DAKS: An R Package for Data Analysis Methods in Knowledge Space Theory

Knowledge space theory is part of psychometrics and provides a theoretical framework for the modeling, assessment, and training of knowledge. It utilizes the idea that some pieces of knowledge may imply others, and is based on order and set theory. We introduce the R package DAKS for performing basic and advanced operations in knowledge space theory. This package implements three inductive item tree analysis algorithms for deriving quasi orders from binary data, the original, corrected, and minimized corrected algorithms, in sample as well as population quantities. It provides functions for computing population and estimated asymptotic variances of and one and two sample Z tests for the diff fit measures, and for switching between test item and knowledge state representations. Other features are a function for computing response pattern and knowledge state frequencies, a data (based on a finite mixture latent variable model) and quasi order simulation tool, and a Hasse diagram drawing device. We describe the functions of the package and demonstrate their usage by real and simulated data examples.

DAKS: An R Package for Data Analysis Methods in Knowledge Space Theory

Knowledge space theory is part of psychometrics and provides a theoretical framework for the modeling, assessment, and training of knowledge. It utilizes the idea that some pieces of knowledge may imply others, and is based on order and set theory. We introduce the R package DAKS for performing basic and advanced operations in knowledge space theory. This package implements three inductive item tree analysis algorithms for deriving quasi orders from binary data, the original, corrected, and minimized corrected algorithms, in sample as well as population quantities. It provides functions for computing population and estimated asymptotic variances of and one and two sample Z tests for the diff fit measures, and for switching between test item and knowledge state representations. Other features are a function for computing response pattern and knowledge state frequencies, a data (based on a finite mixture latent variable model) and quasi order simulation tool, and a Hasse diagram drawing device. We describe the functions of the package and demonstrate their usage by real and simulated data examples

On Verifying and Engineering the Well-gradedness of a Union-closed Family

Current techniques for generating a knowledge space, such as QUERY, guarantees that the resulting structure is closed under union, but not that it satisfies wellgradedness, which is one of the defining conditions for a learning space. We give necessary and sufficient conditions on the base of a union-closed set family that ensures that the family is well-graded. We consider two cases, depending on whether or not the family contains the empty set. We also provide algorithms for efficiently testing these conditions, and for augmenting a set family in a minimal way to one that satisfies these conditions.Comment: 15 page

Generalization from correlated sets of patterns in the perceptron

Generalization is a central aspect of learning theory. Here, we propose a framework that explores an auxiliary task-dependent notion of generalization, and attempts to quantitatively answer the following question: given two sets of patterns with a given degree of dissimilarity, how easily will a network be able to "unify" their interpretation? This is quantified by the volume of the configurations of synaptic weights that classify the two sets in a similar manner. To show the applicability of our idea in a concrete setting, we compute this quantity for the perceptron, a simple binary classifier, using the classical statistical physics approach in the replica-symmetric ansatz. In this case, we show how an analytical expression measures the "distance-based capacity", the maximum load of patterns sustainable by the network, at fixed dissimilarity between patterns and fixed allowed number of errors. This curve indicates that generalization is possible at any distance, but with decreasing capacity. We propose that a distance-based definition of generalization may be useful in numerical experiments with real-world neural networks, and to explore computationally sub-dominant sets of synaptic solutions

ZETA - Zero-Trust Authentication: Relying on Innate Human Ability, not Technology

Reliable authentication requires the devices and channels involved in the process to be trustworthy; otherwise authentication secrets can easily be compromised. Given the unceasing efforts of attackers worldwide such trustworthiness is increasingly not a given. A variety of technical solutions, such as utilising multiple devices/channels and verification protocols, has the potential to mitigate the threat of untrusted communications to a certain extent. Yet such technical solutions make two assumptions: (1) users have access to multiple devices and (2) attackers will not resort to hacking the human, using social engineering techniques. In this paper, we propose and explore the potential of using human-based computation instead of solely technical solutions to mitigate the threat of untrusted devices and channels. ZeTA (Zero Trust Authentication on untrusted channels) has the potential to allow people to authenticate despite compromised channels or communications and easily observed usage. Our contributions are threefold: (1) We propose the ZeTA protocol with a formal definition and security analysis that utilises semantics and human-based computation to ameliorate the problem of untrusted devices and channels. (2) We outline a security analysis to assess the envisaged performance of the proposed authentication protocol. (3) We report on a usability study that explores the viability of relying on human computation in this context

Random Matrix Theories in Quantum Physics: Common Concepts

We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.Comment: 178 pages, Revtex, 45 figures, submitted to Physics Report