Efficient algorithms for finding disjoint paths in grids

The reconfiguration problem on VLSI/WSI processor arrays in the presence of faulty processors can be stated as the following integral multi-source routing problem: Given a set of N nodes (faulty processors or sources) in an m×n rectangular grid where m, n≤N, the problem to be solved is to connect the N nodes to distinct nodes at the grid boundary using a set of `disjoint' paths. This problem can be referred to as an escape problem which can be solved trivially in O(mnN) time. By exploiting all the properties of the network, planarity and regularity of a grid, integral flow, and unit capacity source/sink/flow, we can optimally compress the size of the grid from O(mn) to O(√mnN) and solve the problem in O(d√mnN), where d is the maximum number of disjoint paths found, for both the edge-disjoint and vertex-disjoint cases. In the worst case, d, m, n are O(N) and the result is O(N2.5). Note that this routing problem can also be solved with the same time complexity even if the disjoint paths have to be ended at another set of N nodes (sinks) in the grid instead of the grid boundary.published_or_final_versio

Escaping a grid by edge-disjoint paths

We study the edge-disjoint escape problem in grids: Given a set of n sources in a two-dimensional grid, the problem is to connect all sources to the grid boundary using a set of n edge-disjoint paths. Different from the conventional approach that reduces the problem to network flow problem, we solve the problem by ensuring that no rectangles in the grid contain more sources than outlets, a necessary and sufficient condition for the existence of a solution. Based on this condition, we give a greedy algorithm which finds the paths in O(n2) time, which is faster than the previous approaches. This problem has applications in point-to-point delivery, VLSI reconfiguration and package routing.published_or_final_versio

Optimal simulation of full binary trees on faulty hypercubes

The problem of operating full binary tree based algorithms on a hypercube with faulty nodes was investigated. Developing a method for embedding a full binary tree into the faulty hypercube is the solution to this problem. Two outcomes for embedding an (n-1)-tree into an n-cube with unit dilation and load, that were based on a new embedding technique, were presented. For the problem where the root can be mapped to any nonfaulty hypercube node, the optimum toleration of faults was shown. Moreover, it was demonstrated that the algorithm for the variable root embedding problem is maximal within a class algorithms called recursive embedding algorithms as far as the number of tolerable faults is concerned. Lastly, it was demonstrated that when an O(1/√n) fraction of nodes in the hypercube are faulty, a O(1)-load variable root embedding is not always possible regardless of the significance of the dilation.published_or_final_versio

Finding optimal threshold for correction error reads in DNA assembling

Background: DNA assembling is the problem of determining the nucleotide sequence of a genome from its substrings, called reads. In the experiments, there may be some errors on the reads which affect the performance of the DNA assembly algorithms. Existing algorithms, e.g. ECINDEL and SRCorr, correct the error reads by considering the number of times each length-k substring of the reads appear in the input. They treat those length-k substrings appear at least M times as correct substring and correct the error reads based on these substrings. However, since the threshold M is chosen without any solid theoretical analysis, these algorithms cannot guarantee their performances on error correction. Results: In this paper, we propose a method to calculate the probabilities of false positive and false negative when determining whether a length-k substring is correct using threshold M. Based on this optimal threshold M that minimizes the total errors (false positives and false negatives). Experimental results on both real data and simulated data showed that our calculation is correct and we can reduce the total error substrings by 77.6% and 65.1% when compared to ECINDEL and SRCorr respectively. Conclusion: We introduced a method to calculate the probability of false positives and false negatives of the length-k substring using different thresholds. Based on this calculation, we found the optimal threshold to minimize the total error of false positive plus false negative. © 2009 Chin et al; licensee BioMed Central Ltd.published_or_final_versio

Platelet Activating Factor Blocks Interkinetic Nuclear Migration in Retinal Progenitors through an Arrest of the Cell Cycle at the S/G2 Transition

Nuclear migration is regulated by the LIS1 protein, which is the regulatory subunit of platelet activating factor (PAF) acetyl-hydrolase, an enzyme complex that inactivates the lipid mediator PAF. Among other functions, PAF modulates cell proliferation, but its effects upon mechanisms of the cell cycle are unknown. Here we show that PAF inhibited interkinetic nuclear migration (IKNM) in retinal proliferating progenitors. The lipid did not, however, affect the velocity of nuclear migration in cells that escaped IKNM blockade. The effect depended on the PAF receptor, Erk and p38 pathways and Chk1. PAF induced no cell death, nor a reduction in nucleotide incorporation, which rules out an intra-S checkpoint. Notwithstanding, the expected increase in cyclin B1 content during G2-phase was prevented in the proliferating cells. We conclude that PAF blocks interkinetic nuclear migration in retinal progenitor cells through an unusual arrest of the cell cycle at the transition from S to G2 phases. These data suggest the operation, in the developing retina, of a checkpoint that monitors the transition from S to G2 phases of the cell cycle

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability

Global patient outcomes after elective surgery: prospective cohort study in 27 low-, middle- and high-income countries.

BACKGROUND: As global initiatives increase patient access to surgical treatments, there remains a need to understand the adverse effects of surgery and define appropriate levels of perioperative care. METHODS: We designed a prospective international 7-day cohort study of outcomes following elective adult inpatient surgery in 27 countries. The primary outcome was in-hospital complications. Secondary outcomes were death following a complication (failure to rescue) and death in hospital. Process measures were admission to critical care immediately after surgery or to treat a complication and duration of hospital stay. A single definition of critical care was used for all countries. RESULTS: A total of 474 hospitals in 19 high-, 7 middle- and 1 low-income country were included in the primary analysis. Data included 44 814 patients with a median hospital stay of 4 (range 2-7) days. A total of 7508 patients (16.8%) developed one or more postoperative complication and 207 died (0.5%). The overall mortality among patients who developed complications was 2.8%. Mortality following complications ranged from 2.4% for pulmonary embolism to 43.9% for cardiac arrest. A total of 4360 (9.7%) patients were admitted to a critical care unit as routine immediately after surgery, of whom 2198 (50.4%) developed a complication, with 105 (2.4%) deaths. A total of 1233 patients (16.4%) were admitted to a critical care unit to treat complications, with 119 (9.7%) deaths. Despite lower baseline risk, outcomes were similar in low- and middle-income compared with high-income countries. CONCLUSIONS: Poor patient outcomes are common after inpatient surgery. Global initiatives to increase access to surgical treatments should also address the need for safe perioperative care. STUDY REGISTRATION: ISRCTN5181700

Fast algorithm for computing longest common subsequences of small alphabet size

Given two strings of lengths m and n≥m on an alphabet of size s, the longest common subsequence (LCS) problem is to determine the longest subsequence that can be obtained by deleting zero or more symbols from either string. The first O(mn) algorithm was given by Hirschberg in 1975. The algorithm was later revised to O(ln), where l is the length of an LCS between the two strings. Another strategy given by Hunt and Szymanski takes O(rlogn) time, where r≤mn is the total number of matches between the two strings. Apostolico and Guerra combined the two approaches and derived an O(mlogn + dlog(mn/d)) algorithm, where d≤r is the number of dominant matches (minimal candidates) between the two strings. Efficient algorithms for two similar strings were devised by Nakatsu et al. [7] and Myers [6] with time complexities of O(n(m-l)) and O(n(n-l)), respectively. This paper presents a new algorithm for this problem, which requires preprocessing that is nearly standard for the LCS problem and has time and space complexity of O(ns + min {ds, lm}) and O(ns + d), respectively. This algorithm is particularly efficient when s (the alphabet size) is small. Different data structures are used to obtain variations of the basic algorithm that require different time and space complexities.link_to_subscribed_fulltex

General schedulers for the pinwheel problem based on double-integer reduction

The pinwheel is a hard-real-time scheduling problem for scheduling satellite ground stations to service a number of satellites without data loss. Given a multiset of positive integers (instance) A = {a1, ... an}, the problem is to find an infinite sequence (schedule) of symbols from {1,2, ... n} such that there is at least one symbol i within any interval of ai symbols (slots). Not all instances A can be scheduled; for example, no 'successful' schedule exists for instances whose density is larger than 1. It has been shown that any instance whose density is less than 2/3 can always be scheduled. Two new schedulers are proposed which improve this 2/3 result to a new 0.7 density threshold. These two schedulers can be viewed as a generalization of the previously known schedulers, i.e., they can handle a larger class of pinwheel instances including all instances schedulable by the previously known techniques.link_to_subscribed_fulltex