Cost Sharing under Uncertainty: An Algorithmic Approach to Cooperative Interval-Valued Games

Recently, Branzei, Dimitrov, and Tijs (2003) introduced cooperative interval-valued games. Among other insights, the notion of an interval core has been coined and proposed as a solution concept for interval-valued games. In this paper we will present a general mathematical programming algorithm which can be applied to find an element in the interval core. As an example, we discuss lot sizing with uncertain demand to provide an application for interval-valued games and to demonstrate how interval core elements can be computed. Also, we reveal that pitfalls exist if interval core elements are computed in a straightforward manner by considering the interval borders separately.

The bovine dilated cardiomyopathy locus maps to a 1.0-Mb interval on chromosome 18

Cardiomyopathies are myocardial diseases that lead to cardiac dysfunction, heart failure, arrhythmia, and sudden death. In human medicine, cardiomyopathies frequently warrant heart transplantation in children and adults. Bovine dilated cardiomyopathy (BDCMP) is a heart muscle disorder that has been observed during the last 30 years in cattle of Holstein-Friesian origin. In Switzerland BDCMP affects Swiss Fleckvieh and Red Holstein breeds. BDCMP is characterized by a cardiac enlargement with ventricular remodeling and chamber dilatation. The common symptoms in affected animals are subacute subcutaneous edema, congestion of the jugular veins, and tachycardia with gallop rhythm. A cardiomegaly with dilatation and hypertrophy of all heart chambers, myocardial degeneration, and fibrosis are typical postmortem findings. It was shown that all BDCMP cases reported worldwide traced back to a red factor-carrying Holstein-Friesian bull, ABC Reflection Sovereign. An autosomal recessive mode of inheritance was proposed for BDCMP. Recently, the disease locus was mapped to a 6.7-Mb interval MSBDCMP06-BMS2785 on bovine Chr 18 (BTA18). In the present study the BDCMP locus was fine mapped by using a combined strategy of homozygosity mapping and association study. A BAC contig of 2.9 Mb encompassing the crucial interval was constructed to establish the correct marker order on BTA18. We show that the disease locus is located in a gene-rich interval of 1.0 Mb and is flanked by the microsatellite markers DIK3006 and MSBDCMP51.

Integration of Year-round Forage Management Systems for Spring-calving and Fall-calving Beef Cows (A Progress Report)

Animal production, hay production and feeding, winter forage composition changes, and summer pasture yields and nutrient composition of a year-round grazing system for spring-calving and fall-calving cows were compared to those of a conventional, minimal land system. Cows in the year-round and minimal land systems grazed forage from smooth bromegrassorchardgrass-birdsfoot trefoil (SB-O-T) pastures at 1.67 and 3.33 acres, respectively, per cow in the summer. During the summer, SB-O-T pastures in the year-round grazing system also were grazed by stockers at 1.67 stockers per acre, and spring-calving and fall-calving cows grazed smooth bromegrass–red clover (SB-RC) and endophyte-free tall fescue–red clover (TF-RC) at 2.5 acres per cow for approximately 45 days in midsummer. In the year-round grazing system, spring-calving cows grazed corn crop residues at 2.5 acres per cow and stockpiled SB-RC pastures at 2.5 acres per cow; fallcalving cows grazed stockpiled TF-RC pastures at 2.5 acres per cow during winter. In the minimal land system, in winter, cows were maintained in a drylot on first-cutting hay harvested from 62.5–75% of the pasture acres during summer. Hay was fed to maintain a body condition score of 5 on a 9-point scale for springcalving cows in both systems and a body condition score of 3 for fall-calving cows in the year-round system. Over 3 years, mean body weights of fall-calving cows in the year-round system did not differ from the body weights of spring-calving cows in either system, but fall-calving cows had higher (P < .05) body condition scores compared to spring-calving cows in either system. There were no differences among all groups of cows in body condition score changes over the winter grazing season (P > .05). During the summer grazing season, fall-calving cows in the year- round system and springcalving cows in the minimal land system gained more body condition and more weight (P < .05) than springcalving cows in the year-round grazing system. Fall calves in the year-round system had higher birth weights, lower weaning weights, and lower average preweaning daily gains compared to either group of spring calves (P < .05). However, there were no significant differences for birth weights, weaning weights, or average pre-weaning daily gains between spring calves in either system over the 3-year experiment (P > .05). The amount of total growing animal production (calves and stockers) per acre for each system did not differ in any year (P > .05). Over the 3-year experiment, 1.9 ton more hay was fed per cow and 1 ton more hay was fed per cow–calf pair in the minimal land system compared to the year-round grazing system (P < .05).

Integrating the Use of Spring- and Fall-Calving Beef Cows in a Year-round Grazing System (A Progress Report)

Animal production, hay production and feeding, and the yields and composition of forage from summer and winter grass-legume pastures and winter corn crop residue fields from a year-round grazing system were compared with those of a conventional system. The year-round grazing system utilized 1.67 acres of smooth bromegrass-orchardgrass-birdsfoot trefoil pasture per cow in the summer, and 1.25 acres of stockpiled tall fescue-red clover pasture per cow, 1.25 acres of stockpiled smooth bromegrass-red clover pasture per cow, and 1.25 acres of corn crop residues per cow during winter for spring- and fall-calving cows and stockers. First-cutting hay was harvested from the tall fescue-red clover and smooth bromegrass-red clover pastures to meet supplemental needs of cows and calves during winter. In the conventional system (called the minimal land system), spring-calving cows grazed smooth bromegrass-orchardgrass-birdsfoot trefoil pastures at 3.33 acres/cow during summer with first cutting hay removed from one-half of these acres. This hay was fed to these cows in a drylot during winter. All summer grazing was done by rotational stocking for both systems, and winter grazing of the corn crop residues and stockpiled forages for pregnant spring-calving cows and lactating fall-calving cows in the year-round system was managed by strip-stocking. Hay was fed to springcalving cows in both systems to maintain a mean body condition score of 5 on a 9-point scale, but was fed to fall-calving cows to maintain a mean body condition score of greater than 3. Over winter, fall-calving cows lost more body weight and condition than spring calving cows, but there were no differences in body weight or condition score change between spring-calving cows in either system. Fall- and spring-calving cows in the yearround grazing system required 934 and 1,395 lb. hay dry matter/cow for maintenance during the winter whereas spring-calving cows in drylot required 4,776 lb. hay dry matter/cow. Rebreeding rates were not affected by management system. Average daily gains of spring-born calves did not differ between systems, but were greater than fall calves. Because of differences in land areas for the two systems, weight production of calves per acre of cows in the minimal land system was greater than those of the year-round grazing system, but when the additional weight gains of the stocker cattle were considered, production of total growing animals did not differ between the two systems.

Evaluation of Year-round Forage Management Systems for Spring- and Fall-Calving Beef Cows (A Progress Report)

A year-round grazing system for spring- and fall-calving cows was developed to compare animal production and performance, hay production and feeding, winter forage composition changes, and summer pasture yield and nutrient composition to that from a conventional, or minimal land system. Systems compared forage from smooth bromegrass-orchardgrass-birdsfoot trefoil pastures for both systems in the summer and corn crop residues and stockpiled grass-legume pastures for the year-round system to drylot hay feeding during winter for the minimal land system. The year-round grazing system utilized 1.67 acres of smooth bromegrassorchardgrass- birdsfoot trefoil (SB-O-T) pasture per cow in the summer, compared with 3.33 acres of (SB-O-T) pasture per cow in the control (minimal land) system. In addition to SB-O-T pastures, the year-round grazing system utilized 2.5 acres of tall fescue-red clover (TFRC) and 2.5 acres of smooth bromegrass-red clover (SBRC) per cow for grazing in both mid-summer and winter for fall- and spring-calving cows, respectively. First-cutting hay was harvested from the TF-RC and SB-RC pastures, and regrowth was grazed for approximately 45 days in the summer. These pastures were then fertilized with 40 lbs N/acre and stockpiled for winter grazing. Also utilized during the winter for spring-calving cows in the year-round grazing system were corn crop residue (CCR) pastures at an allowance of 2.5 acres per cow. In the minimal land system, hay was harvested from three-fourths of the area in SB-O-T pastures and stored for feeding in a drylot through the winter. Summer grazing was managed with rotational stocking for both systems, and winter grazing of stockpiled forages and corn crop residues by year-round system cows was managed by strip-stocking. Hay was fed to maintain a body condition score of 5 on a 9 point scale for spring-calving cows in both systems. Hay was supplemented as needed to maintain a body condition score of 3 for fall-calving cows nursing calves through the winter. Although initial condition scores for cows in both systems were different at the initiation of grazing for both winter and summer, there were no significant differences (P > .05) in overall condition score changes throughout both grazing seasons. In year 1, fall-calving cows in the year-round grazing system lost more (P < .05) body weight during winter than spring-calving cows in either system. In year 2, there were no differences seen in weight changes over winter for any group of cows. Average daily gains of fall calves in the yearround system were 1.9 lbs/day compared with weight gains of 2.5 lbs/day for spring calves from both systems. Yearly growing animal production from pastures for both years did not differ between systems when weight gains of stockers that grazed summer pastures in the year-round grazing system were added to weight gains of suckling calves. Carcass characteristics for all calves finished in the feedlot for both systems were similar. There were no significant differences in hay production between systems for year 1; however, amounts of hay needed to maintain cows were 923, 1373, 4732 lbs dry matter/cow for year-round fall-calving, year-round spring-calving, and minimal land spring-calving cows, respectively. In year 2, hay production per acre in the minimal land system was greater (P < .05) than for the year-round system, but the amounts of hay required per cow were 0, 0, and 4720 lbs dry matter/cow for yearround fall-calving, year-round spring-calving, and minimal land spring-calving cows, respectively.

Electrocardiographic PR interval and adverse outcomes in older adults: the Health, Aging, and Body Composition study

BACKGROUND The electrocardiographic PR interval increases with aging, differs by race, and is associated with atrial fibrillation (AF), pacemaker implantation, and all-cause mortality. We sought to determine the associations between PR interval and heart failure, AF, and mortality in a biracial cohort of older adults. METHODS AND RESULTS The Health, Aging, and Body Composition (Health ABC) Study is a prospective, biracial cohort. We used multivariable Cox proportional hazards models to examine PR interval (hazard ratios expressed per SD increase) and 10-year risks of heart failure, AF, and all-cause mortality. Multivariable models included demographic, anthropometric, and clinical variables in addition to established cardiovascular risk factors. We examined 2722 Health ABC participants (aged 74±3 years, 51.9% women, and 41% black). We did not identify significant effect modification by race for the outcomes studied. After multivariable adjustment, every SD increase (29 ms) in PR interval was associated with a 13% greater 10-year risk of heart failure (95% confidence interval, 1.02-1.25) and a 13% increased risk of incident AF (95% confidence interval, 1.04-1.23). PR interval >200 ms was associated with a 46% increased risk of incident heart failure (95% confidence interval, 1.11-1.93). PR interval was not associated with increased all-cause mortality. CONCLUSIONS We identified significant relationships of PR interval to heart failure and AF in older adults. Our findings extend prior investigations by examining PR interval and associations with adverse outcomes in a biracial cohort of older men and women.

Effects of beta-alanine supplementation and interval training on physiological determinants of severe exercise performance.

INTRODUCTION We aimed to manipulate physiological determinants of severe exercise performance. We hypothesized that (1) beta-alanine supplementation would increase intramuscular carnosine and buffering capacity and dampen acidosis during severe cycling, (2) that high-intensity interval training (HIT) would enhance aerobic energy contribution during severe cycling, and (3) that HIT preceded by beta-alanine supplementation would have greater benefits. METHODS Sixteen active men performed incremental cycling tests and 90-s severe (110 % peak power) cycling tests at three time points: before and after oral supplementation with either beta-alanine or placebo, and after an 11-days HIT block (9 sessions, 4 × 4 min), which followed supplementation. Carnosine was assessed via MR spectroscopy. Energy contribution during 90-s severe cycling was estimated from the O2 deficit. Biopsies from m. vastus lateralis were taken before and after the test. RESULTS Beta-alanine increased leg muscle carnosine (32 ± 13 %, d = 3.1). Buffering capacity and incremental cycling were unaffected, but during 90-s severe cycling, beta-alanine increased aerobic energy contribution (1.4 ± 1.3 %, d = 0.5), concurrent with reduced O2 deficit (-5.0 ± 5.0 %, d = 0.6) and muscle lactate accumulation (-23 ± 30 %, d = 0.9), while having no effect on pH. Beta-alanine also enhanced motivation and perceived state during the HIT block. There were no between-group differences in adaptations to the training block, namely increased buffering capacity (+7.9 ± 11.9 %, p = 0.04, d = 0.6, n = 14) and glycogen storage (+30 ± 47 %, p = 0.04, d = 0.5, n = 16). CONCLUSIONS Beta-alanine did not affect buffering considerably, but has beneficial effects on severe exercise metabolism as well as psychological parameters during intense training phases.

Recognition memory across the lifespan: the impact of word frequency and study-test interval on estimates of familiarity and recollection

The goal of this study was to investigate recognition memory performance across the lifespan and to determine how estimates of recollection and familiarity contribute to performance. In each of three experiments, participants from five groups from 14 up to 85 years of age (children, young adults, middle-aged adults, young-old adults, and old-old adults) were presented with high- and low-frequency words in a study phase and were tested immediately afterwards and/or after a one day retention interval. The results showed that word frequency and retention interval affected recognition memory performance as well as estimates of recollection and familiarity. Across the lifespan, the trajectory of recognition memory followed an inverse u-shape function that was neither affected by word frequency nor by retention interval. The trajectory of estimates of recollection also followed an inverse u-shape function, and was especially pronounced for low-frequency words. In contrast, estimates of familiarity did not differ across the lifespan. The results indicate that age differences in recognition memory are mainly due to differences in processes related to recollection while the contribution of familiarity-based processes seems to be age-invariant.

Multiple independent genetic factors at NOS1AP modulate the QT interval in a multi-ethnic population.

Extremes of electrocardiographic QT interval are associated with increased risk for sudden cardiac death (SCD); thus, identification and characterization of genetic variants that modulate QT interval may elucidate the underlying etiology of SCD. Previous studies have revealed an association between a common genetic variant in NOS1AP and QT interval in populations of European ancestry, but this finding has not been extended to other ethnic populations. We sought to characterize the effects of NOS1AP genetic variants on QT interval in the multi-ethnic population-based Dallas Heart Study (DHS, n = 3,072). The SNP most strongly associated with QT interval in previous samples of European ancestry, rs16847548, was the most strongly associated in White (P = 0.005) and Black (P = 3.6 x 10(-5)) participants, with the same direction of effect in Hispanics (P = 0.17), and further showed a significant SNP x sex-interaction (P = 0.03). A second SNP, rs16856785, uncorrelated with rs16847548, was also associated with QT interval in Blacks (P = 0.01), with qualitatively similar results in Whites and Hispanics. In a previously genotyped cohort of 14,107 White individuals drawn from the combined Atherosclerotic Risk in Communities (ARIC) and Cardiovascular Health Study (CHS) cohorts, we validated both the second locus at rs16856785 (P = 7.63 x 10(-8)), as well as the sex-interaction with rs16847548 (P = 8.68 x 10(-6)). These data extend the association of genetic variants in NOS1AP with QT interval to a Black population, with similar trends, though not statistically significant at P<0.05, in Hispanics. In addition, we identify a strong sex-interaction and the presence of a second independent site within NOS1AP associated with the QT interval. These results highlight the consistent and complex role of NOS1AP genetic variants in modulating QT interval.

Sudden Increase in Tidal Response Linked to Calving and Acceleration at a Large Greenland Outlet Glacier

Large calving events at Greenland's largest outlet glaciers are associated with glacial earthquakes and near instantaneous increases in glacier flow speed. At some glaciers and ice streams, flow is also modulated in a regular way by ocean tidal forcing at the terminus. At Helheim Glacier, analysis of geodetic data shows decimeter-level periodic position variations in response to tidal forcing. However, we also observe transient increases of more than 100% in the glacier's responsiveness to such tidal forcing following glacial-earthquake calving events. The timing and amplitude of the changes correlate strongly with the step-like increases in glacier speed and longitudinal strain rate associated with glacial earthquakes. The enhanced response to the ocean tides may be explained by a temporary disruption of the subglacial drainage system and a concomitant reduction of the friction at the ice-bedrock interface, and suggests a new means by which geodetic data may be used to infer glacier properties. Citation: de Juan, J., et al. (2010), Sudden increase in tidal response linked to calving and acceleration at a large Greenland outlet glacier, Geophys. Res. Lett., 37, L12501, doi: 10.1029/2010GL043289.

Theoretical Calving Rates from Glaciers Along Ice Walls Grounded in Water of Variable Depths

Calving has been studied for glaciers ranging from slow polar glaciers that calve on dry land, such as on Deception Island (63.0-degrees-S, 60.6-degrees-W) in Antarctica, through temperate Alaskan tide-water glaciers, to fast outlet glaciers that float in fiords and calve in deep water, such as Jakobshavns Isbrae (69.2-degrees-N, 49.9-degrees-W) in Greenland. Calving from grounded ice walls and floating ice shelves is the main ablation mechanism for the Antarctic and Greenland ice sheets, as it was along marine and lacustrine margins of former Pleistocene ice sheets, and is for tide-water and polar glaciers. Yet, the theory of ice calving is underdeveloped because of inherent dangers in obtaining field data to test and constrain calving models. An attempt is made to develop a calving theory for ice walls grounded in water of variable depth, and to relate slab calving from ice walls to tabular calving from ice shelves. A calving law is derived in which calving rates from ice walls are controled by bending creep behind the ice wall, and depend on wall height h, forward bending angle-theta, crevasse distance c behind the ice wall and depth d of water in front of the ice wall. Reasonable agreement with calving rates reported by Brown and others (1982) for Alaskan tide-water glaciers is obtained when c depends on wall height, wall height above water and water depth. More data are needed to determine which of these dependencies is correct. A calving ratio c/h is introduced to understand the transition from slab calving to tabular calving as water deepens and the calving glacier becomes afloat.

Step-Wise Changes in Glacier Flow Speed Coincide With Calving and Glacial Earthquakes at Helheim Glacier, Greenland

Geodetic observations show several large, sudden increases in flow speed at Helheim Glacier, one of Greenland's largest outlet glaciers, during summer, 2007. These step-like accelerations, detected along the length of the glacier, coincide with teleseismically detected glacial earthquakes and major iceberg calving events. No coseismic offset in the position of the glacier surface is observed; instead, modest tsunamis associated with the glacial earthquakes implicate glacier calving in the seismogenic process. Our results link changes in glacier velocity directly to calving-front behavior at Greenland's largest outlet glaciers, on timescales as short as minutes to hours, and clarify the mechanism by which glacial earthquakes occur. Citation: Nettles, M., et al. (2008), Step-wise changes in glacier flow speed coincide with calving and glacial earthquakes at Helheim Glacier, Greenland, Geophys. Res. Lett., 35, L24503, doi: 10.1029/2008GL036127.

Calving Giant Icebergs: Old Principles, New Applications

Earth-orbiting satellites can now monitor calving of large icebergs from ice shelves bordering the marine West Antarctic Ice Sheet, and recent calving events have stimulated interest in calving mechanisms. To advance this interest pioneering work in brittle and ductile fracture mechanics is reviewed, leading to a new application to calving of giant icebergs from Antarctic ice shelves. The aim is to view iceberg calving as more than terminal events for Antarctic ice when glaciologists lose interest. Instead calving launches Antarctic ice into the larger dynamic system of Earth's climate machine. This encourages a holistic approach to glaciology.

Bending Shear: The Rate-Controlling Mechanism for Calving Ice Walls

Bending shear was observed to produce nearly vertical shear bands in a calving ice wall standing on dry land on Deception Island (Iat. 63.0 oS., long. 60.6 W.), and slabs calved straight downward when shear rupture occurred along these shear bands (Hughes, 1989). A formula for the calving rate was developed from the Deception Island data, and we have attempted to justify generalizing this formula to include ice walls standing along beaches or in water. These are environments in which a wave-washed groove develops along the base of the ice wall or along a water line above the base. The rate of wave erosion provides an alternative mechanism for controlling the calving rate in these environments. We have determined that the rate at which bending creep produces nearly vertical shear bands, along which shear r upture occurs, controls the calving rate in all environments. Shear rupture occurs at a calving shear stress of about I bar. Our results justify using the calving formula to compute the calving rate of ice walls in computer models of ice-sheet dynamics. This is especially important in simulating retreat of Northern Hemisphere ice sheets during the last deglaciation, when marine and lacustrine environments were common along retreating ice margins. These margins would have been ice walls standing along beaches or in water, because floating ice shelves are not expected in the ablation zone of retreating ice sheets.

Glacier Calving: A Numerical Model of Forces in the Calving-Speed/Water-Depth Relation

Empirical data suggest that the race of calving of grounded glaciers terminating in water is directly proportional to the water depth. Important controls on calving may be the extent to which a calving face tends to become oversteepened by differential flow within the ice and the extent to which bending moments promote extrusion and bottom crevassing at the base of a calving face. Numerical modelling suggests that the tendency to become oversteepened increases roughly linearly with water depth. In addition, extending longitudinal deviatoric stresses at the base of a calving face increase with water depth. These processes provide a possible physical explanation for the observed calving-rate/water-depth relation.