On statistical bounds of heuristic solutions to location problems

Solutions to combinatorial optimization problems, such as problems of locating facilities, frequently rely on heuristics to minimize the objective function. The optimum is sought iteratively and a criterion is needed to decide when the procedure (almost) attains it. Pre-setting the number of iterations dominates in OR applications, which implies that the quality of the solution cannot be ascertained. A small, almost dormant, branch of the literature suggests using statistical principles to estimate the minimum and its bounds as a tool to decide upon stopping and evaluating the quality of the solution. In this paper we examine the functioning of statistical bounds obtained from four different estimators by using simulated annealing on p-median test problems taken from Beasley’s OR-library. We find the Weibull estimator and the 2nd order Jackknife estimator preferable and the requirement of sample size to be about 10 being much less than the current recommendation. However, reliable statistical bounds are found to depend critically on a sample of heuristic solutions of high quality and we give a simple statistic useful for checking the quality. We end the paper with an illustration on using statistical bounds in a problem of locating some 70 distribution centers of the Swedish Post in one Swedish region. 

Stochastic discount factor bounds and rare events: a review

We aim to provide a review of the stochastic discount factor bounds usually applied to diagnose asset pricing models. In particular, we mainly discuss the bounds used to analyze the disaster model of Barro (2006). Our attention is focused in this disaster model since the stochastic discount factor bounds that are applied to study the performance of disaster models usually consider the approach of Barro (2006). We first present the entropy bounds that provide a diagnosis of the analyzed disaster model which are the methods of Almeida and Garcia (2012, 2016); Ghosh et al. (2016). Then, we discuss how their results according to the disaster model are related to each other and also present the findings of other methodologies that are similar to these bounds but provide different evidence about the performance of the framework developed by Barro (2006).

Gravitational and quantum bounds on the photon mass

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Localization of the optimal solution and a posteriori bounds for aggregation

After an aggregated problem has been solved, it is often desirable to estimate the accuracy loss due to the fact that a simpler problem than the original one has been solved. One way of measuring this loss in accuracy is the difference in objective function values. To get the bounds for this difference, Zipkin (Operations Research 1980;28:406) has assumed, that a simple (knapsack-type) localization of an original optimal solution is known. Since then various extensions of Zipkin's bound have been proposed, but under the same assumption. A method to compute the bounds for variable aggregation for convex problems, based on general localization of the original solution is proposed. For some classes of the original problem it is shown how to construct the localization. Examples are given to illustrate the main constructions and a small numerical study is presented.

Bounds on contact interactions from LEP1 data and high-Q2 HERA events

A contact four-fermion interaction between light quarks and electrons has been evoked as a possible explanation for the excess of events observed by HERA at high-Q2. We explore the 1-loop effects of such interaction in Γ(Z0 → e+e-) measured at LEP and impose strong bounds on the lower limit of the effective scale. Our results are able to discard some of the contact interactions as possible explanation for the HERA events. © 1997 Elsevier Science B.V.

Bounds on Higgs and gauge-boson interactions from LEP2 data

We derive bounds on Higgs and gauge-boson anomalous interactions using the LEP2 data on the production of three photons and photon pairs in association with hadrons. In the framework of SU(2)L ⊗ U(1)Y effective Lagrangians, we examine all dimension-six operators that lead to anomalous Higgs interactions involving γ and Z. The search for Higgs boson decaying to γγ pairs allow us to obtain constrains on these anomalous couplings that are comparable with the ones originating from the analysis of pp̄ collisions at the Tevatron. Our results also show that if the coefficients of all blind operators are assumed to have the same magnitude, the indirect constraints on the anomalous couplings obtained from this analysis, for Higgs masses MH ≲ 140 GeV, are more restrictive than the ones coming from the W+W- production. © 1998 Elsevier Science B.V. All rights reserved.

Novel 12S mtDNA findings in sloths (Pilosa, Folivora) and anteaters (Pilosa, Vermilingua) suggest a true case of long branch attraction

We sequenced 12S RNA mtDNA for the majority of the extant species of sloths and anteaters and compared our results with previous data obtained by our group using 16S RNA mtDNA in the same specimens and to GenBank sequences of the extinct giant sloth Mylodon. Our results suggest that pigmy-anteaters may be a case of the long-branch attraction phenomenon and also show the large genetic difference between the Amazonian and Atlantic forest three-toed sloths, contrasting with the small differences observed between the two non-Atlantic forest forms of sloths. These results have important implications for the taxonomy of sloths and anteaters and strongly suggest the placement of pigmy anteaters in their own family (Cyclopidae) and raising the taxonomic status of Bradypus torquatus to a genus.

Error Upper Bounds for a Computational Method for Nonlinear Boundary and Initial-Value Problems

This work develops a computational approach for boundary and initial-value problems by using operational matrices, in order to run an evolutive process in a Hilbert space. Besides, upper bounds for errors in the solutions and in their derivatives can be estimated providing accuracy measures.

Global and Regional Ventricular Repolarization Study by Body Surface Potential Mapping in Patients with Left Bundle-Branch Block and Heart Failure Undergoing Cardiac Resynchronization Therapy

Background: The controversial effects promoted by cardiac resynchronization therapy (CRT) on the ventricular repolarization (VR) have motivated VR evaluation by body surface potential mapping (BSPM) in CRT patients. Methods: Fifty-two CRT patients, mean age 58.8 +/- 12.3 years, 31 male, LVEF 27.5 +/- 9.2, NYHA III-IV heart failure with QRS181.5 +/- 14.2 ms, underwent 87-lead BSPM in sinus rhythm (BASELINE) and biventricular pacing (BIV). Measurements of mean and corrected QT intervals and dispersion, mean and corrected T peak end intervals and their dispersion, and JT intervals characterized global and regional (RV, Intermediate, and LV regions) ventricular repolarization response. Results: Global QTm (P < 0.001) and QTcm (P < 0.05) were decreased in BIV; QTm was similar across regions in both modes (P = ns); QTcm values were lower in RV/LV than in Intermediate region in BASELINE and BIV (P < 0.001); only RV/Septum showed a significant difference (P < 0.01) in the BIV mode. QTD values both of BASELINE (P < 0.01) and BIV (P < 0.001) were greater in the Intermediate than in the LV region. CRT effect significantly reduced global/regional QTm and QTcm values. QTD was globally decreased in RV/LV (Intermediate: P = ns). BIV mode significantly reduced global T peak end mean and corrected intervals and their dispersion. JT values were not significant. Conclusions: Ventricular repolarization parameters QTm, QTcm, and QTD global/regional values, as assessed by BSPM, were reduced in patients under CRT with severe HF and LBBB. Greater recovery impairment in the Intermediate region was detected by the smaller variation of its dispersion.

Differences in neointimal thickness between the adluminal and the abluminal sides of malapposed and side-branch struts in a polylactide bioresorbable scaffold: evidence in vivo about the abluminal healing process

The goal of this study was to describe the neointimal healing on the abluminal side (ABL) of malapposed (ISA) struts and nonapposed side-branch (NASB) struts in terms of coverage by optical coherence tomography (OCT) and in comparison with the adluminal side (ADL).

Using Micro-Gravity Techniques to Map Alluvium Thickness and Pleistocene Location of the West Branch of the Susquehanna River Near Muncy, Pennsylvania

Laurentide glaciation during the early Pleistocene (~970 ka) dammed the southeast-flowing West Branch of the Susquehanna River (WBSR), scouring bedrock and creating 100-km-long glacial Lake Lesley near the Great Bend at Muncy, Pennsylvania (Ramage et al., 1998). Local drill logs and well data indicate that subsequent paleo-outwash floods and modern fluvial processes have deposited as much as 30 meters of alluvium in this area, but little is known about the valley fill architecture and the bedrock-alluvium interface. By gaining a greater understanding of the bedrock-alluvium interface the project will not only supplement existing depth to bedrock information, but also provide information pertinent to the evolution of the Muncy Valley landscape. This project determined if variations in the thickness of the valley fill were detectable using micro-gravity techniques to map the bedrock-alluvium interface. The gravity method was deemed appropriate due to scale of the study area (~30 km2), ease of operation by a single person, and the available geophysical equipment. A LaCoste and Romberg Gravitron unit was used to collect gravitational field readings at 49 locations over 5 transects across the Muncy Creek and Susquehanna River valleys (approximately 30 km2), with at least two gravity base stations per transect. Precise latitude, longitude and ground surface elevation at each location were measured using an OPUS corrected Trimble RTK-GPS unit. Base stations were chosen based on ease of access due to the necessity of repeat measurements. Gravity measurement locations were selected and marked to provide easy access and repeat measurements. The gravimeter was returned to a base station within every two hours and a looping procedure was used to determine drift and maximize confidence in the gravity measurements. A two-minute calibration reading at each station was used to minimize any tares in the data. The Gravitron digitally recorded finite impulse response filtered gravity measurements every 20 seconds at each station. A measurement period of 15 minutes was used for each base station occupation and a minimum of 5 minutes at all other locations. Longer or multiple measurements were utilized at some sites if drift or other externalities (i.e. train or truck traffic) were effecting readings. Average, median, standard deviation and 95% confidence interval were calculated for each station. Tidal, drift, latitude, free-air, Bouguer and terrain corrections were then applied. The results show that the gravitational field decreases as alluvium thickness increases across the axes of the Susquehanna River and Muncy Creek valleys. However, the location of the gravity low does not correspond with the present-day location of the West Branch of the Susquehanna River (WBSR), suggesting that the WBSR may have been constrained along Bald Eagle Mountain by a glacial lobe originating from the Muncy Creek Valley to the northeast. Using a 3-D inversion model, the topography of the bedrock-alluvium interface was determined over the extent of the study area using a density contrast of -0.8 g/cm3. Our results are consistent with the bedrock geometry of the area, and provide a low-cost, non-invasive and efficient method for exploring the subsurface and for supplementing existing well data.