Some Results on Superpatterns for Preferential Arrangements

A {\it superpattern} is a string of characters of length $n$ that contains as a subsequence, and in a sense that depends on the context, all the smaller strings of length $k$ in a certain class. We prove structural and probabilistic results on superpatterns for {\em preferential arrangements}, including (i) a theorem that demonstrates that a string is a superpattern for all preferential arrangements if and only if it is a superpattern for all permutations; and (ii) a result that is reminiscent of a still unresolved conjecture of Alon on the smallest permutation on $[n]$ that contains all $k$-permutations with high probability.Comment: 13 page

BL-WoLF: A Framework For Loss-Bounded Learnability In Zero-Sum Games

We present BL-WoLF, a framework for learnability in repeated zero-sum games where the cost of learning is measured by the losses the learning agent accrues (rather than the number of rounds). The game is adversarially chosen from some family that the learner knows. The opponent knows the game and the learner's learning strategy. The learner tries to either not accrue losses, or to quickly learn about the game so as to avoid future losses (this is consistent with the Win or Learn Fast (WoLF) principle; BL stands for ``bounded loss''). Our framework allows for both probabilistic and approximate learning. The resultant notion of {\em BL-WoLF}-learnability can be applied to any class of games, and allows us to measure the inherent disadvantage to a player that does not know which game in the class it is in. We present {\em guaranteed BL-WoLF-learnability} results for families of games with deterministic payoffs and families of games with stochastic payoffs. We demonstrate that these families are {\em guaranteed approximately BL-WoLF-learnable} with lower cost. We then demonstrate families of games (both stochastic and deterministic) that are not guaranteed BL-WoLF-learnable. We show that those families, nevertheless, are {\em BL-WoLF-learnable}. To prove these results, we use a key lemma which we derive

The Sedentary Survey of Extreme High Energy Peaked BL Lacs III. Results from Optical Spectroscopy

The multi-frequency Sedentary Survey is a flux limited, statistically well-defined sample of highly X-ray dominated BL Lacertae objects (HBLs) which includes 150 sources. In this paper, the third of the series, we report the results of a dedicated optical spectroscopy campaign that, together with results from other independent optical follow up programs, led to the spectroscopic identification of all sources in the sample. We carried out a systematic spectroscopic campaign for the observation of all unidentified objects of the sample using the ESO 3.6m, the KPNO 4m, and the TNG optical telescopes. We present new identifications and optical spectra for 76 sources, 50 of which are new BL Lac objects, 18 are sources previously referred as BL Lacs but for which no redshift information was available, and 8 are broad emission lines AGNs. We find that the multi-frequency selection technique used to build the survey is highly efficient (about 90%) in selecting BL Lacs objects. We present positional and spectroscopic information for all confirmed BL Lac objects. Our data allowed us to determined 36 redshifts out of the 50 new BL Lacs and 5 new redshifts for the previously known objects. The redshift distribution of the complete sample is presented and compared with that of other BL Lacs samples. For 26 sources without recognizable absorption features, we calculated lower limits to the redshift using a method based on simulated optical spectra with different ratios between jet and galaxy emission. For a subsample of 38 object with high-quality spectra, we find a correlation between the optical spectral slope, the 1.4 GHz radio luminosity, and the Ca H&K break value, indicating that for powerful/beamed sources the optical light is dominated by the non-thermal emission from the jet.Comment: 23 pages, accepted by A&

The changing clinical pattern of endemic Burkitt lymphoma in Western Africa: Experience from a tertiary center in Ghana

Abstract Background Burkitt lymphoma (BL) is the most common childhood cancer in Ghana, where the endemic variant is the predominant subtype and historically presents as a highly chemo-sensitive jaw tumor. This study aimed to update the current epidemiological characteristics of childhood BL in our institution. Procedure Patient data for all children diagnosed with BL and seen at Korle Bu Teaching Hospital between January 2007 and December 2012 were retrospectively analyzed. Results BL was diagnosed in 173 children