相关论文: Alan M. Turing: The Applications of Probability to…

Uniquely among the sciences, quantum cryptography has driven both foundational research as well as practical real-life applications. We review the progress of quantum cryptography in the last decade, covering quantum key distribution and…

This paper discusses digital online mathematics examinations -- a discussion ranging from high school to university level examinations. In particular, we consider the nature of mathematical writing, what is distinctive about mathematical…

Topological data analysis involves the statistical characterization of the shape of data. Persistent homology is a primary tool of topological data analysis, which can be used to analyze topological features and perform statistical…

The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The…

Masking is a widely-used effective countermeasure against power side-channel attacks for implementing cryptographic algorithms. Surprisingly, few formal verification techniques have addressed a fundamental question, i.e., whether the masked…

This is a chapter on quantum cryptography for the book "A Multidisciplinary Introduction to Information Security" to be published by CRC Press in 2011/2012. The chapter aims to introduce the topic to undergraduate-level and…

In topological data analysis, persistent homology characterizes robust topological features in data and it has a summary representation, called a persistence diagram. Statistical research for persistence diagrams have been actively…

Password authentication is a common approach to the system security and it is also a very important procedure to gain access to user resources. In the conventional password authentication methods a server has to authenticate the legitimate…

In this article, we study a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures. We analyze several classes of extraction procedures: a…

A system of session types is introduced as induced by a Curry Howard correspondence applied to Bounded Linear Logic, and then extending the thus obtained type system with probabilistic choices and ground types. The obtained system satisfies…

We show how to store good approximations of probability distributions in small space.

This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…

The information theoretic approach to security entails harnessing the correlated randomness available in nature to establish security. It uses tools from information theory and coding and yields provable security, even against an adversary…

A fruitful way of obtaining meaningful, possibly concrete, algorithmically random numbers is to consider a potential behaviour of a Turing machine and its probability with respect to a measure (or semi-measure) on the input space of binary…

The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…

The aim of a probabilistic resource analysis is to derive a probability distribution of possible resource usage for a program from a probability distribution of its input. We present an automated multi- phase rewriting based method to…

Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…

We solve university level probability and statistics questions by program synthesis using OpenAI's Codex, a Transformer trained on text and fine-tuned on code. We transform course problems from MIT's 18.05 Introduction to Probability and…

Earlier techniques of text mining included algorithms like k-means, Naive Bayes, SVM which classify and cluster the text document for mining relevant information about the documents. The need for improving the mining techniques has us…

Automated Teller Machines (ATMs) represent the most used system for withdrawing cash. The European Central Bank reported more than 11 billion cash withdrawals and loading/unloading transactions on the European ATMs in 2019. Although ATMs…