Related papers: The Monster and black-box groups
We describe a generalization of the concept of a pc presentation that applies to groups with a nontrivial solvable radical. Such a representation can be much more efficient in terms of memory use and even of arithmetic, than permuattion and…
We show the details of certain computations that are used in the paper "Verification of the conjugacy classes and ordinary character table of the Monster".
We employ the recently developed hybrid and mmgroup computational models for groups to calculate the character table of $N(\rm{2B}^5) \cong 2^{5+10+20}.( \rm{S}_3 \times \rm{L}_5 {2} )$, a maximal subgroup of the Monster sporadic simple…
We explain a conjecture relating the monster simple group to an algebraic variety that was discovered in a non-monstrous context.
As a contribution to an eventual solution of the problem of determination of the maximal subgroups of the Monster we show that there is a unique conjugacy class of subgroups isomorphic to $PSU_3(8)$. The argument depends on some…
We review the construction of monsters in classical general relativity. Monsters have finite ADM mass and surface area, but potentially unbounded entropy. From the curved space perspective they are objects with large proper volume that can…
We show the details of certain computations that are described in [BMW19].
This book describes some computational methods to deal with modular characters of finite groups. It is the theoretical background of the MOC system of the same authors. This system was, and is still used, to compute the modular character…
With the increasing adoption of Artificial Intelligence (AI) in all fields and daily activities, a heated debate is found about the advantages and challenges of AI and the need for navigating the concerns associated with AI to make the best…
Black box machine learning models are currently being used for high stakes decision-making throughout society, causing problems throughout healthcare, criminal justice, and in other domains. People have hoped that creating methods for…
Explaining the behavior of a black box machine learning model at the instance level is useful for building trust. However, it is also important to understand how the model behaves globally. Such an understanding provides insight into both…
We show interesting relations between extremal partition functions of a family of conformal field theories and dimensions of the irreducible representations of the Fischer-Griess Monster sporadic group. We argue that these relations can be…
We prove the correctness of the character table of the sporadic simple Baby Monster group that is shown in the Atlas of Finite Groups.
We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the…
We present an interpretable companion model for any pre-trained black-box classifiers. The idea is that for any input, a user can decide to either receive a prediction from the black-box model, with high accuracy but no explanations, or…
Machine learning models are becoming increasingly popular in different types of settings. This is mainly caused by their ability to achieve a level of predictive performance that is hard to match by human experts in this new era of big…
Clustering algorithms play a fundamental role as tools in decision-making and sensible automation processes. Due to the widespread use of these applications, a robustness analysis of this family of algorithms against adversarial noise has…
Many machine learning models are vulnerable to adversarial examples: inputs that are specially crafted to cause a machine learning model to produce an incorrect output. Adversarial examples that affect one model often affect another model,…
Black-box complexity is a complexity theoretic measure for how difficult a problem is to be optimized by a general purpose optimization algorithm. It is thus one of the few means trying to understand which problems are tractable for genetic…
In the scenario of black-box adversarial attack, the target model's parameters are unknown, and the attacker aims to find a successful adversarial perturbation based on query feedback under a query budget. Due to the limited feedback…