Joint swing-up and stabilization of the Reaction Wheel Pendulum using Discontinuous Integral algorithm

In this paper, a third-order discontinuous integral controller is designed to jointly swing-up and robustly stabilize in finite-time the upright position of the Reaction Wheel Pendulum (RWP) system, despite some uncertainties and perturbations. To show this, a numerical estimation of the domain of attraction of the controller is used. The control algorithm produces a continuous control signal, thus reducing the usual chattering effect of the sliding-mode controllers. The theoretical results of the paper are verified by simulations and experiments in a laboratory setup.     

A constraints-aware Reweighted Feasibility Pump approach

We extend the Reweighted Feasibility Pump (RFP) approach of De Santis et al. (2014) [9], De Santis et al. (2013) [8], which is based on the interpretation of the (main step of the) Feasibility Pump as the Frank-Wolfe method applied to an appropriate penalty function that drives the search towards integer solutions. We modify the function that is minimized by incorporating barrier terms that provide information about how much changing a variable is possible due to it being involved in (almost) active constraints. The corresponding Constraints-Aware RWP is experimentally tested on two sets of hard pure binary feasibility problems, and the results show that, all other things being equal, the modification leads to a more effective and robust method w.r.t. the original RFP one.     

Nonexistence of Markovian time dynamics for graphical models of correlated default

Filiz et al. (in arXiv:0809.1393 (2008)) proposed a model for the pattern of defaults seen among a group of firms at the end of a given time period. The ingredients in the model are a graph G=(V,E), where the vertices V correspond to the firms and the edges E describe the network of interdependencies between the firms, a parameter for each vertex that captures the individual propensity of that firm to default, and a parameter for each edge that captures the joint propensity of the two connected firms to default. The correlated default model can be rewritten as a standard Ising model on the graph by identifying the set of defaulting firms in the default model with the set of sites in the Ising model for which the {±1}-valued spin is +1. We ask whether there is a suitable continuous-time Markov chain (X _t ) _t??0 taking values in the subsets of V such that X ₀=?, X _r ?X _s for r??s (that is, once a firm defaults, it stays in default), the distribution of X _T for some fixed time T is the one given by the default model, and the distribution of X _t for other times t is described by a probability distribution in the same family as the default model. In terms of the equivalent Ising model, this corresponds to asking if it is possible to begin at time 0 with a configuration in which every spin is ?1 and then flip spins one at a time from ?1 to +1 according to Markovian dynamics so that the configuration of spins at each time is described by some Ising model and at time T the configuration is distributed according to the prescribed Ising model. We show for three simple but financially natural special cases that this is not possible outside of the trivial case where there is complete independence between the firms.     

Measuring efficiency at U.S. banks: Accounting for heterogeneity is important

Estimates of bank cost efficiency can be biased if bank heterogeneity is ignored. I compare X-inefficiency derived from a model constraining the cost frontier to be the same for all banks in the U.S. and a model allowing for different frontiers and error terms across Federal Reserve Districts. I find that the data reject the single cost function model; X-inefficiency measures based on the single cost function model are, on average, higher than those based on the separate cost functions model; the distributions of the one-sided error terms are wider for the single cost function model than for the separate cost functions model; and the ranking of Districts by the level of X-inefficiency differs in the two models. The results suggest it is important when studying X-inefficiency to account for differences across the markets in which banks are operating and that since X-inefficiency is, by construction, a residual, it will be particulary sensitive to omissions in the basic model.     

Homotopical algebraic geometry I: topos theory

This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts. In this first part we investigate a notion of higher topos.For this, we use S-categories (i.e. simplicially enriched categories) as models for certain kind of ∞-categories, and we develop the notions of S-topologies, S-sites and stacks over them. We prove in particular, that for an S-category T endowed with an S-topology, there exists a model category of stacks over T, generalizing the model category structure on simplicial presheaves over a Grothendieck site of Joyal and Jardine. We also prove some analogs of the relations between topologies and localizing subcategories of the categories of presheaves, by proving that there exists a one-to-one correspondence between S-topologies on an S-category T, and certain left exact Bousfield localizations of the model category of pre-stacks on T. Based on the above results, we study the notion of model topos introduced by Rezk, and we relate it to our model categories of stacks over S-sites.In the second part of the paper, we present a parallel theory where S-categories, S-topologies and S-sites are replaced by model categories, model topologies and model sites. We prove that a canonical way to pass from the theory of stacks over model sites to the theory of stacks over S-sites is provided by the simplicial localization construction of Dwyer and Kan. As an example of application, we propose a definition of étale K-theory of ring spectra, extending the étale K-theory of commutative rings.     

Existence and uniqueness for several non-linear elliptic problems arising in lubrication theory

We consider the non-linear elliptic equation ∇·(A(x,p)∇p)=∇·b(x,p) with positive Dirichlet boundary data. The coefficients A and b are taken from models used in lubrication theory, and in particular are not defined for negative values of p. We prove some general existence and uniqueness results for a family of models, which extend related results in the literature. These results allow us to prove existence, uniqueness and positivity of the solution to advanced compressible lubrication models such as the kinetic-based Fukui-Kaneko model and the second-order-slip model. We also consider a spring-like model of compliant-foil compressible bearing, and weaken some hypotheses of previous results on more classical models such as the standard Reynolds model and the first-order-slip model.     

A fuzzy algorithm for continuous capacitated location allocation model with risk consideration

This paper presents a continuous capacitated location-allocation model with fixed cost as a risk management model. In the presented model, the fixed cost consists of production and installation costs. The model considers risk as percent of unsatisfied demands. The fixed cost is assigned to a zone with a predetermined radius from its center. Because of uncertain environment, demand in each zone is investigated as a fuzzy number. The model is solved by a fuzzy algorithm based on α-cut method. After solving the model based on different α-values, the zones with the largest possibilities are determined for locating new facilities and the best locations are calculated based on the obtained possibilities. Then, the model is solved based on different α-values to determine best allocation values. Also, this paper proposes a Cross Entropy (CE) algorithm considering multivariate normal and multinomial density functions for solving large scale instances and is compared with GAMS. Finally, a numerical example is expressed to illustrate the proposed model.     

Comparative error bound theory for three location models: continuous demand versus discrete demand

We develop a unified error bound theory to compare a given p-median, p-center or covering location model with continuously distributed demand points in R ⁿ to a corresponding given original model of the same type having a finite collection of demand points in R ⁿ . We give ways to construct either a continuous or finite demand point model from the other model and also control the error bound. Our work uses Voronoi tilings extensively, and is related to earlier error bound theory for aggregating finitely many demand points.     

Nagata's conjecture and countably compact hulls in generic extensions

Nagata conjectured that every M-space is homeomorphic to a closed subspace of the product of a countably compact space and a metric space. Although this conjecture was refuted by Burke and van Douwen, and A. Kato, independently, but we can show that there is a c.c.c. poset P of size ω² such that in VP Nagata's conjecture holds for each first countable regular space from the ground model (i.e. if a first countable regular space X∈V is an M-space in VP then it is homeomorphic to a closed subspace of the product of a countably compact space and a metric space in VP). By a result of Morita, it is enough to show that every first countable regular space from the ground model has a first countable countably compact extension in VP. As a corollary, we also obtain that every first countable regular space from the ground model has a maximal first countable extension in model VP.     

Optimal manufacturer’s replenishment policies in the EPQ model under two levels of trade credit policy

In 2007, Huang proposed the optimal retailer’s replenishment decisions in the EPQ model under two levels of trade credit policy, in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides its customer a permissible delay period N (with N < M). In this paper, we extend his EPQ model to complement the shortcoming of his model. In addition, we relax the dispensable assumptions of N < M and others. We then establish an appropriate EPQ model to the problem, and develop the proper theoretical results to obtain the optimal solution. Finally, a numerical example is used to illustrate the proposed model and its optimal solution.     

Bidimensional shallow water model with polynomial dependence on depth through vorticity

In this paper, we obtain a bidimensional shallow water model with polynomial dependence on depth. With this aim, we introduce a small non-dimensional parameter ε and we study three-dimensional Euler equations in a domain depending on ε (in such a way that, when ε becomes small, the domain has small depth). Then, we use asymptotic analysis to study what happens when ε approaches to zero. Asymptotic analysis allows us to obtain a new bidimensional shallow water model that not only computes the average velocity (as the classical model does) but also provides the horizontal velocity at different depths. This represents a significant improvement over the classical model. We must also remark that we obtain the model without making assumptions about velocity or pressure behavior (only the usual ansatz in asymptotic analysis). Finally, we present some numerical results showing that the new model is able to approximate the non-constant in depth solutions to Euler equations, whereas the classical model can only obtain the average velocity.     

Indeterminacy in portfolio selection

This paper develops the indeterminacy in “portfolio selection” putting together a modification of a device of measure theory used in our previous papers [Atti del XXI Convegno Annuale AMASES, 1997, pp. 635–647; Soft Computing in Financial Engineering, 1999, pp. 425–432] and Shannon's entropy of information. We obtain an expectation, variance and indeterminacy (E–V–I) functional which is a generalization of the expectation quadratic utility. If I=0 our model is more coherent with the expectation–variance (E–V) model than the classical model and if I≠0 our model yields a warning about the risk from indeterminacy that expectation quadratic utility model does not. A numerical method and its statistical application with Italian data illustrates the results.     

G-symmetric spectra,semistability and the multiplicative norm

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in between Mandell's equivariant symmetric spectra and the G-orthogonal spectra of Mandell and May and is Quillen equivalent to the two. We further discuss equivariant semistability, construct model structures on module, algebra and commutative algebra categories and describe the homotopical properties of the multiplicative norm in this context.     

New Faddeev-Niemi-Type variables for the static Yang-Mills theory

Faddeev and Niemi introduced a nonlinear sigma model as a natural extension of the Faddeev $\mathbb{S}^2 $ chiral model. The field variables in the extended model are two chiral fields taking values in SU(3)/(U(1)×U(1)) and SU(3)/(SU(2)×U(1)). Shabanov showed that the energy functional of the extended model is bounded from below by a topological invariant and can therefore support knotlike excitations and a mass gap. We introduce new variables of the Faddeev-Niemi type for the static SU(3) Yang-Mills theory, which reveal a structure of a nonlinear sigma model in the Lagrangian.     

Integrating DEA-oriented performance assessment and target setting using interactive MOLP methods

Data envelopment analysis (DEA) and multiple objective linear programming (MOLP) are tools that can be used in management control and planning. Whilst these two types of model are similar in structure, DEA is directed to assessing past performances as part of management control function and MOLP to planning future performance targets. This paper is devoted to investigating equivalence models and interactive tradeoff analysis procedures in MOLP, such that DEA-oriented performance assessment and target setting can be integrated in a way that the decision makers’ preferences can be taken into account in an interactive fashion. Three equivalence models are investigated between the output-oriented dual DEA model and the minimax reference point formulations, namely the super-ideal point model, the ideal point model and the shortest distance model. These models can be used to support efficiency analysis in the same way as the conventional DEA model does and also support tradeoff analysis for setting target values by individuals or groups. A case study is conducted to illustrate how DEA-oriented efficiency analysis can be conducted using the MOLP methods and how such performance assessment can be integrated into an interactive procedure for setting realistic target values.     

Parametric scaling of mathematical models

Parametric scaling, the process of extrapolation of a modelling result to new parametric conditions, is often required in model optimization, and can be important if the effects of parametric uncertainty on model predictions are to be quantified. Knowledge of the functional relationship between the model solution (y) and the system parameters (α) may also provide insight into the physical system underlying the model. This paper examines strategies for parametric scaling, assuming that only the nominal model solution y(α) and the associated parametric sensitivity coefficients (?y/?α, ?²y/?α², etc.) are known. The truncated Taylor series is shown to be a poor choice for parametric scaling, when y has known bounds. Alternate formulae are proposed which ‘build-in’ the constraints on y, thus expanding the parametric region in which the extrapolation may be valid. In the case where y has a temporal as well as a parametric dependence, the extrapolation may be further improved by removing from the Taylor series coefficients the ‘secular’ components, which refer to changes in the time scale of y(t), not to changes in y as a function of α.     

Covering location problem of emergency service facilities in an uncertain environment

In practical location problems on networks, the response time between any pair of vertices and the demands of vertices are usually indeterminate. This paper employs uncertainty theory to address the location problem of emergency service facilities under uncertainty. We first model the location set covering problem in an uncertain environment, which is called the uncertain location set covering model. Using the inverse uncertainty distribution, the uncertain location set covering model can be transformed into an equivalent deterministic location model. Based on this equivalence relation, the uncertain location set covering model can be solved. Second, the maximal covering location problem is investigated in an uncertain environment. This paper first studies the uncertainty distribution of the covered demand that is associated with the covering constraint confidence level α. In addition, we model the maximal covering location problem in an uncertain environment using different modelling ideas, namely, the (α, β)-maximal covering location model and the α-chance maximal covering location model. It is also proved that the (α, β)-maximal covering location model can be transformed into an equivalent deterministic location model, and then, it can be solved. We also point out that there exists an equivalence relation between the (α, β)-maximal covering location model and the α-chance maximal covering location model, which leads to a method for solving the α-chance maximal covering location model. Finally, the ideas of uncertain models are illustrated by a case study.     

Inner models with large cardinal features usually obtained by forcing

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2 ^κ ?=?κ ⁺, another for which 2 ^κ ?=?κ ⁺⁺ and another in which the least strongly compact cardinal is supercompact. If there is a strongly compact cardinal, then there is an inner model with a strongly compact cardinal, for which the measurable cardinals are bounded below it and another inner model W with a strongly compact cardinal κ, such that ${H^{V}_{\kappa^+} \subseteq {\rm HOD}^W}$ . Similar facts hold for supercompact, measurable and strongly Ramsey cardinals. If a cardinal is supercompact up to a weakly iterable cardinal, then there is an inner model of the Proper Forcing Axiom and another inner model with a supercompact cardinal in which GCH?+?V?=?HOD holds. Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between strong compactness and supercompactness. If a cardinal is strongly compact up to a weakly iterable cardinal, then there is an inner model in which the least measurable cardinal is strongly compact. If there is a weakly iterable limit δ of <δ-supercompact cardinals, then there is an inner model with a proper class of Laver-indestructible supercompact cardinals. We describe three general proof methods, which can be used to prove many similar results.     

Upper bounds for the risk in the α — t utility function

Fishburn's α — t model is an important example of a utility function involving a target for a random variable. Simple upper bounds for the risk function in this model are proposed for cases in which the probability distribution is either unknown, or produces complicated or intractable statements of the model.     

Representability theorems for presheaves of spectra

Suppose that M is a simplicial model category and that F is a contravariant simplicial functor defined on M which takes values in pointed simplicial sets. This note displays conditions on the simplicial model category M and the functor F such that F is representable up to weak equivalence. The conditions on F are homotopy coherent versions of the classical conditions for Brown representability, while M should have the fundamental properties of the stable model structure for presheaves of spectra on a Grothendieck site.