Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments

The assortment problem in revenue management is the problem of deciding which subset of products to offer to consumers in order to maximise revenue. A simple and natural strategy is to select the best assortment out of all those that are constructed by fixing a threshold revenue $\pi$ and then choosing all products with revenue at least $\pi$. This is known as the revenue-ordered assortments strategy. In this paper we study the approximation guarantees provided by revenue-ordered assortments when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the set is enlarged. This rationality assumption, known as regularity, is satisfied by almost all discrete choice models considered in the revenue management and choice theory literature, and in particular by random utility models. The bounds we obtain are tight and improve on recent results in that direction, such as for the Mixed Multinomial Logit model by Rusmevichientong et al. (2014). An appealing feature of our analysis is its simplicity, as it relies only on the regularity condition. We also draw a connection between assortment optimisation and two pricing problems called unit demand envy-free pricing and Stackelberg minimum spanning tree: These problems can be restated as assortment problems under discrete choice models satisfying the regularity condition, and moreover revenue-ordered assortments correspond then to the well-studied uniform pricing heuristic. When specialised to that setting, the general bounds we establish for revenue-ordered assortments match and unify the best known results on uniform pricing.Comment: Minor changes following referees' comment

High dietary fat consumption impairs axonal mitochondrial function in vivo

Peripheral neuropathy (PN) is the most common complication of prediabetes and diabetes. PN causes severe morbidity for Type 2 diabetes (T2D) and prediabetes patients, including limb pain followed by numbness resulting from peripheral nerve damage. PN in T2D and prediabetes is associated with dyslipidemia and elevated circulating lipids; however, the molecular mechanisms underlying PN development in prediabetes and T2D are unknown. Peripheral nerve sensory neurons rely on axonal mitochondria to provide energy for nerve impulse conduction under homeostatic conditions. Models of dyslipidemia in vitro demonstrate mitochondrial dysfunction in sensory neurons exposed to elevated levels of exogenous fatty acids. Herein, we evaluated the effect of dyslipidemia on mitochondrial function and dynamics in sensory axons of the saphenous nerve of a male high-fat diet (HFD)-fed murine model of prediabetes to identify mitochondrial alterations that correlate with PN pathogenesis in vivo. We found that the HFD decreased mitochondrial membrane potential (MMP) in axonal mitochondria and reduced the ability of sensory neurons to conduct at physiological frequencies. Unlike mitochondria in control axons, which dissipated their MMP in response to increased impulse frequency (from 1 to 50 Hz), HFD mitochondria dissipated less MMP in response to axonal energy demand, suggesting a lack of reserve capacity. The HFD also decreased sensory axonal Ca^{2+} levels and increased mitochondrial lengthening and expression of PGC1α, a master regulator of mitochondrial biogenesis. Together, these results suggest that mitochondrial dysfunction underlies an imbalance of axonal energy and Ca^{2+} levels and impairs impulse conduction within the saphenous nerve in prediabetic PN

Munchausen by internet: current research and future directions.

The Internet has revolutionized the health world, enabling self-diagnosis and online support to take place irrespective of time or location. Alongside the positive aspects for an individual's health from making use of the Internet, debate has intensified on how the increasing use of Web technology might have a negative impact on patients, caregivers, and practitioners. One such negative health-related behavior is Munchausen by Internet

Existence, uniqueness and structure of second order absolute minimisers

Let ⊆ Rn be a bounded open C1,1 set. In this paper we prove the existence of a unique second order absolute minimiser u∞ of the functional E∞(u, O) := F(·, u)L∞(O), O ⊆ measurable, with prescribed boundary conditions for u and Du on ∂ and under natural assumptions on F. We also show that u∞ is partially smooth and there exists a harmonic function f∞ ∈ L1() such that F(x, u∞(x)) = e∞ sgn f∞(x) for all x ∈ { f∞ = 0}, where e∞ is the infimum of the global energy

Cardiac magnetic resonance visualizes acute and chronic myocardial injuries in myocarditis

Our objective was to evaluate the ability of CMR to visualize myocardial injuries over the course of myocarditis. We studied 42 patients (39 males, 3 females; age 37 ± 14 years) with myocarditis during the acute phase and after 12 ± 9 months. CMR included function analyses, T2-weighted imaging (T2 ratio), T1-weighted imaging before and after i.v. gadolinium injection (global relative enhancement; gRE), and late gadolinium enhancement (LGE). In the acute phase, the T2 ratio was elevated in 57%, gRE in 31%, and LGE was present in 64% of the patients. In 32 patients (76%) were any two (or more) out of three sequences abnormal. At follow-up, there was an increase in ejection fraction (57.4 ± 11.9% vs. 61.4 ± 7.6; P < 0.05) while both T2 ratio (2.04 ± 0.32 vs. 1.70 ± 0.28; P < 0.001) and gRE (4.07 ± 1.63 vs. 3.11 ± 1.22; P < 0.05) significantly decreased. The LGE persisted in 10 patients. Dilated cardiomyopathy was present in 3 patients and 4 patients received a defibrillator or a pacemaker. A comprehensive CMR approach is a useful tool to visualize myocardial tissue injuries over the course of myocarditis. CMR may help to differentiate acute from healed myocarditis, and add information for the differential diagnoses

Does the biomarker search paradigm need re-booting?

The clinical problem of bladder cancer is its high recurrence and progression, and that the most sensitive and specific means of monitoring is cystoscopy, which is invasive and has poor patient compliance. Biomarkers for recurrence and progression could make a great contribution, but in spite of decades of research, no biomarkers are commercially available with the requisite sensitivity and specificity. In the post-genomic age, the means to search the entire genome for biomarkers has become available, but the conventional approaches to biomarker discovery are entirely inadequate to yield results with the new technology. Finding clinically useful biomarker panels with sensitivity and specificity equal to that of cystoscopy is a problem of systems biology

Multidisciplinary teams, and parents, negotiating common ground in shared-care of children with long-term conditions: A mixed methods study

Background: Limited negotiation around care decisions is believed to undermine collaborative working between parents of children with long-term conditions and professionals, but there is little evidence of how they actually negotiate their respective roles. Using chronic kidney disease as an exemplar this paper reports on a multi-method study of social interaction between multidisciplinary teams and parents as they shared clinical care. Methods. Phases 1 and 2: a telephone survey mapping multidisciplinary teams' parent-educative activities, and qualitative interviews with 112 professionals (Clinical-psychologists, Dietitians, Doctors, Nurses, Play-specialists, Pharmacists, Therapists and Social-workers) exploring their accounts of parent-teaching in the 12 British children's kidney units. Phase 3: six ethnographic case studies in two units involving observations of professional/parent interactions during shared-care, and individual interviews. We used an analytical framework based on concepts drawn from Communities of Practice and Activity Theory. Results: Professionals spoke of the challenge of explaining to each other how they are aware of parents' understanding of clinical knowledge, and described three patterns of parent-educative activity that were common across MDTs: Engaging parents in shared practice; Knowledge exchange and role negotiation, and Promoting common ground. Over time, professionals had developed a shared repertoire of tools to support their negotiations with parents that helped them accomplish common ground during the practice of shared-care. We observed mutual engagement between professionals and parents where a common understanding of the joint enterprise of clinical caring was negotiated. Conclusions: For professionals, making implicit knowledge explicit is important as it can provide them with a language through which to articulate more clearly to each other what is the basis of their intuition-based hunches about parents' support needs, and may help them to negotiate with parents and accelerate parents' learning about shared caring. Our methodology and results are potentially transferrable to shared management of other conditions. © 2013 Swallow et al.; licensee BioMed Central Ltd

Mapping gene associations in human mitochondria using clinical disease phenotypes

Nuclear genes encode most mitochondrial proteins, and their mutations cause diverse and debilitating clinical disorders. To date, 1,200 of these mitochondrial genes have been recorded, while no standardized catalog exists of the associated clinical phenotypes. Such a catalog would be useful to develop methods to analyze human phenotypic data, to determine genotype-phenotype relations among many genes and diseases, and to support the clinical diagnosis of mitochondrial disorders. Here we establish a clinical phenotype catalog of 174 mitochondrial disease genes and study associations of diseases and genes. Phenotypic features such as clinical signs and symptoms were manually annotated from full-text medical articles and classified based on the hierarchical MeSH ontology. This classification of phenotypic features of each gene allowed for the comparison of diseases between different genes. In turn, we were then able to measure the phenotypic associations of disease genes for which we calculated a quantitative value that is based on their shared phenotypic features. The results showed that genes sharing more similar phenotypes have a stronger tendency for functional interactions, proving the usefulness of phenotype similarity values in disease gene network analysis. We then constructed a functional network of mitochondrial genes and discovered a higher connectivity for non-disease than for disease genes, and a tendency of disease genes to interact with each other. Utilizing these differences, we propose 168 candidate genes that resemble the characteristic interaction patterns of mitochondrial disease genes. Through their network associations, the candidates are further prioritized for the study of specific disorders such as optic neuropathies and Parkinson disease. Most mitochondrial disease phenotypes involve several clinical categories including neurologic, metabolic, and gastrointestinal disorders, which might indicate the effects of gene defects within the mitochondrial system. The accompanying knowledgebase (http://www.mitophenome.org/) supports the study of clinical diseases and associated genes

Accuracy of cardiovascular magnetic resonance in myocarditis: comparison of MR and histological findings in an animal model

Background: Because Endomyocardial Biopsy has low sensitivity of about 20%, it can be performed near to myocardium that presented as Late Gadolinium Enhancement (LGE) in cardiovascular magnetic resonance (CMR). However the important issue of comparing topography of CMR and histological findings has not yet been investigated. Thus the current study was performed using an animal model of myocarditis. Results: In 10 male Lewis rats Experimental Autoimmune myocarditis was induced, 10 rats served as control. On day 21 animals were examined by CMR to compare topographic distribution of LGE to histological inflammation. Sensitivity, specificity, positive and negative predictive values for LGE in diagnosing myocarditis were determined for each segment of myocardium. Latter diagnostic values varied widely depending on topographic distribution of LGE and inflammation as well as on the used CMR sequence. Sensitivity of LGE was up to 76% (left lateral myocardium) and positive predictive values were up to 85% (left lateral myocardium), whereas sensitivity and positive predictive value dropped to 0 - 33% (left inferior myocardium). Conclusions: Topographic distribution of LGE and histological inflammation seem to influence sensitivity, specifity, positive and negative predictive values. Nevertheless, positive predictive value for LGE of up to 85% indicates that Endomyocardial Biopsy should be performed "MR-guided". LGE seems to have greater sensitivity than Endomyocardial Biopsy for the diagnosis of myocarditis