Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

Hierarchical Approach for Survivable Network Design

A central design challenge facing network planners is how to select a cost-effective network configuration that can provide uninterrupted service despite edge failures. In this paper, we study the Survivable Network Design (SND) problem, a core model underlying the design of such resilient networks that incorporates complex cost and connectivity trade-offs. Given an undirected graph with specified edge costs and (integer) connectivity requirements between pairs of nodes, the SND problem seeks the minimum cost set of edges that interconnects each node pair with at least as many edge-disjoint paths as the connectivity requirement of the nodes. We develop a hierarchical approach for solving the problem that integrates ideas from decomposition, tabu search, randomization, and optimization. The approach decomposes the SND problem into two subproblems, Backbone design and Access design, and uses an iterative multi-stage method for solving the SND problem in a hierarchical fashion. Since both subproblems are NP-hard, we develop effective optimization-based tabu search strategies that balance intensification and diversification to identify near-optimal solutions. To initiate this method, we develop two heuristic procedures that can yield good starting points. We test the combined approach on large-scale SND instances, and empirically assess the quality of the solutions vis-à-vis optimal values or lower bounds. On average, our hierarchical solution approach generates solutions within 2.7% of optimality even for very large problems (that cannot be solved using exact methods), and our results demonstrate that the performance of the method is robust for a variety of problems with different size and connectivity characteristics.

The Choice of Expedient Regulatory Controls on Housing Market Using Short-Term Equilibria Model

Khutoretsky dealt with the problem of maximising a linear utility function (MUF) over the set of short-term equilibria in a housing market by reducing it to a linear programming problem, and suggested a combinatorial algorithm for this problem. Two approaches to the market adjustment were considered: the funding of housing construction and the granting of housing allowances. In both cases, locally optimal regulatory measures can be developed using the corresponding dual prices. The optimal effects (with the regulation expenditures restricted by an amount K) can be found using specialised models based on MUF: a model M1 for choice of the optimum structure of investment in housing construction, and a model M2 for optimum distribution of housing allowances. The linear integer optimisation problems corresponding to these models are initially difficult but can be solved after slight modifications of the parameters. In particular, the necessary modification of K does not exceed the maximum construction cost of one dwelling (for M1) or the maximum size of one housing allowance (for M2). The result is particularly useful since slight modification of K is not essential in practice.

Method of Detecting System Function by Measuring Frequency Response

Methods of rapidly measuring an impedance spectrum of an energy storage device in-situ over a limited number of logarithmically distributed frequencies are described. An energy storage device is excited with a known input signal, and aresponse is measured to ascertain the impedance spectrum. An excitation signal is a limited time duration sum-of-sines consisting of a select number offrequencies. In one embodiment, magnitude and phase of each frequency ofinterest within the sum-of-sines is identified when the selected frequencies and sample rate are logarithmic integer steps greater than two. This technique requires a measurement with a duration of one period of the lowest frequency. In another embodiment, where selected frequencies are distributed in octave steps, the impedance spectrum can be determined using a captured time record that is reduced to a half-period of the lowest frequency.

Entwicklung eines Dispositionsleitstandes zur Bestimmung optimaler Torbelegungen in Stückgutspeditionsanlagen

Im operativen Betrieb einer Stückgutspeditionsanlage entscheidet der Betriebslenker bzw. der Disponent in einem ersten Schritt darüber, an welche Tore die Fahrzeuge zur Be- und Entladung andocken sollen. Darüber hinaus muss er für jede Tour ein Zeitfenster ausweisen innerhalb dessen sie das jeweilige Tor belegt. Durch die örtliche und zeitliche Fahrzeug-Tor-Zuordnung wird der für den innerbetrieblichen Umschlagprozess erforderliche Ressourcenaufwand in Form von zu fahrenden Wegstrecken oder aber Gabelstaplerstunden bestimmt. Ein Ziel der Planungsaufgabe ist somit, die Zuordnung der Fahrzeuge an die Tore so vorzunehmen, dass dabei minimale innerbetriebliche Wegstrecken entstehen. Dies führt zu einer minimalen Anzahl an benötigten Umschlagmittelressourcen. Darüber hinaus kann es aber auch zweckmäßig sein, die Fahrzeuge möglichst früh an die Tore anzudocken. Jede Tour verfügt über einen individuellen Fahrplan, der Auskunft über den Ankunftszeitpunkt sowie den Abfahrtszeitpunkt der jeweiligen Tour von der Anlage gibt. Nur innerhalb dieses Zeitfensters darf der Disponent die Tour einem der Tore zuweisen. Geschieht die Zuweisung nicht sofort nach Ankunft in der Anlage, so muss das Fahrzeug auf einer Parkfläche warten. Eine Minimierung der Wartezeiten ist wünschenswert, damit das Gelände der Anlage möglichst nicht durch zuviele Fahrzeuge gleichzeitig belastet wird. Es kann vor allem aber auch im Hinblick auf das Reservieren der Tore für zeitkritische Touren sinnvoll sein, Fahrzeuge möglichst früh abzufertigen. Am Lehrstuhl Verkehrssysteme und -logistik (VSL) der Universität Dortmund wurde die Entscheidungssituation im Rahmen eines Forschungsprojekts bei der Stiftung Industrieforschung in Anlehnung an ein zeitdiskretes Mehrgüterflussproblem mit unsplittable flow Bedingungen modelliert. Die beiden Zielsetzungen wurden dabei in einer eindimensionalen Zielfunktion integriert. Das resultierende Mixed Integer Linear Programm (MILP) wurde programmiert und für mittlere Szenarien durch Eingabe in den Optimization Solver CPlex mit dem dort implementierten exakten Branch-and-Cut Verfahren gelöst. Parallel wurde im Rahmen einer Kooperation zwischen dem Lehrstuhl VSL und dem Unternehmen hafa Docking Systems, einem der weltweit führenden Tor und Rampenhersteller, für die gleiche Planungsaufgabe ein heuristisches Scheduling Verfahren sowie ein Dispositionsleitstand namens LoadDock Navigation entwickelt. Der Dispositionsleitstand dient der optimalen Steuerung der Torbelegungen in logistischen Anlagen. In dem Leitstand wird planerische Intelligenz in Form des heuristischen Schedulingverfahrens, technische Neuerungen in der Rampentechnik in Form von Sensoren und das Expertenwissen des Disponenten in einem Tool verbunden. Das mathematische Modell sowie der Prototyp mit der integrierten Heuristik werden im Rahmen dieses Artikels vorgestellt.

Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up

In reverse logistics networks, products (e.g., bottles or containers) have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP) is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

MQN-Mapplet: Visualization of Chemical Space with Interactive Maps of DrugBank, ChEMBL, PubChem, GDB-11, and GDB-13

The MQN-mapplet is a Java application giving access to the structure of small molecules in large databases via color-coded maps of their chemical space. These maps are projections from a 42-dimensional property space defined by 42 integer value descriptors called molecular quantum numbers (MQN), which count different categories of atoms, bonds, polar groups, and topological features and categorize molecules by size, rigidity, and polarity. Despite its simplicity, MQN-space is relevant to biological activities. The MQN-mapplet allows localization of any molecule on the color-coded images, visualization of the molecules, and identification of analogs as neighbors on the MQN-map or in the original 42-dimensional MQN-space. No query molecule is necessary to start the exploration, which may be particularly attractive for nonchemists. To our knowledge, this type of interactive exploration tool is unprecedented for very large databases such as PubChem and GDB-13 (almost one billion molecules). The application is freely available for download at www.gdb.unibe.ch.

Patient classification system: An integrated method for measuring nursing intensity and optimizing resource allocation

A patient classification system was developed integrating a patient acuity instrument with a computerized nursing distribution method based on a linear programming model. The system was designed for real-time measurement of patient acuity (workload) and allocation of nursing personnel to optimize the utilization of resources.^ The acuity instrument was a prototype tool with eight categories of patients defined by patient severity and nursing intensity parameters. From this tool, the demand for nursing care was defined in patient points with one point equal to one hour of RN time. Validity and reliability of the instrument was determined as follows: (1) Content validity by a panel of expert nurses; (2) predictive validity through a paired t-test analysis of preshift and postshift categorization of patients; (3) initial reliability by a one month pilot of the instrument in a practice setting; and (4) interrater reliability by the Kappa statistic.^ The nursing distribution system was a linear programming model using a branch and bound technique for obtaining integer solutions. The objective function was to minimize the total number of nursing personnel used by optimally assigning the staff to meet the acuity needs of the units. A penalty weight was used as a coefficient of the objective function variables to define priorities for allocation of staff.^ The demand constraints were requirements to meet the total acuity points needed for each unit and to have a minimum number of RNs on each unit. Supply constraints were: (1) total availability of each type of staff and the value of that staff member (value was determined relative to that type of staff's ability to perform the job function of an RN (i.e., value for eight hours RN = 8 points, LVN = 6 points); (2) number of personnel available for floating between units.^ The capability of the model to assign staff quantitatively and qualitatively equal to the manual method was established by a thirty day comparison. Sensitivity testing demonstrated appropriate adjustment of the optimal solution to changes in penalty coefficients in the objective function and to acuity totals in the demand constraints.^ Further investigation of the model documented: correct adjustment of assignments in response to staff value changes; and cost minimization by an addition of a dollar coefficient to the objective function. ^

A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The short-term scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500–1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient. We present a hybrid method consisting of three phases. First, the set of operations is divided into several subsets. Second, these subsets are iteratively scheduled using a generic and flexible MILP formulation. Third, a novel critical path-based improvement procedure is applied to the resulting schedule. We develop several strategies for the integration of the MILP model into this heuristic framework. Using these strategies, high-quality feasible solutions to large-scale instances can be obtained within reasonable CPU times using standard optimisation software. We have applied the proposed hybrid method to a set of industrial problem instances and found that the method outperforms state-of-the-art methods.

Daytime Low Stratiform Cloud Detection on AVHRR Imagery

The near-real time retrieval of low stratiform cloud (LSC) coverage is of vital interest for such disciplines as meteorology, transport safety, economy and air quality. Within this scope, a novel methodology is proposed which provides the LSC occurrence probability estimates for a satellite scene. The algorithm is suited for the 1 × 1 km Advanced Very High Resolution Radiometer (AVHRR) data and was trained and validated against collocated SYNOP observations. Utilisation of these two combined data sources requires a formulation of constraints in order to discriminate cases where the LSC is overlaid by higher clouds. The LSC classification process is based on six features which are first converted to the integer form by step functions and combined by means of bitwise operations. Consequently, a set of values reflecting a unique combination of those features is derived which is further employed to extract the LSC occurrence probability estimates from the precomputed look-up vectors (LUV). Although the validation analyses confirmed good performance of the algorithm, some inevitable misclassification with other optically thick clouds were reported. Moreover, the comparison against Polar Platform System (PPS) cloud-type product revealed superior classification accuracy. From the temporal perspective, the acquired results reported a presence of diurnal and annual LSC probability cycles over Europe.

A novel clinical scoring system for outcome prediction in dogs with acute kidney injury managed by hemodialysis.

BACKGROUND No reliable tool to predict outcome of acute kidney injury (AKI) exists. HYPOTHESIS A statistically derived scoring system can accurately predict outcome in dogs with AKI managed with hemodialysis. ANIMALS One hundred and eighty-two client-owned dogs with AKI. METHODS Logistic regression analyses were performed initially on clinical variables available on the 1st day of hospitalization for relevance to outcome. Variables with P< or = .1 were considered for further analyses. Continuous variables outside the reference range were divided into quartiles to yield quartile-specific odds ratios (ORs) for survival. Models were developed by incorporating weighting factors assigned to each quartile based on the OR, using either the integer value of the OR (Model A) or the exact OR (Models B or C, when the etiology was known). A predictive score for each model was calculated for each dog by summing all weighting factors. In Model D, actual values for continuous variables were used in a logistic regression model. Receiver-operating curve analyses were performed to assess sensitivities, specificities, and optimal cutoff points for all models. RESULTS Higher scores were associated with decreased probability of survival (P < .001). Models A, B, C, and D correctly classified outcomes in 81, 83, 87, and 76% of cases, respectively, and optimal sensitivities/specificities were 77/85, 81/85, 83/90 and 92/61%, respectively. CONCLUSIONS AND CLINICAL RELEVANCE The models allowed outcome prediction that corresponded with actual outcome in our cohort. However, each model should be validated further in independent cohorts. The models may also be useful to assess AKI severity.

Scheduling in service systems: an application in the event-tourism industry

This paper deals with an event-bus tour booked by Bollywood film fans. During the tour, the participants visit selected locations of famous Bollywood films at various sites in Switzerland. Moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour; for organizational reasons, two or more buses cannot stay at the same location simultaneously. The planning problem is how to compute a feasible schedule for each bus such that the total waiting time (primary objective) and the total travel time (secondary objective) are minimized. We formulate this problem as a mixed-integer linear program, and we report on computational results obtained with the Gurobi solver.

The triplite–triploidite supergroup: structural modulation in wagnerite, discreditation of magniotriplite, and the new mineral hydroxylwagnerite

Electron-microprobe analysis, single-crystal X-ray diffraction with an area detector, and high-resolution transmission electron microscopy show that minerals related to wagnerite, triplite and triploidite, which are monoclinic Mg, Fe and Mn phosphates with the formula Me2+ 2PO4(F,OH), constitute a modulated series based on the average triplite structure. Modulation occurs along b and may be commensurate with (2b periodicity) or incommensurate but generally close to integer values (∼3b, ∼5b, ∼7b, ∼9b), i.e. close to polytypic behaviour. As a result, the Mg- and F-dominant minerals magniotriplite and wagnerite can no longer be considered polymorphs of Mg2PO4F, i.e., there is no basis for recognizing them as distinct species. Given that wagnerite has priority (1821 vs. 1951), the name magniotriplite should be discarded in favour of wagnerite. Hydroxylwagnerite, end-member Mg2PO4OH, occurs in pyrope megablasts along with talc, clinochlore, kyanite, rutile and secondary apatite in two samples from lenses of pyrope–kyanite–phengite–quartz-schist within metagranite in the coesite-bearing ultrahigh-pressure metamorphic unit of the Dora-Maira Massif, western Alps, Vallone di Gilba, Val Varaita, Piemonte, Italy. Electron microprobe analyses of holotype hydroxylwagnerite and of the crystal with the lowest F content gave in wt%: P2O5 44.14, 43.99; SiO2 0.28, 0.02; SO3 –, 0.01; TiO2 0.20, 0.16; Al2O3 0.06, 0.03; MgO 48.82, 49.12; FeO 0.33, 0.48; MnO 0.01, 0.02; CaO 0.12, 0.10; Na2O 0.01, –; F 5.58, 4.67; H2O (calc) 2.94, 3.36; –O = F 2.35, 1.97; Sum 100.14, 99.98, corresponding to (Mg1.954Fe0.007Ca0.003Ti0.004Al0.002Na0.001)Σ=1.971(P1.003Si0.008)Σ=1.011O4(OH0.526F0.474)Σ=1 and (Mg1.971Fe0.011Ca0.003Ti0.003Al0.001)Σ=1.989(P1.002Si0.001)Σ=1.003O4(OH0.603F0.397)Σ=1, respectively. Due to the paucity of material, H2O could not be measured, so OH was calculated from the deficit in F assuming stoichiometry, i.e., by assuming F + OH = 1 per formula unit. Holotype hydroxylwagnerite is optically biaxial (+), α 1.584(1), β 1.586(1), γ 1.587(1) (589 nm); 2V Z(meas.) = 43(2)°; orientation Y = b. Single-crystal X-ray diffraction gives monoclinic symmetry, space group P21/c, a = 9.646(3) Å, b = 12.7314(16) Å, c = 11.980(4) Å, β = 108.38(4) , V = 1396.2(8) Å3, Z = 16, i.e., hydroxylwagnerite is the OH-dominant analogue of wagnerite [β-Mg2PO4(OH)] and a high-pressure polymorph of althausite, holtedahlite, and α- and ε-Mg2PO4(OH). We suggest that the group of minerals related to wagnerite, triplite and triploidite constitutes a triplite–triploidite super-group that can be divided into F-dominant phosphates (triplite group), OH-dominant phosphates (triploidite group), O-dominant phosphates (staněkite group) and an OH-dominant arsenate (sarkinite). The distinction among the three groups and a potential fourth group is based only on chemical features, i.e., occupancy of anion or cation sites. The structures of these minerals are all based on the average triplite structure, with a modulation controlled by the ratio of Mg, Fe2+, Fe3+ and Mn2+ ionic radii to (O,OH,F) ionic radii.