13,400 research outputs found
A Proof of the G\"ottsche-Yau-Zaslow Formula
Let S be a complex smooth projective surface and L be a line bundle on S.
G\"ottsche conjectured that for every integer r, the number of r-nodal curves
in |L| is a universal polynomial of four topological numbers when L is
sufficiently ample. We prove G\"ottsche's conjecture using the algebraic
cobordism group of line bundles on surfaces and degeneration of Hilbert schemes
of points. In addition, we prove the the G\"ottsche-Yau-Zaslow Formula which
expresses the generating function of the numbers of nodal curves in terms of
quasi-modular forms and two unknown series.Comment: 29 page
Adversarial Discriminative Domain Adaptation
Adversarial learning methods are a promising approach to training robust deep
networks, and can generate complex samples across diverse domains. They also
can improve recognition despite the presence of domain shift or dataset bias:
several adversarial approaches to unsupervised domain adaptation have recently
been introduced, which reduce the difference between the training and test
domain distributions and thus improve generalization performance. Prior
generative approaches show compelling visualizations, but are not optimal on
discriminative tasks and can be limited to smaller shifts. Prior discriminative
approaches could handle larger domain shifts, but imposed tied weights on the
model and did not exploit a GAN-based loss. We first outline a novel
generalized framework for adversarial adaptation, which subsumes recent
state-of-the-art approaches as special cases, and we use this generalized view
to better relate the prior approaches. We propose a previously unexplored
instance of our general framework which combines discriminative modeling,
untied weight sharing, and a GAN loss, which we call Adversarial Discriminative
Domain Adaptation (ADDA). We show that ADDA is more effective yet considerably
simpler than competing domain-adversarial methods, and demonstrate the promise
of our approach by exceeding state-of-the-art unsupervised adaptation results
on standard cross-domain digit classification tasks and a new more difficult
cross-modality object classification task
Hidden regret in insurance markets: adverse and advantageous selection
We examine insurance markets with two types of customers: those who regret suboptimal decisions and those who don.t. In this setting, we characterize the equilibria under hidden information about the type of customers and hidden action. We show that both pooling and separating equilibria can exist. Furthermore, there exist separating equilibria that predict a positive correlation between the amount of insurance coverage and risk type, as in the standard economic models of adverse selection, but there also exist separating equilibria that predict a negative correlation between the amount of insurance coverage and risk type, i.e. advantageous selection. Since optimal choice of regretful customers depends on foregone alternatives, any equilibrium includes a contract which is o¤ered but not purchased
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