Approximation algorithms for stochastic and risk-averse optimization

We present improved approximation algorithms in stochastic optimization. We prove that the multi-stage stochastic versions of covering integer programs (such as set cover and vertex cover) admit essentially the same approximation algorithms as their standard (non-stochastic) counterparts; this improves upon work of Swamy \& Shmoys which shows an approximability that depends multiplicatively on the number of stages. We also present approximation algorithms for facility location and some of its variants in the $2$-stage recourse model, improving on previous approximation guarantees. We give a $2.2975$-approximation algorithm in the standard polynomial-scenario model and an algorithm with an expected per-scenario $2.4957$-approximation guarantee, which is applicable to the more general black-box distribution model.Comment: Extension of a SODA'07 paper. To appear in SIAM J. Discrete Mat

Additional file 2: of Cell type-specific analysis of transcriptome changes in the porcine endometrium on Day 12 of pregnancy

Table S2. Differentially expressed genes in luminal epithelium, glandular epithelium, stroma, and complete tissue. (XLSX 1826 kb

Additional file 1: of Cell type-specific analysis of transcriptome changes in the porcine endometrium on Day 12 of pregnancy

Table S1. Raw data statistic of RNA-seq (DOCX 15 kb

Additional file 3: of Cell type-specific analysis of transcriptome changes in the porcine endometrium on Day 12 of pregnancy

Table S3. Selected function found in luminal epithelium, glandular epithelium, stroma, and complete tissue. (XLSX 58 kb

Additional file 2 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Figure S2. Schema of the Galaxy pipeline: 1) to collapse FastQ file into the sequence and number of appearance ranked by the counts. 2) converts FASTA files into the Galaxy data file type “tabular” (tab-separated text files). 3) converts dashes in to tabs and 4) extracts selected columns of a given tabular file. 5) joins files by a selected identifier column. (PNG 4714 kb

Additional file 3: Table S2. of Expression of microRNAs and isomiRs in the porcine endometrium: implications for gene regulation at the maternal-conceptus interface

List of sequences annotated and not annotated to known porcine and mammalian miRNAs. In total, 873 sequences, showing 100 % homology to the reference sequence, were annotated to mature or stem-loop miRNAs represented in miRBase v. 18, Ensembl, EMBL or NCBI databases. (XLSX 781 kb

Additional file 14: Table S8. of Expression of microRNAs and isomiRs in the porcine endometrium: implications for gene regulation at the maternal-conceptus interface

miRNA/isomiR names, sequences and assays ID of molecules validated by stem-loop real-time RT-PCR in the porcine endometrium. (DOCX 18 kb

Additional file 10 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Table S4. EdgeR result of all comparisons on isomiR level. (XLSX 32902 kb

L'Auto-vélo : automobilisme, cyclisme, athlétisme, yachting, aérostation, escrime, hippisme / dir. Henri Desgranges

27 mars 19261926/03/27 (A27,N9233)

Additional file 7 of Small RNA-seq analysis of single porcine blastocysts revealed that maternal estradiol-17beta exposure does not affect miRNA isoform (isomiR) expression

Figure S4. Known and novel miRNAs and species annotation - unique sequences and read counts. In the outer ring the mapped unique sequences are shown related to mapped species. The inner cycle represents the corresponding read counts per species. (PNG 468 kb