Explore the vast range of titles available.

A well-known observation of Serre and Tate is that the Hecke algebra acts locally nilpotently on modular forms mod 2 on SL 2 ( Z ) . We give an algorithm for calculating the degree of Hecke nilpotency for cusp forms, and we obtain a formula for the total number of cusp forms mod 2 of any given degree of nilpotency. Using these results, we find that the degrees of Hecke nilpotency in spaces M k have no limiting distribution as k → ∞ . As an application, we study the parity of the partition function using Hecke nilpotency.

Lorcaserin is a selective serotonin 2C receptor (5-HT2C) agonist approved in the United States for use in chronic weight management as an adjunct to a reduced-calorie diet and increased physical activity. Its pharmacologic activity is limited to 5-HT subtype 2 receptors. The potency of lorcaserin for the 5-HT2C receptor is 14-fold greater than its potency for the 5-HT2A receptor and 61-fold greater than its potency for the 5-HT2B receptor. Although 5-HT receptors have been implicated in serotonin syndrome, the precise pathogenesis is unknown. Given a theoretic risk for this syndrome in patients administered lorcaserin either alone or in combination with certain serotonergic agents (eg, selective serotonin reuptake inhibitors [SSRIs] and serotonin–norepinephrine reuptake inhibitors [SNRIs]), patients taking prohibited serotonergic agents were excluded from the Phase III clinical trials. This retrospective analysis evaluated the tolerability of lorcaserin in patients who took protocol-allowed or proscribed serotonergic agents for varying durations of up to 1 year during the BLOOM, BLOSSOM, and BLOOM-DM studies. Patients randomly assigned to receive either lorcaserin 10 mg QD, lorcaserin 10 mg BID, or placebo and who took a spectrum of serotonergic agents were evaluated at week 52 of treatment (814 and 624 patients receiving lorcaserin and placebo, respectively, were found to have taken allowed or prohibited serotonergic agents during these trials). After the use of a proscribed serotonergic agent was discovered, these patients were discontinued from the trial and followed. None of the patients in the serotonergic agent subpopulation or in the overall safety population met the clinical criteria of serotonin syndrome. The proportions of patients experiencing any adverse event (AE) were balanced in the lorcaserin and placebo groups in the prohibited serotonergic agent subpopulation. The prevalences of the most common AEs were similar between the serotonergic agent subpopulation and the overall safety population. The concurrent use of lorcaserin and prohibited or allowed serotonergic agents did not appear to have increased the spectrum or intensity of AEs potentially associated with serotonin excess in this limited dataset. However, the sample population was too small to rule out an effect on a rare event such as serotonin syndrome. ClinicalTrials.gov identifiers: NCT00395135, NCT00603902, and NCT00603291.

How does plasticity evolve over relatively short timescales? Through a series of common garden and reciprocal transplant experiments, Walter et al. found distinct patterns of variation in the phenotype and gene expression for two closely related Sicilian daisy species of the genus Senecio across an elevational gradient. This suggests that adaptive divergence may produce interspecific differences in both the magnitude and direction of plasticity. The nonadaptive nature of the plasticity found in Senecio aethnensis has important implications for conservation efforts and evolutionary modeling.

Evaluation drives and tracks progress in every field. Metrics of evaluation are designed to assess important criteria in an area, and aid us in understanding the quantitative differences between one breakthrough and another. In machine learning, evaluation metrics have historically acted as north stars towards which researchers have optimized and organized their methods and findings. While evaluation metrics have been straightforward to construct and implement in some subfields of machine learning, they have been notoriously difficult to design in generative models. Several reasons emerge to explain this: (1) there are no gold standard outputs to compare against, unlike held-out test sets, (2) because of their diverse training methods and formulations, inherent model properties are difficult to measure consistently, and sampled outputs are often used for evaluation instead, (3) dependence on external (pretrained) models that add another layer of bias and uncertainty, and (4) inconsistent results without a large number of samples. As a result, generative models have suffered from noisy assessments that occupy a changing evaluation landscape, in contrast to the relative stability of their discriminative counterparts. In this manuscript, we examine several important criteria for generative models and introduce evaluation metrics to address each one while discussing the aforementioned issues in generative model evaluation. In particular, we examine the challenge of measuring the perceptual realism of generated outputs and introduce a human-in-the-loop evaluation system that leverages psychophysics theory to ground the method in human perception literature and crowdsourcing techniques to construct an efficient, reliable, and consistent method for comparing different models. In addition to this, we analyze disentanglement, an increasingly important property for assessing learned representations, by measuring an intrinsic property of a generative model's data manifold using persistent homology. The final work in this manuscript takes a step towards assessing a generative model and its different modes with a key application in mind, specifically the stylistic fidelity across different generated modes in a multimodal setting.

Data augmentation has led to substantial improvements in the performance and generalization of deep models, and remains a highly adaptable method to evolving model architectures and varying amounts of data—in particular, extremely scarce amounts of available training data. In this paper, we present a novel method of applying Möbius transformations to augment input images during training. Möbius transformations are bijective conformal maps that generalize image translation to operate over complex inversion in pixel space. As a result, Möbius transformations can operate on the sample level and preserve data labels. We show that the inclusion of Möbius transformations during training enables improved generalization over prior sample-level data augmentation techniques such as cutout and standard crop-and-flip transformations, most notably in low data regimes.

With success on controlled tasks, deep generative models are being increasingly applied to humanitarian applications (Nie et al 2017 Int. Conf. on Medical Image Computing and Computer-Assisted Intervention (Berlin: Springer) pp 417–25, Yanardag et al 2017 Deep Empathy ). In this paper, we focus on the evaluation of a conditional generative model that illustrates the consequences of climate change-induced flooding to encourage public interest and awareness on the issue. Because metrics for comparing the realism of different modes in a conditional generative model do not exist, we propose several automated and human-based methods for evaluation. To do this, we adapt several existing metrics and assess the automated metrics against gold standard human evaluation. We find that using Fréchet Inception Distance with embeddings from an intermediary Inception-v3 layer that precedes the auxiliary classifier produces results most correlated with human realism. While insufficient alone to establish a human-correlated automatic evaluation metric, we believe this work begins to bridge the gap between human and automated generative evaluation procedures, and to generate more realistic images of the future consequences of climate change.

With success on controlled tasks, deep generative models are being increasingly applied to humanitarian applications (Nie et al 2017 Int. Conf. on Medical Image Computing and Computer-Assisted Intervention (Berlin: Springer) pp 417–25, Yanardag et al 2017 Deep Empathy). In this paper, we focus on the evaluation of a conditional generative model that illustrates the consequences of climate change-induced flooding to encourage public interest and awareness on the issue. Because metrics for comparing the realism of different modes in a conditional generative model do not exist, we propose several automated and human-based methods for evaluation. To do this, we adapt several existing metrics and assess the automated metrics against gold standard human evaluation. We find that using Fréchet Inception Distance with embeddings from an intermediary Inception-v3 layer that precedes the auxiliary classifier produces results most correlated with human realism. While insufficient alone to establish a human-correlated automatic evaluation metric, we believe this work begins to bridge the gap between human and automated generative evaluation procedures, and to generate more realistic images of the future consequences of climate change.

With success on controlled tasks, deep generative models are being increasingly applied to humanitarian applications (Nie et al 2017 Int. Conf. on Medical Image Computing and Computer-Assisted Intervention (Berlin: Springer) pp 417-25, Yanardag et al 2017 Deep Empathy). In this paper, we focus on the evaluation of a conditional generative model that illustrates the consequences of climate change-induced flooding to encourage public interest and awareness on the issue. Because metrics for comparing the realism of different modes in a conditional generative model do not exist, we propose several automated and human-based methods for evaluation. To do this, we adapt several existing metrics and assess the automated metrics against gold standard human evaluation. We find that using Fréchet Inception Distance with embeddings from an intermediary Inception-v3 layer that precedes the auxiliary classifier produces results most correlated with human realism. While insufficient alone to establish a human-correlated automatic evaluation metric, we believe this work begins to bridge the gap between human and automated generative evaluation procedures, and to generate more realistic images of the future consequences of climate change.