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John Rossi

Publications and source records attributed to John Rossi.

4 recordsLinked to original sources
arXiv2021

Asymptotic functions of entire functions

If $f$ is an entire function and $a$ is a complex number, $a$ is said to be an asymptotic value of $f$ if there exists a path $γ$ from $0$ to infinity such that $f(z) - a$ tends to $0$ as $z$ tends to infinity along $γ$. The Denjoy--Carleman--Ahlfors Theorem asserts that if $f$ has $n$ distinct asymptotic values, then the rate of growth of $f$ is at least order $n/2$, mean type. A long-standing problem asks whether this conclusion holds for entire functions having $n$ distinct asymptotic (entire) functions, each of growth at most order $1/2$, minimal type. In this paper conditions on the function $f$ and associated asymptotic paths are obtained that are sufficient to guarantee that $f$ satisfies the conclusion of the Denjoy--Carleman--Ahlfors Theorem. In addition, for each positive integer $n$, an example is given of an entire function of order $n$ having $n$ distinct, prescribed asymptotic functions, each of order less than $1/2$.

math.CV↗
arXiv2016

AptaTRACE: Elucidating Sequence-Structure Binding Motifs by Uncovering Selection Trends in HT-SELEX Experiments

Aptamers, short synthetic RNA/DNA molecules binding specific targets with high affinity and specificity, are utilized in an increasing spectrum of bio-medical applications. Aptamers are identified in vitro via the Systematic Evolution of Ligands by Exponential Enrichment (SELEX) protocol. SELEX selects binders through an iterative process that, starting from a pool of random ssDNA/RNA sequences, amplifies target-affine species through a series of selection cycles. HT-SELEX, which combines SELEX with high throughput sequencing, has recently transformed aptamer development and has opened the field to even more applications. HT-SELEX is capable of generating over half a billion data points, challenging computational scientists with the task of identifying aptamer properties such as sequence structure motifs that determine binding. While currently available motif finding approaches suggest partial solutions to this question, none possess the generality or scalability required for HT-SELEX data, and they do not take advantage of important properties of the experimental procedure. We present AptaTRACE, a novel approach for the identification of sequence-structure binding motifs in HT-SELEX derived aptamers. Our approach leverages the experimental design of the SELEX protocol and identifies sequence-structure motifs that show a signature of selection. Because of its unique approach, AptaTRACE can uncover motifs even when these are present in only a minuscule fraction of the pool. Due to these features, our method can help to reduce the number of selection cycles required to produce aptamers with the desired properties, thus reducing cost and time of this rather expensive procedure. The performance of the method on simulated and real data indicates that AptaTRACE can detect sequence-structure motifs even in highly challenging data.

q-bio.QM↗
arXiv2013

Wiman-Valiron theory for a class of functions meromorphic in the unit disc

Analogues of the key results of Wiman-Valiron theory are proved for a class of functions meromorphic in the unit disc, based on an approach developed by Bergweiler, Rippon and Stallard for the plane setting. The results give local approximations for the function and its logarithmic derivative and, in the case of positive order of growth, for higher order logarithmic derivatives as well.

math.CV↗