Rank, select and access in grammar-compressed strings

Given a string $S$ of length $N$ on a fixed alphabet of $\sigma$ symbols, a grammar compressor produces a context-free grammar $G$ of size $n$ that generates $S$ and only $S$. In this paper we describe data structures to support the following operations on a grammar-compressed string: \mbox{rank}_c(S,i) (return the number of occurrences of symbol $c$ before position $i$ in $S$); \mbox{select}_c(S,i) (return the position of the $i$th occurrence of $c$ in $S$); and \mbox{access}(S,i,j) (return substring $S[i,j]$). For rank and select we describe data structures of size $O(n\sigma\log N)$ bits that support the two operations in $O(\log N)$ time. We propose another structure that uses $O(n\sigma\log (N/n)(\log N)^{1+\epsilon})$ bits and that supports the two queries in $O(\log N/\log\log N)$, where $\epsilon>0$ is an arbitrary constant. To our knowledge, we are the first to study the asymptotic complexity of rank and select in the grammar-compressed setting, and we provide a hardness result showing that significantly improving the bounds we achieve would imply a major breakthrough on a hard graph-theoretical problem. Our main result for access is a method that requires $O(n\log N)$ bits of space and $O(\log N+m/\log_\sigma N)$ time to extract $m=j-i+1$ consecutive symbols from $S$. Alternatively, we can achieve $O(\log N/\log\log N+m/\log_\sigma N)$ query time using $O(n\log (N/n)(\log N)^{1+\epsilon})$ bits of space. This matches a lower bound stated by Verbin and Yu for strings where $N$ is polynomially related to $n$.Comment: 16 page

Canonical treatment of two dimensional gravity as an anomalous gauge theory

The extended phase space method of Batalin, Fradkin and Vilkovisky is applied to formulate two dimensional gravity in a general class of gauges. A BRST formulation of the light-cone gauge is presented to reveal the relationship between the BRST symmetry and the origin of $SL(2,R)$ current algebra. From the same principle we derive the conformal gauge action suggested by David, Distler and Kawai.Comment: 11 pages, KANAZAWA-92-1

Effects of the geometrical configuration of air-water mixer on the size and distribution of micro-bubbles in aeration systems

The objective of this work is to present a novel geometrical configuration for microbubble generators (MBGs) to improve dissolved-oxygen levels in water. Among various methodologies from the literature, Orifice and Venturi tubes have been considered as baseline cases. Experimental data from the literature are used to verify a computational fluid dynamics (CFD) case developed for a better understanding of the dynamics of MBGs. As a result, the validated CFD setup has been implemented on a modified Venturi-type generator, where air is injected coaxially with respect to the tube axis, whereas a helicoid wall at variable pitch angle is used. Results show a reduction in the mean bubble diameter distribution from the baseline Venturi tubes, particularly, at low-speed inlet velocities. This is of interest, especially to decrease the energy requirement for most common water aeration systems

A cycling state that can lead to glassy dynamics in intracellular transport

Power-law dwell times have been observed for molecular motors in living cells, but the origins of these trapped states are not known. We introduce a minimal model of motors moving on a two-dimensional network of filaments, and simulations of its dynamics exhibit statistics comparable to those observed experimentally. Analysis of the model trajectories, as well as experimental particle tracking data, reveals a state in which motors cycle unproductively at junctions of three or more filaments. We formulate a master equation for these junction dynamics and show that the time required to escape from this vortex-like state can account for the power-law dwell times. We identify trends in the dynamics with the motor valency for further experimental validation. We demonstrate that these trends exist in individual trajectories of myosin II on an actin network. We discuss how cells could regulate intracellular transport and, in turn, biological function, by controlling their cytoskeletal network structures locally

Sexuality & Perspective

Panel Chair: Whitney Pisani Papers Presented: Siren\u27s Song of Sapiosexuality by Emma Tabei Abstract: Gender and male and female communications is discussed just as much if not more than politics currently. As we get more and more interested in understanding communication between genders, perhaps we need to look at where we came from instead of guessing what will happen next. Homer\u27s, Odyssey, specifically the Siren\u27s Song, pits male and female gender roles and perspectives against each other resulting in an untraditional look at modern female and male communications far ahead of Homer’s time; departing from the stereotypical gender looking glass. The Soiled Fertility of Female Script by Emily Ellison You Are What You Repeat by Tyrell J. Osborn The Perspective of Crush by Ileana Garnan

Queries on LZ-Bounded Encodings

We describe a data structure that stores a string $S$ in space similar to that of its Lempel-Ziv encoding and efficiently supports access, rank and select queries. These queries are fundamental for implementing succinct and compressed data structures, such as compressed trees and graphs. We show that our data structure can be built in a scalable manner and is both small and fast in practice compared to other data structures supporting such queries

Block trees

Let string S[1..n] be parsed into z phrases by the Lempel-Ziv algorithm. The corresponding compression algorithm encodes S in O(z) space, but it does not support random access to S. We introduce a data structure, the block tree, that represents S in O(z log(n/z)) space and extracts any symbol of S in time O(log(n/z)), among other space-time tradeoffs. The structure also supports other queries that are useful for building compressed data structures on top of S. Further, block trees can be built in linear time and in a scalable manner. Our experiments show that block trees offer relevant space-time tradeoffs compared to other compressed string representations for highly repetitive strings. (C) 2020 Elsevier Inc. All rights reserved.Peer reviewe