Supercharacters,symmetric functions in noncommuting variables,and related Hopf algebras

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.     

Multigraded combinatorial Hopf algebras and refinements of odd and even subalgebras

We develop a theory of multigraded (i.e., ℕ ^l -graded) combinatorial Hopf algebras modeled on the theory of graded combinatorial Hopf algebras developed by Aguiar et al. (Compos. Math. 142:1–30, 2006). In particular we introduce the notion of canonical k-odd and k-even subalgebras associated with any multigraded combinatorial Hopf algebra, extending simultaneously the work of Aguiar et al. and Ehrenborg. Among our results are specific categorical results for higher level quasisymmetric functions, several basis change formulas, and a generalization of the descents-to-peaks map.     

Dynamics of one-dimensional granular arrays with pre-compression

Nonlinear Dynamics - Bifurcations of periodic orbits and band zones of a one-dimensional granular array are numerically investigated in this study. A conservative two-bead system is first...     

Recent Developments in Targeting RAS Downstream Effectors for RAS-Driven Cancer Therapy

Aberrant activity of oncogenic rat sarcoma virus (RAS) protein promotes tumor growth and progression. RAS-driven cancers comprise more than 30% of all human cancers and are refractory to frontline treatment strategies. Since direct targeting of RAS has proven challenging, efforts have been centered on the exploration of inhibitors for RAS downstream effector kinases. Two major RAS downstream signaling pathways, including the Raf/MEK/Erk cascade and the phosphatidylinositol-3-kinase (PI3K) pathway, have become compelling targets for RAS-driven cancer therapy. However, the main drawback in the blockade of a single RAS effector is the multiple levels of crosstalk and compensatory mechanisms between these two pathways that contribute to drug resistance against monotherapies. A growing body of evidence reveals that the sequential or synergistic inhibition of multiple RAS effectors is a more convenient route for the efficacy of cancer therapy. Herein, we revisit the recent developments and discuss the most promising modalities targeting canonical RAS downstream effectors for the treatment of RAS-driven cancers.     

On Hopf Algebras and Their Generalizations

We survey Hopf algebras and their generalizations. In particular, we compare and contrast three well-studied generalizations (quasi-Hopf algebras, weak Hopf algebras, and Hopf algebroids), and two newer ones (Hopf monads and hopfish algebras). Each of these notions was originally introduced for a specific purpose within a particular context; our discussion favors applicability to the theory of dynamical quantum groups. Throughout the note, we provide several definitions and examples in order to make this exposition accessible to readers with differing backgrounds.     

Ramanujan sums as supercharacters

The theory of supercharacters, recently developed by Diaconis-Isaacs and André, is used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas. In addition to exhibiting a new application of supercharacter theory, this article also serves as a blueprint for future work since some of the abstract results we develop are applicable in much greater generality.     

More Than Meets the Eye in Bacterial Cellulose: Biosynthesis,Bioprocessing, and Applications in Advanced Fiber Composites

Bacterial cellulose (BC) nanofibers are one of the stiffest organic materials produced by nature. It consists of pure cellulose without the impurities that are commonly found in plant‐based cellulose. This review discusses the metabolic pathways of cellulose‐producing bacteria and the genetic pathways of Acetobacter xylinum. The fermentative production of BC and the bioprocess parameters for the cultivation of bacteria are also discussed. The influence of the composition of the culture medium, pH, temperature, and oxygen content on the morphology and yield of BC are reviewed. In addition, the progress made to date on the genetic modification of bacteria to increase the yield of BC and the large‐scale production of BC using various bioreactors, namely static and agitated cultures, stirred tank, airlift, aerosol, rotary, and membrane reactors, is reviewed. The challenges in commercial scale production of BC are thoroughly discussed and the efficiency of various bioreactors is compared. In terms of the application of BC, particular emphasis is placed on the utilization of BC in advanced fiber composites to manufacture the next generation truly green, sustainable and renewable hierarchical composites.     

A new multiobjective simulated annealing algorithm

A new multiobjective simulated annealing algorithm for continuous optimization problems is presented. The algorithm has an adaptive cooling schedule and uses a population of fitness functions to accurately generate the Pareto front. Whenever an improvement with a fitness function is encountered, the trial point is accepted, and the temperature parameters associated with the improving fitness functions are cooled. Beside well known linear fitness functions, special elliptic and ellipsoidal fitness functions, suitable for the generation on non-convex fronts, are presented. The effectiveness of the algorithm is shown through five test problems. The parametric study presented shows that more fitness functions as well as more iteration gives more non-dominated points closer to the actual front. The study also compares the linear and elliptic fitness functions. The success of the algorithm is also demonstrated by comparing the quality metrics obtained to those obtained for a well-known evolutionary multiobjective algorithm.     

A new paradigm for protein design and biological self-assembly

Very few molecules with biological origins contain the element fluorine. Nature's inability to incorporate fluorine into biomolecules is related to the low concentration of free fluoride in sea and surface water. However, judicious introduction of fluorine into proteins, nucleic acids, lipids and carbohydrates has allowed mechanistic scrutiny of enzyme catalysis, control of protein oligomerization in membranes, clustered display of ligands on surfaces of living cells, and in increasing the protease stability of protein and peptide therapeutics.