On recursions for coefficients of mock theta functions

We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoglu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order mock theta functions. Additionally, we discuss an application of this identity to other mock theta functions.Comment: 21 pages, to appear in Research in Number Theor

Variations of Andrews-Beck type congruences

We prove three variations of recent results due to Andrews on congruences for $NT(m,k,n)$, the total number of parts in the partitions of $n$ with rank congruent to $m$ modulo $k$. We also conjecture new congruences and relations for $NT(m,k,n)$ and for a related crank-type function.Comment: 15 pages, typos corrected, to appear in the Journal of Mathematical Analysis and Application

Worldwide genetic variation of the IGHV and TRBV immune receptor gene families in humans.

The immunoglobulin heavy variable (IGHV) and T cell beta variable (TRBV) loci are among the most complex and variable regions in the human genome. Generated through a process of gene duplication/deletion and diversification, these loci can vary extensively between individuals in copy number and contain genes that are highly similar, making their analysis technically challenging. Here, we present a comprehensive study of the functional gene segments in the IGHV and TRBV loci, quantifying their copy number and single-nucleotide variation in a globally diverse sample of 109 (IGHV) and 286 (TRBV) humans from over a 100 populations. We find that the IGHV and TRBV gene families exhibit starkly different patterns of variation. In addition to providing insight into the different evolutionary paths of the IGHV and TRBV loci, our results are also important to the adaptive immune repertoire sequencing community, where the lack of frequencies of common alleles and copy number variants is hampering existing analytical pipelines

Hashing for Similarity Search: A Survey

Similarity search (nearest neighbor search) is a problem of pursuing the data items whose distances to a query item are the smallest from a large database. Various methods have been developed to address this problem, and recently a lot of efforts have been devoted to approximate search. In this paper, we present a survey on one of the main solutions, hashing, which has been widely studied since the pioneering work locality sensitive hashing. We divide the hashing algorithms two main categories: locality sensitive hashing, which designs hash functions without exploring the data distribution and learning to hash, which learns hash functions according the data distribution, and review them from various aspects, including hash function design and distance measure and search scheme in the hash coding space

Smart Heritage for Urban Sustainability: A Review of Current Definitions and Future Developments

Smart heritage is still novel in heritage discourse, with a few relevant review articles. In this regard, a specific interpretation of smart architectural heritage and a framework for instructing its development is lacking. This article reviews the literature on smart heritage in sustainable development to fill the knowledge gap. As a methodology for this study, the integrative review approach and thematic analysis are adopted to review references located at the crossroads of historic, smart, and sustainable disciplines. The review and interpretation draw on literature from relevant fields to understand implementations, current states, and support to interpret smart heritage. Review outcomes indicate that smart heritage is becoming dynamic as technologies are increasingly applied to more detailed heritage branches. This article lists the factors that heritage should possess to be defined as smart, and it provides a framework that might be followed to achieve the aims of this discourse by stating that smart heritage discussions are relevant to smart cities, as they may have a mutual effect and interact to promote each other.