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Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
DNA data storage offers a high-density, long-term alternative to traditional storage systems, addressing the exponential growth of digital data. Composite DNA extends this paradigm by leveraging mixtures of nucleotides to increase storage…
A pedigree is a directed graph in which each vertex (except the founder vertices) has two parents. The main result in this paper is a construction of an infinite family of counter examples to a reconstruction problem on pedigrees, thus…
Composite DNA is a recent novel method to increase the information capacity of DNA-based data storage above the theoretical limit of 2 bits/symbol. In this method, every composite symbol does not store a single DNA nucleotide but a mixture…
The ongoing effort to detect and characterize physical entanglement in biopolymers has so far established that knots are present in many globular proteins and also abound in viral DNA packaged inside bacteriophages. RNA molecules, on the…
Proteomics will celebrate its 20th year in 2014. In this relatively short period of time, it has invaded most areas of biology and its use will probably continue to spread in the future. These two decades have seen a considerable increase…
Minuscule molecular forces can transform DNA into a structure that is elongated by more than half its original length. We demonstrate that this pronounced conformational transition is of relevance to ongoing experimental and theoretical…
The plethystic transformation $f[X] \mapsto f[X/(1-t)]$ and LLT polynomials are central to the theory of symmetric Macdonald polynomials. In this work, we introduce and study nonsymmetric flagged LLT polynomials. We show that these admit…
Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the…
Despite nearly two scores of research on RNA secondary structure and RNA-RNA interaction prediction, the accuracy of the state-of-the-art algorithms are still far from satisfactory. Researchers have proposed increasingly complex energy…
The weight systems of finite-dimensional representations of complex, simple Lie algebras exhibit patterns beyond Weyl-group symmetry. These patterns occur because weight systems can be decomposed into lattice polytopes in a natural way.…
Genetic information is stored in a linear sequence of base-pairs; however, thermal fluctuations and complex DNA conformations such as folds and loops make it challenging to order genomic material for in vitro analysis. In this work, we…
Covering alignment problems arise from recent developments in genomics; so called pan-genome graphs are replacing reference genomes, and advances in haplotyping enable full content of diploid genomes to be used as basis of sequence…
The Weihrauch degrees and strong Weihrauch degrees are partially ordered structures representing degrees of unsolvability of various mathematical problems. Their study has been widely applied in computable analysis, complexity theory, and…
Locations of DNA replication initiation in prokaryotes, called "origins of replication", are well-characterized. However, a mechanistic understanding of the sequence-dependence of the local unzipping of double-stranded DNA, the first step…
We provided explicit formulas for the number of stringy points over finite fields of parabolic type A character varieties with generic semisimple monodromy. This leads to formulas for their stringy E-polynomials. In particular, they satisfy…
We give a precise estimate for the number of lattice points in certain bounded subsets of $\mathbb{R}^{n}$ that involve `hyperbolic spikes' and occur naturally in multiplicative Diophantine approximation. We use Wilkie's o-minimal structure…
This paper addresses enforcing non-vanishing constraints for solutions to a second order elliptic partial differential equation by appropriate choices of boundary conditions. We show that, in dimension $d\geq2$, under suitable regularity…
Complex systems with tightly coadapted parts frequently appear in living systems and are difficult to account for through Darwinian evolution, that is random variation and natural selection, if the constituent parts are independently coded…
We show that a certain superfield formalism can be used to find an off-shell supersymmetric description for some supersymmetric field theories where conventional superfield formalism does not work. This "new" formalism contains even…