A Note on Outliers in Linear Regression : A Case of Japanese Typical Households Behaviour

We study the notions of disjunctivity and alternativity of orthomodular posets in the context of orthoprojections or skew projections in C*-algebras

Some remarks on measures on orthogonal rational projections and the rational sphere

We examine measures on the quantum logic of all projections with rational n x n-matrices and on its sublogic generated by all projections onto one-dimensional subspaces in ℚn passing through elements of the unit sphere in ℚn

Gleason-type theorems for signed measures on orthomodular posets of projections on linear spaces

We consider some orthomodular posets which are not lattices and the Gleason-type theorems for signed measures on them. © 1995 Plenum Publishing Corporation

Gleason-type theorem for linear spaces over the field of four elements

We prove an analog of the famous Gleason theorem for additive functions on the orthomodular poset of all projections defined on an n-dimensional linear space over the field consisting of four elements. An essential part of the proof consists in a computer calculation

LogShield: A Transformer-based APT Detection System Leveraging Self-Attention

Cyber attacks are often identified using system and network logs. There have been significant prior works that utilize provenance graphs and ML techniques to detect attacks, specifically advanced persistent threats, which are very difficult to detect. Lately, there have been studies where transformer-based language models are being used to detect various types of attacks from system logs. However, no such attempts have been made in the case of APTs. In addition, existing state-of-the-art techniques that use system provenance graphs, lack a data processing framework generalized across datasets for optimal performance. For mitigating this limitation as well as exploring the effectiveness of transformer-based language models, this paper proposes LogShield, a framework designed to detect APT attack patterns leveraging the power of self-attention in transformers. We incorporate customized embedding layers to effectively capture the context of event sequences derived from provenance graphs. While acknowledging the computational overhead associated with training transformer networks, our framework surpasses existing LSTM and Language models regarding APT detection. We integrated the model parameters and training procedure from the RoBERTa model and conducted extensive experiments on well-known APT datasets (DARPA OpTC and DARPA TC E3). Our framework achieved superior F1 scores of 98% and 95% on the two datasets respectively, surpassing the F1 scores of 96% and 94% obtained by LSTM models. Our findings suggest that LogShield's performance benefits from larger datasets and demonstrates its potential for generalization across diverse domains. These findings contribute to the advancement of APT attack detection methods and underscore the significance of transformer-based architectures in addressing security challenges in computer systems

A probabilistic inequality for sums of bounded symmetric independent random variables

An inequality ∫x x+2 P{|∑i=1 n ξi| ≥ t} dt ≤ ∫x x+2 P{|∑i=1 n εi| ≥ t} dt is proved which describes an extremal property of a two-point distribution within the class of symmetric distributions with bounded support. © 1997 Plenum Publishing Corporation

The gleason theorem for the field of rational numbers and residue fields

Charges μ taking values in a field F and defined on orthomodular partially ordered sets (logics) of all projectors in some finite-dimensional linear space over F are considered. In the cases where F is the field of rational numbers or a residue field, the Gleason representation μ(P) = tr(T μP), where T μ is a linear operator, is proved. © 1999 Kluwcr Academic/Plenum Publishers

Linear spaces with probability measures, ultraproducts and contiguity

The ultraproducts of measurable linear spaces with probability measure are considered. We study some properties (sometimes exotic) of these probability spaces. Connections between the notions of ultraproduct, equivalence and contiguity, singularity and entire separateness are established. © 2014 Pleiades Publishing, Ltd

The haagerup problem on subadditive weights on W *-algebras

In 1975 U. Haagerup stated the following question: Is every normal subadditive weight on a W *-algebra sigma-weakly lower semicontinuous? Here we positively answer this question in a particular case of abelian W *-algebras and present a general form of normal subadditive weights on these algebras. © Allerton Press, Inc., 2011

Disjunctivity and alternativity in projection logics

We study the notions of disjunctivity and alternativity of orthomodular posets in the context of orthoprojections or skew projections in C*-algebras