Faster subsequence recognition in compressed strings

Computation on compressed strings is one of the key approaches to processing massive data sets. We consider local subsequence recognition problems on strings compressed by straight-line programs (SLP), which is closely related to Lempel--Ziv compression. For an SLP-compressed text of length $\bar m$, and an uncompressed pattern of length $n$, C{\'e}gielski et al. gave an algorithm for local subsequence recognition running in time $O(\bar mn^2 \log n)$. We improve the running time to $O(\bar mn^{1.5})$. Our algorithm can also be used to compute the longest common subsequence between a compressed text and an uncompressed pattern in time $O(\bar mn^{1.5})$; the same problem with a compressed pattern is known to be NP-hard

Carbon Consequences of Forest Disturbance and Recovery Across the Conterminous United States

Forests of North America are thought to constitute a significant long term sink for atmospheric carbon. The United States Forest Service Forest Inventory and Analysis (FIA) program has developed a large data base of stock changes derived from consecutive estimates of growing stock volume in the US. These data reveal a large and relatively stable increase in forest carbon stocks over the last two decades or more. The mechanisms underlying this national increase in forest stocks may include recovery of forests from past disturbances, net increases in forest area, and growth enhancement driven by climate or fertilization by CO2 and Nitrogen. Here we estimate the forest recovery component of the observed stock changes using FIA data on the age structure of US forests and carbon stocks as a function of age. The latter are used to parameterize forest disturbance and recovery processes in a carbon cycle model. We then apply resulting disturbance/recovery dynamics to landscapes and regions based on the forest age distributions. The analysis centers on 28 representative climate settings spread about forested regions of the conterminous US. We estimate carbon fluxes for each region and propagate uncertainties in calibration data through to the predicted fluxes. The largest recovery-driven carbon sinks are found in the South central, Pacific Northwest, and Pacific Southwest regions, with spatially averaged net ecosystem productivity (NEP) of about 100 g C / square m / a driven by forest age structure. Carbon sinks from recovery in the Northeast and Northern Lake States remain moderate to large owing to the legacy of historical clearing and relatively low modern disturbance rates from harvest and fire. At the continental scale, we find a conterminous U.S. forest NEP of only 0.16 Pg C/a from age structure in 2005, or only 0.047 Pg C/a of forest stock change after accounting for fire emissions and harvest transfers. Recent estimates of NEP derived from inventory stock change, harvest, and fire data show twice the NEP sink we derive from forest age distributions. We discuss possible reasons for the discrepancies including modeling errors and the possibility of climate and/or fertilization (CO2 or N) growth enhancements

Impacts of disturbance history on forest carbon stocks and fluxes: Merging satellite disturbance mapping with forest inventory data in a carbon cycle model framework

Forest carbon stocks and fluxes are highly dynamic following stand-clearing disturbances from severe fire and harvest and this presents a significant challenge for continental carbon budget assessments. In this work we use forest inventory data to parameterize a carbon cycle model to represent post-disturbance carbon trajectories of carbon pools and fluxes for specific forest types growing in high and low site productivity class settings. We then apply these trajectories to landscapes and regions based on forest age distributions derived from either the FIA data or from Landsat time series stacks (1985–2006) for 54 representative scenes throughout most of the conterminous United States.Weestimate the net carbon uptake in forests caused by post-disturbance growth and decomposition (“regrowth sink”) for forested regions across the country. At the landscape scale, the prevailing condition of positive net ecosystem productivity (NEP) is in stark contrast to local patcheswith large sources, particularly in the west where fires and clear cuts create contiguous disturbed patches. At the continental scale, regional differences in disturbance rates reflect management patterns of high disturbance rates in the Southeastern and South Central states, and lower disturbance rates in the Northeast andNorthern Lakes States. Despite low contemporary disturbance rates in the Northeast and Northern Lakes States (0.61 and 0.74% y−1), the regrowth sink there remains of moderate to large strength (88 and 57 g C m−2 y−1) owing to the continued legacy from historical clearing. Large regrowth sinks are also found in the Southeast, South Central, and Pacific Southwest regions (85, 86, and 95 g C m−2 y−1) where disturbance rates also tend to be higher (1.59, 1.38, and 0.93% y−1). Overall, the Landsat-derived disturbance rates are elevated relative to FIA-derived rates (1.19 versus 0.93% y−1) particularly for western regions. The differences only modestly adjust regional- and continental-scale carbon budgets, reducing NEP from forest regrowth by about 8%

Dynamic Set Intersection

Consider the problem of maintaining a family $F$ of dynamic sets subject to insertions, deletions, and set-intersection reporting queries: given $S,S'\in F$, report every member of $S\cap S'$ in any order. We show that in the word RAM model, where $w$ is the word size, given a cap $d$ on the maximum size of any set, we can support set intersection queries in $O(\frac{d}{w/\log^2 w})$ expected time, and updates in $O(\log w)$ expected time. Using this algorithm we can list all $t$ triangles of a graph $G=(V,E)$ in $O(m+\frac{m\alpha}{w/\log^2 w} +t)$ expected time, where $m=|E|$ and $\alpha$ is the arboricity of $G$. This improves a 30-year old triangle enumeration algorithm of Chiba and Nishizeki running in $O(m \alpha)$ time. We provide an incremental data structure on $F$ that supports intersection {\em witness} queries, where we only need to find {\em one} $e\in S\cap S'$. Both queries and insertions take O\paren{\sqrt \frac{N}{w/\log^2 w}} expected time, where $N=\sum_{S\in F} |S|$. Finally, we provide time/space tradeoffs for the fully dynamic set intersection reporting problem. Using $M$ words of space, each update costs $O(\sqrt {M \log N})$ expected time, each reporting query costs $O(\frac{N\sqrt{\log N}}{\sqrt M}\sqrt{op+1})$ expected time where $op$ is the size of the output, and each witness query costs $O(\frac{N\sqrt{\log N}}{\sqrt M} + \log N)$ expected time.Comment: Accepted to WADS 201

Continuity of Landsat Obersvations: Short Term Considerations

As of writing in mid-2010, both Landsat-5 and -7 continue to function, with sufficient fuel to enable data collection until the launch of the Landsat Data Continuity Mission (LDCM) scheduled for December of 2012. Failure of one or both of Landsat-5 or -7 may result in a lack of Landsat data for a period of time until the 2012 launch. Although the potential risk of a component failure increases the longer the sensor\u27s design life is exceeded, the possible gap in Landsat data acquisition is reduced with each passing day and the risk of Landsat imagery being unavailable diminishes for all except a handful of applications that are particularly data demanding. Advances in Landsat data compositing and fusion are providing opportunities to address issues associated with Landsat-7 SLC-off imagery and to mitigate a potential acquisition gap through the integration of imagery from different sensors. The latter will likely also provide short-term, regional solutions to application-specific needs for the continuity of Landsat-like observations. Our goal in this communication is not to minimize the community\u27s concerns regarding a gap in Landsat observations, but rather to clarify how the current situation has evolved and provide an up-to-date understanding of the circumstances, implications, and mitigation options related to a potential gap in the Landsat data record

The generalized localization lengths in one dimensional systems with correlated disorder

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared. Generalized entropic localization lengths are introduced in order to characterize the states and compared with their behavior for exponential localization. An acceptable agreement is obtained, however, the exponential form seems to be an oversimplification in the presence of correlated disorder. According to our analysis in the case of the random dimer model and the two new models the presence of power-law localization cannot be ruled out.Comment: 7 pages, LaTeX (IOP style), 2 figure

Fast Searching in Packed Strings

Given strings $P$ and $Q$ the (exact) string matching problem is to find all positions of substrings in $Q$ matching $P$. The classical Knuth-Morris-Pratt algorithm [SIAM J. Comput., 1977] solves the string matching problem in linear time which is optimal if we can only read one character at the time. However, most strings are stored in a computer in a packed representation with several characters in a single word, giving us the opportunity to read multiple characters simultaneously. In this paper we study the worst-case complexity of string matching on strings given in packed representation. Let $m \leq n$ be the lengths $P$ and $Q$, respectively, and let $\sigma$ denote the size of the alphabet. On a standard unit-cost word-RAM with logarithmic word size we present an algorithm using time O\left(\frac{n}{\log_\sigma n} + m + \occ\right). Here \occ is the number of occurrences of $P$ in $Q$. For $m = o(n)$ this improves the $O(n)$ bound of the Knuth-Morris-Pratt algorithm. Furthermore, if $m = O(n/\log_\sigma n)$ our algorithm is optimal since any algorithm must spend at least \Omega(\frac{(n+m)\log \sigma}{\log n} + \occ) = \Omega(\frac{n}{\log_\sigma n} + \occ) time to read the input and report all occurrences. The result is obtained by a novel automaton construction based on the Knuth-Morris-Pratt algorithm combined with a new compact representation of subautomata allowing an optimal tabulation-based simulation.Comment: To appear in Journal of Discrete Algorithms. Special Issue on CPM 200

Neurology

Contains reports on seven research projects.U. S. Public Health Service (B-3055-3,U. S. Public Health Service (B-3090-3)U. S. Public Health Service (38101-22)Office of Naval Research (Nonr-1841 (70))Air Force (AF33(616)-7588)Air Force (AFAOSR 155-63)Army Chemical Corps (DA-18-108-405-Cml-942)National Institutes of Health (Grant MH-04734-03

Neurology

Contains reports on six research projects.U. S. Public Health Service (B-3055-4, B-3090-4, MH-06175-02)U. S. Air Force (AF49(638)-1313)U.S. Navy. Office of Naval Research (Nonr-1841(70)