are met: authenticity, inclusion, and impact. We discuss the significance of each criterion and the role of DTHs in advancing recursive representation in a parliamentary system.

Critique and consequence

After describing the landscape in macroeconomics and econometrics in Spring 1973 when Robert E. Lucas (1976) first presented his Critique at the inaugural Carnegie-Rochester conference, I add a fourth example based on Sargent and Wallace (1973) to those in section 5 of Lucas’s paper. To portray consequences of Lucas’s Critique, I use it as a vehicle to describe the time inconsistency of optimal plans and their credibility. A theory of government policy affects chains of influence among money creation and inflation rates at different dates. Different theories of policy bring different state vectors in recursive representations of inflation-money-supply outcomes.

A recursive representation for decoupling time-state dependent jumps from jump-diffusion processes

We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbounded intensity, not of Lévy-driven type that essentially benefits a lot from independent and stationary increments. The recursive representation, along with a few related ones, are derived by making use of a jump time of the underlying dynamics as an information relay point in passing the past on to a previous iteration step to fill in the missing information on the unobserved trajectory ahead. We prove that the proposed recursive representations are convergent exponentially fast in the limit, and can be represented in a similar form to Picard iterates under the probability measure with its jump component suppressed. On the basis of each iterate, we construct upper and lower bounding functions that are also convergent towards the true solution as the iterations proceed. We provide numerical results to justify our theoretical findings.

Recursive Processing Algorithm for Low Complexity Decoding of Polar Codes With Large Kernels

A reduced complexity algorithm is presented for computing the log-likelihood ratios (LLRs) arising in the successive cancellation (SC) decoder for polar codes with large kernels of arbitrary dimension. The proposed algorithm exploits a recursive trellis representation of the codes generated by submatrices of the polarization kernel and enables polar codes based on large kernels to be decoded with lower complexity compared to the codes based on the Arıkan kernel with the same performance. Extensions to the case of non-binary kernels are presented.

Backpropagation-Free Deep Learning with Recursive Local Representation Alignment

Training deep neural networks on large-scale datasets requires significant hardware resources whose costs (even on cloud platforms) put them out of reach of smaller organizations, groups, and individuals. Backpropagation (backprop), the workhorse for training these networks, is an inherently sequential process that is difficult to parallelize. Furthermore, researchers must continually develop various specialized techniques, such as particular weight initializations and enhanced activation functions, to ensure stable parameter optimization. Our goal is to seek an effective, neuro-biologically plausible alternative to backprop that can be used to train deep networks. In this paper, we propose a backprop-free procedure, recursive local representation alignment, for training large-scale architectures. Experiments with residual networks on CIFAR-10 and the large benchmark, ImageNet, show that our algorithm generalizes as well as backprop while converging sooner due to weight updates that are parallelizable and computationally less demanding. This is empirical evidence that a backprop-free algorithm can scale up to larger datasets.

Multigrid Incomplete Factorization Methods in Krylov Subspaces

The paper studies multigrid methods for solving systems of linear algebraic equations resulting from the seven-point discretization of the three-dimensional Dirichlet problem for an elliptic differential equation of the second order in a parallepipedal domain on a regular grid. The algorithms suggested are presented as special iteration processes of incomplete factorization in Krylov subspaces with a hierarchical recursive vector structure that corresponds to a sequence of embedded grids and gives rise to a block tridiagonal recursive representation of the coefficient matrix of the original linear algebraic system. The convergence of iterations is enhanced by using the principle of compensation of the row sums and also the symmetric successive block overrelaxation. An arbitrary m-grid method is defined recursively, based on the two-grid method. For simplicity, the algorithms are considered for linear systems with Stieltjes coefficient matrices. Issues related to generalization of the algorithms to larger classes of problems and, in particular, those with unsymmetric matrices are discussed.

Generalized de Boor–Cox Formulas and Pyramids for Multi-Degree Spline Basis Functions

The conventional B-splines possess the de Boor–Cox formula, which relates to a pyramid algorithm. However, for multi-degree splines, a de Boor–Cox-type evaluation algorithm only exists in some special cases. This paper considers any multi-degree spline with arbitrary degree and continuity, and provides two generalized de Boor–Cox-type relations. One uses several lower degree polynomials to build a combination to evaluate basis functions, whose form is similar to using the de Boor–Cox formula several times. The other is a linear combination of two functions out of the recursive definition, which keeps the combination coefficient polynomials of degree 1, so it is more similar to the de Boor–Cox formula and can be illustrated by several pyramids with different heights. In the process of calculating the recursions, a recursive representation using the Bernstein basis is used and numerically analyzed.

Density regression and uncertainty quantification with Bayesian deep noise neural networks.

Deep neural network (DNN) models have achieved state-of-the-art predictive accuracy in a wide range of applications. However, it remains a challenging task to accurately quantify the uncertainty in DNN predictions, especially those of continuous outcomes. To this end, we propose the Bayesian deep noise neural network (B-DeepNoise), which generalizes standard Bayesian DNNs by extending the random noise variable from the output layer to all hidden layers. Our model is capable of approximating highly complex predictive density functions and fully learn the possible random variation in the outcome variables. For posterior computation, we provide a closed-form Gibbs sampling algorithm that circumvents tuning-intensive Metropolis-Hastings methods. We establish a recursive representation of the predictive density and perform theoretical analysis on the predictive variance. Through extensive experiments, we demonstrate the superiority of B-DeepNoise over existing methods in terms of density estimation and uncertainty quantification accuracy. A neuroimaging application is included to show our model's usefulness in scientific studies.

New Generalized Hypergeometric Functions

The classical Gauss hypergeometric function and the Kumar confluent hypergeometric function are defined using a classical Pochammer symbol , and a factorial function. This research paper will present a two-parameter Pochhammer symbol, and discuss some of its properties such as recursive formulae and integral representation. In addition, the generalized Gauss and Kumar confluent hypergeometric functions are defined using a two-parameter Pochhammer symbol and two-parameter factorial function and some of the properties of the new generalized hypergeometric functions were also discussed.

Learning Asymmetric and Local Features in Multi-Dimensional Data Through Wavelets With Recursive Partitioning

Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images. It requires methods that are sensitive to local details while fast enough to handle massive numbers of images of ever increasing sizes. We introduce a probabilistic model-based framework that achieves these objectives by incorporating adaptivity into discrete wavelet transforms (DWT) through Bayesian hierarchical modeling, thereby allowing wavelet bases to adapt to the geometric structure of the data while maintaining the high computational scalability of wavelet methods-linear in the sample size (e.g., the resolution of an image). We derive a recursive representation of the Bayesian posterior model which leads to an exact message passing algorithm to complete learning and inference. While our framework is applicable to a range of problems including multi-dimensional signal processing, compression, and structural learning, we illustrate its work and evaluate its performance in the context of image reconstruction using real images from the ImageNet database, two widely used benchmark datasets, and a dataset from retinal optical coherence tomography and compare its performance to state-of-the-art methods based on basis transforms and deep learning.

Color-gradient lattice Boltzmann model for immiscible fluids with density contrast.

We present a color-gradient-based lattice Boltzmann model for immiscible fluids with a large density contrast. The model employs the velocity-based equilibrium distribution function, initially proposed for the phase-field-based model by Zu and He [Phys. Rev. E 87, 043301 (2013)1539-375510.1103/PhysRevE.87.043301], with a modification necessary to satisfy the kinematic condition at the interface. Different from the existing color-gradient models, the present model allows to specify interface mobility that is independent of the fluid density ratio. Further, we provide a unified framework, which uses the recursive representation of the lattice Boltzmann equation, to derive the governing equationsof the system. The emergent color dynamics thus obtained, through an analysis of the segregation operator, is shown to obey the locally conservative Allen-Cahn equation. We use a series of benchmarks, which include a stationary drop, a layered Poiseuille flow, translation of a drop under a forced velocity field, the Rayleigh-Taylor instability, and the capillary intrusion test to demonstrate the model's ability in dealing with complex flow problems.

Competitive equilibriums and social shaping for multi-agent systems

In this paper, we study multi-agent systems with decentralized resource allocations. Agents have local demand and resource supply, and are interconnected through a network designed to support sharing of the local resource; and the network has no external resource supply. It is known from classical welfare economics theory that by pricing the flow of resource, balance between the demand and supply is possible. Agents decide on the consumed resource, and perhaps further the traded resource as well, to maximize their payoffs considering both the utility of the consumption, and the income from the trading. When the network supply and demand are balanced, a competitive equilibrium is achieved if all agents maximize their individual payoffs, and a social welfare equilibrium is achieved if the total agent utilities are maximized. First, we consider multi-agent systems with static local allocations, and prove from duality theory that under general concavity assumptions, the competitive equilibrium and the social welfare equilibrium exist and agree. Next, we show that the agent utility functions can be prescribed in a family of socially admissible functions, under which the resource price at the competitive equilibrium is kept below a threshold. Finally, we extend the study to dynamical multi-agent systems where agents are associated with dynamical states from linear processes, and prove that the dynamic competitive equilibrium and the dynamic social welfare equilibrium continue to exist and coincide with each other. In addition, we also present a recursive representation of the competitive equilibriums using dynamic programming, and a receding horizon approach for smoothing the dynamic pricing as a dynamic competitive equilibrium social shaping method.

Recursive Convex Model for Optimal Power Flow Solution in Monopolar DC Networks

This paper presents a new optimal power flow (OPF) formulation for monopolar DC networks using a recursive convex representation. The hyperbolic relation between the voltages and power at each constant power terminal (generator or demand) is represented as a linear constraint for the demand nodes and generators. To reach the solution for the OPF problem a recursive evaluation of the model that determines the voltage variables at the iteration t+1 (vt+1) by using the information of the voltages at the iteration t (vt) is proposed. To finish the recursive solution process of the OPF problem via the convex relaxation, the difference between the voltage magnitudes in two consecutive iterations less than the predefined tolerance is considered as a stopping criterion. The numerical results in the 85-bus grid demonstrate that the proposed recursive convex model can solve the classical power flow problem in monopolar DC networks, and it also solves the OPF problem efficiently with a reduced convergence error when compared with semidefinite programming and combinatorial optimization methods. In addition, the proposed approach can deal with radial and meshed monopolar DC networks without modifications in its formulation. All the numerical implementations were in the MATLAB programming environment and the convex models were solved with the CVX and the Gurobi solver.

Robust multimodel control for uncertain nonlinear MIMO systems based on ARX-Laguerre multimodel and LSDP approach

In this paper, we propose a new alternative for the robust control of nonlinear MIMO (multiple-input multiple-output) systems based on the multimodel approach and LSDP (Loop-Shaping Design Procedure)approach in the discrete case. First, the multimodel approach is exploited by representing each linear sub-model in the form of the recent linear MIMO ARX (Auto-Regressive with eXogenous inputs) -Laguerre model which guarantees a significant parameters number reduction compared with the MIMO ARX model. Thus, the resulting multivariable multimodel, entitled MIMO ARX-Laguerre multimodel, ensures a reduction of the parametric complexity with a simple recursive vector representation. However, this reduction is conditioned by an optimal choice of the pole characterising each Laguerre base. To deal with this, we propose the identification, using the genetic algorithm, of the Laguerre poles as well as the weighting function parameters of the MIMO ARX-Laguerre multimodel. This latter allows to generate a set of linear MIMO ARX-Laguerre sub-models which are exploited to propose a robust multimodel control for uncertain nonlinear MIMO systems. In fact, for each identified sub-model, we combine the LSDP approach and the RGA (Relative Gain Array) theory to develop a local robust controller. Then, a multivariable roust multimodel control algorithm is developed where the overall control strategy by multimodel approach amounts to incorporating the same weighting functions used in the considered multivariable multimodel in order to interpolate the control laws calculated from each local robust controller. The optimisation of Laguerre poles and weighting functions parameters as well as the proposed multivariable robust multimodel control algorithm are validated on the experimental prototype Quanser Aero system.

On two elastodynamic homogenization methods for periodic composites

Two-scale asymptotic method and Willis’ method are jointly examined for the elastodynamic homogenization of periodic composites. The effective elastodynamic constitutive law given by Willis’ method, non-local both in time and space, is first reformulated so as to make appear a compact expression for the effective impedance tensor characterizing it. The two-scale asymptotic method is then revisited by exploiting the fact that the results obtained by it constitute an approximation to the general ones delivered by Willis’ method. The solutions for the hierarchical motion equations issuing from asymptotic analysis are shown to admit a compact recursive representation. A generic compact expression is derived for the effective impedance tensor associated with the nth-order approximation of asymptotic analysis. Remarkably, this expression turns out to be formally identical to the one of the effective impedance tensor obtained via Willis’ method. As an example of illustration, the elastodynamic homogenization of a layered composite undergoing anti-plane shear is investigated in detail.

Recursive Sparse Representation for Identifying Multiple Concurrent Occupants Using Floor Vibration Sensing

In this paper, we present a multiple concurrent occupant identification approach through footstep-induced floor vibration sensing. Identification of human occupants is useful in a variety of indoor smart structure scenarios, with applications in building security, space allocation, and healthcare. Existing approaches leverage sensing modalities such as vision, acoustic, RF, and wearables, but are limited due to deployment constraints such as line-of-sight requirements, sensitivity to noise, dense sensor deployment, and requiring each walker to wear/carry a device. To overcome these restrictions, we use footstep-induced structural vibration sensing. Footstep-induced signals contain information about the occupants' unique gait characteristics, and propagate through the structural medium, which enables sparse and passive identification of indoor occupants. The primary research challenge is that multiple-person footstep-induced vibration responses are a mixture of structurally-codependent overlapping individual responses with unknown timing, spectral content, and mixing ratios. As such, it is difficult to determine which part of the signal corresponds to each occupant. We overcome this challenge through a recursive sparse representation approach based on cosine distance that identifies each occupant in a footstep event in the order that their signals are generated, reconstructs their portion of the signal, and removes it from the mixed response. By leveraging sparse representation, our approach can simultaneously identify and separate mixed/overlapping responses, and the use of the cosine distance error function reduces the influence of structural codependency on the multiple walkers' signals. In this way, we isolate and identify each of the multiple occupants' footstep responses. We evaluate our approach by conducting real-world walking experiments with three concurrent walkers and achieve an average F1 score for identifying all persons of 0.89 (1.3x baseline improvement), and with a 10-person "hybrid" dataset (simulated combination of single-walker real-world data), we identify 2, 3, and 4 concurrent walkers with a trace-level accuracy of 100%, 93%, and 73%, respectively, and observe as much as a 2.9x error reduction over a naive baseline approach.

Recursive Sample Scaling Low-Rank Representation

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.