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In the highly competitive area of telecommunications, cost, quality, and network management are among the most important aspects to be considered when designing a network. We study the problem of dimensioning a telecommunication network that is still operating in case of a failure of a network component. Given a demand between each pair of nodes of a telecommunication network and a finite set of possible capacities for each edge of the network, we consider the problem of deciding what capacity to install on each edge of the network in order to minimize the building cost of the network and to satisfy the demand between each pair of nodes, even if a network component fails. The routing of the demands must satisfy the following additional restrictions: (a) there is a maximum number of nodes allowed in each path between any pair of nodes (path length restriction), and (b) there is a maximum percentage of the demand between each pair of nodes that can be routed through any network component (diversification restriction). Moreover, the chosen capacities must be such that, for every single node or single edge failure, a certain percentage of the demand between any pair of nodes is reroutable (i.e. it ``survives'' the particular failure). We formulate the problem as a mixed integer linear programming problem and present a cutting plane algorithm as well as several heuristics for its solution. Furthermore, we discuss several ways to implement survivability into a telecommunication network.
Background
We assessed the novel MACC1 gene to further stratify stage II colon cancer patients with proficient mismatch repair (pMMR).
Patients and methods
Four cohorts with 596 patients were analyzed: Charité 1 discovery cohort was assayed for MACC1 mRNA expression and MMR in cryo-preserved tumors. Charité 2 comparison cohort was used to translate MACC1 qRT-PCR analyses to FFPE samples. In the BIOGRID 1 training cohort MACC1 mRNA levels were related to MACC1 protein levels from immunohistochemistry in FFPE sections; also analyzed for MMR. Chemotherapy-naïve pMMR patients were stratified by MACC1 mRNA and protein expression to establish risk groups based on recurrence-free survival (RFS). Risk stratification from BIOGRID 1 was confirmed in the BIOGRID 2 validation cohort. Pooled BIOGRID datasets produced a best effect-size estimate.
Results
In BIOGRID 1, using qRT-PCR and immunohistochemistry for MACC1 detection, pMMR/MACC1-low patients had a lower recurrence probability versus pMMR/MACC1-high patients (5-year RFS of 92% and 67% versus 100% and 68%, respectively). In BIOGRID 2, longer RFS was confirmed for pMMR/MACC1-low versus pMMR/MACC1-high patients (5-year RFS of 100% versus 90%, respectively). In the pooled dataset, 6.5% of patients were pMMR/MACC1-low with no disease recurrence, resulting in a 17% higher 5-year RFS (95% CI (12.6-21.3%)) versus pMMR/MACC1-high patients (P=0.037). Outcomes were similar for pMMR/MACC1-low and deficient MMR (dMMR) patients (5-year RFS of 100% and 96%, respectively).
Conclusions
MACC1 expression stratifies colon cancer patients with unfavorable pMMR status. Stage II colon cancer patients with pMMR/MACC1-low tumors have a similar favorable prognosis to those with dMMR with potential implications for the role of adjuvant therapy.
Background
We assessed the novel MACC1 gene to further stratify stage II colon cancer
patients with proficient mismatch repair (pMMR).
Patients and methods
Four cohorts with 596 patients were analyzed: Charité 1 discovery cohort
was assayed for MACC1 mRNA expression and MMR in cryo-preserved
tumors. Charité 2 comparison cohort was used to translate MACC1 qRT-
PCR analyses to FFPE samples. In the BIOGRID 1 training cohort MACC1
mRNA levels were related to MACC1 protein levels from
immunohistochemistry in FFPE sections; also analyzed for MMR.
Chemotherapy-naïve pMMR patients were stratified by MACC1 mRNA and
protein expression to establish risk groups based on recurrence-free
survival (RFS). Risk stratification from BIOGRID 1 was confirmed in the
BIOGRID 2 validation cohort. Pooled BIOGRID datasets produced a best
effect-size estimate.
Results
In BIOGRID 1, using qRT-PCR and immunohistochemistry for MACC1
detection, pMMR/MACC1-low patients had a lower recurrence probability
versus pMMR/MACC1-high patients (5-year RFS of 92% and 67% versus
100% and 68%, respectively). In BIOGRID 2, longer RFS was confirmed
for pMMR/MACC1-low versus pMMR/MACC1-high patients (5-year RFS of
100% versus 90%, respectively). In the pooled dataset, 6.5% of patients
were pMMR/MACC1-low with no disease recurrence, resulting in a 17%
higher 5-year RFS (95% CI (12.6-21.3%)) versus pMMR/MACC1-high
patients (P=0.037). Outcomes were similar for pMMR/MACC1-low and
deficient MMR (dMMR) patients (5-year RFS of 100% and 96%,
respectively).
Conclusions
MACC1 expression stratifies colon cancer patients with unfavorable pMMR
status. Stage II colon cancer patients with pMMR/MACC1-low tumors have
a similar favorable prognosis to those with dMMR with potential
implications for the role of adjuvant therapy.