Differential Calculus the Study of the Growth and Decay of an Entity’s Population

Population Growth and Decay study of the growth or the decrease of a population of a given entity, is carried out according to the environment. In an infinite environment, i.e. when the resources are unlimited, a population P believes according to the following differential equation P’ = KP, with the application of the differential calculus we obtasin an exponential function of the variable time (t). The function of which we can predict approximately a population according to the signs of k and time (t). If k > 0, we speak of the Malthusian croissant. On the other hand, in a finite environment i.e. when resources are limited, the population cannot exceed a certain value. and it satisfies the logistic equation proposed by the economist Francois Verhulst: P’ = P(1-P).

Differentiable Deformation Graph-Based Neural Non-rigid Registration

The traditional pipeline for non-rigid registration is to iteratively update the correspondence and alignment such that the transformed source surface aligns well with the target surface.Among the pipeline,the correspondence construction and iterative manner are key to the results,while existing strategies might result in local optima.In this paper,we adopt the widely used deformation graph-based representation,while replacing some key modules with neural learning-based strategies.Specifically,we design a neural network to predict the correspondence and its reliability confidence rather than the strategies like nearest neighbor search and pair rejection.Besides,we adopt the GRU-based recurrent network for iterative refinement,which is more robust than the traditional strategy.The model is trained in a self-supervised manner and thus can be used for arbitrary datasets without ground-truth.Extensive experiments demonstrate that our proposed method outperforms the state-of-the-art methods by a large margin.

On the Differential Polynomial of a Graph

We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x^(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.