The Theory of Competitive Markets

Chapter 2 explains how the theory of competitive markets became the benchmark for economic analysis, implicitly leading to the assumption that firms actually compete in real-world markets rather than acting as oligopolies. The chapter begins by showing how competition theoretically maximizes resource allocation and constrains the behavior of firms. Then it analyzes the assumptions that underlie the theory, emphasizing the problems that stem from the assumption of consumer sovereignty and the ability of producers to manipulate consumer preferences. It also explains how the assumption that markets are competitive became the paradigm of economic education, as advocated by Alfred Marshall, rather than recognizing the prevalence of monopolies and oligopolies, as advocated by Marshall’s successor, Joan Robinson. Finally, the chapter shows how the assumption that real-world markets are competitive is used to justify opposition to government regulation, based on the notion that competition already provides the only necessary constraints.

MINLP formulations for continuous piecewise linear function fitting

We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y) for piecewise linear function fitting. We show that this MINLP model is incomplete and can result in a piecewise linear curve that is not the graph of a function, because it misses a set of necessary constraints. We provide two counterexamples to illustrate this effect, and propose three alternative models that correct this behavior. We investigate the theoretical relationship between these models and evaluate their computational performance.

Modeling of traversable wormholes in exponential f(R,T) gravity

In the present communication, we have studied the existence of wormholes described by a logarithmic shape function, in the exponential f(R, T) gravity given by f(R, T) = R + 2ξe^{ςt} where ξ and ς are arbitrary constants, under three different set of physical constraints. The logarithmic shape function is found to be well behaved satisfying all the necessary constraints for traversable and asymptotically flat wormholes. The obtained wormhole solutions are analyzed from the energy conditions for different values of involved physical constants. It has been observed that our proposed shape function for the exponential form of f(R, T) gravity, represents the existence of exotic matter with a standard violation of the NEC. Moreover, for the trace T=0 i.e. for the general relativity case with R being replaced by R+2, the wormhole geometry has been analyzed to prove the existence of exotic matter. Further, the behaviour of physical parameters such as the energy density ρ, the trace T, anisotropy parameter △ describing the geometry of the universe has been presented with the help of graphs.

A Triple-Moment Representation of Ice in the Predicted Particle Properties (P3) Microphysics Scheme

In the original Predicted Particle Properties (P3) bulk microphysics scheme, all ice-phase hydrometeors are represented by one or more “free” ice categories, where the physical properties evolve smoothly through changes to the four prognostic variables (per category,) and with a 2-moment representation of the particle size distribution. As such, the spectral dispersion cannot evolve independently, which thus results in limitations in representation of ice – in particular hail – due to necessary constraints in the scheme to prevent excessive gravitational size sorting. To overcome this, P3 has been modified to include a 3-moment representation of the size distribution of each ice category through the addition of a fifth prognostic variable, the sixth moment of the size distribution.The details of the 3-moment ice parameterization in P3 are provided. The behavior of the modified scheme, with the single-ice-category configuration, is illustrated through simulations in a simple 1D kinematic model framework as well as with near large-eddy-resolving (250-m grid spacing) 3D simulations of a hail-producing supercell. It is shown that the 3-moment ice configuration controls size sorting in a physically-based way and leads to an improved capacity to simulate large, heavily-rimed ice (hail), including mean and maximum sizes and reflectivity, and thus an overall improvement in the representation of ice-phase particles in the P3 scheme.

Adaptive Multilevel Collaborative Passenger Flow Control in Peak Hours for a Subway Line

Due to contradiction of large-scale passenger demand and limited transportation capacity, the passengers who cannot be transported away in time accumulate and congest in stations. To ensure travel safety, improve travel efficiency, and ameliorate waiting environments for passengers, this paper proposes an adaptive multilevel collaborative passenger flow control strategy integrating the control of station entrance and station hall. An integer linear programming model is constructed, which aims at minimizing the total passenger waiting time and taking the safe capacity of each key area of all stations as the necessary constraints. The model is applied in two scenarios with different scales of passenger demand in the morning peak of the Batong line. The results show that the proposed model can adaptively activate the appropriate control level, limit the amount of accumulated passengers in each key area of the station within its safe capacity, and shorten the total passenger waiting time.

Automatic Detection of Amplitude-Distorted Samples from Clipped Seismic Waveforms

Seismic waveforms are essential for seismology but are clipped when their actual amplitudes are too high to be faithfully recorded by seismometers. The clipping effects are popular for both big earthquakes and small earthquakes within a short epicentral distance. Here, we illustrate potential risks of direct usage of clipped waveforms by examining the frequency leakage and show the failure of bandpass filtering for different clipping levels; then we summarize two characteristics of clipped records: (1) The temporal gradient is unusually large around the clipped segment compared with the unclipped portions, and (2) the clipped samples cluster into one segment or several if many samples are involved. Next, we propose three criteria for distinguishing clipped samples from the perfect samples based on these two characteristics. Finally, we design a numerical algorithm for automatic detection of clipped samples using constraints on the gradient, amplitude, and gradient-varying range. Numerical experiments show the excellent performance of our algorithm on automatically detecting the clipped samples. Our algorithm seamlessly integrates all necessary constraints for both flat-top type and back-to-zero type and thus can correctly recognize these two types simultaneously; in addition, it is basically data driven and thus can work well without considering seismometer configuration and instrument type, which would be helpful for real-time detection of clipped records without interruption from human operations. As a robust and swift tool of automatic detection on amplitude-clipped samples, our algorithm could identify most typical clipped records and reduce potential risks due to using unrecognizable clipped waveforms; furthermore, it would be helpful for fast detection and possible restoration of clipped waveforms in the presence of huge volumes of data.

Analysis of the Influence of Suspension Actuator Limitations on Ride Comfort in Passenger Cars Using Model Predictive Control

Active suspension systems help to deliver superior ride comfort and can be used to resolve the objective conflict between ride comfort and road-holding. Currently, there exists no method for analyzing the influence of actuator limitations, such as maximum force and maximum rate of change, on the achievable ride comfort. This research paper presents a method that is capable of doing this. It uses model predictive control to eliminate the influence of feedback controller performance and to integrate both actuator limitations and necessary constraints on dynamic wheel-load variation and suspension travel. Various scenarios are simulated, such as driving over a speed bump and inner city driving, as well as driving on a country road and motorway driving, using a state-of-the-art quarter-car model, parameterized for a luxury class vehicle. It is analyzed how comfort, or in one scenario road-holding, can be improved with consideration for the actuator limitations. The results indicate that actuator rate limitation has a strong influence on vertical vehicle dynamics control system performance, and that relatively small maximum forces of around 1000 to 2000 N are sufficient to successfully reject disturbances from road irregularities, provided the actuator is capable of supplying the forces at a sufficiently high rate of change.

On Functions Computed on Trees

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function that takes as inputs two numbers from its children and produces one output. Since thinking about functions in terms of computation graphs is becoming popular, we may want to know which functions can be implemented on a given tree. Here, we describe a set of necessary constraints in the form of a system of nonlinear partial differential equations that must be satisfied. Moreover, we prove that these conditions are sufficient in contexts of analytic and bit-valued functions. In the latter case, we explicitly enumerate discrete functions and observe that there are relatively few. Our point of view allows us to compare different neural network architectures in regard to their function spaces. Our work connects the structure of computation graphs with the functions they can implement and has potential applications to neuroscience and computer science.

A RELEVANCE-THEORETIC ANALYSIS OF YEAH AS A DISCOURSE MARKER

The paper attempts to explain English native speakers’ use of the discourse marker yeah from a relevance-theoretic perspective (Sperber & Wilson, 1995). As a discourse marker, yeah normally functions as a continuer, an agreement marker, a turn-taking marker, or a disfluency marker. However, according to Relevance Theory, yeah can also be considered a procedural expression, and therefore, is expected to help yield necessary constraints on the contexts, which facilitates understanding in human communication by encoding one of the three contextual effects (contextual implication, strengthening, or contradiction) or reorienting the audience to certain assumptions which lead to the intended interpretation. Analyses of examples taken from conversations with a native speaker of English suggest that each use of yeah as a discourse marker is able to put a certain type of constraints on the relevance of the accompanying utterance. These initial analyses serve as a foundation for further research to confirm its multi-functionality as a procedural expression when examined within the framework of Relevance Theory.

3D Multi-Beam and Null Synthesis by Phase-Only Control for 5G Antenna Arrays

This paper presents an iterative algorithm for the synthesis of the three-dimensional (3D) radiation pattern generated by an antenna array of arbitrary geometry. The algorithm is conceived to operate in fifth-generation (5G) millimeter-wave scenarios, thus enabling the support of multi-user mobile streaming and massive peer-to-peer communications, which require the possibility to synthesize 3D patterns with wide null regions and multiple main beams. Moreover, the proposed solution adopts a phase-only control approach to reduce the complexity of the feeding network and is characterized by a low computational cost, thanks to the closed-form expressions derived to estimate the phase of each element at the generic iteration. These expressions are obtained from the minimization of a weighted cost function that includes all the necessary constraints. To finally check its versatility in a 5G environment, the developed method is validated by numerical examples involving planar and conformal arrays, considering desired patterns with different numbers of main beams and nulls.