Efficient LZ78 factorization of grammar compressed text

We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string. Given an SLP of size $n$ representing a text $S$ of length $N$, our algorithm computes the LZ78 factorization of $T$ in $O(n\sqrt{N}+m\log N)$ time and $O(n\sqrt{N}+m)$ space, where $m$ is the number of resulting LZ78 factors. We also show how to improve the algorithm so that the $n\sqrt{N}$ term in the time and space complexities becomes either $nL$, where $L$ is the length of the longest LZ78 factor, or $(N - \alpha)$ where $\alpha \geq 0$ is a quantity which depends on the amount of redundancy that the SLP captures with respect to substrings of $S$ of a certain length. Since $m = O(N/\log_\sigma N)$ where $\sigma$ is the alphabet size, the latter is asymptotically at least as fast as a linear time algorithm which runs on the uncompressed string when $\sigma$ is constant, and can be more efficient when the text is compressible, i.e. when $m$ and $n$ are small.Comment: SPIRE 201

Beyond shared signals: The role of downward gaze in the stereotypical representation of sad facial expressions

According to the influential shared signal hypothesis, perceived gaze direction influences the recognition of emotion from the face, for example, gaze averted sideways facilitates the recognition of sad expressions because both gaze and expression signal avoidance. Importantly, this approach assumes that gaze direction is an independent cue that influences emotion recognition. But could gaze direction also impact emotion recognition because it is part of the stereotypical representation of the expression itself? In Experiment 1, we measured gaze aversion in participants engaged in a facial expression posing task. In Experiment 2, we examined the use of gaze aversion when constructing facial expressions on a computerized avatar. Results from both experiments demonstrated that downward gaze plays a central role in the representation of sad expressions. In Experiment 3, we manipulated gaze direction in perceived facial expressions and found that sadness was the only expression yielding a recognition advantage for downward, but not sideways gaze. Finally, in Experiment 4 we independently manipulated gaze aversion and eyelid closure, thereby demonstrating that downward gaze enhances sadness recognition irrespective of eyelid position. Together, these findings indicate that (1) gaze and expression are not independent cues and (2) the specific type of averted gaze is critical. In consequence, several premises of the shared signal hypothesis may need revision. (PsycINFO Database Record (c) 2019 APA, all rights reserved

Compressed Subsequence Matching and Packed Tree Coloring

We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses $O(n+\frac{n\sigma}{w})$ space and $O(n+\frac{n\sigma}{w}+m\log N\log w\cdot occ)$ or $O(n+\frac{n\sigma}{w}\log w+m\log N\cdot occ)$ time. Here $w$ is the word size and $occ$ is the number of occurrences of the pattern. Our algorithm uses less space than previous algorithms and is also faster for $occ=o(\frac{n}{\log N})$ occurrences. The algorithm uses a new data structure that allows us to efficiently find the next occurrence of a given character after a given position in a compressed string. This data structure in turn is based on a new data structure for the tree color problem, where the node colors are packed in bit strings.Comment: To appear at CPM '1

Tropical tele-connections to the Mediterranean climate and weather

Some strong natural fluctuations of climate in the Eastern Mediterranean (EM) region are shown to be connected to the major tropical systems. Potential relations between EM rainfall extremes to tropical systems, e.g. El Niño, Indian Monsoon and hurricanes, are demonstrated. For a specific event, high resolution modelling of the severe flood on 3-5 December 2001 in Israel suggests a relation to hurricane Olga. In order to understand the factors governing the EM climate variability in the summer season, the relationship between extreme summer temperatures and the Indian Monsoon was examined. Other tropical factors like the Red-Sea Trough system and the Saharan dust are also likely to contribute to the EM climate variability

Processing and Transmission of Information

Contains reports on two research projects.Lincoln Laboratory (Purchase Order DDL-B-00306)United States ArmyUnited States NavyUnited States Air Force (Contract AF19(604)-5200

Factorised Steady States in Mass Transport Models

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and random sequential dynamics and includes models such as the Zero-range process and Asymmetric random average process as special cases. We derive a necessary and sufficient condition for the steady state to factorise, which takes a rather simple form.Comment: 6 page

Processing and Transmission of Information

Contains reports on four research projects.Lincoln Laboratory (Purchase Order B-00306)United States ArmyUnited States NavyUnited States Air Force (Contract AF19(604)-7400

Pervasive Rise of Small-scale Deforestation in Amazonia

Understanding forest loss patterns in Amazonia, the Earth’s largest rainforest region, is critical for effective forest conservation and management. Following the most detailed analysis to date, spanning the entire Amazon and extending over a 14-year period (2001–2014), we reveal significant shifts in deforestation dynamics of Amazonian forests. Firstly, hotspots of Amazonian forest loss are moving away from the southern Brazilian Amazon to Peru and Bolivia. Secondly, while the number of new large forest clearings (>50 ha) has declined significantly over time (46%), the number of new small clearings (<1 ha) increased by 34% between 2001–2007 and 2008–2014. Thirdly, we find that small-scale low-density forest loss expanded markedly in geographical extent during 2008–2014. This shift presents an important and alarming new challenge for forest conservation, despite reductions in overall deforestation rates

Fingerprints in Compressed Strings

The Karp-Rabin fingerprint of a string is a type of hash value that due to its strong properties has been used in many string algorithms. In this paper we show how to construct a data structure for a string S of size N compressed by a context-free grammar of size n that answers fingerprint queries. That is, given indices i and j, the answer to a query is the fingerprint of the substring S[i,j]. We present the first O(n) space data structures that answer fingerprint queries without decompressing any characters. For Straight Line Programs (SLP) we get O(logN) query time, and for Linear SLPs (an SLP derivative that captures LZ78 compression and its variations) we get O(log log N) query time. Hence, our data structures has the same time and space complexity as for random access in SLPs. We utilize the fingerprint data structures to solve the longest common extension problem in query time O(log N log l) and O(log l log log l + log log N) for SLPs and Linear SLPs, respectively. Here, l denotes the length of the LCE