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About 10,000 papers for “Random sequence”

On random strings and sequence comparisons

David E. Foulser · 1986

Sequence analysis is concerned with the comparison of finitely long strings of letters drawn from a finite alphabet. This dissertation considers two models of comparing random strings and examines the random length of their resulting features, the longest generalized success run in a semi-Markov chain and the longest common subsequence of two or more compared sequences. The first chapter examines a semi-Markov renewal process in which certain durations are labeled success durations and the remainder are failure durations. We derive the limiting distribution of the first passage time until a success duration of length at least x. We also characterize the limiting behavior of the longest observed success duration until epoch t and provide its lower and upper limiting distributions. Applications of these results include long runs of heads in many tosses of a Markov dependent coin, runs of general patterned types in Markov dependent sequences, runs admitting a prescribed number of errors, and the longest continous occupation time of the positive axis in a random walk on the integers. The second principal subject of the dissertation examines the behavior of long monotone paths. The longest common subsequence (LCS) of two or more target sequences is a common measure of sequence similarity. We derive asymptotic lower and upper bounds on the expected LCS fraction, the expected ratio of LCS length to target sequence length, assuming non-uniform letter densities. A related problem considers the longest monotone path (LMP) through matches located at random on a square lattice. New asymptotic bounds for this process are also displayed. The third principal division investigates special versions of the LCS and LMP problems. We produce exact asymptotic match fractions and variances for a case in which one target sequence obeys a deterministic pattern. Exact asymptotic match fractions are also given for LCS and LMP calculations in which the longest monotone path is required to remain within a finite-width band centered on the main diagonal.

Cited by 4

Characterization of Sequence Distributions in Random and Semi-Random Copolymers

Michael Cole, Jordan Fitch, Tara Y. Meyer · Macromolecules · 2026

We report a strategy for analyzing and distinguishing the sequence distributions of random and semirandom poly(lactic-co-glycolic acid) (PLGA) analogs using selective digestion at cleavable olefin-containing monomer units. Semirandom copolymers were synthesized via a parallel-successive (P-S) approach that enables coarse-grained sequence control by coupling telechelic oligomers of varied composition and length. Following cross-metathesis digestion, the resulting fragment distributions were fractionated and analyzed via NMR, SEC, and MALDI-MS. These postdigestion data directly reflect the microstructural arrangement of the cleavable units in the predigestion copolymers. Monte Carlo simulations were employed to model both random and P-S copolymerizations, offering in silico digestion data that elucidate the influence of oligomer feed ratios and dispersity on the resulting block-length distributions. Experimental and simulated results demonstrate that P-S copolymers exhibit broader and sometimes bimodal fragment distributions compared to their random analogs, validating the method’s capacity to encode and detect distinct microstructural features. This approach provides a scalable, analytically tractable platform for tuning and characterizing sequence distributions in degradable polyesters and potentially other polymer systems where sequence plays a critical role in material properties.

Cited by 0Open access

An improved pseudo random sequence based on the m-sequence

Da-guo Zheng, Gang Wang, Bo Li et al. · 2011

m-sequence is the earliest pseudo random sequence that was used widely, it has good randomness and balance. But it has a disadvantage in the amount of address code. This paper puts forward a method which use at last two m-sequence to output in the order. The new sequence has good correlation function and it has a big promotion in the amount of address and the variety of the period that make it has extensive applications in CDMA and communication encryption.

Cited by 0

EQUIVALENCE OF NON-NEGATIVE RANDOM TRANSLATES OF AN IID RANDOM SEQUENCE

Aoi Honda, Yoshiaki Okazaki, Hiroshi Sato · Taiwanese Journal of Mathematics · 2009

Let $\bf X=\{X_k\}$ be an IID random sequence and $\bf Y=\{Y_k\}$ be an independent random sequence also independent of $\bf X$. Denote by $\mu_{\bf X}$ and $\mu_{\bf X+\bf Y}$ the probability measures on the sequence space induced by $\bf X$ and $\bf X+\bf Y =\{X_k+Y_k\}$, respectively. The problem is to characterize $\mu_{\bf X+\bf Y}\sim\mu_{\bf X}$ in terms of $\mu_{\bf Y}$ in the case where $\bf X$ is non-negative. Sato and Tamashiro [6] first discussed this problem assuming the existence of ${f_{\bf X}(x)=\frac{d\mu_{X_1}}{dx}(x)}$. They gave several necessary or sufficient conditions for $\mu_{\bf X+\bf Y}\sim\mu_{\bf X}$ under some additional assumptions on $f_{\bf X}$ or on $\bf Y$. The authors precisely improve these results. First they rationalize the assumption of the existence of $f_{\bf X}$. Then they prove that the condition (C.6) is necessary for wider classes of $f_\bf X$ with local regularities. They also prove if the $p$-integral $I_p^0(\bf X)\lt \infty$ and $\bf Y\in \ell_p^+$ a.s., then (C.6) is necessary and sufficient. Furthermore, in the typical case where $\bf X$ is exponentially distributed, they prove an explicit necessary and sufficient condition for $\mu_{\bf X+\bf Y}\sim \mu_\bf X$.

Cited by 0Open access

Exploring Antibody Recognition of Sequence Space through Random-Sequence Peptide Microarrays

Rebecca F. Halperin, Phillip Stafford, Stephen Albert Johnston · Molecular & Cellular Proteomics · 2010

A universal platform for efficiently mapping antibody epitopes would be of great use for many applications, ranging from antibody therapeutic development to vaccine design. Here we tested the feasibility of using a random peptide microarray to map antibody epitopes. Although peptide microarrays are physically constrained to ∼10(4) peptides per array, compared with 10(8) permitted in library panning approaches such as phage display, they enable a much more high though put and direct measure of binding. Long (20 mer) random sequence peptides were chosen for this study to look at an unbiased sampling of sequence space. This sampling of sequence space is sparse, as an exact epitope sequence is unlikely to appear. Commercial monoclonal antibodies with known linear epitopes or polyclonal antibodies raised against engineered 20-mer peptides were used to evaluate this array as an epitope mapping platform. Remarkably, peptides with the most sequence similarity to known epitopes were only slightly more likely to be recognized by the antibody than other random peptides. We explored the ability of two methods singly and in combination to predict the actual epitope from the random sequence peptides bound. Though the epitopes were not directly evident, subtle motifs were found among the top binding peptides for each antibody. These motifs did have some predictive ability in searching for the known epitopes among a set of decoy sequences. The second approach using a windowing alignment strategy, was able to score known epitopes of monoclonal antibodies well within the test dataset, but did not perform as well on polyclonals. Random peptide microarrays of even limited diversity may serve as a useful tool to prioritize candidates for epitope mapping or antigen identification.

Cited by 67Open access

Exp 3: Comparing a random dot sequence to forward dot sequence.

Taylor Burchfield (8871659), Ernest Greene (79006) · Figshare · 2020

<p>Presenting the letter dots in a random sequence (green) produced a larger decline in letter recognition than was produced by the forward sequence (blue)–p < 0.0001.</p>

Cited by 0Open access

Sequence Dependence of Self-Interacting Random Chains

Irback, Anders, Schwarze, Holm · arXiv (Cornell University) · 1995

We study the thermodynamic behavior of the random chain model proposed by Iori, Marinari and Parisi, and how this depends on the actual sequence of interactions along the chain. The properties of randomly chosen sequences are compared to those of designed ones, obtained through a simulated annealing procedure in sequence space. We show that the transition to the folded phase takes place at a smaller strength of the quenched disorder for designed sequences. As a result, folding can be relatively fast for these sequences.

Cited by 0Open access

Sequential effects in random sequence generation task.

Hanan Shteingart (3045207), Yonatan Loewenstein (46302) · Figshare · 2016

<p>A. The conditional probabilities Pr(<i>x</i><sub>0</sub> = <i>H</i>|<i>x</i><sub><i>k</i></sub> = <i>H</i>) of generating <i>H</i> in a current trial (<i>x</i><sub>0</sub> = <i>H</i>), conditioned on a choice <i>H</i>–<i>k</i> trials ago. B. Logistic regression model's coefficients. Dashed gray line represents the null hypothesis of no sequential effect. Error bars represents the confidence interval at significance level of 0.005 (Bonferroni correction for multiple comparison) and stars denoted statistical significance assuming normal distribution of noise (t-test).</p>

Cited by 0Open access

How Long Until a Random Sequence Decreases?

Jacob Siehler · Mathematics Magazine · 2010

0.0478, 0.1429, 0.1667, 0.2204, 0.8124, 0.8226, 0.3101 ..., with the first decrease occurring in the seventh position, you might feel that this was an unusually long time to wait for that first decrease—even if you’re not exactly sure how long such a run “usually” lasts in a random sequence. The average position of the first decrease in a stream of random numbers depends on precisely what you mean by random; that is, it depends on the distribution of random numbers that you’re sampling. Surprisingly, though, for continuous distributions, the question has a very specific (and delightful) answer that is independent of how the random numbers are distributed. We will uncover the answer in due time—in Proposition 2, to be precise. In the meantime, exercise your intuition by making a guess in advance about how long, on average, a monotone run like the one above will last in a sequence of random numbers. If you’ve been around math much, you can probably make a shrewd guess based solely on the fact that I described the answer as “delightful.” But we will start by discussing a special case of the problem, when the random numbers are generated simply by rolling dice.

Cited by 1

Waiting time for ATG in random sequence

Daniel Standage · Figshare · 2013

I used my random sequence generator to create 5000 random sequences with even nucleotide distribution. I then determined the position of the first occurrence of "ATG" in each sequence and plotted the distribution of these positions. The mean position (63.41) was very close to the expected waiting time (64) from the analytical solution.

Cited by 0Open access

Random graphs with a given degree sequence

Guillem Córdoba Perarnau · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · 2023

Des de l’aparició de la noció de xarxes complexes, els grafs aleatoris han resultat una eina fonamental per modelar-les i estudiar-les. En aquest article tractarem l’estudi dels grafs aleatoris amb una seqüència de graus donada, en què el grau de cada vèrtex és fixat a priori per després triar una instància aleatòria que respecti aquestes restriccions. El nostre objectiu és introduir en aquest tema el lector que no hi està familiaritzat, enunciant els resultats més rellevants en l’àrea i explicant perquè són certs, sense donar-ne proves rigoroses.

Cited by 0Open access

Random graphs with a given degree sequence

Sourav Chatterjee, Persi Diaconis, Allan Sly · The Annals of Applied Probability · 2011

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovász and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. The argument proceeds by studying a natural exponential model having the degree sequence as a sufficient statistic. The maximum likelihood estimate (MLE) of the parameters is shown to be unique and consistent with high probability. Thus n parameters can be consistently estimated based on a sample of size one. A fast, provably convergent, algorithm for the MLE is derived. These ingredients combine to prove the graph limit theorem. Along the way, a continuous version of the Erdős–Gallai characterization of degree sequences is derived.

Cited by 165Open access

Sequence Similarity Estimation by Random Subsequence Sketching

Chen, Ke, Pattar, Vinamratha, Shao, Mingfu · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2025

Sequence similarity estimation is essential for many bioinformatics tasks, including functional annotation, phylogenetic analysis, and overlap graph construction. Alignment-free methods aim to solve large-scale sequence similarity estimation by mapping sequences to more easily comparable features that can approximate edit distances efficiently. Substrings or k-mers, as the dominant choice of features, face an unavoidable compromise between sensitivity and specificity when selecting the proper k-value. Recently, subsequence-based features have shown improved performance, but they are computationally demanding, and determining the ideal subsequence length remains an intricate art. In this work, we introduce SubseqSketch, a novel alignment-free scheme that maps a sequence to an integer vector, where the entries correspond to dynamic, rather than fixed, lengths of random subsequences. The cosine similarity between these vectors exhibits a strong correlation with the edit similarity between the original sequences. Through experiments on benchmark datasets, we demonstrate that SubseqSketch is both efficient and effective across various alignment-free tasks, including nearest neighbor search and phylogenetic clustering. A C++ implementation of SubseqSketch is openly available at https://github.com/Shao-Group/SubseqSketch.

Cited by 0Open access