Methods for visualizing protein or nucleic acid motifs have traditionally relied upon residue frequencies to graphically scale character heights. We describe the pLogo, a motif visualization in which residue heights are scaled relative to their statistical significance. A pLogo generation tool is publicly available at http://plogo.uconn.edu/ and supports real-time conditional probability calculations and visualizations.
Network motifs are statistically overrepresented sub-structures (sub-graphs) in a network, and have been recognized as 'the simple building blocks of complex networks'. Study of biological network motifs may reveal answers to many important biological questions. The main difficulty in detecting larger network motifs in biological networks lies in the facts that the number of possible sub-graphs increases exponentially with the network or motif size (node counts, in general), and that no known polynomial-time algorithm exists in deciding if two graphs are topologically equivalent. This article discusses the biological significance of network motifs, the motivation behind solving the motif-finding problem, and strategies to solve the various aspects of this problem. A simple classification scheme is designed to analyze the strengths and weaknesses of several existing algorithms. Experimental results derived from a few comparative studies in the literature are discussed, with conclusions that lead to future research directions.
Blockchain data structures maintained via the longest-chain rule have emerged as a powerful algorithmic tool for consensus algorithms. e technique-popularized by the Bitcoin protocol-has proven to be remarkably flexible and now supports consensus algorithms in a wide variety of se ings. Despite such broad applicability and adoption, current analytic understanding of the technique is highly dependent on details of the protocol's leader election scheme. A particular challenge appears in the proof-of-stake se ing, where existing analyses suffer from quadratic dependence on suffix length.We describe an axiomatic theory of blockchain dynamics that permits rigorous reasoning about the longestchain rule in quite general circumstances and establish bounds-optimal to within a constant-on the probability of a consistency violation. is se les a critical open question in the proof-of-stake se ing where we achieve linear consistency for the first time.Operationally, blockchain consensus protocols achieve consistency by instructing parties to remove a suffix of a certain length from their local blockchain. While the analysis of Bitcoin guarantees consistency with error 2 −k by removing O(k) blocks, recent work on proof-of-stake (PoS) blockchains has suffered from quadratic dependence: (PoS) blockchain protocols, exemplified by Ouroboros (Crypto 2017), Ouroboros Praos (Eurocrypt 2018) and Sleepy Consensus (Asiacrypt 2017), can only establish that the length of this suffix should be Θ(k 2 ).is consistency guarantee is a fundamental design parameter for these systems, as the length of the suffix is a lower bound for the time required to wait for transactions to se le. Whether this gap is an intrinsic limitation of PoS-due to issues such as the "nothing-at-stake" problem-has been an urgent open question, as deployed PoS blockchains further rely on consistency for protocol correctness: in particular, security of the protocol itself relies on this parameter. Our general theory directly improves the required suffix length from Θ(k 2 ) to Θ(k). us we show, for the first time, how PoS protocols can match proof-of-work blockchain protocols for exponentially decreasing consistency error.Our analysis focuses on the articulation of a two-dimensional stochastic process that captures the features of interest, an exact recursive closed form for the critical functional of the process, and tail bounds established for associated generating functions that dominate the failure events. Finally, the analysis provides an explicit polynomial-time algorithm for exactly computing the exponentially-decaying error function which can directly inform practice.Direct consequences. Our results establish consistency bounds in a quite general se ing-see below: In particular, they directly imply exp(−Θ(k)) consistency for the Sleepy consensus (Snow White) [21], Ouroboros [13], Ouroboros Praos [6], and Ouroboros Genesis [2] blockchain protocols. ( e Ouroboros Praos and Ouroboros Genesis analyses in fact directly relied on an earlier e-print version of the present...
We improve the fundamental security threshold of Proof-of-Stake (PoS) blockchain protocols, reflecting for the first time the positive effect of rounds with multiple honest leaders. Current analyses of the longest-chain rule in PoS blockchain protocols reduce consistency to the dynamics of an abstract, round-based block creation process that is determined by three probabilities:• pA, the probability that a round has at least one adversarial leader;• ph, the probability that a round has a single honest leader; and• pH, the probability that a round has multiple, but honest, leaders.We present a consistency analysis that achieves the optimal threshold ph + pH > pA. is is a first in the literature and can be applied to both the simple synchronous se ing and the se ing with bounded delays. Moreover, we achieve the optimal consistency error e −Θ (k) where k is the confirmation time.e consistency analyses in Ouroboros Praos (Eurocrypt 2018) and Genesis (CCS 2018) assume that the probability of a uniquely honest round exceeds that of the other two events combined (i.e., ph − pH > pA); the analyses in Sleepy Consensus (Asiacrypt 2017) and Snow White (Fin. Crypto 2019) assume that a uniquely honest round is more likely than an adversarial round (i.e., ph > pA). us existing analyses either incur a penalty for multiply honest rounds, or treat them neutrally. In addition, previous analyses completely break down when uniquely honest rounds become less frequent, i.e., ph < pA. Our new results can be directly applied to improve consistency of these existing protocols. We emphasize that these thresholds determine the critical tradeoff between honest majority, network delays, and consistency error.We complement our results with a consistency analysis in the se ing where uniquely honest slots are rare, even le ing ph = 0, under the added assumption that honest players adopt a consistent chain selection rule. Our analysis provides a direct connection between the Ouroboros analysis by Blum et al. (SODA 2020) focusing on "relative margin" and the Sleepy consensus analysis focusing on "strong pivots.
BackgroundMany consensus-based and Position Weight Matrix-based methods for recognizing transcription factor binding sites (TFBS) are not well suited to the variability in the lengths of binding sites. Besides, many methods discard known binding sites while building the model. Moreover, the impact of Information Content (IC) and the positional dependence of nucleotides within an aligned set of TFBS has not been well researched for modeling variable-length binding sites. In this paper, we propose ML-Consensus (Mixed-Length Consensus): a consensus model for variable-length TFBS which does not exclude any reported binding sites.MethodsWe consider Pairwise Score (PS) as a measure of positional dependence of nucleotides within an alignment of TFBS. We investigate how the prediction accuracy of ML-Consensus is affected by the incorporation of IC and PS with a particular binding site alignment strategy. We perform cross-validations for datasets of six species from the TRANSFAC public database, and analyze the results using ROC curves and the Wilcoxon matched-pair signed-ranks test.ResultsWe observe that the incorporation of IC and PS in ML-Consensus results in statistically significant improvement in the prediction accuracy of the model. Moreover, the existence of a core region among the known binding sites (of any length) is witnessed by the pairwise coexistence of nucleotides within the core length.ConclusionsThese observations suggest the possibility of an efficient multiple sequence alignment algorithm for aligning TFBS, accommodating known binding sites of any length, for optimal (or near-optimal) TFBS prediction. However, designing such an algorithm is a matter of further investigation.
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