Unavoidable Sets of Partial Words

The notion of an unavoidable set of words appears frequently in the fields of mathematics and theoretical computer science, in particular with its connection to the study of combinatorics on words. The theory of unavoidable sets has seen extensive study over the past twenty years. In this paper we extend the definition of unavoidable sets of words to unavoidable sets of partial words. Partial words, or finite sequences that may contain a number of ?do not know? symbols or ?holes,? appear naturally in several areas of current interest such as molecular biology, data communication, and DNA computing. We demonstrate the utility of the notion of unavoidability of sets of partial words by making use of it to identify several new classes of unavoidable sets of full words. Along the way we begin work on classifying the unavoidable sets of partial words of small cardinality. We pose a conjecture, and show that affirmative proof of this conjecture gives a sufficient condition for classifying all the unavoidable sets of partial words of size two. We give a result which makes the conjecture easy to verify for a significant number of cases. We characterize many forms of unavoidable sets of partial words of size three over a binary alphabet, and completely characterize such sets over a ternary alphabet. Finally, we extend our results to unavoidable sets of partial words of size k over a k-letter alphabet

Number of Holes in Unavoidable Sets of Partial Words I

Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. We consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem of fully characterizing all unavoidable sets of partial words of size three

Testing avoidability on sets of partial words is hard

We prove that the problem of deciding whether a finite set of partial words is unavoidable is NP-hard for any alphabet of size larger than or equal to two, which is in contrast with the well-known feasability results for unavoidability of a set of full words. We raise some related questions on avoidability of sets of partial words

Computing the Partial Word Avoidability Indices of Ternary Patterns

We study pattern avoidance in the context of partial words. The problem of classifying the avoidable binary patterns has been solved, so we move on to ternary and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patterns' avoidability indices or at least give bounds for them

Outpatient Emergency Department Utilization: Measurement and Prediction: A Dissertation

Approximately half of all emergency department (ED) visits are primary-care sensitive (PCS) – meaning that they could potentially be avoided with timely, effective primary care. Reducing undesirable types of healthcare utilization (including PCS ED use) requires the ability to define, measure, and predict such use in a population. In this retrospective, observational study, we quantified ED use in 2 privately insured populations and developed ED risk prediction models. One dataset, obtained from a Massachusetts managed-care network (MCN), included data from 2009-11. The second was the MarketScan database, with data from 2007-08. The MCN study included 64,623 individuals enrolled for at least 1 base-year month and 1 prediction-year month in Massachusetts whose primary care provider (PCP) participated in the MCN. The MarketScan study included 15,136,261 individuals enrolled for at least 1 base-year month and 1 prediction-year month in the 50 US states plus DC, Puerto Rico, and the US Virgin Islands. We used medical claims to identify principal diagnosis codes for ED visits, and scored each according to the New York University Emergency Department algorithm. We defined primary-care sensitive (PCS) ED visits as those in 3 subcategories: nonemergent, emergent but primary-care treatable, and emergent but preventable/avoidable. We then: 1) defined and described the distributions of 3 ED outcomes: any ED use; number of ED visits; and a new outcome, based on the NYU algorithm, that we call PCS ED use; 2) built and validated predictive models for these outcomes using administrative claims data; 3) compared the performance of models predicting any ED use, number of ED visits, and PCS ED use; 4) enhanced these models by adding enrollee characteristics from electronic medical records, neighborhood characteristics, and payor/provider characteristics, and explored differences in performance between the original and enhanced models. In the MarketScan sample, 10.6% of enrollees had at least 1 ED visit, with about half of utilization scored as PCS. For the top risk group (those in the 99.5th percentile), the model’s sensitivity was 3.1%, specificity was 99.7%, and positive predictive value (PPV) was 49.7%. The model predicting PCS visits yielded sensitivity of 3.8%, specificity of 99.7%, and PPV of 40.5% for the top risk group. In the MCN sample, 14.6% (±0.1%) had at least 1 ED visit during the prediction period, with an overall rate of 18.8 (±0.2) visits per 100 persons and 7.6 (±0.1) PCS ED visits per 100 persons. Measuring PCS ED use with a threshold-based approach resulted in many fewer visits counted as PCS, discarding information unnecessarily. Out of 45 practices, 5 to 11 (11-24%) had observed values that were statistically significantly different from their expected values. Models predicting ED utilization using age, sex, race, morbidity, and prior use only (claims-based models) had lower R2 (ranging from 2.9% to 3.7%) and poorer predictive ability than the enhanced models that also included payor, PCP type and quality, problem list conditions, and covariates from the EMR, Census tract, and MCN provider data (enhanced model R2 ranged from 4.17% to 5.14%). In adjusted analyses, age, claims-based morbidity score, any ED visit in the base year, asthma, congestive heart failure, depression, tobacco use, and neighborhood poverty were strongly associated with increased risk for all 3 measures (all P\u3c.001)

Fusion Based Safety Application for Pedestrian Detection with Danger Estimation

Proceedings of: 14th International Conference on Information Fusion (FUSION 2011). Chicago, Illinois, USA 5-8 July 2011.Road safety applications require the most reliable data. In recent years data fusion is becoming one of the main technologies for Advance Driver Assistant Systems (ADAS) to overcome the limitations of isolated use of the available sensors and to fulfil demanding safety requirements. In this paper a real application of data fusion for road safety for pedestrian detection is presented. Two sets of automobile-emplaced sensors are used to detect pedestrians in urban environments, a laser scanner and a stereovision system. Both systems are mounted in the automobile research platform IVVI 2.0 to test the algorithms in real situations. The different safety issues necessary to develop this fusion application are described. Context information such as velocity and GPS information is also used to provide danger estimation for the detected pedestrians.This work was supported by the Spanish Government through the Cicyt projects FEDORA (GRANT TRA2010- 20225-C03-01 ) , VIDAS-Driver (GRANT TRA2010-21371-C03-02 ).Publicad

Antitrust Analysis for the Internet Upstream Market: A BGP Approach

In this paper we study concentration in the European Internet upstream access market. The possibility of measuring market concentration depends on a correct definition of the market itself; however, this is not always possible, since, as it is the case of the Internet industry, very often Antitrust authorities lack reliable pricing and traffic data. This difficulty motivates our paper. We present an alternative approach based on the inference of the Internet Operators interconnection policies using micro-data sourced from their Border Gateway Protocol tables. We assess market concentration following a two step process: firstly we propose a price-independent algorithm for defining both the vertical and geographical relevant market boundaries, then we calculate market concentration indexes using two novel metrics. These assess, for each undertaking, both itsrole in terms of essential network facility and of wholesale market dominance. The results, applied to four leading Internet Exchange Points in London, Amsterdam, Frankfurt and Milan, show that some vertical segments of these markets are highly concentrated, while others are extremely competitive. According to the Merger Guidelines some of the estimated market concentration values would immediately fall within the special attention category.Technology and Industry, Other Topics

Healthy minds in healthy bodies: An international comparison of education-related inequality in physical health among older adults

Education is arguably the most important correlate of health We study education-related inequality in the physical of older adults across 11 European countries and the US. Combining data from HRS 2002, ELSA 2002 and SHARE 2004, our results suggest that education is strongly correlated with health both across and within countries. Education-related inequality in health is larger in Mediterranean and Anglo-Saxon countries than in western European countries. We find no evidence of a trade-off between health levels and equity in health. Education-related inequality in health hardly driven by income or wealth effects (except in the US), and differences in health behaviors (smoking) by education level contribute surprisingly little health differences across education groups