A Mathematical Model for the Origin of Name Brands and Generics

Firms in the U.S. spend over 200 billion dollars each year advertising their products to consumers, around one percent of the country's gross domestic product. It is of great interest to understand how that aggregate expenditure affects prices, market efficiency, and overall welfare. Here, we present a mathematical model for the dynamics of competition through advertising and find a surprising prediction: when advertising is relatively cheap compared to the maximum benefit advertising offers, rational firms split into two groups, one with significantly less advertising (a "generic" group) and one with significantly more advertising (a "name brand" group). Our model predicts that this segmentation will also be reflected in price distributions; we use large consumer data sets to test this prediction and find good qualitative agreement.Comment: 24 pages, 11 figure

Holography and Defect Conformal Field Theories

We develop both the gravity and field theory sides of the Karch-Randall conjecture that the near-horizon description of a certain D5-D3 brane configuration in string theory, realized as AdS_5 x S^5 bisected by an AdS_4 x S^2 "brane", is dual to N=4 Super Yang-Mills theory in R^4 coupled to an R^3 defect. We propose a complete Lagrangian for the field theory dual, a novel "defect superconformal field theory" wherein a subset of the fields of N=4 SYM interacts with a d=3 SU(N) fundamental hypermultiplet on the defect preserving conformal invariance and 8 supercharges. The Kaluza-Klein reduction of wrapped D5 modes on AdS_4 x S^2 leads to towers of short representations of OSp(4|4), and we construct the map to a set of dual gauge-invariant defect operators O_3 possessing integer conformal dimensions. Gravity calculations of and are given. Spacetime and N-dependence matches expectations from dCFT, while the behavior as functions of lambda = g^2 N at strong and weak coupling is generically different. We comment on a class of correlators for which a non-renormalization theorem may still exist. Partial evidence for the conformality of the quantum theory is given, including a complete argument for the special case of a U(1) gauge group. Some weak coupling arguments which illuminate the duality are presented.Comment: 47 pages, LaTeX, 2 figures, feynmf. v2: fixed minor errors, added references. v3: fixed more typo

Master crossover behavior of parachor correlations for one-component fluids

The master asymptotic behavior of the usual parachor correlations, expressing surface tension $\sigma$ as a power law of the density difference $\rho_{L}-\rho_{V}$ between coexisting liquid and vapor, is analyzed for a series of pure compounds close to their liquid-vapor critical point, using only four critical parameters $(\beta_{c})^{-1}$, $\alpha_{c}$, $Z_{c}$ and $Y_{c}$, for each fluid. ... The main consequences of these theoretical estimations are discussed in the light of engineering applications and process simulations where parachor correlations constitute one of the most practical method for estimating surface tension from density and capillary rise measurements

Systematic Overestimation of Machine Learning Performance in Neuroimaging Studies of Depression

We currently observe a disconcerting phenomenon in machine learning studies in psychiatry: While we would expect larger samples to yield better results due to the availability of more data, larger machine learning studies consistently show much weaker performance than the numerous small-scale studies. Here, we systematically investigated this effect focusing on one of the most heavily studied questions in the field, namely the classification of patients suffering from Major Depressive Disorder (MDD) and healthy controls. Drawing upon a balanced sample of $N = 1,868$ MDD patients and healthy controls from our recent international Predictive Analytics Competition (PAC), we first trained and tested a classification model on the full dataset which yielded an accuracy of 61%. Next, we mimicked the process by which researchers would draw samples of various sizes ($N=4$ to $N=150$) from the population and showed a strong risk of overestimation. Specifically, for small sample sizes ($N=20$), we observe accuracies of up to 95%. For medium sample sizes ($N=100$) accuracies up to 75% were found. Importantly, further investigation showed that sufficiently large test sets effectively protect against performance overestimation whereas larger datasets per se do not. While these results question the validity of a substantial part of the current literature, we outline the relatively low-cost remedy of larger test sets

Adrenocortical tumours in children and adolescents: The EXPeRT/PARTNER diagnostic and therapeutic recommendations

Adrenocortical tumours (ACTs) are rare during childhood. A complete surgical resection provides the best chance of cure, but the role and efficacy of the adjuvant therapy are still controversial. Various histologic criteria of malignancy for ACTs adopted in children do not facilitate comparative studies and are not completely shared. Therefore, a sharp demarcation between benign and malignant lesions has not been recognised, making it difficult to identify who potentially needs perioperative therapy. This manuscript presents the internationally harmonised recommendations for the diagnosis and treatment of ACTs in children and adolescents, established by the European Cooperative Study Group for Paediatric Rare Tumours (EXPeRT) group within the EU-funded project PARTNER (Paediatric Rare Tumours Network - European Registry)

Dung‐visiting beetle diversity is mainly affected by land use, while community specialization is driven by climate

Dung beetles are important actors in the self‐regulation of ecosystems by driving nutrient cycling, bioturbation, and pest suppression. Urbanization and the sprawl of agricultural areas, however, destroy natural habitats and may threaten dung beetle diversity. In addition, climate change may cause shifts in geographical distribution and community composition. We used a space‐for‐time approach to test the effects of land use and climate on α‐diversity, local community specialization (H (2)′) on dung resources, and γ‐diversity of dung‐visiting beetles. For this, we used pitfall traps baited with four different dung types at 115 study sites, distributed over a spatial extent of 300 km × 300 km and 1000 m in elevation. Study sites were established in four local land‐use types: forests, grasslands, arable sites, and settlements, embedded in near‐natural, agricultural, or urban landscapes. Our results show that abundance and species density of dung‐visiting beetles were negatively affected by agricultural land use at both spatial scales, whereas γ‐diversity at the local scale was negatively affected by settlements and on a landscape scale equally by agricultural and urban land use. Increasing precipitation diminished dung‐visiting beetle abundance, and higher temperatures reduced community specialization on dung types and γ‐diversity. These results indicate that intensive land use and high temperatures may cause a loss in dung‐visiting beetle diversity and alter community networks. A decrease in dung‐visiting beetle diversity may disturb decomposition processes at both local and landscape scales and alter ecosystem functioning, which may lead to drastic ecological and economic damage