We assume that all combinatorial objects that we refer to (graphs, boolean formulas, families of sets) are represented as binary strings. For a binary string x, we denote its length as |x|. We represent a decision problem as a language, that is, as the set of all inputs for which the answer is YES. We define P as the class of languages that can be decided in polynomial time. We define NP as the...

We begin by recalling the flow time minimization problem on unrelated machines from last lecture: Given a set of machines and a set of jobs, define: rj ∈ Z, to be the release time of job j, pi,j ∈ Z, is the run time of job j on machine i, Cj is the time at which job j is completed and the flow time of j is Fj = Cj − rj . Our goal is to find a schedule S, s.t. ∑ j∈J Fj is minimized. In the onlin...

PKS\,1351$-$018 at a redshift of $z=3.71$ is one the most luminous, steady synchrotron sources with luminosity $> 10^{47}$\,erg~s$^{-1}$. The does not seem to vary by more than $\sim 25\%$ over 35 years. In order appreciate this remarkable behavior, if it were $z=0.5$, would have flux density 15 GHz in range $110 - 137$\,Jy 11 yrs. spite two strong $\gamma$-ray flares $\lesssim 10^{49}$\,erg~s$...

In order to develop a curriculum especially for educable mentally retarded students at the high school level, this federally funded 1-year research project aimed to establish unique parameters involved in vocational adjustment for these students and to develop a tentative curriculum with this information. A literature review was conducted, and a research team interviewed supervisors, vocational...

Polymorphism is a key feature of amyloid fibril structures but it remains challenging to explain these variations for a particular sample. Here, we report electron cryomicroscopy-based reconstructions from different fibril morphologies formed by a peptide fragment from an amyloidogenic immunoglobulin light chain. The observed fibril morphologies vary in the number and cross-sectional arrangemen...

This article has been retracted. Please see the Retraction Notice for more detail: https://doi.org/10.1186/s40550-018-0064-3.