When the convolution of two natural exponential families is still a natural exponential family, then these families are either Gaussian or Poisson. We generalize this result of Letac in the case of n (n > 2) families.doi:10.1016/S0764-4442(99)80299-7Denys Pommeret...
The limit can be easily computed for two particular assignment choices of λk, first using the geometric series and second using the exponential series. Setting λk=λk, i.e., to a geometric series, we obtain the geometric random walk kernel which is defined as (29)k×(G,G′)=∫i,...
From rectangles, triangles, unit step function, negative exponential, ramp, sine, cosine, and ending in the periodic pulse, we mix and match what we can fit and describe the intricate details of convolution. We wrap the chapter with the important topic of convolution with the delta function....
The convolution of two finite sequences is defined by extending the sequences to finitely supported functions on the set of integers. When the sequences are the coefficients of two polynomials, then the coefficients of the ordinary product of the two polynomials are the convolution of the original...
Answer to: Find the convolution of the two functions: f(x)=5e^{-x} and g(x)=\cos(x) By signing up, you'll get thousands of step-by-step solutions...
Differentiable biology: using deep learning for biophysics-based and data-driven modeling of molecular mechanisms Article 04 October 2021 Improving representations of genomic sequence motifs in convolutional networks with exponential activations Article 08 February 2021 Transfer learning enables predictions...
In this paper, we consider a general notion of convolution. LetDbe a finite domain and letD^nbe the set ofn-length vectors (tuples) ofD. Letf :D\times D\rightarrow Dbe a function and let\oplus _fbe a coordinate-wise application off. Thef-Convolutionof two functionsg,h :D^n \right...
If we had decided to place the soldering iron at a different location than the origin, we would expect the same heat distribution to result, and so this process is translation invariant. Had we placed two soldering irons, we would expect the result to be the sum of two dispersing heat wav...
A Journey Through Divisibility of Class Numbers of Imaginary Quadratic Fields by 16:01 On Two Variable Artin’s Conjecture by Suhita Hazra 13:16 Diophantine Approximation with Prime Restriction inReal Quadratic Number Fields 14:21 Monochromatic exponential pattern in Ramsey theory by Sayan Goswami...
From the previous chapter we understand that, in general, the linear convolution of two N-point sequences will result in a sequence longer than N. Obviously, convolution via DFT is not exactly the same as linear convolution. It is called circular convolution. The convolution is circular because...