New Classes of Finite Dimensional Filters with Nonmaximal Rank Estimation Algebra on State Dimension $n$ and Linear Rank $n-2$

2020 ◽  
Vol 58 (6) ◽  
pp. 3413-3427
Author(s):  
Xiao-pei Jiao ◽  
Stephen S.-T. Yau
Keyword(s):  
Rank Estimation ◽  
Linear Rank ◽  
Finite Dimensional ◽  
Estimation Algebra

scholarly journals Characteristic-dependent linear rank inequalities in 21 variables

2019 ◽  
Vol 43 (169) ◽  
pp. 764-770
Author(s):  
Victor Peña-Macias ◽  
Humberto Sarria - Zapata
Keyword(s):  
Finite Field ◽  
Linear Inequality ◽  
Binary Matrix ◽  
The Third ◽  
Linear Rank ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Characteristic 2 ◽  
Characteristic 3 ◽  
New Inequalities

In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of spans of vector subspaces of a finite dimensional vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. This paper shows a preliminary result in the production of these inequalities. We produce three new inequalities in 21 variables using as guide a particular binary matrix, with entries in a finite field, whose rank is 8, with characteristic 2; 9 with characteristic 3; or 10 with characteristic neither 2 nor 3. The first inequality is true over fields whose characteristic is 2; the second inequality is true over fields whose characteristic is 2 or 3; the third inequality is true over fields whose characteristic is neither 2 nor 3.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

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