Real Estate Appraisal: A Double Perspective Data Envelopment Analysis Approach

This paper proposes a new methodology for the assessment of the value range for real estate units. The theoretical basis of the methodology is built on the Data Envelopment Analysis—DEA approach, which has its original concept adapted to the case where the units under assessment consist of transactions among sellers and buyers. The proposed approach—christened Double Perspective-Data Envelopment Analysis (DP-DEA)—is applied to a database comprising the prices and features of the units under assessment. It is shown that the DP-DEA presents some specific advantages when compared to the usual regression analysis method employed in real estate value assessment.     

The position value is the Myerson value,in a sense

We characterize the position value for TU games with a cooperation structure in terms of the Myerson value of some natural modification of the original game—the link agent form. This construction is extended to TU games with a conference structure.      

The cartesian closed bicategory of generalised species of structures

The concept of generalised species of structures between smallcategories and, correspondingly, that of generalised analyticfunctor between presheaf categories are introduced. An operationof substitution for generalised species, which is the counterpartto the composition of generalised analytic functors, is alsoput forward. These definitions encompass most notions of combinatorialspecies considered in the literature — including of courseJoyal's original notion — together with their associatedsubstitution operation. Our first main result exhibits the substitutioncalculus of generalised species as arising from a Kleisli bicategoryfor a pseudo-comonad on profunctors. Our second main resultestablishes that the bicategory of generalised species of structuresis cartesian closed.     

On the asymptotic distribution of the likelihood ratio under the regularity conditions due to doob

Summary The concepts of the asymptotic maximum likelihood estimates—AMLEs in short—and their asymptotic identity are introduced in section 1. They seem to be more adequate than the usual one for uses in the large sample theory. The AMLE is a slightly weakened version of the usual maximum likelihood estimate and therefore it should have a bit wider applicability than the original one. The asymptotic normality of a consistent AMLE and Wilks’ theorem concerning the asymptotic distribution of the statistic —2 log λ, where λ is the likelihood ratio, can be obtained under the regularity conditions due to Doob in section 2. A set of conditions which assure the existence of a unique and consistent AMLE is presented in section 3 and in the final section 4 the proof of the existence of the unique and consistent AMLE under those conditions is given. This work has been motivated by the work of Ogawa, Moustafa and Roy [3].     

Coreduction Homology Algorithm for Regular CW-Complexes

In this paper we present a new algorithm for computing the homology of regular CW-complexes. This algorithm is based on the coreduction algorithm due to Mrozek and Batko and consists essentially of a geometric preprocessing algorithm for the standard chain complex generated by a CW-complex. By employing the concept of S-complexes the original chain complex can—in all known practical cases—be reduced to a significantly smaller S-complex with isomorphic homology, which can then be computed using standard methods. Furthermore, we demonstrate that in the context of non-uniform cubical grids this method significantly improves currently available algorithms based on uniform cubical grids.     

Leaving us in tiers: can homophily be used to generate tiering effects?

Substantial evidence indicates that our social networks are divided into tiers in which people have a few very close social support group, a larger set of friends, and a much larger number of relatively distant acquaintances. Because homophily—the principle that like seeks like—has been suggested as a mechanism by which people interact, it may also provide a mechanism that generates such frequencies and distributions. However, our multi-agent simulation tool, Construct, suggests that a slight supplement to a knowledge homophily model—the inclusion of several highly salient personal facts that are infrequently shared—can more successfully lead to the tiering behavior often observed in human networks than a simplistic homophily model. Our findings imply that homophily on both general and personal facts is necessary in order to achieve realistic frequencies of interaction and distributions of interaction partners. Implications of the model are discussed, and recommendations are provided for simulation designers seeking to use homophily models to explain human interaction patterns.     

Investment under ambiguity with the best and worst in mind

Recent literature on optimal investment has stressed the difference between the impact of risk and the impact of ambiguity—also called Knightian uncertainty—on investors’ decisions. In this paper, we show that a decision maker’s attitude towards ambiguity is similarly crucial for investment decisions. We capture the investor’s individual ambiguity attitude by applying α-MEU preferences to a standard investment problem. We show that the presence of ambiguity often leads to an increase in the subjective project value, and entrepreneurs are more eager to invest. Thereby, our investment model helps to explain differences in investment behavior in situations which are objectively identical.     

An interpretation of the Vakulenko—Kapitansky estimate

Introducing a concept of twisted tubes, we provide a speculative interpretation of exponent 3/4 in the Vakulenko—Kapitansky estimate for the Faddeev—Skyrme model. This allows us to make an assumption about the domain of applicability of the fit derived from the VK estimate. We propose an example of a sequence of knotted configurations which may be utilized in construction of static solutions with high energies. Bibliography: 9 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 317, 2004, pp. 57–65.     

C 1 Lohner Algorithm

Abstract. We present a modification of the Lohner algorithm for the computation of rigorous bounds for solutions of ordinary differential equations together with partial derivatives with respect to initial conditions. The modified algorithm requires essentially the same computational effort as the original one. We applied the algorithm to show the existence of several periodic orbits for R?ssler equations and the 14-dimensional Galerkin projection of the Kuramoto—Sivashinsky partial differential equation.     

On the best approximation matrix problem and matrix Fourier series

In this paper the concept of positive definite bilinear matrix moment functional, acting on the space of all the matrix valued continuous functions defined on a bounded interval [a,b] is introduced. The best approximation matrix problem with respect to such a functional is solved in terms of matrix Fourier series. Basic properties of matrix Fourier series such as the Riemann—Lebesgue, matrix property and the bessel—parseval matrix inequality are proved. The concept of total set with respect to a positive definite matrix functional is introduced, and the totallity of an orthonormal sequence of matrix polynomials with respect to the functional is established.     

A relax-and-cut framework for Gomory mixed-integer cuts

Gomory mixed-integer cuts (GMICs) are widely used in modern branch-and-cut codes for the solution of mixed-integer programs. Typically, GMICs are iteratively generated from the optimal basis of the current linear programming (LP) relaxation, and immediately added to the LP before the next round of cuts is generated. Unfortunately, this approach is prone to instability. In this paper we analyze a different scheme for the generation of rank-1 GMICs read from a basis of the original LP—the one before the addition of any cut. We adopt a relax-and-cut approach where the generated GMICs are not added to the current LP, but immediately relaxed in a Lagrangian fashion. Various elaborations of the basic idea are presented, that lead to very fast—yet accurate—variants of the basic scheme. Very encouraging computational results are presented, with a comparison with alternative techniques from the literature also aimed at improving the GMIC quality. We also show how our method can be integrated with other cut generators, and successfully used in a cut-and-branch enumerative framework.     

Groves of Phylogenetic Trees

A major challenge in biological sciences is the reconstruction of the Tree of Life. To this effect, large genomic databases like GenBank and SwissProt are being mined for clusters from which phylogenies can be inferred. Systematists and comparative biologists commonly combine such phylogenies into informative supertrees that reveal information which was not explicitly displayed in any of the original phylogenies. However, whether a supertree is informative depends on particular overlap properties among the clusters from which it originates. In this work we formally introduce the concept of groves — sets of clusters with the potential to construct informative supertrees. Thus maximal potential candidate clusters for informative supertree construction can be identified in large databases through groves, prior to inferring trees for each cluster. Groves also have the potential to lead to informative supermatrix construction. We developed methods that (i) efficiently identify particular types of groves and (ii) find lower and upper bounds on the minimal number of groves needed to cover all the trees or data sets in a database. Finally, we apply our methods to the green plant sequences from GenBank.     

On the Kurosh theorem

We introduce the concept of a projective family of subgroups, which behaves well under passage to subgroups, and then relate it to the notion of a wreath product. This does indeed deliver a new proof of the Kurosh theorem on subgroups of a free product, in which use is actually made of just categorical properties of a free product—all earlier proofs had a combinatorial bearing. Translated fromAlgebra i Logika, Vol. 37, No. 4, pp. 381–393, July–August, 1998.     

Explicit and Efficient Formulas for the Lattice Point Count in Rational Polygons Using Dedekind—Rademacher Sums

Abstract. We give explicit, polynomial-time computable formulas for the number of integer points in any two-dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of our formulas are Dedekind—Rademacher sums , which are polynomial-time computable finite Fourier series. As a by-product we rederive a reciprocity law for these sums due to Gessel, which generalizes the reciprocity law for the classical Dedekind sums. In addition, our approach shows that Gessel's reciprocity law is a special case of the one for Dedekind—Rademacher sums, due to Rademacher.     

A combinatorial Lefschetz fixed point formula

We define a class of simplicial maps — those which are “expanding directions preserving” — from a barycentric subdivision to the original simplicial complex. These maps naturally induce a self map on the links of their fixed points. The local index at a fixed point of such a map turns out to be the Lefschetz number of the induced map on the link of the fixed point in relative homology. We also show that a weakly hyperbolic [4] simplicial map sdⁿK →K is expanding directions preserving.     

A Newton’s method for perturbed second-order cone programs

We develop optimality conditions for the second-order cone program. Our optimality conditions are well-defined and smooth everywhere. We then reformulate the optimality conditions into several systems of equations. Starting from a solution to the original problem, the sequence generated by Newton’s method converges Q-quadratically to a solution of the perturbed problem under some assumptions. We globalize the algorithm by (1) extending the gradient descent method for differentiable optimization to minimizing continuous functions that are almost everywhere differentiable; (2) finding a directional derivative of the equations. Numerical examples confirm that our algorithm is good for “warm starting” second-order cone programs—in some cases, the solution of a perturbed instance is hit in two iterations. In the progress of our algorithm development, we also generalize the nonlinear complementarity function approach for two variables to several variables.     

On local and global sigma-pi neural networks a common link

In general, there is a great difference between usual three-layer feedforward neural networks with local basis functions in the hidden processing elements and those with standard sigmoidal transfer functions (in the following often called global basis functions). The reason for this difference in nature can be seen in the ridge-type arguments which are commonly used. It is the aim of this paper to show that the situation completely changes when instead of ridge-type arguments were so-called hyperbolic-type arguments. In detail, we show that usual sigmoidal transfer functions evaluated at hyperbolic-type arguments—usually called sigma—pi units—can be used to construct local basis functions which vanish at infinity and, moreover, are integrable and give rise to a partition of unity, both in Cauchy's principal value sense. At this point, standard strategies for approximation with local basis functions can be used without giving up the concept of non-local sigmoidal transfer functions.     

A large-deviations analysis of the GI/GI/1 SRPT queue

We consider a GI/GI/1 queue with the shortest remaining processing time discipline (SRPT) and light-tailed service times. Our interest is focused on the tail behavior of the sojourn-time distribution. We obtain a general expression for its large-deviations decay rate. The value of this decay rate critically depends on whether there is mass in the endpoint of the service-time distribution or not. An auxiliary priority queue, for which we obtain some new results, plays an important role in our analysis. We apply our SRPT results to compare SRPT with FIFO from a large-deviations point of view. 2000 Mathematics Subject Classification: Primary—60K25; Secondary—60F10; 90B22     

Viscosity Solutions of an Infinite-Dimensional Black—Scholes—Barenblatt Equation

We study an infinite-dimensional Black—Scholes—Barenblatt equation which is a Hamilton—Jacobi—Bellman equation that is related to option pricing in the Musiela model of interest rate dynamics. We prove the existence and uniqueness of viscosity solutions of the Black—Scholes—Barenblatt equation and discuss their stochastic optimal control interpretation. We also show that in some cases the solution can be locally uniformly approximated by solutions of suitable finite-dimensional Hamilton—Jacobi—Bellman equations.     

Approximation of impulse controls

The application of impulse controls—delta-function and its higher derivatives—essentially improves our ability to control various systems. However, the delta-function and its derivatives are “idealizations.” Controls applied to model and control real systems are finite (although possibly quite large in magnitude). In this article we consider bounded approximations of impulse controls—so-called fast controls—and examine methods of their construction.