New algorithm shows simpler unrecognizable 4-manifold.
problem How to simplify the construction of unrecognizable 4-manifolds.
method Removed Markov's trick and decreased deficiency in Adian-Rabin set.
result Showed #_9(S^2 x S^2) is unrecognizable.
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8 results for “unrecognizable”
Proof shows homeomorphism problem is unsolvable.
problem Unsolvable homeomorphism problem in topology.
method Detailed proof of Markov's theorem.
result Existence of unrecognizable manifolds in higher dimensions.
We describe theoretical backgrounds for a computer program that recognizes all closed orientable 3-manifolds up to complexity 8. The program can treat also not necessarily closed 3-manifolds of bigger complexities, but here some unrecognizable (by the program) 3-manifolds may occur.
A good cover in R^d is a collection of open contractible sets in R^d such that the intersection of any subcollection is either contractible or empty. Motivated by an analogy with convex sets, intersection patterns of good covers were studied intensively. Our main result is that intersection patterns of good covers are …
Let be -group terms in the variables . Let be their associated piecewise homogeneous linear functions. Let be the -group generated by in the free -generator -group We prove: (i) the problem …
Gödel's sentence is an adversarial example but unsolvable.
problem The existence and unsolvability of adversarial examples.
method Analysis of non-isomorphic natural explanations and computability theory.
result Gödel's sentence is an adversarial example that cannot be solved.
With the increasing adoption of AI, inherent security and privacy vulnerabilities formachine learning systems are being discovered. One such vulnerability makes itpossible for an adversary to obtain private information about the types of instancesused to train the targeted machine learning model. This so-called model i…
Adversarial robustness of amortized Bayesian inference is studied, showing it can be improved.
problem Adversarial robustness of amortized Bayesian inference.
method Simulation-based estimation, regularization scheme based on Fisher information.
result Adversarial robustness can be improved with a regularization scheme.