Finding Skewed Subcubes Under a Distribution

Say that we are given samples from a distribution ? over an n-dimensional space. We expect or desire ? to behave like a product distribution (or a k-wise independent distribution over its marginals for small k). We propose the problem of enumerating/list-decoding all large subcubes where the distribution ? deviates markedly from what we expect; we refer to such subcubes as skewed subcubes. Skewed subcubes are certificates of dependencies between small subsets of variables in ?. We motivate this problem by showing that it arises naturally in the context of algorithmic fairness and anomaly detection. In this work we focus on the special but important case where the space is the Boolean hypercube, and the expected marginals are uniform. We show that the obvious definition of skewed subcubes can lead to intractable list sizes, and propose a better definition of a minimal skewed subcube, which are subcubes whose skew cannot be attributed to a larger subcube that contains it. Our main technical contribution is a list-size bound for this definition and an algorithm to efficiently find all such subcubes. Both the bound and the algorithm rely on Fourier-analytic techniques, especially the powerful hypercontractive inequality. On the lower bounds side, we show that finding skewed subcubes is as hard as the sparse noisy parity problem, and hence our algorithms cannot be improved on substantially without a breakthrough on this problem which is believed to be intractable. Motivated by this, we study alternate models allowing query access to ? where finding skewed subcubes might be easier

The Number of Hierarchical Orderings

An ordered set-partition (or preferential arrangement) of n labeled elements represents a single ``hierarchy''; these are enumerated by the ordered Bell numbers. In this note we determine the number of ``hierarchical orderings'' or ``societies'', where the n elements are first partitioned into m <= n subsets and a hierarchy is specified for each subset. We also consider the unlabeled case, where the ordered Bell numbers are replaced by the composition numbers. If there is only a single hierarchy, we show that the average rank of an element is asymptotic to n/(4 log 2) in the labeled case and to n/4 in the unlabeled case.Comment: 7 page

A JSON Token-Based Authentication and Access Management Schema for Cloud SaaS Applications

Cloud computing is significantly reshaping the computing industry built around core concepts such as virtualization, processing power, connectivity and elasticity to store and share IT resources via a broad network. It has emerged as the key technology that unleashes the potency of Big Data, Internet of Things, Mobile and Web Applications, and other related technologies, but it also comes with its challenges - such as governance, security, and privacy. This paper is focused on the security and privacy challenges of cloud computing with specific reference to user authentication and access management for cloud SaaS applications. The suggested model uses a framework that harnesses the stateless and secure nature of JWT for client authentication and session management. Furthermore, authorized access to protected cloud SaaS resources have been efficiently managed. Accordingly, a Policy Match Gate (PMG) component and a Policy Activity Monitor (PAM) component have been introduced. In addition, other subcomponents such as a Policy Validation Unit (PVU) and a Policy Proxy DB (PPDB) have also been established for optimized service delivery. A theoretical analysis of the proposed model portrays a system that is secure, lightweight and highly scalable for improved cloud resource security and management.Comment: 6 Page

Generation of All Possible Multiselections from a Multiset

The concept of a [k1, k2,..., kK]-selection applied on a multiset is introduced and an algorithm is outlined to generate all [k1, k2,..., kK]-selections from a given multiset. Key words: Multiselection; Mutiset; Contingency matrix; Combinatorie