Multidimensional Discrete Signals Description Using Rotation and Scale Invariant Pattern Spectrum

1989 ◽  
pp. 83-89
Author(s):  
M. Binaghi ◽  
V. Cappellini ◽  
C. Raspollini
Keyword(s):  
Scale Invariant ◽  
Pattern Spectrum ◽  
Discrete Signals

scholarly journals How simple cell to cell communication rules can generate and maintain scale invariant gradients of signalling activity across a multicellular population

2020 ◽  
Author(s):  
Jack Oldham
Keyword(s):  
Thought Experiment ◽  
Cell Communication ◽  
Simple Cell ◽  
Scale Invariant ◽  
Discrete Signals ◽  
Graph Type ◽  
Signalling Molecule ◽  
Gradient Formation ◽  
Local Cell ◽  
Intuitive Method

AbstractThis paper shows computationally and conceptually how gradients of signalling activity can be generated and dynamically maintained across a population of cells using very simple cell to cell communication rules. The rules work on the basis of cells regulating their production rate of a signalling molecule according to the production rates of their immediate neighbours. Highly stable, scale invariant signalling gradients can be formed across the population, with highest rates at the centre and lowest at the periphery.The cell to cell communication behaviour that causes gradient formation is first explained in a descriptive, thought experiment type manner. It is then defined more formally using a conceptual, mathematically discrete computational model, which provides a network or graph type framework in which it is easy to analyse and control discrete signals that are sent between neighbouring cells. This provides an intuitive method of explaining how the signalling gradient emerges as a result of local cell to cell communication. Finally, examples of gradient formation are shown using software implementations of the model.

Scale-Invariant Theory of Optical Properties of Fractal Clusters

1990 ◽  
Author(s):  
Vadim A. Markel ◽  
Leonid S. Muratov ◽  
Mark I. Stockman ◽  
Thomas F. George
Keyword(s):  
Optical Properties ◽  
Invariant Theory ◽  
Scale Invariant ◽  
Fractal Clusters

PROBABILITY OF BPSK SIGNAL RECEPTION ERROR IN PRESENCE OF SIMILAR HINDRANCE

2019 ◽  
pp. 55-59
Author(s):  
V. V. Zvonarev ◽  
I. A. Karabelnikov ◽  
A. S. Popov
Keyword(s):  
Initial Phase ◽  
Information Transfer ◽  
Radio Channel ◽  
Mutual Coherence ◽  
Coherent Noise ◽  
Probability Of Error ◽  
Discrete Signals ◽  
Average Probability ◽  
Correlation Receiver ◽  
Computer Type

The paper considers the problem of calculation of average probability of error of optimum symbol‑by‑symbol coherent reception of binary opposite phase‑shift keyed signals (BPSK) in the presence of similar synchronous noise. The noise similar to signal of PSK‑2 (BPSK), synchronous on clock periods, matching on frequency, differing in sequence of information characters and, perhaps, on initial phase of the bearing fluctuation is considered, up to mutual coherence of signal and noise. Formulas for calculation of probability of error are derived and results of partial computer type of diagrams of tension are given in some points of the correlation receiver. Optimum reception of discrete signals is carried out by means of the correlation receiver or the coordinated filter configured on signal in lack of noise in the presence of only receiver noises. It is shown that availability of synchronous similar or harmonious coherent noise, aim on structure, leads to decrease in noise stability of radio channel of information transfer. Than the level of noise is higher, that the probability of error is more.

Best Matching: Technical Details

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Point Particle ◽  
Euclidean Group ◽  
Scale Invariant ◽  
Similarity Group ◽  
N Body Problem ◽  
Technical Details ◽  
Matching Procedure ◽  
Principal Fibre ◽  
Principal Fibre Bundle ◽  
Gauge Connection

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

Singularities

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Stokes Equations ◽  
Negative Answer ◽  
Three Dimensions ◽  
Picard Iteration ◽  
Navier Stokes ◽  
Scale Invariant ◽  
Navier Stokes Equations ◽  
L2 Norm ◽  
Two Dimensional Flow ◽  
Physical Consequences

The initial value problem of the incompressible Navier–Stokes equations is explained. Leray’s classic study of it (using Picard iteration) is simplified and described in the language of physics. The ideas of Lebesgue and Sobolev norms are explained. The L2 norm being the energy, cannot increase. This gives sufficient control to establish existence, regularity and uniqueness in two-dimensional flow. The L3 norm is not guaranteed to decrease, so this strategy fails in three dimensions. Leray’s proof of regularity for a finite time is outlined. His attempts to construct a scale-invariant singular solution, and modern work showing this is impossible, are then explained. The physical consequences of a negative answer to the regularity of Navier–Stokes solutions are explained. This chapter is meant as an introduction, for physicists, to a difficult field of analysis.

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