A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

Individual Classification of Mild Cognitive Impairment Subtypes by Support Vector Machine Analysis of White Matter DTI.

BACKGROUND AND PURPOSE: MCI was recently subdivided into sd-aMCI, sd-fMCI, and md-aMCI. The current investigation aimed to discriminate between MCI subtypes by using DTI. MATERIALS AND METHODS: Sixty-six prospective participants were included: 18 with sd-aMCI, 13 with sd-fMCI, and 35 with md-aMCI. Statistics included group comparisons using TBSS and individual classification using SVMs. RESULTS: The group-level analysis revealed a decrease in FA in md-aMCI versus sd-aMCI in an extensive bilateral, right-dominant network, and a more pronounced reduction of FA in md-aMCI compared with sd-fMCI in right inferior fronto-occipital fasciculus and inferior longitudinal fasciculus. The comparison between sd-fMCI and sd-aMCI, as well as the analysis of the other diffusion parameters, yielded no significant group differences. The individual-level SVM analysis provided discrimination between the MCI subtypes with accuracies around 97%. The major limitation is the relatively small number of cases of MCI. CONCLUSIONS: Our data show that, at the group level, the md-aMCI subgroup has the most pronounced damage in white matter integrity. Individually, SVM analysis of white matter FA provided highly accurate classification of MCI subtypes.

Beyond Smith's rule: An optimal dynamic index, rule for single machine stochastic scheduling with convex holding costs

Most research on single machine scheduling has assumedthe linearity of job holding costs, which is arguablynot appropriate in some applications. This motivates ourstudy of a model for scheduling $n$ classes of stochasticjobs on a single machine, with the objective of minimizingthe total expected holding cost (discounted or undiscounted). We allow general holding cost rates that are separable,nondecreasing and convex on the number of jobs in eachclass. We formulate the problem as a linear program overa certain greedoid polytope, and establish that it issolved optimally by a dynamic (priority) index rule,whichextends the classical Smith's rule (1956) for the linearcase. Unlike Smith's indices, defined for each class, ournew indices are defined for each extended class, consistingof a class and a number of jobs in that class, and yieldan optimal dynamic index rule: work at each time on a jobwhose current extended class has larger index. We furthershow that the indices possess a decomposition property,as they are computed separately for each class, andinterpret them in economic terms as marginal expected cost rate reductions per unit of expected processing time.We establish the results by deploying a methodology recentlyintroduced by us [J. Niño-Mora (1999). "Restless bandits,partial conservation laws, and indexability. "Forthcomingin Advances in Applied Probability Vol. 33 No. 1, 2001],based on the satisfaction by performance measures of partialconservation laws (PCL) (which extend the generalizedconservation laws of Bertsimas and Niño-Mora (1996)):PCL provide a polyhedral framework for establishing theoptimality of index policies with special structure inscheduling problems under admissible objectives, which weapply to the model of concern.

Intravitreal ranibizumab for age-related macular degeneration : optical coherence tomography guided retreatment intervals and their intra- and inter-individual variability

Purpose: To determine whether the need for retreatment after an initial phase of 3 monthly intravitreal injections of ranibizumab shows an intra-individual regular rhythm and to what degree it varies between different patients. Methods: Prospective study with 42 patients with exudative AMD, treatment naïve. Loading dose of 3 monthly doses of ranibizumab (0,5 mg), followed by a 12 months pro re nata (PRN) regimen according to early exudative signs on HD-OCT Cirrus, Zeiss. The follow-up visits were intensified (week 4, 5, 6, 7, 8, 10, 12, 14, 16, 20, etc after each injection) in order to detect recurrences early, and injection followed within 3 days in cases of subretinal fluid, cysts, or central thickness increase of>50microns. Intervals were calculated between injections for the 12 month follow-up with PRN treatment. Variability was expressed as standard deviation (SD). Results: Visual acuity (VA) improved from a mean ETDRS score of 61.6 (SD 10.8) at baseline to 68.0 (SD 10.2) at month 3 and to 74.7(SD 9.0) at month 12. The 15 patients who have already completed the study showed maintenance of the VA improvement. Central foveal thickness improved from a mean value of 366 microns (baseline) to 253 microns (month 3), well maintained thereafter. Mean number of injections was 8.8 (SD 3.5,range 0-12) per 12 months of follow-up (after 3 doses), with mean individual treatment-recurrence (TR) intervals ranging from 28->365 days (mean 58). Intraindividual variability of TR intervals (SD) was 7.1 days as a mean value (range 1.7¡V22.6). It ranged within 20% of the mean intra-individual interval for 30 (91%) and within 15% for 21 patients (64%). The first interval was within 1 week of the mean intra-individual interval in 64% and within 2 weeks in 89% of patients. Conclusions: The majority of AMD patients showed a relatively stable rhythm for PRN injections of ranibizumab after initial loading phase, associated with excellent functional/anatomical results. The initial interval last loading dose-first recurrence may have a predictive value for further need of treatment, potentially facilitating follow-up and patient care.

Pseudomonas fluorescens CHA0 produces enantio-pyochelin, the optical antipode of the Pseudomonas aeruginosa siderophore pyochelin.

The siderophore pyochelin is made by a thiotemplate mechanism from salicylate and two molecules of cysteine. In Pseudomonas aeruginosa, the first cysteine residue is converted to its D-isoform during thiazoline ring formation whereas the second cysteine remains in its L-configuration, thus determining the stereochemistry of the two interconvertible pyochelin diastereoisomers as 4'R, 2''R, 4''R (pyochelin I) and 4'R, 2''S, 4''R (pyochelin II). Pseudomonas fluorescens CHA0 was found to make a different stereoisomeric mixture, which promoted growth under iron limitation in strain CHA0 and induced the expression of its biosynthetic genes, but was not recognized as a siderophore and signaling molecule by P. aeruginosa. Reciprocally, pyochelin promoted growth and induced pyochelin gene expression in P. aeruginosa, but was not functional in P. fluorescens. The structure of the CHA0 siderophore was determined by mass spectrometry, thin-layer chromatography, NMR, polarimetry, and chiral HPLC as enantio-pyochelin, the optical antipode of the P. aeruginosa siderophore pyochelin. Enantio-pyochelin was chemically synthesized and confirmed to be active in CHA0. Its potential biosynthetic pathway in CHA0 is discussed.

The extraordinarily bright optical afterglow of GRB 991208 and its host galaxy

Observations of the extraordinarily bright optical afterglow (OA) of GRB 991208 started 2.1 d after the event. The flux decay constant of the OA in the R-band is -2.30 +/- 0.07 up to 5 d, which is very likely due to the jet effect, and after that it is followed by a much steeper decay with constant -3.2 +/- 0.2, the fastest one ever seen in a GRB OA. A negative detection in several all-sky films taken simultaneously to the event implies either a previous additional break prior to 2 d after the occurrence of the GRB (as expected from the jet effect). The existence of a second break might indicate a steepening in the electron spectrum or the superposition of two events. Once the afterglow emission vanished, contribution of a bright underlying SN is found, but the light curve is not sufficiently well sampled to rule out a dust echo explanation. Our determination of z = 0.706 indicates that GRB 991208 is at 3.7 Gpc, implying an isotropic energy release of 1.15 x 10E53 erg which may be relaxed by beaming by a factor > 100. Precise astrometry indicates that the GRB coincides within 0.2' with the host galaxy, thus given support to a massive star origin. The absolute magnitude is M_B = -18.2, well below the knee of the galaxy luminosity function and we derive a star-forming rate of 11.5 +/- 7.1 Mo/yr. The quasi-simultaneous broad-band photometric spectral energy distribution of the afterglow is determined 3.5 day after the burst (Dec 12.0) implying a cooling frequency below the optical band, i.e. supporting a jet model with p = -2.30 as the index of the power-law electron distribution.