Related papers: Rational tangle surgery and Xer recombination on c…
We consider the question of which Dehn surgeries along a given knot bound rational homology balls. We use Ozsv\'ath and Szab\'o's correction terms in Heegaard Floer homology to obtain general constraints on the surgery coefficients. We then…
We present a calculation technique for modeling inhomogeneous DNA replication kinetics, where replication factors such as initiation rates or fork speeds can change with both position and time. We can use our model to simulate data sets…
Organization and maintenance of the chromosomal DNA in living cells strongly depends on the DNA interactions with a plethora of DNA-binding proteins. Single-molecule studies show that formation of nucleoprotein complexes on DNA by such…
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's…
The Sine-Gordon model is obtained by tilting the law of a log-correlated Gaussian field $X$ defined on a subset of $\mathbb{R}^d$ by the exponential of its cosine, namely $\exp(\alpha \smallint \cos (\beta X))$. It is an important model in…
For a knot $K$ in the 3-sphere and a simply connected closed 4-manifold $X$, we define the $X$-double slice genus of $K$, extending the notion from the case when $X$ is the 4-sphere. We show that for each integer $n$, there exists an…
It is well known that the structural deformations (stressed states) of DNA molecule play a crucial role in its biological functions including gene expression. For instance, looping in DNA (often mediated by protein binding) is a crucial…
The strong bending of polymers is poorly understood. We propose a general quantitative framework of polymer bending that includes both the weak and strong bending regimes on the same footing, based on a single general physical principle. As…
Collagen crosslinking of the cornea (CXL) is commonly employed to prevent or treat keratoconus. Although the change of corneal stiffness induced by CXL surgery can be monitored with non-contact dynamic Optical Coherence Elastography (OCE)…
This paper studies the problem of reconstructing binary matrices that are only accessible through few evaluations of their discrete X-rays. Such question is prominently motivated by the demand in material science for developing a tool for…
A Charge Transport (CT) mechanism has been proposed in several papers (e.g., Yavin, et al. PNAS, v102 3546 (2005)) to explain the localization of Base Excision Repair (BER) enzymes to lesions on DNA. The CT mechanism relies on redox…
DNA supercoiling, the under or overwinding of DNA, is a key physical mechanism both participating to compaction of bacterial genomes and making genomic sequences adopt various structural forms. DNA supercoiling may lead to the formation of…
Being a dual purpose enzyme, the DNA polymerase is responsible for elongation of the newly formed DNA strand as well as cleaving the erroneous growth in case of a misincorporation. The efficiency of replication depends on the coordination…
Surgery on a knot in $S^3$ is said to be an alternating surgery if it yields the double branched cover of an alternating link. The main theoretical contribution is to show that the set of alternating surgery slopes is algorithmically…
For a knot $K$ in a homology $3$-sphere $\Sigma$, let $M$ be the result of $2/q$-surgery on $K$, and let $X$ be the universal abelian covering of $M$. Our first theorem is that if the first homology of $X$ is finite cyclic and $M$ is a…
Given a generic rational curve $C$ in the group of Euclidean displacements we construct a linkage such that the constrained motion of one of the links is exactly $C$. Our construction is based on the factorization of polynomials over dual…
Substring kernels are classical tools for representing biological sequences or text. However, when large amounts of annotated data are available, models that allow end-to-end training such as neural networks are often preferred. Links…
A new class of micromechanically motivated chain network models for soft biological tissues is presented. On the microlevel, it is based on the statistics of long chain molecules. A wormlike chain model is applied to capture the behavior of…
Ultrasound-guided percutaneous needle insertion is a standard procedure employed in both biopsy and ablation in clinical practices. However, due to the complex interaction between tissue and instrument, the needle may deviate from the…
A tandem cell is proposed for DNA sequencing in which an exonuclease enzyme cleaves bases (mononucleotides) from a strand of DNA for identification inside a nanopore. It has two nanopores and three compartments with the structure [cis1,…