We introduce Backstr\"om pairs and rings, study their derived categories construct for them a sort of categorical resolutions. For the latter we define global dimension, semi-orthogonal decomposition category deduce that dimension ring is at most $2$. Using this decomposition, description module as elements special bimodule. also partial tilting pair to triangular matrices latter.

This article gives a natural decomposition of the suspension of a generalized moment-angle complex or partial product space which arises as the polyhedral product functor described below. The introduction and application of the smash product moment-angle complex provides a precise identification of the stable homotopy type of the values of the polyhedral product functor. One direct consequence ...

The decomposition theory of sequential machines aims to find answers to the following important practical problem: how to decompose a complex sequential machine into a number of simpler partial machines in order to: simplify the design, implementation and verification process; make it possible to process (to optimize, to implement, to test, ••. ) the separate partial machines al though it may b...

The Partial Information Decomposition (PID) [1] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a two-predictor partial information decomposition (PID) over discrete spaces [2]. A lattice of maximum entropy probability models is constructed based on marginal dependency c...

Latent semantic indexing (LSI) is a method of information retrieval that relies heavily on the partial singular value decomposition (PSVD) of the term-document matrix representation of a dataset. Calculating the PSVD of large term-document matrices is computationally expensive; hence in the case where terms or documents are merely added to an existing dataset, it is extremely beneficial to upda...

Approximations of expressions of the form If := trace(W T f(A)W ), where A ∈ Rm×m is a large symmetric matrix, W ∈ Rm×k with k ≪ m, and f is a function, can be computed without evaluating f(A) by applying a few steps of the global block Lanczos method to A with initial block-vector W . This yields a partial global Lanczos decomposition of A. We show that for suitable functions f upper and lower...

-Empirical Mode Decomposition (EMD) has recently been introduced as a local and fully data-driven technique aimed at analyzing nonstationary signals, by decomposing nonstationary signals into Intrinsic Mode Functions (IMFs). In this contribution, we employ it to process the signals of partial discharge, a typical type of nonstationary signal. Based on the IMFs extracted from the corrupted signa...

Both Sylvester matrix and convolution are defined by two polynomials. If one of them has small degree, then the associated Sylvester linear system can be solved fast by using its PFD interpretation of the convolution equation. This can immediately simplify the refinement of approximate convolution by means of Newton’s iteration, where we also incorporate the PFD refinement techniques or alterna...

In this work we study the distributed representations learnt by generative neural network models. In particular, we investigate the properties of redundant and synergistic information that groups of hidden neurons contain about the target variable. To this end, we use an emerging branch of information theory called partial information decomposition (PID) and track the informational properties o...