Multi-angle and nonuniform ground motions on cable-stayed bridges

The definition of the spatial variability of the ground motion (SVGM) is a complex and multi-parametric problem. Its effect on the seismic response of cable-stayed bridges is important, yet not entirely understood to date. This work examines the effect of the SVGM on the seismic response of cable-stayed bridges by means of the time delay of the ground motion at different supports, the loss of coherency of the seismic waves, and the incidence angle of the seismic waves. The focus herein is the effect of the SVGM on cable-stayed bridges with various configurations in terms of their length and of design parameters such as the pylon shape and the pylon–cable system configuration. The aim of this article is to provide general conclusions that are applicable to a wide range of canonical cable-stayed bridges and to contribute to the ongoing effort to interpret and predict the effect of the SVGM in long structures. This work shows that the effect of the SVGM on the seismic response of cable-stayed bridges varies depending on the pylon shape, height, and section dimensions; on the cable-system configuration; and on the response quantity of interest. Furthermore, the earthquake incidence angle defines whether the SVGM is important to the seismic response of the cable-stayed bridges. It is also confirmed that the SVGM excites vibration modes of the bridges that do not contribute to their seismic response when identical support motion is considered.

On critical Kirchhoff problems driven by the fractional Laplacian

We study a nonlocal parametric problem driven by the fractional Laplacian operator combined with a Kirchhoff-type coefficient and involving a critical nonlinearity term in the Sobolev embedding sense. Our approach is of variational and topological nature. The obtained results can be viewed as a nontrivial extension to the nonlocal setting of some recent contributions already present in the literature.

Regularized Orthogonal Machine Learning for Nonlinear Semiparametric Models

This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we estimate by modern machine learning tools. We first adjust the moment function so that the gradient of the future loss function is insensitive (formally, Neyman-orthogonal) with respect to the first-stage regularization bias, preserving the single index property. We then take the loss function to be an indefinite integral of the adjusted moment function with respect to the single index. The proposed Lasso estimator converges at the oracle rate, where the oracle knows the nuisance function and solves only the parametric problem. We demonstrate our method by estimating the short-term heterogeneous impact of Connecticut’s Jobs First welfare reform experiment on women’s welfare participation decision.

An approximation algorithm for a general class of parametric optimization problems

In a (linear) parametric optimization problem, the objective value of each feasible solution is an affine function of a real-valued parameter and one is interested in computing a solution for each possible value of the parameter. For many important parametric optimization problems including the parametric versions of the shortest path problem, the assignment problem, and the minimum cost flow problem, however, the piecewise linear function mapping the parameter to the optimal objective value of the corresponding non-parametric instance (the optimal value function) can have super-polynomially many breakpoints (points of slope change). This implies that any optimal algorithm for such a problem must output a super-polynomial number of solutions. We provide a method for lifting approximation algorithms for non-parametric optimization problems to their parametric counterparts that is applicable to a general class of parametric optimization problems. The approximation guarantee achieved by this method for a parametric problem is arbitrarily close to the approximation guarantee of the algorithm for the corresponding non-parametric problem. It outputs polynomially many solutions and has polynomial running time if the non-parametric algorithm has polynomial running time. In the case that the non-parametric problem can be solved exactly in polynomial time or that an FPTAS is available, the method yields an FPTAS. In particular, under mild assumptions, we obtain the first parametric FPTAS for each of the specific problems mentioned above and a $$(3/2 + \varepsilon )$$ ( 3 / 2 + ε ) -approximation algorithm for the parametric metric traveling salesman problem. Moreover, we describe a post-processing procedure that, if the non-parametric problem can be solved exactly in polynomial time, further decreases the number of returned solutions such that the method outputs at most twice as many solutions as needed at minimum for achieving the desired approximation guarantee.

SDO and LDO relaxation approaches to complex fractional quadratic optimization

This paper examines a complex fractional quadratic optimization problem subject to two quadratic constraints. The original problem is transformed into a parametric quadratic programming problem by the well-known classical Dinkelbach method. Then a semidefinite and Lagrangian dual optimization approaches are presented to solve the nonconvex parametric problem at each iteration of the bisection and generalized Newton algorithms. Finally, the numerical results demonstrate the effectiveness of the proposed approaches.

On the effect of multi-angle and spatially variable ground motions on cable-stayed bridges

The definition of the Spatial Variability of the Ground Motion (SVGM) is a com- plex and multi-parametric problem. Its effect on the seismic response of long and multiply-supported structures in general, and on cable-stayed bridges, in particular, is important but not entirely understood. This work examines the effect of the SVGM on the seismic response of cable-stayed bridges by means of the time delay of the earth- quake at different supports and of the loss of coherency of the seismic waves. The focus herein is the effect of the SVGM on cable-stayed bridges with various configu- rations in terms of their length and of design parameters, such as the pylon shape and the pylon–cable system configuration, combined with the influence of the incidence angle of the seismic waves. The aim of this paper is to provide general conclusions that are applicable to a wide range of cable-stayed bridges and to contribute to the ongoing effort to interpret and predict the effect of the SVGM. It has been found that the influence of the multi-support excitation on the seismic response of the bridges is strongly affected by the shape of the pylons, by the pylon–cable system configura- tion and by and the earthquake’s incidence angle. It is also observed that the SVGM excites vibration modes of the bridges that do not contribute to their seismic response when identical support motion is considered.

The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations

In this paper, we consider intuitionistic fuzzy partial functional differential equations with local and nonlocal initial conditions using the Banach fixed point theorem. A new complete intuitionistic fuzzy metric space is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems. We use the level-set representation of intuitionistic fuzzy functions and define the solution to an intuitionistic fuzzy partial functional differential equation problem through a corresponding parametric problem and further develop theoretical results on the existence and uniqueness of the solution. An example is presented to illustrate the results with some numerical simulation for α-cuts of the intuitionistic fuzzy solutions: we give the representation of the surface of intuitionistic fuzzy solutions.

Minoan Group Design: The ‘View from the Bridge’

The aim of this chapter is to address the so-called Minoan Palace as a design object. To detect and unfold, in other words, the design logic that produced this hybrid configuration standing somewhere between a large building and an urban compound. As a starting point, it is pertinent to emphasize that the production of built space is a dynamic process involving poly-parametric problem solving. It requires formulating the tasks, checking requirements versus constraints, evaluating tolerance and capacity, and finally making choices and decisions based on optimization. Planning and designing architectural space, in other words, is a nebulous task, notoriously difficult to capture, describe, or teach for that matter. In Rowe’s (1982: 18) lucid account, it has ‘“wicked problems”: they have no definitive formulation, no explicit “stopping rule”, they have more than one plausible explanation, and their solutions cannot be strictly correct or false’. Moreover, this procedure does not take place once and for all. It is re-enacted every time one interferes with a work of architecture, even if only to whitewash a wall or block a door. Since buildings, as a rule, survive their original creators and users by several generations, such interventions are frequent and vary in scale, in compliance with the life cycles that the building will serve till it exists nomore or has become the object of archaeological investigation. With such variety of intertwined and obscured parameters at play, one wonders: what sort of answers do archaeologists expect to find from the surviving remnants of the architectural palimpsest they are dealing with? Is it because of the innate difficulties in capturing and analysing the dynamic process of architectural production that we have lingered for too long over the static data of the end product (see chapter 1)? The situation however is not that hopeless, for ‘architecture is not the field of creative freedom some have imagined it to be, but a system of rules for giving society what it expects in the way of architecture’ (Eco 1997: 194).