In the online version of the well-known graph coloring problem, the vertices appear one after the other together with the edges to the already known vertices and have to be irrevocably colored immediately after their appearance. We consider this problem on bipartite, i. e., two-colorable graphs. We prove that at least 1.13746 · log 2 (n) − 0.49887 colors are necessary for any deterministic online algorithm to be able to color any given bipartite graph on n vertices, thus improving on the previously known lower bound of log 2 n +1 for sufficiently large n.Recently, the advice complexity was introduced as a method for a fine-grained analysis of the hardness of online problems. We apply this method to the online coloring problem and prove (almost) tight linear upper and lower bounds on the advice complexity of coloring a bipartite graph online optimally or using 3 colors. Moreover, we prove that O( √ n) advice bits are sufficient for coloring any bipartite graph on n vertices with at most log 2 n colors.

A large Italian multicenter observational retrospective study was conducted on the use of brentuximab vedotin (BV) for patients with relapsed Hodgkin’s lymphoma (HL) to check if clinical trial results are confirmed even in a real life context. 234 CD30+ HL patients were enrolled. Best response was observed after a median of 4 cycles in 140 patients (59.8%): 74 (31.6%) patients obtained a complete response (CR) and 66 (28.2%) achieved a partial response (PR); overall response rate at the end of the treatment was 48.3% (62 CR and 51 PR). The best response rate was higher in the elderly subset: 14 (50%) CR and 5 (17.8%) PR. Disease free survival was 26.3% at 3 years and progression free survival 31.9% at 4.5 years. Duration of response did not differ for who achieved at least PR and then either did or did not undergo consolidative transplant. Overall, the treatment was well tolerated and no death has been linked to BV-induced toxicity.Our report confirms activity in elderly patients, duration of response unrelated to the consolidation with transplant procedure, the relevance of the CR status at first restaging, and the role of BV as a bridge to transplant for chemorefractory patients.

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In an L(2, 1)-coloring of a graph, the vertices are colored with colors from an ordered set such that neighboring vertices get colors that have distance at least 2 and vertices at distance 2 in the graph get different colors. We consider the problem of finding an L(2, 1)-coloring using a minimum range of colors in an online setting where the vertices arrive in consecutive time steps together with information about their neighbors and vertices at distance 2 among the previously revealed vertices. For this, we restrict our attention to paths and cycles.Offline, paths can easily be colored within the range {0, . . . , 4} of colors. We prove that, considering deterministic algorithms in an online setting, the range {0, . . . , 6} is necessary and sufficient while a simple greedy strategy needs range {0, . . . , 7}.Advice complexity is a recently developed framework to measure the complexity of online problems. The idea is to measure how many bits of advice about the yet unknown parts of the input an online algorithm needs to compute a solution of a certain quality. We show a sharp threshold on the advice complexity of the online L(2, 1)-coloring problem on paths and cycles. While achieving color range {0, . . . , 6} does not need any advice, improving over this requires a number of advice bits that is linear in the size of the input. Thus, the L(2, 1)-coloring problem is the first known example of an online problem for which sublinear advice does not help.We further use our advice complexity results to prove that no randomized online algorithm can achieve a better expected competitive ratio than 5 4 (1 − δ), for any δ > 0.

The mammalian target of rapamycin (mTOR) is a central processor of intra- and extracellular signals, regulating many fundamental cellular processes such as metabolism, growth, proliferation, and survival. Strong evidences have indicated that mTOR dysregulation is deeply implicated in leukemogenesis. This has led to growing interest in the development of modulators of its activity for leukemia treatment. This review intends to provide an outline of the principal biological and molecular functions of mTOR. We summarize the current understanding of how mTOR interacts with microRNAs, with components of cell metabolism, and with controllers of apoptotic machinery. Lastly, from a clinical/translational perspective, we recapitulate the therapeutic results in leukemia, obtained by using mTOR inhibitors as single agents and in combination with other compounds.