Locally Decodable Codes for Edit Distance

Abstract. Locally decodable codes (LDC) [1,5] are error correcting codes that allow decoding (any) individual symbol of the message, by reading only few symbols of the codeword. Consider an application such as storage solutions for large data, where errors may occur in the disks (or some disks may just crush). In such an application, it is often de-sirable to recover only small portions of the data (have random access). Thus, in such applications, using LDC provides enormous efficiency gains over standard error correcting codes (ECCs), that need to read the en-tire encoded message to learn even a single bit of information. Typically, LDC’s, as well as standard ECC’s decode the encoded messaged if upto some bounded fraction of the symbols had been modified. This corre-sponds to decoding strings of bounded Hamming distance from a valid codeword. An often more realistic metric is the edit distance, measur-ing the shortest sequence of insertions and deletions (indel.) of symbols leading from one word to another. For example, (few) indel. modifica

Incremental prognostic value of coronary computed tomography angiography over coronary calcium scoring for major adverse cardiac events in elderly asymptomatic individuals

Aims Coronary computed tomography angiography (CCTA) and coronary artery calcium score (CACS) have prognostic value for coronary artery disease (CAD) events beyond traditional risk assessment. Age is a risk factor with very high weight and little is known regarding the incremental value of CCTA over CAC for predicting cardiac events in older adults. Methods and results Of 27 125 individuals undergoing CCTA, a total of 3145 asymptomatic adults were identified. This study sample was categorized according to tertiles of age (cut-off points: 52 and 62 years). CAD severity was classified as 0, 1-49, and ≥50% maximal stenosis in CCTA, and further categorized according to number of vessels ≥50% stenosis. The Framingham 10-year risk score (FRS) and CACS were employed as major covariates. Major adverse cardiovascular events (MACE) were defined as a composite of all-cause death or non-fatal MI. During a median follow-up of 26 months (interquartile range: 18-41 months), 59 (1.9%) MACE occurred. For patients in the top age tertile, CCTA improved discrimination beyond a model included FRS and CACS (C-statistic: 0.75 vs. 0.70, P-value = 0.015). Likewise, the addition of CCTA improved category-free net reclassification (cNRI) of MACE in patients within the highest age tertile (e.g. cNRI = 0.75; proportion of events/non-events reclassified were 50 and 25%, respectively; P-value <0.05, all). CCTA displayed no incremental benefit beyond FRS and CACS for prediction of MACE in the lower age tertiles. Conclusion CCTA provides added prognostic value beyond cardiac risk factors and CACS for the prediction of MACE in asymptomatic older adults

Effects of the high-density lipoprotein mimetic agent CER-001 on coronary atherosclerosis in patients with acute coronary syndromes: a randomized trial†

Aim High-density lipoproteins (HDLs) have several potentially protective vascular effects. Most clinical studies of therapies targeting HDL have failed to show benefits vs. placebo. Objective To investigate the effects of an HDL-mimetic agent on atherosclerosis by intravascular ultrasonography (IVUS) and quantitative coronary angiography (QCA). Design and setting A prospective, double-blinded, randomized trial was conducted at 51 centres in the USA, the Netherlands, Canada, and France. Intravascular ultrasonography and QCA were performed to assess coronary atherosclerosis at baseline and 3 (2-5) weeks after the last study infusion. Patients Five hundred and seven patients were randomized; 417 and 461 had paired IVUS and QCA measurements, respectively. Intervention Patients were randomized to receive 6 weekly infusions of placebo, 3 mg/kg, 6 mg/kg, or 12 mg/kg CER-001. Main outcome measures The primary efficacy parameter was the nominal change in the total atheroma volume. Nominal changes in per cent atheroma volume on IVUS and coronary scores on QCA were also pre-specified endpoints. Results The nominal change in the total atheroma volume (adjusted means) was −2.71, −3.13, −1.50, and −3.05 mm3 with placebo, CER-001 3 mg/kg, 6 mg/kg, and 12 mg/kg, respectively (primary analysis of 12 mg/kg vs. placebo: P = 0.81). There was also no difference among groups for the nominal change in per cent atheroma volume (0.02, −0.02, 0.01, and 0.19%; nominal P = 0.53 for 12 mg/kg vs. placebo). Change in the coronary artery score was −0.022, −0.036, −0.022, and −0.015 mm (nominal P = 0.25, 0.99, 0.55), and change in the cumulative coronary stenosis score was −0.51, 2.65, 0.71, and −0.77% (compared with placebo, nominal P = 0.85 for 12 mg/kg and nominal P = 0.01 for 3 mg/kg). The number of patients with major cardiovascular events was 10 (8.3%), 16 (13.3%), 17 (13.7%), and 12 (9.8%) in the four groups. Conclusion CER-001 infusions did not reduce coronary atherosclerosis on IVUS and QCA when compared with placebo. Whether CER-001 administered in other regimens or to other populations could favourably affect atherosclerosis must await further study. Name of the trial registry: Clinicaltrials.gov; Registry's URL: http://clinicaltrials.gov/ct2/show/NCT01201837?term=cer-001&rank=2; Trial registration number: NCT0120183

Incremental prognostic value of coronary computed tomography angiography over coronary calcium scoring for major adverse cardiac events in elderly asymptomatic individuals

Aims Coronary computed tomography angiography (CCTA) and coronary artery calcium score (CACS) have prognostic value for coronary artery disease (CAD) events beyond traditional risk assessment. Age is a risk factor with very high weight and little is known regarding the incremental value of CCTA over CAC for predicting cardiac events in older adults. Methods and results Of 27 125 individuals undergoing CCTA, a total of 3145 asymptomatic adults were identified. This study sample was categorized according to tertiles of age (cut-off points: 52 and 62 years). CAD severity was classified as 0, 1-49, and >= 50% maximal stenosis in CCTA, and further categorized according to number of vessels >= 50% stenosis. The Framingham 10-year risk score (FRS) and CACS were employed as major covariates. Major adverse cardiovascular events (MACE) were defined as a composite of all-cause death or non-fatal MI. During a median follow-up of 26 months (interquartile range: 18-41months), 59 (1.9%) MACE occurred. For patients in the top age tertile, CCTA improved discrimination beyond a model included FRS and CACS (C-statistic: 0.75 vs. 0.70, P-value = 0.015). Likewise, the addition of CCTA improved category-free net reclassification (cNRI) of MACE in patients within the highest age tertile (e.g. cNRI = 0.75; proportion of events/non-events reclassified were 50 and 25%, respectively; P-value <0.05, all). CCTA displayed no incremental benefit beyond FRS and CACS for prediction of MACE in the lower age tertiles. Conclusion CCTA provides added prognostic value beyond cardiac risk factors and CACS for the prediction of MACE in asymptomatic older adults

Optimal Coding for Streaming Authentication and Interactive Communication

We consider the task of communicating a data stream-a long, possibly infinite message not known in advance to the sender-over a channel with adversarial noise. For any given noise rate c 1/2