We propose a fast local level set method for the inverse problem of gravimetry. The theoretical foundation for our approach is based on the following uniqueness result: if an open set D is star-shaped or x₃-convex with respect to its center of gravity, then its exterior potential uniquely determines the open set D. To achieve this purpose constructively, the first challenge is how to parametrize this open set D as its boundary may have a variety of possible shapes. To describe those different shapes we propose to use a level-set function to parametrize the unknown boundary of this open set. The second challenge is how to deal with the issue of partial data as gravimetric measurements are only made on a part of a given reference domain . To overcome this difficulty we propose a linear numerical continuation approach based on the single layer representation to find potentials on the boundary of some artificial domain

Numerical encoding plays an important role in DNA sequence analysis via computational methods, in which numerical values are associated with corresponding symbolic characters. After numerical representation, digital signal processing methods can be exploited to analyze DNA sequences. To reflect the biological properties of the original sequence, it is vital that the representation is one-to-one. Chaos Game Representation (CGR) is an iterative mapping technique that assigns each nucleotide in a DNA sequence to a respective position on the plane that allows the depiction of the DNA sequence in the form of image. Using CGR, a biological sequence can be transformed one-to-one to a numerical sequence that preserves the main features of the original sequence. In this research, we propose to encode DNA sequences by considering 2D CGR coordinates as complex numbers, and apply digital signal processing methods to analyze their evolutionary relationship. Computational experiments indicate that this approach gives comparable results to the state-of-the-art multiple sequence alignment method, Clustal Omega, and is significantly faster. The MATLAB code for our method can be accessed from: www.mathworks.com/matlabcentral/fileexchange/57152

We give an overview of our philosophy of pictures in mathematics. We emphasize a bidirectional process between picture lan- guage and mathematical concepts: abstraction and simulation. This motivates a program to understand different subjects, using virtual and real mathematical concepts simulated by pictures.

The bran fraction of wheat grain is known to contain significant quantities of bioactive components. This study evaluated the potential of solid-state yeast fermentation to improve the health beneficial properties of wheat bran, including extractable antioxidant properties, protein contents, and soluble and insoluble fiber compositions. Three commercial food grade yeast preparations were evaluated in the study along with the effects of yeast dose, treatment time, and their interaction with the beneficial components. Solid-state yeast treatments were able to significantly increase releasable antioxidant properties ranging from 28 to 65, from 0 to 20, from 13 to 19, from 0 to 25, from 50 to 100, and from 3 to 333% for scavenging capacities against peroxyl (ORAC), ABTS cation, DPPH and hydroxyl radicals, total phenolic contents (TPC), and phenolic acids, respectively. Yeast treatment increased protein content 11-12% but did not significantly alter the fiber composition of wheat bran. Effects of solid-state yeast treatment on both ORAC and TPC of wheat bran were altered by yeast dose, treatment time, and their interaction. Results suggest that solid-state yeast treatment may be a commercially viable postharvest procedure for improving the health beneficial properties of wheat bran and other wheat-based food ingredients.

Recent understandings of molecular evolution, together with the fossil records, have established that there are both linear and nonlinear processes in the creation of novel species, which is strikingly similar to the generation of prime numbers and human creativity. Each creation of a more complex species is like a prime number, unpredictable, discontinuous, and yet can be modeled by a smooth curve in relation to time. The mystery behind the complexity increases in nature and human civilizations might well turn out to be similar to that behind the appearances of prime numbers. Here we show that an algorithm for the creative process of humans can create prime numbers in a lawful and yet unpredictable fashion. The essence of primes is the duality of uniqueness and uniformity together with the creation algorithm. The algorithm consists of the non-linear process of uniformity selection to create the unique and the linear process of uniqueness selection to form the uniformity. The iterations of this algorithm can create an infinite number of primes. The algorithm appears to have been hardwired in the human brain as shown by recent experimental studies. This new understanding can deduce some of the best-known properties of primes and may explain the nearly constant and yet seemingly random creation of novelty in relation to time.