Bayesian Forecasting of Dynamic Extreme Quantiles

In this paper, we provide a novel Bayesian solution to forecasting extreme quantile thresholds that are dynamic in nature. This is an important problem in many fields of study including climatology, structural engineering, and finance. We utilize results from extreme value theory to provide the backdrop for developing a state-space model for the unknown parameters of the observed time-series. To solve for the requisite probability densities, we derive a Rao-Blackwellized particle filter and, most importantly, a computationally efficient, recursive solution. Using the filter, the predictive distribution of future observations, conditioned on the past data, is forecast at each time-step and used to compute extreme quantile levels. We illustrate the improvement in forecasting ability, versus traditional methods, using simulations and also apply our technique to financial market data.

Iterative Regression Based Hybrid Localization for Wireless Sensor Networks

Among various localization methods, a localization method that uses a radio frequency signal-based wireless sensor network has been widely applied due to its robustness against noise factors and few limits on installation location. In this paper, we focus on an iterative localization scheme for a mobile with a limited number of time difference of arrival (TDOA) and angle of arrival (AOA) data measured from base stations. To acquire the optimal location of a mobile, we propose a recursive solution for localization using an iteratively reweighted-recursive least squares (IR-RLS) algorithm. The proposed IR-RLS scheme can obtain the optimal solution with a fast computational speed when additional TDOA and/or AOA data is measured from base stations. Moreover, while the number of measured TDOA/AOA data was limited, the proposed IR-RLS scheme could obtain the precise location of a mobile. The performance of the proposed IR-RLS method is confirmed through some simulation results.

Static Upper/Lower Thrust and Kinematic Work Balance Stationarity for Least-Thickness Circular Masonry Arch Optimization

This paper re-considers a recent analysis on the so-called Couplet–Heyman problem of least-thickness circular masonry arch structural form optimization and provides complementary and novel information and perspectives, specifically in terms of the optimization problem, and its implications in the general understanding of the Mechanics (statics) of masonry arches. First, typical underlying solutions are independently re-derived, by a static upper/lower horizontal thrust and a kinematic work balance, stationary approaches, based on a complete analytical treatment; then, illustrated and commented. Subsequently, a separate numerical validation treatment is developed, by the deployment of an original recursive solution strategy, the adoption of a discontinuous deformation analysis simulation tool and the operation of a new self-implemented Complementarity Problem/Mathematical Programming formulation, with a full matching of the achieved results, on all the arch characteristics in the critical condition of minimum thickness.

Recursive Solution of Queue Length Distribution for Geo/G/1 Queue with Delayed Min(N, D)-Policy

In this paper we consider a discrete-time Geo/G/1 queue with delayed Min(N, D)-policy. Using renewal process theory, total probability decomposition technique and z-transform, we study the transient and equilibrium properties of the queue length from an arbitrary initial state, and obtain both the recursive expressions of the transient state queue length distribution and the steady state queue length distribution at arbitrary time epoch n+. Furthermore, we derive the important relations between equilibrium queue length distributions at different time epochs n–, n and n+. Finally, we give some numerical examples about capacity decision in queueing systems to demonstrate the application of the analytical results reported in this paper.

Zeroth-Order Deterministic Local and Delay Pandemic Models Comparison

Delay differential equations are set up for zeroth-order pandemic models in analogy with traditional SIR and SEIR models by specifying individual times of incubation and infectiousness prior to recovery. Independent linear delay relations in addition to a nonlinear delay differential equation are found for characterizing time-dependent compartmental populations. Asymptotic behavior allows a link between parameters of the delay and traditional models for their comparison. In analogy with transformation of the traditional equations into linear form giving populations and time in parametric form, expansion in the delay provides a simple recursive solution. Also, a soliton-like solution in terms of a logistic function can be applied for accurate approximation. Otherwise, straightforward numerical solution is effected in terms of linearized boundary conditions specifying the distribution of instigators as to their initial infection progress--in contrast to traditional models specifying only initial average infectious and exposed populations. Examples contrasting asymptotically-linked traditional and delay models are given.

Reduced-Order Algorithm for Eigenvalue Assignment of Singularly Perturbed Linear Systems

In this paper, we present an algorithm for eigenvalue assignment of linear singularly perturbed systems in terms of reduced-order slow and fast subproblem matrices. No similar algorithm exists in the literature. First, we present an algorithm for the recursive solution of the singularly perturbed algebraic Sylvester equation used for eigenvalue assignment. Due to the presence of a small singular perturbation parameter that indicates separation of the system variables into slow and fast, the corresponding algebraic Sylvester equation is numerically ill-conditioned. The proposed method for the recursive reduced-order solution of the algebraic Sylvester equations removes ill-conditioning and iteratively obtains the solution in terms of four reduced-order numerically well-conditioned algebraic Sylvester equations corresponding to slow and fast variables. The convergence rate of the proposed algorithm is Oε, where ε is a small positive singular perturbation parameter.

Identification of Structural Parameters and Unknown Inputs Based on Revised Observation Equation: Approach and Validation

The identification of parameters of linear or nonlinear systems under unknown inputs and limited outputs is an important but still challenging topic in the context of structural health monitoring. Time-domain analysis methodologies, such as extend Kalman filter (EKF), have been actively studied and shown to be powerful for parameter identification. However, the conventional EKF is not applicable when the input is unknown or unmeasured. In this paper, by introducing a projection matrix in the observation equation, a time-domain EKF-based approach is proposed for the simultaneous identification of structural parameters and the unknown excitations with limited outputs. A revised version of observation equation is presented. The unknown inputs are identified using the least squares estimation based on the limited observations and the estimated structural parameters at the current time step. Particularly, an analytical recursive solution is derived. The accuracy and effectiveness of the proposed approach is first demonstrated via several numerical examples. Then it was validated by the shaking table tests on a five-story building model for the robustness in application to real structures. The results show that the proposed approach can satisfactorily identify the parameters of linear or nonlinear structures under unknown inputs.

Numerical modeling for the urban drainage gallery systems design

ABSTRACT Considering the frequent flooding of urban centers, the financial limitations and the inefficient management of Urban Drainage (UD) systems in Brazilian municipalities, it is necessary that projects be developed efficiently. These objectives are achieved with the correct definition of the diameter and galleries slope, resulting in adequate hydraulic ratios. It is also necessary to guarantee the flow without backwater, by verifying the energy grade line along the network. There are software capable of assisting the calculation, which, however, do not report optimized solutions. A vector-based numerical modeling is presented for the optimized sizing of a UD gallery system. This model was applied in an area and its results were compared with those obtained by two software in the Brazilian market. It is demonstrated the optimization developed contributes to increases the efficiency in the design. The main scientific contributions are: to characterize and model the typical design slopes, to obtain the optimum slope combined with the smaller diameter; to explore the potential of the hydraulic ratios above those normally employed, with positive effects on the definition of {D, ig} and the economy in the system; and to implement a recursive solution from a cycle of interdependent information, ensuring accuracy of results.

Recursive Contracts

We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.

Chain of matrices, loop equations, and topological recursion

This article considers the so-called loop equations satisfied by integrals over random matrices coupled in a chain as well as their recursive solution in the perturbative case when the matrices are Hermitian. Random matrices are used in fields such as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces, both of which are based on the analysis of a matrix integral. However, this term can be confusing since the definition of a matrix integral in these two applications is not the same. The article discusses these two definitions, perturbative and non-perturbative, along with their relationship. It first provides an overview of a matrix integral before comparing convergent and formal matrix integrals. It then describes the loop equations and their solution in the one-matrix model. It also examines matrices coupled in a chain plus external field and concludes with a generalization of the topological recursion.