Related papers: On Double-Entry Bookkeeping: The Mathematical Trea…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of `doubled kets' (i.e. mixing), and by tracing out part of a `doubled' two-system ket (i.e. dilation). Both…
Large-scale sharing of dialogue data is key to advancing the science of teaching and learning, yet rigorous de-identification remains a major barrier. In mathematics tutoring transcripts, numeric expressions frequently resemble structured…
We consider a problem, which we call secure grouping, of dividing a number of parties into some subsets (groups) in the following manner: Each party has to know the other members of his/her group, while he/she may not know anything about…
Deep Ensemble (DE) is an effective alternative to Bayesian neural networks for uncertainty quantification in deep learning. The uncertainty of DE is usually conveyed by the functional inconsistency among the ensemble members, say, the…
This paper introduces a novel theoretical framework for auditing differential privacy (DP) in a black-box setting. Leveraging the concept of $f$-differential privacy, we explicitly define type I and type II errors and propose an auditing…
Metric learning involves learning a discriminative representation such that embeddings of similar classes are encouraged to be close, while embeddings of dissimilar classes are pushed far apart. State-of-the-art methods focus mostly on…
A double Poisson bracket, in the sense of M. Van den Bergh, is an operation on an associative algebra $A$ which induces a Poisson bracket on each representation space $\operatorname{Rep}(A,n)$ in an explicit way. In this note, we study the…
Science and mathematics help people better to understand world, eliminating different fallacies and misconceptions. One of such misconception is related to arithmetic, which is so important both for science and everyday life. People think…
In this paper we propose a formal framework for studying privacy in information systems. The proposal follows a two-axes schema where the first axis considers privacy as a taxonomy of rights and the second axis involves the ways an…
Authentication is a process by which an entity,which could be a person or intended computer,establishes its identity to another entity.In private and public computer networks including the Internet,authentication is commonly done through…
As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…
Separation logic is used to reason locally about stateful programs. State of the art program logics for higher-order store are usually built on top of untyped operational semantics, in part because traditional denotational methods have…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
Integration by parts (IBP) has acquired a bad reputation. While it allows us to compute a wide variety of integrals when other methods fall short, its implementation is often seen as plodding and confusing. Readers familiar with tabular IBP…
Differential privacy (DP) has become the de facto standard of privacy preservation due to its strong protection and sound mathematical foundation, which is widely adopted in different applications such as big data analysis, graph data…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
Entity Resolution, also called record linkage or deduplication, refers to the process of identifying and merging duplicate versions of the same entity into a unified representation. The standard practice is to use a Rule based or Machine…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…