The Alternating Stock Size Problem and the Gasoline Puzzle

Given a set S of integers whose sum is zero, consider the problem of finding a permutation of these integers such that: (i) all prefix sums of the ordering are nonnegative, and (ii) the maximum value of a prefix sum is minimized. Kellerer et al. referred to this problem as the "Stock Size Problem" and showed that it can be approximated to within 3/2. They also showed that an approximation ratio of 2 can be achieved via several simple algorithms. We consider a related problem, which we call the "Alternating Stock Size Problem", where the number of positive and negative integers in the input set S are equal. The problem is the same as above, but we are additionally required to alternate the positive and negative numbers in the output ordering. This problem also has several simple 2-approximations. We show that it can be approximated to within 1.79. Then we show that this problem is closely related to an optimization version of the gasoline puzzle due to Lov\'asz, in which we want to minimize the size of the gas tank necessary to go around the track. We present a 2-approximation for this problem, using a natural linear programming relaxation whose feasible solutions are doubly stochastic matrices. Our novel rounding algorithm is based on a transformation that yields another doubly stochastic matrix with special properties, from which we can extract a suitable permutation

The Alternating Stock Size Problem and the Gasoline Puzzle

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Supported Metal Nanohydrides for Hydrogen Storage

Producción CientíficaAdsorption of hydrogen on graphdiyne (GDY) and boron-graphdiyne (BGDY) doped with palladium clusters has been investigated by performing density functional calculations. Pd6 fits well on the large holes of those porous layers, preserving its octahedral structure in GDY and changing it to a capped trigonal bipyramid structure in BGDY. Pd6GDY adsorbs up to five H2 molecules with sizable adsorption energies, two dissociated and three nondissociated. The dissociation barrier of H2 on the Pd6GDY cluster is 0.58 eV. Pd6BGDY can adsorb up to six molecules, three dissociated and three nondissociated, and the dissociation barrier of H2 on Pd6BGDY is 0.23 eV. In both cases, the dissociation barriers are substantially smaller than the corresponding dissociation barriers on undoped GDY and BGDY. The Pd clusters saturated with hydrogen can be viewed as nanohydrides. Spilling of the adsorbed hydrogen atoms toward the GDY and BGDY substrates is hindered by large activation barriers. We then propose using BGDY and GDY layers as support platforms for metal nanohydrides. The amount of stored hydrogen using Pd as the dopant is below the target of 6% of hydrogen in weight, but replacing Pd by a lighter metal with similar or higher affinity for hydrogen would substantially enhance the storage.Ministerio de Ciencia e Innovación (MCIN/AEI/ 10.13039/501100011033)(Grant PID2019-104924RB-I00

Global economic burden of unmet surgical need for appendicitis

Background: There is a substantial gap in provision of adequate surgical care in many low-and middle-income countries. This study aimed to identify the economic burden of unmet surgical need for the common condition of appendicitis. Methods: Data on the incidence of appendicitis from 170 countries and two different approaches were used to estimate numbers of patients who do not receive surgery: as a fixed proportion of the total unmet surgical need per country (approach 1); and based on country income status (approach 2). Indirect costs with current levels of access and local quality, and those if quality were at the standards of high-income countries, were estimated. A human capital approach was applied, focusing on the economic burden resulting from premature death and absenteeism. Results: Excess mortality was 4185 per 100 000 cases of appendicitis using approach 1 and 3448 per 100 000 using approach 2. The economic burden of continuing current levels of access and local quality was US $92 492 million using approach 1 and$73 141 million using approach 2. The economic burden of not providing surgical care to the standards of high-income countries was $95 004 million using approach 1 and$75 666 million using approach 2. The largest share of these costs resulted from premature death (97.7 per cent) and lack of access (97.0 per cent) in contrast to lack of quality. Conclusion: For a comparatively non-complex emergency condition such as appendicitis, increasing access to care should be prioritized. Although improving quality of care should not be neglected, increasing provision of care at current standards could reduce societal costs substantially

Pooled analysis of WHO Surgical Safety Checklist use and mortality after emergency laparotomy

Background The World Health Organization (WHO) Surgical Safety Checklist has fostered safe practice for 10 years, yet its place in emergency surgery has not been assessed on a global scale. The aim of this study was to evaluate reported checklist use in emergency settings and examine the relationship with perioperative mortality in patients who had emergency laparotomy. Methods In two multinational cohort studies, adults undergoing emergency laparotomy were compared with those having elective gastrointestinal surgery. Relationships between reported checklist use and mortality were determined using multivariable logistic regression and bootstrapped simulation. Results Of 12 296 patients included from 76 countries, 4843 underwent emergency laparotomy. After adjusting for patient and disease factors, checklist use before emergency laparotomy was more common in countries with a high Human Development Index (HDI) (2455 of 2741, 89.6 per cent) compared with that in countries with a middle (753 of 1242, 60.6 per cent; odds ratio (OR) 0.17, 95 per cent c.i. 0.14 to 0.21, P <0001) or low (363 of 860, 422 per cent; OR 008, 007 to 010, P <0.001) HDI. Checklist use was less common in elective surgery than for emergency laparotomy in high-HDI countries (risk difference -94 (95 per cent c.i. -11.9 to -6.9) per cent; P <0001), but the relationship was reversed in low-HDI countries (+121 (+7.0 to +173) per cent; P <0001). In multivariable models, checklist use was associated with a lower 30-day perioperative mortality (OR 0.60, 0.50 to 073; P <0.001). The greatest absolute benefit was seen for emergency surgery in low- and middle-HDI countries. Conclusion Checklist use in emergency laparotomy was associated with a significantly lower perioperative mortality rate. Checklist use in low-HDI countries was half that in high-HDI countries.Peer reviewe

Global variation in anastomosis and end colostomy formation following left-sided colorectal resection

Background End colostomy rates following colorectal resection vary across institutions in high-income settings, being influenced by patient, disease, surgeon and system factors. This study aimed to assess global variation in end colostomy rates after left-sided colorectal resection. Methods This study comprised an analysis of GlobalSurg-1 and -2 international, prospective, observational cohort studies (2014, 2016), including consecutive adult patients undergoing elective or emergency left-sided colorectal resection within discrete 2-week windows. Countries were grouped into high-, middle- and low-income tertiles according to the United Nations Human Development Index (HDI). Factors associated with colostomy formation versus primary anastomosis were explored using a multilevel, multivariable logistic regression model. Results In total, 1635 patients from 242 hospitals in 57 countries undergoing left-sided colorectal resection were included: 113 (6·9 per cent) from low-HDI, 254 (15·5 per cent) from middle-HDI and 1268 (77·6 per cent) from high-HDI countries. There was a higher proportion of patients with perforated disease (57·5, 40·9 and 35·4 per cent; P < 0·001) and subsequent use of end colostomy (52·2, 24·8 and 18·9 per cent; P < 0·001) in low- compared with middle- and high-HDI settings. The association with colostomy use in low-HDI settings persisted (odds ratio (OR) 3·20, 95 per cent c.i. 1·35 to 7·57; P = 0·008) after risk adjustment for malignant disease (OR 2·34, 1·65 to 3·32; P < 0·001), emergency surgery (OR 4·08, 2·73 to 6·10; P < 0·001), time to operation at least 48 h (OR 1·99, 1·28 to 3·09; P = 0·002) and disease perforation (OR 4·00, 2·81 to 5·69; P < 0·001). Conclusion Global differences existed in the proportion of patients receiving end stomas after left-sided colorectal resection based on income, which went beyond case mix alone

Approximation algorithms for classical-quantum channel coding

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Extension complexity of the correlation polytope

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Comparison of multicenter MRI protocols for visualizing the spinal cord gray matter

PURPOSE: Spinal cord gray-matter imaging is valuable for a number of applications, but remains challenging. The purpose of this work was to compare various MRI protocols at 1.5 T, 3 T, and 7 T for visualizing the gray matter. METHODS: In vivo data of the cervical spinal cord were collected from nine different imaging centers. Data processing consisted of automatically segmenting the spinal cord and its gray matter and co-registering back-to-back scans. We computed the SNR using two methods (SNR_single using a single scan and SNR_diff using the difference between back-to-back scans) and the white/gray matter contrast-to-noise ratio per unit time. Synthetic phantom data were generated to evaluate the metrics performance. Experienced radiologists qualitatively scored the images. We ran the same processing on an open-access multicenter data set of the spinal cord MRI (N = 267 participants). RESULTS: Qualitative assessments indicated comparable image quality for 3T and 7T scans. Spatial resolution was higher at higher field strength, and image quality at 1.5 T was found to be moderate to low. The proposed quantitative metrics were found to be robust to underlying changes to the SNR and contrast; however, the SNR_single method lacked accuracy when there were excessive partial-volume effects. CONCLUSION: We propose quality assessment criteria and metrics for gray-matter visualization and apply them to different protocols. The proposed criteria and metrics, the analyzed protocols, and our open-source code can serve as a benchmark for future optimization of spinal cord gray-matter imaging protocols