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We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact). Our results improve and extend earlier and recent ones in the literature.

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to weigh the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider peoples incentives and interactions in the data-collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, <i>finite population learning</i>, to address whether with high probability, a large fraction of people in a given finite population network can make good inference. Serving as a foundation, this concept enables

New heterotic torsional geometries are constructed as orbifolds of T^ 2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed curves. We give explicit constructions when the base K3 is Kummer or algebraic. The orbifold geometries can preserve N= 1, 2 supersymmetry in four dimensions or be non-supersymmetric.

In 2017, Ward Beullenset al.submitted Lifted Unbalanced Oil andVinegar, which is a modification to the Unbalanced Oil and Vinegar Schemeby Patarin. Previously, Dinget al.proposed the Subfield Differential Attack which prompted a change of parameters by the authors of LUOV for the sec-ond round of the NIST post quantum standardization competition. In this paper we propose a modification to the Subfield Differential Attack called the Nested Subset Differential Attack which fully breaks half of the pa-rameter sets put forward. We also show by experimentation that this attack ispractically possible to do in under 210 minutes for the level I security param-eters and not just a theoretical attack. The Nested Subset Differential attack isa large improvement of the Subfield differential attack which can be used inreal world circumstances. Moreover, we will only use what is called the "lifted"structure of LUOV, and our attack can be thought as a development of solving"lifted" quadratic systems.

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!

No abstract uploaded!