Jeff Kinne

Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds

The area of derandomization attempts to provide efficient deterministic simulations of randomized algorithms in various algorithmic settings. Goldreich and Wigderson introduced a notion of “typically-correct” deterministic simulations, which are allowed to err on few inputs. In this paper, we further the study of typically-correct derandomization in two ways.First, we develop a generic approach for constructing typically-correct derandomizations based on seed-extending pseudorandom generators, which are pseudorandom generators that reveal their seed. We use our approach to obtain both conditional and unconditional typically-correct derandomization results in various algorithmic settings. We show that our technique strictly generalizes an earlier approach by Shaltiel based on randomness extractors and simplifies the proofs of some known results. We also demonstrate that our approach is applicable in algorithmic settings where earlier work did not apply. For example, we present a typically-correct polynomial-time simulation for every language in BPP based on a hardness assumption that is (seemingly) weaker than the ones used in earlier work.Second, we investigate whether typically-correct derandomization of BPP implies circuit lower bounds. Extending the work of Kabanets and Impagliazzo for the zero-error case, we establish a positive answer for error rates in the range considered by Goldreich and Wigderson. In doing so, we provide a simpler proof of the zero-error result. Our proof scales better than the original one and does not rely on the result by Impagliazzo, Kabanets, and Wigderson that NEXP having polynomialsize circuits implies that NEXP coincides with EXP.

On derandomization and average-case complexity of monotone functions

We investigate whether circuit lower bounds for monotone circuits can be used to derandomize randomized monotone circuits. We show that, in fact, any derandomization of randomized monotone computations would derandomize all randomized computations, whether monotone or not. We prove similar results in the settings of pseudorandom generators and average-case hard functions - that a pseudorandom generator secure against monotone circuits is also secure with somewhat weaker parameters against general circuits, and that an average-case hard function for monotone circuits is also hard with somewhat weaker parameters for general circuits.

On TC0 Lower Bounds for the Permanent

In this paper we consider the problem of proving lower bounds for the permanent. An ongoing line of research has shown super-polynomial lower bounds for slightly-non-uniform small-depth threshold and arithmetic circuits [1,2,3,4]. We prove a new parameterized lower bound that includes each of the previous results as sub-cases. Our main result implies that the permanent does not have Boolean threshold circuits of the following kinds. 1 Depth O(1), poly − log(n) bits of non-uniformity, and size s(n) such that for all constants c, s (c)(n) < 2 n . The size s must satisfy another technical condition that is true of functions normally dealt with (such as compositions of polynomials, logarithms, and exponentials). 2 Depth o(loglogn), poly − log(n) bits of non-uniformity, and size n O(1). 3 Depth O(1), n o(1) bits of non-uniformity, and size n O(1).

Identification of genome-wide non-canonical spliced regions and analysis of biological functions for spliced sequences using Read-Split-Fly

BackgroundIt is generally thought that most canonical or non-canonical splicing events involving U2- and U12 spliceosomes occur within nuclear pre-mRNAs. However, the question of whether at least some U12-type splicing occurs in the cytoplasm is still unclear. In recent years next-generation sequencing technologies have revolutionized the field. The “Read-Split-Walk” (RSW) and “Read-Split-Run” (RSR) methods were developed to identify genome-wide non-canonical spliced regions including special events occurring in cytoplasm. As the significant amount of genome/transcriptome data such as, Encyclopedia of DNA Elements (ENCODE) project, have been generated, we have advanced a newer more memory-efficient version of the algorithm, “Read-Split-Fly” (RSF), which can detect non-canonical spliced regions with higher sensitivity and improved speed. The RSF algorithm also outputs the spliced sequences for further downstream biological function analysis.ResultsWe used open access ENCODE project RNA-Seq data to search spliced intron sequences against the U12-type spliced intron sequence database to examine whether some events could occur as potential signatures of U12-type splicing. The check was performed by searching spliced sequences against 5’ss and 3’ss sequences from the well-known orthologous U12-type spliceosomal intron database U12DB. Preliminary results of searching 70 ENCODE samples indicated that the presence of 5’ss with U12-type signature is more frequent than U2-type and prevalent in non-canonical junctions reported by RSF. The selected spliced sequences have also been further studied using miRBase to elucidate their functionality. Preliminary results from 70 samples of ENCODE datasets show that several miRNAs are prevalent in studied ENCODE samples. Two of these are associated with many diseases as suggested in the literature. Specifically, hsa-miR-1273 and hsa-miR-548 are associated with many diseases and cancers.ConclusionsOur RSF pipeline is able to detect many possible junctions (especially those with a high RPKM) with very high overall accuracy and relative high accuracy for novel junctions. We have incorporated useful parameter features into the pipeline such as, handling variable-length read data, and searching spliced sequences for splicing signatures and miRNA events. We suggest RSF, a tool for identifying novel splicing events, is applicable to study a range of diseases across biological systems under different experimental conditions.

Disparities in second‐generation DNA metabarcoding results exposed with accessible and repeatable workflows

Different second‐generation sequencing technologies may have taxon‐specific biases when DNA metabarcoding prey in predator faeces. Our major objective was to examine differences in prey recovery from bat guano across two different sequencing workflows using the same faecal DNA extracts. We compared results between the Ion Torrent PGM and the Illumina MiSeq with similar library preparations and the same analysis pipeline. We focus on repeatability and provide an R Notebook in an effort towards transparency for future methodological improvements. Full documentation of each step enhances the accessibility of our analysis pipeline. We tagged DNA from insectivorous bat faecal samples, targeted the arthropod cytochrome c oxidase I minibarcode region and sequenced the product on both second‐generation sequencing platforms. We developed an analysis pipeline with a high operational taxonomic unit (OTU) clustering threshold (i.e., ≥98.5%) followed by copy number filtering to avoid merging rare but genetically similar prey into the same OTUs. With this workflow, we detected 297 unique prey taxa, of which 74% were identified at the species level. Of these, 104 (35%) prey OTUs were detected by both platforms, 176 (59%) OTUs were detected by the Illumina MiSeq system only, and 17 (6%) OTUs were detected using the Ion Torrent system only. Costs were similar between platforms but the Illumina MiSeq recovered six times more reads and four additional insect orders than did Ion Torrent. The considerations we outline are particularly important for long‐term ecological monitoring; a more standardized approach will facilitate comparisons between studies and allow faster recognition of changes within ecological communities.

Additional file 3: of Read-Split-Run: an improved bioinformatics pipeline for identification of genome-wide non-canonical spliced regions using RNA-Seq data

Statistics reported by RSR for 64 test cases for the Dtt sample. This file contains all supplementary results for 64 test cases for the Dtt sample. (XLSX 79 kb)