Abstract: Resource allocation systems (aka distributed ledgers) can overcome scalability issues while still ensuring both that system resource amounts are not corrupted and that resource recipients can trust in resources delivered to them by requiring distributed nodes maintaining account histories—in return, for instance, for transaction fees—to probabilistically verify transaction history and maintain reserve resources in their own accounts for the repair of transactions impaired by invalid previous transactions. Even in a permissionless environment, such systems can maintain eventual consistency of transaction history without impairment of the accounts of non-maintaining users.

Abstract: A method and apparatus for providing information to a plurality of users based on the relevancy of the information to the users are disclosed. An incoming message is received. Similarity scores are generated indicating similarities of the incoming message to features of a plurality of messages. Relevancy scores are generated for the plurality of users, the relevancy scores indicating relevancies of the incoming message to the plurality of users based on the similarity scores and a plurality of user profiles including information descriptive of the plurality of users' preferences for the features of the plurality of users. Message information derived from the incoming message, the relevancy scores, and the plurality of user profiles is delivered to at least some of the plurality of users.

Abstract: A file protection scheme for fixed content in a distributed data archive uses computations that leverage permutation operators of a cyclic code. In an illustrative embodiment, an N+K coding technique is described for use to protect data that is being distributed in a redundant array of independent nodes (RAIN). The data itself may be of any type, and it may also include system metadata. According to the invention, the data to be distributed is encoded by a dispersal operation that uses a group of permutation ring operators. In a preferred embodiment, the dispersal operation is carried out using a matrix of the form [IN—C] where IN is an n×n identity sub-matrix and C is a k×n sub-matrix of code blocks. The identity sub-matrix is used to preserve the data blocks intact. The sub-matrix C preferably comprises a set of permutation ring operators that are used to generate the code blocks. The operators are preferably superpositions that are selected from a group ring of a permutation group with base ring Z2.

Abstract: A method and apparatus for providing information to a plurality of users based on the relevancy of the information to the users are disclosed. An incoming message is received. Similarity scores are generated indicating similarities of the incoming message to features of a plurality of messages. Relevancy scores are generated for the plurality of users, the relevancy scores indicating relevancies of the incoming message to the plurality of users based on the similarity scores and a plurality of user profiles including information descriptive of the plurality of users' preferences for the features of the plurality of users. Message information derived from the incoming message, the relevancy scores, and the plurality of user profiles is delivered to at least some of the plurality of users.

Abstract: A file protection scheme for fixed content in a distributed data archive uses computations that leverage permutation operators of a cyclic code. In an illustrative embodiment, an N+K coding technique is described for use to protect data that is being distributed in a redundant array of independent nodes (RAIN). The data itself may be of any type, and it may also include system metadata. According to the invention, the data to be distributed is encoded by a dispersal operation that uses a group of permutation ring operators. In a preferred embodiment, the dispersal operation is carried out using a matrix of the form [IN—C] where IN is an n×n identity sub-matrix and C is a k×n sub-matrix of code blocks. The identity sub-matrix is used to preserve the data blocks intact. The sub-matrix C preferably comprises a set of permutation ring operators that are used to generate the code blocks. The operators are preferably superpositions that are selected from a group ring of a permutation group with base ring Z2.

Abstract: A method and apparatus for providing information to a plurality of users based on the relevancy of the information to the users are disclosed. An incoming message is received. Similarity scores are generated indicating similarities of the incoming message to features of a plurality of messages. Relevancy scores are generated for the plurality of users, the relevancy scores indicating relevancies of the incoming message to the plurality of users based on the similarity scores and a plurality of user profiles including information descriptive of the plurality of users' preferences for the features of the plurality of users. Message information derived from the incoming message, the relevancy scores, and the plurality of user profiles is delivered to at least some of the plurality of users.

Abstract: A method and apparatus for providing information to a plurality of users based on the relevancy of the information to the users are disclosed. An incoming message is received. Similarity scores are generated indicating similarities of the incoming message to features of a plurality of messages. Relevancy scores are generated for the plurality of users, the relevancy scores indicating relevancies of the incoming message to the plurality of users based on the similarity scores and a plurality of user profiles including information descriptive of the plurality of users' preferences for the features of the plurality of users. Message information derived from the incoming message, the relevancy scores, and the plurality of user profiles is delivered to at least some of the plurality of users.

Abstract: A method and system for evaluating the relevancy of an incoming message to a plurality of users are disclosed. Similarity scores indicating similarities of the incoming message to features of a plurality of messages are generated. Relevancy scores are generated for the plurality of users indicating relevancies of the incoming message to the plurality of users based on the similarity scores and a plurality of user profiles including information descriptive of the plurality of users' preferences for the features.