EXAGRAPH: Graph and combinatorial methods for enabling exascale applications

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.

Rational design of hyperstable antibacterial peptides for food preservation

We describe the design of peptides with properties like thermostability, pH stability, and antibacterial activity against a few bacterial food pathogens. Insights obtained from classical structure-function analysis of natural peptides and their mutants through antimicrobial and enzymatic assays are used to rationally develop a set of peptides. pH and thermostability assays were performed to demonstrate robust antimicrobial activity post-treatment with high temperatures and at wide pH ranges. We have also investigated the mode of action of these hyperstable peptides using membrane permeability assays, electron microscopy, and molecular dynamics simulations. Notably, through mutational studies, we show that these peptides elicit their antibacterial action via both membrane destabilization and inhibition of intracellular trypsin—the two functions attributable to separate peptide segments. Finally, toxicity studies and food preservation assays demonstrate the safety and efficacy of the designed peptides for food preservation. Overall, the study provides a general ‘blueprint’ for the development of stable antimicrobial peptides (AMPs). Insights obtained from this work may also be combined with combinatorial methods in high-throughput studies for future development of antimicrobials for various applications.

On the Norms of RFMLR-Circulant Matrices with the Exponential and Trigonometric Functions

In this paper, based on combinatorial methods and the structure of RFMLR-circulant matrices, we study the spectral norms of RFMLR-circulant matrices involving exponential forms and trigonometric functions. Firstly, we give some properties of exponential forms and trigonometric functions. Furthermore, we study Frobenius norms, the lower and upper bounds for the spectral norms of RFMLR-circulant matrices involving exponential forms and trigonometric functions by some ingenious algebra methods, and then we obtain new refined results.

Construction Of Three-Variable High-Order Defferential Equation Polynomial Solutions By Combinatorics Method

In this paper, we study how basic systems of polynomial solutions of a differential equation of high order with mixed derivatives of a function of three variables are constructed using combinatorial methods

Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Combinatorial Constructions Of Ordered Orthogonal Arrays & Ordered Covering Arrays

In this thesis, we consider combinatorial objects called ordered orthogonal arrays, which are related to orthogonal arrays and Latin squares. We also introduce a new combinatorial method to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays, which generalize covering arrays. We adapt existing combinatorial methods to the construction of these objects, as well as developing new ones. We discuss the applications of ordered orthogonal arrays and ordered covering arrays to quasi-Monte Carlo integration through the construction of point sets called (t,m,s)-nets and a new object we call (t,m,s)-covering nets.

Random tensor models—the U(N)D-invariant model

In the first section we give a briefly presentation of the U(N)D-invariant tensor models (N being again the size of the tensor, and D being the dimension). The next section is then dedicated to the analysis of the Dyson–Schwinger equations (DSE) in the large N limit. These results are essential to implement the double scaling limit mechanism of the DSEs, which is done in the third section. The main result of this chapter is the doubly-scaled 2-point function for a model with generic melonic interactions. However, several assumptions on the large N scaling of cumulants are made along the way. They are proved using various combinatorial methods.