Longest Increasing Subsequence under Persistent Comparison Errors

We study the problem of computing a longest increasing subsequence in a sequence $S$ of $n$ distinct elements in the presence of persistent comparison errors. In this model, every comparison between two elements can return the wrong result with some fixed (small) probability $p$, and comparisons cannot be repeated. Computing the longest increasing subsequence exactly is impossible in this model, therefore, the objective is to identify a subsequence that (i) is indeed increasing and (ii) has a length that approximates the length of the longest increasing subsequence. We present asymptotically tight upper and lower bounds on both the approximation factor and the running time. In particular, we present an algorithm that computes an $O(\log n)$-approximation in time $O(n\log n)$, with high probability. This approximation relies on the fact that that we can approximately sort $n$ elements in $O(n\log n)$ time such that the maximum dislocation of an element is at most $O(\log n)$. For the lower bounds, we prove that (i) there is a set of sequences, such that on a sequence picked randomly from this set every algorithm must return an $\Omega(\log n)$-approximation with high probability, and (ii) any $O(\log n)$-approximation algorithm for longest increasing subsequence requires $\Omega(n \log n)$ comparisons, even in the absence of errors

Bayesian astrostatistics: a backward look to the future

This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by astronomers; and (3) multilevel (hierarchical) Bayesian modeling as a major future direction for research in Bayesian astrostatistics, exemplified in part by presentations at the first ISI invited session on astrostatistics, commemorated in this volume. It closes with an intentionally provocative recommendation for astronomical survey data reporting, motivated by the multilevel Bayesian perspective on modeling cosmic populations: that astronomers cease producing catalogs of estimated fluxes and other source properties from surveys. Instead, summaries of likelihood functions (or marginal likelihood functions) for source properties should be reported (not posterior probability density functions), including nontrivial summaries (not simply upper limits) for candidate objects that do not pass traditional detection thresholds.Comment: 27 pp, 4 figures. A lightly revised version of a chapter in "Astrostatistical Challenges for the New Astronomy" (Joseph M. Hilbe, ed., Springer, New York, forthcoming in 2012), the inaugural volume for the Springer Series in Astrostatistics. Version 2 has minor clarifications and an additional referenc

Inversions from Sorting with Distance-Based Errors

ISSN:0302-9743ISSN:1611-334

Longest Increasing Subsequence Under Persistent Comparison Errors

ISSN:0302-9743ISSN:1611-334

Radiofrequency ablation in pancreatic cancer

Introduction and aim. Radiofrequency ablation (RFA) is effective in the treatment of unresectable hepatic tumors and promising results have also been described in tumors of kidney, lung, brain, prostate, and breast. The radiofrequency destruction of solid pancreatic tumors sounds logical but also seems risky due to the friable pancreatic parenchyma, the fear of pancreatitis and the prejudiced myth of ‘the pancreas is not your friend’. Patients and methods. We present our initial experience and we describe our technique during intraoperative RFA in four patients with locally advanced and unresectable pancreatic adenocarcinoma (head of pancreas, three; body-tail, one; diameter, 3–12 cm). In all the patients, the RFA was followed by bypass palliative procedures (cholecystojejunostomy and Brown's anastomosis and/or gastrojejunostomy). A drainage tube was left close to the ablated area. Serum amylase and fluid amylase (drain) were measured for 5–7 days postoperatively. Sandostatin was also administered prophylactically for 3–5 days. Results. The postoperative period was uneventful in all the patients, without complications or evidence of pancreatitis. The post RFA CT scan showed remarkable changes in the density and the characteristics of the tumors in all the patients. All the patients are alive, at 12, 8, 5 and 3 months postoperatively, respectively. In one patient (with cancer of the body of the pancreas) who was receiving morphine because of intolerable pain, significant pain relief has been observed. Conclusions. From our initial results, RFA seems to be a feasible, potentially safe and promising option in patients with locally advanced and unresectable pancreatic cancer. Nevertheless, larger series of cases are needed to secure our encouraging results