There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

An overview of the self-organizing map algorithm, on which the papers in this issue are based, is presented in this article.

The Self-Organizing Map

Federated learning (FL) is a machine learning setting where many clients (e.g. mobile devices or whole organizations) collaboratively train a model under the orchestration of a central server (e.g. service provider), while keeping the training data decentralized. FL embodies the principles of focused data collection and minimization, and can mitigate many of the systemic privacy risks and costs resulting from traditional, centralized machine learning and data science approaches. Motivated by the explosive growth in FL research, this paper discusses recent advances and presents an extensive collection of open problems and challenges.

Advances and Open Problems in Federated Learning

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the “bible of computer algebra”, gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany oneor two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Modern computer algebra

Journal of the ACM

A unified approach to domination problems on interval graphs

Linear algorithm for optimal path cover problem on interval graphs

Thank you for reading progress in cryptology indocrypt 2004 5th international conference on cryptology in india chennai india december 20 22 2004 proceedings. As you may know, people have search hundreds times for their chosen books like this progress in cryptology indocrypt 2004 5th international conference on cryptology in india chennai india december 20 22 2004 proceedings, but end up in malicious downloads. Rather than reading a good book with a cup of coffee in the afternoon, instead they juggled with some harmful bugs inside their laptop.

Progress in Cryptology – INDOCRYPT 2007

We study the interplay of network connectivity and perfectly secure message transmission under the corrupting influence of generalized Byzantine adversaries. It is known that in the threshold adversary model, where the Byzantine adversary can corrupt upto any t among the n players (nodes), perfectly secure communication among any pair of players is possible if and only if the underlying synchronous network is (2t + 1)-connected. Strictly generalizing these results to the non-threshold setting, we show that perfectly secure communication among any pair of players is possible if and only if the union of no two sets in the adversary structure is a vertex cutset of the synchronous network. The computation and communication complexities of the transmission protocol are polynomial in the size of the network and the maximal basis of the adversary structure.

On perfectly secure communication over arbitrary networks

In the perfectly secure message transmission (PSMT) problem, two synchronized non-faulty players (or processors), the Sender S and the Receiver R are connected by n wires (each of which facilitates 2-way communication); S has an l-bit message that he wishes to send to R; after exchanging messages in phases R should correctly obtain S’s message, while an adversary listening on and actively controlling any set of t (or less) wires should have no information about S’s message.

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C. Pandu Rangan

Papers

A unified approach to domination problems on interval graphs

Linear algorithm for optimal path cover problem on interval graphs

Progress in Cryptology – INDOCRYPT 2007

On perfectly secure communication over arbitrary networks

Optimal Perfectly Secure Message Transmission