Revisiting the Problem of Searching on a Line

We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the first tight bounds on the exact optimal competitive ratio achievable, parameterized in terms of the given bounds on D, along with an optimal search strategy that achieves this competitive ratio. We prove that this optimal strategy is unique. We characterize the conditions under which an optimal strategy can be computed exactly and, when it cannot, we explain how numerical methods can be used efficiently. In addition, we answer several related open questions, including the maximal reach problem, and we discuss how to generalize these results to m rays, for any m >= 2

Suffix Tree of Alignment: An Efficient Index for Similar Data

We consider an index data structure for similar strings. The generalized suffix tree can be a solution for this. The generalized suffix tree of two strings $A$ and $B$ is a compacted trie representing all suffixes in $A$ and $B$. It has $|A|+|B|$ leaves and can be constructed in $O(|A|+|B|)$ time. However, if the two strings are similar, the generalized suffix tree is not efficient because it does not exploit the similarity which is usually represented as an alignment of $A$ and $B$. In this paper we propose a space/time-efficient suffix tree of alignment which wisely exploits the similarity in an alignment. Our suffix tree for an alignment of $A$ and $B$ has $|A| + l_d + l_1$ leaves where $l_d$ is the sum of the lengths of all parts of $B$ different from $A$ and $l_1$ is the sum of the lengths of some common parts of $A$ and $B$. We did not compromise the pattern search to reduce the space. Our suffix tree can be searched for a pattern $P$ in $O(|P|+occ)$ time where $occ$ is the number of occurrences of $P$ in $A$ and $B$. We also present an efficient algorithm to construct the suffix tree of alignment. When the suffix tree is constructed from scratch, the algorithm requires $O(|A| + l_d + l_1 + l_2)$ time where $l_2$ is the sum of the lengths of other common substrings of $A$ and $B$. When the suffix tree of $A$ is already given, it requires $O(l_d + l_1 + l_2)$ time.Comment: 12 page

Effect of previous water conditions on vine response to rewatering

A comparative study of stomatal responses to rewatering was conducted on grapevines previously subjected to conditions of water stress and no water stress. Two cultivars were grown in 35 L lysimeters: 'Airén', from the dry zone of La Mancha, and 'Chardonnay', from the humid zone of Burgundy. The day after rewatering no significant differences in soil water content were found between water treatments or cultivars. However, predawn leaf water potential was significantly higher under non-stress than under stressed conditions, differences between cultivars were also found. Water consumption during the 5 d after rewatering was directly related to vine leaf area development. Vines grown under water stress conditions showed more uniform stomatal behaviour after rewatering. One day after rewatering rates of leaf conductance, transpiration and net photosynthesis were significantly higher in non-stressed vines, while 3 d after rewatering leaf conductance and transpiration were significantly higher in vines previously subjected to water stress. Net photosynthesis was significantly higher in water-stressed vines 5 d after rewatering. No differences were found between cultivars with regard to leaf conductance. The differences in the relationship between net photosynthesis and leaf conductance between stressed and non-stressed vines before rewatering were not found after rewatering. The only permanent adaptation mechanism to water stress was a lowering of leaf area development, which allowed water-stressed vines to consume less water to maintain a higher water availability and high or constant stomatal conductance.

Fast Two-Robot Disk Evacuation with Wireless Communication

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.Comment: 18 pages, 10 figure

Where Are My Intelligent Assistant's Mistakes? A Systematic Testing Approach

Intelligent assistants are handling increasingly critical tasks, but until now, end users have had no way to systematically assess where their assistants make mistakes. For some intelligent assistants, this is a serious problem: if the assistant is doing work that is important, such as assisting with qualitative research or monitoring an elderly parent’s safety, the user may pay a high cost for unnoticed mistakes. This paper addresses the problem with WYSIWYT/ML (What You See Is What You Test for Machine Learning), a human/computer partnership that enables end users to systematically test intelligent assistants. Our empirical evaluation shows that WYSIWYT/ML helped end users find assistants’ mistakes significantly more effectively than ad hoc testing. Not only did it allow users to assess an assistant’s work on an average of 117 predictions in only 10 minutes, it also scaled to a much larger data set, assessing an assistant’s work on 623 out of 1,448 predictions using only the users’ original 10 minutes’ testing effort

Expected length of the longest common subsequence for large alphabets

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that the expected value of L, when normalized by n, converges to a constant C_k. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that C_k\sqrt{k} goes to 2 as k goes to infinity.Comment: 14 pages, 1 figure, LaTe

Post-fire Regeneration Traits of Understorey Shrub Species Modulate Successional Responses to High Severity Fire in Mediterranean Pine Forests

Recurrent fires can impede the spontaneous recruitment capacity of pine forests. Empirical studies have suggested that this can lead to a prolonged replacement of pine forest by shrubland, especially if shrub species are pyrophytic. Model-based studies, however, have suggested that post-fire succession of pine forest under current climatic conditions will eventually tend towards the dominance of oaks under high fire severity and recurrence. These previous modelling studies did not address the role of the various post-fire regeneration traits of the understory shrub species. Considering the dichotomy of obligate seeder vs. resprouter species, either obligate or facultative resprouter, we hypothesized that when the shrubs present are post-fire seeders, the oaks steadily occupy the forest, whereas resprouter shrub species might compete with oaks and delay or arrest post-fire succession. To test this hypothesis, we developed a dynamic, cellular automaton model for simulating post-fire successional transitions in pine forests, including shrubs, pines and oaks, and stochastic fires of regular frequency. Our results showed a strong tendency towards oak dominance as final model state and a very reduced role of fire recurrence in this final state, with low yearly acorn input delaying oak dominance. Most relevantly, and in line with our hypothesis, the trend towards oak dominance depended markedly on the two types of shrub species, being delayed by resprouter species, which extended the shrub-dominated succession stage for several centuries. Our simulation results supported the view that the type of understorey species should be a key consideration in post-fire restoration strategies aiming to enhance fire resilience.This research has received funding from the European Union Seventh Framework Programme (FP7/2007-2013) under the grant agreement no. 283068 (CASCADE project). Thanks are due to FCT/MCTES for the financial support to CESAM (UIDP/50017/2020+UIDB/50017/2020), through national funds and the post-doctoral research contract of Jacob Keizer (FCT-IF/01465/2015), and to the Spanish Ministry of Science and Innovation for financial support (CGL2017-89804-R) of the work of Susana Bautista. The work of Paula Maia was partially supported by the project SuSPiRe (PTDC/ASP-SIL/30983/2017) funded by FCT, through COMPETE2020—Programa Operacional Competitividade e Internacionalização (POCI)

Increased aridity drives post‐fire recovery of Mediterranean forests towards open shrublands

Recent observations suggest that repeated fires could drive Mediterranean forests to shrublands, hosting flammable vegetation that regrows quickly after fire. This feedback supposedly favours shrubland persistence and may be strengthened in the future by predicted increased aridity. An assessment was made of how fires and aridity in combination modulated the dynamics of Mediterranean ecosystems and whether the feedback could be strong enough to maintain shrubland as an alternative stable state to forest. A model was developed for vegetation dynamics, including stochastic fires and different plant fire‐responses. Parameters were calibrated using observational data from a period up to 100 yr ago, from 77 sites with and without fires in Southeast Spain and Southern France. The forest state was resilient to the separate impact of fires and increased aridity. However, water stress could convert forests into open shrublands by hampering post‐fire recovery, with a possible tipping point at intermediate aridity. Projected increases in aridity may reduce the resilience of Mediterranean forests against fires and drive post‐fire ecosystem dynamics toward open shrubland. The main effect of increased aridity is the limitation of post‐fire recovery. Including plant fire‐responses is thus fundamental when modelling the fate of Mediterranean‐type vegetation under climate‐change scenarios