The impact of special days in call arrivals forecasting: A neural network approach to modelling special days

A key challenge for call centres remains the forecasting of high frequency call arrivals collected in hourly or shorter time buckets. In addition to the complex intraday, intraweek and intrayear seasonal cycles, call arrival data typically contain a large number of anomalous days, driven by the occurrence of holidays, special events, promotional activities and system failures. This study evaluates the use of a variety of univariate time series forecasting methods for forecasting intraday call arrivals in the presence of such outliers. Apart from established, statistical methods, we consider artificial neural networks (ANNs). Based on the modelling flexibility of the latter, we introduce and evaluate different methods to encode the outlying periods. Using intraday arrival series from a call centre operated by one of Europe’s leading entertainment companies, we provide new insights on the impact of outliers on the performance of established forecasting methods. Results show that ANNs forecast call centre data accurately, and are capable of modelling complex outliers using relatively simple outlier modelling approaches. We argue that the relative complexity of ANNs over standard statistical models is offset by the simplicity of coding multiple and unknown effects during outlying periods.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.     

Minimal varieties of residuated lattices

In this paper we investigate the atomic level in the lattice of subvarieties of residuated lattices. In particular, we give infinitely many commutative atoms and construct continuum many non-commutative, representable atoms that satisfy the idempotent law; this answers Problem 8.6 of [12]. Moreover, we show that there are only two commutative idempotent atoms and only two cancellative atoms. Finally, we study the connections with the subvariety lattice of residuated bounded-lattices. We modify the construction mentioned above to obtain a continuum of idempotent, representable minimal varieties of residuated bounded-lattices and illustrate how the existing construction provides continuum many covers of the variety generated by the three-element non-integral residuated bounded-lattice.In Celebration of the Sixtieth Birthday of Ralph N. McKenzieReceived August 1, 2003; accepted in final form April 27, 2004.     

On p-logistic equations of equidiffusive type

We consider a p-logistic equation with equidiffusive reaction. We study the existence, nonexistence and uniqueness of positive solutions as the parameter \(\lambda >0\) varies. In the case of a unique positive solution \(u_{\lambda }\), we investigate the monotonicity and continuity properties of the map \(\lambda \rightarrow u_{\lambda }\).     

Nonhomogeneous Hemivariational Inequalities with Indefinite Potential and Robin Boundary Condition

We consider a nonlinear, nonhomogeneous Robin problem with an indefinite potential and a nonsmooth primitive in the reaction term. In fact, the right-hand side of the problem (reaction term) is the Clarke subdifferential of a locally Lipschitz integrand. We assume that asymptotically this term is resonant with respect the principal eigenvalue (from the left). We prove the existence of three nontrivial smooth solutions, two of constant sign and the third nodal. We also show the existence of extremal constant sign solutions. The tools come from nonsmooth critical point theory and from global optimization (direct method).     

Gluing Eguchi‐Hanson Metrics and a Question of Page

In 1978, Gibbons‐Pope and Page proposed a physical picture for the Ricci flat Kähler metrics on the K3 surface based on a gluing construction. In this construction, one starts from a flat torus with 16 orbifold points and resolves the orbifold singularities by gluing in 16 small Eguchi‐Hanson manifolds that all have the same orientation. This construction was carried out rigorously by Topiwala, LeBrun‐Singer, and Donaldson. In 1981, Page asked whether the above construction can be modified by reversing the orientations of some of the Eguchi‐Hanson manifolds. This is a subtle question: if successful, this construction would produce Einstein metrics that are neither Kähler nor self‐dual. In this paper, we focus on a configuration of maximal symmetry involving eight small Eguchi‐Hanson manifolds of each orientation that are arranged according to a chessboard pattern. By analyzing the interactions between Eguchi‐Hanson manifolds with opposite orientation, we identify a nonvanishing obstruction to the gluing problem, thereby destroying any hope of producing a metric of zero Ricci curvature in this way. Using this obstruction, we are able to understand the dynamics of such metrics under Ricci flow as long as the Eguchi‐Hanson manifolds remain small. In particular, for the configuration described above, we obtain an ancient solution to the Ricci flow with the property that the maximum of the Riemann curvature tensor blows up at a rate of , while the maximum of the Ricci curvature converges to 0.© 2016 Wiley Periodicals, Inc.     

Identifying preferred solutions to Multi-Objective Binary Optimisation problems,with an application to the Multi-Objective Knapsack Problem

In this paper we present a new framework for identifying preferred solutions to multi-objective binary optimisation problems. We develop the necessary theory which leads to new formulations that integrate the decision space with the space of criterion weights. The advantage of this is that it allows for incorporating preferences directly within a unique binary optimisation problem which identifies efficient solutions and associated weights simultaneously. We discuss how preferences can be incorporated within the formulations and also describe how to accommodate the selection of weights when the identification of a unique solution is required. Our results can be used for designing interactive procedures for the solution of multi-objective binary optimisation problems. We describe one such procedure for the multi-objective multi-dimensional binary knapsack formulation of the portfolio selection problem.     

Improper hydrogen bonded cyclohexane C-Hax···Yax contacts: theoretical predictions and experimental evidence from 1H NMR spectroscopy of suitable axial cyclohexane models

C-H(ax)···Y(ax) contacts are a textbook prototype of steric hindrance in organic chemistry. The nature of these contacts is investigated in this work. MP2/6-31+G(d,p) calculations predicted the presence of improper hydrogen bonded C-H(ax)···Y(ax) contacts of different strength in substituted cyclohexane rings. To support the theoretical predictions with experimental evidence, several synthetic 2-substituted adamantane analogues (1-24) with suitable improper H-bonded C-H(ax)···Y(ax) contacts of different strength were used as models of a substituted cyclohexane ring. The (1)H NMR signal separation, Δδ(γ-CH(2)), within the cyclohexane ring γ-CH(2)s is raised when the MP2/6-31+G(d,p) calculated parameters, reflecting the strength of the H-bonded C-H(ax)···Y(ax) contact, are increased. In molecules with enhanced improper H-bonded contacts C-H(ax)···Y(ax), like those having sterically crowded contacts (Y(ax) = t-Bu) or contacts including considerable electrostatic attractions (Y(ax) = O-C or O═C) the calculated DFT steric energies of the γ-axial hydrogens are considerably reduced reflecting their electron cloud compression. The results suggest that the proton H(ax) electron cloud compression, caused by the C-H(ax)···Y(ax) contacts, and the resulting increase in Δδ(γ-CH(2)) value can be effected not just from van der Waals spheres compression, but more generally from electrostatic attraction forces and van der Waals repulsion, both of which are improper H-bonding components.