Topologies on Types: Connections

For different purposes, economists may use different topologies on types. We char- acterize the relationship among these various topologies. First, we show that for any general types, convergence in the uniform-weak topology implies convergence in both the strategic topology and the uniform strategic topology. Second, we explicitly con- struct a type which is not the limit of any …finite types under the uniform strategic topology, showing that the uniform strategic topology is strictly fi…ner than the strategic topology. With these results, we can linearly rank various topologies on the universal type space, which gives a clear picture of the relationship between the implication of types for beliefs and their implication for behaviors.the universal type space, the strategic topology; the uniform strategic topology; the uniform-weak topology; interim correlated rationalizable actions

Identification of Two Thermotolerance-Related Genes in Agaricus bisporus

To characterize thermotolerance-related genes in Agaricus bisporus strain 02, we employed differential display PCR (DD-PCR) to analyze total RNA samples extracted from the mycelia grown at different temperatures. Two partial DNA fragments (023-11A and 023-11B) were cloned thus far, the expression of which was correlated with the culturing temperature. The sequences of the two DNA fragments were determined and the results showed that the nucleotide sequence of 023-11A was unknown, and 023-11B was highly similar in nucleotide sequence (identities 24 %, positives 45 %) to a gene coding for the karyopherin docking complex of the nuclear pore complex of Saccharomyces cerevisiae. It is possible to use the two fragments for further characterization of full-length coding sequences, which can potentially be used for generating new thermotolerant mushroom strains by transgenic technique

Topologies on types: connections

For diþerent purposes, economists may use diþerent topologies on types. We characterize the relationship among these various topologies. First, we show that for any general types, convergence in the uniform-weak topology implies convergence in both the strategic topology and the uniform strategic topology. Second, we explicitly construct a type which is not the limit of any .nite types under the uniform strategic topology, showing that the uniform strategic topology is strictly .ner than the strategic topology. With these results, we can linearly rank various topologies on the universal type space, which gives a clear picture of the relationship between the implication of types for beliefs and their implication for behaviors

Uniform Topologies on Types

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet (1989)). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris (2006)). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games.Rationalizability, Incomplete information, Higher-order beliefs, Strategic topology, Electronic mail game

Uniform topologies on types

We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet 1989). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris 2006). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games.Rationalizability, incomplete information, higher-order beliefs, strategic topology, electronic mail game

Dual Adversarial Alignment for Realistic Support-Query Shift Few-shot Learning

Support-query shift few-shot learning aims to classify unseen examples (query set) to labeled data (support set) based on the learned embedding in a low-dimensional space under a distribution shift between the support set and the query set. However, in real-world scenarios the shifts are usually unknown and varied, making it difficult to estimate in advance. Therefore, in this paper, we propose a novel but more difficult challenge, RSQS, focusing on Realistic Support-Query Shift few-shot learning. The key feature of RSQS is that the individual samples in a meta-task are subjected to multiple distribution shifts in each meta-task. In addition, we propose a unified adversarial feature alignment method called DUal adversarial ALignment framework (DuaL) to relieve RSQS from two aspects, i.e., inter-domain bias and intra-domain variance. On the one hand, for the inter-domain bias, we corrupt the original data in advance and use the synthesized perturbed inputs to train the repairer network by minimizing distance in the feature level. On the other hand, for intra-domain variance, we proposed a generator network to synthesize hard, i.e., less similar, examples from the support set in a self-supervised manner and introduce regularized optimal transportation to derive a smooth optimal transportation plan. Lastly, a benchmark of RSQS is built with several state-of-the-art baselines among three datasets (CIFAR100, mini-ImageNet, and Tiered-Imagenet). Experiment results show that DuaL significantly outperforms the state-of-the-art methods in our benchmark.Comment: Best student paper in PAKDD 202