相关论文: Waiting for regulatory sequences to appear

Human reading behavior is tuned to the statistics of natural language: the time it takes human subjects to read a word can be predicted from estimates of the word's probability in context. However, it remains an open question what…

Humans and chimpanzees are believed to have shared a common ancestor about 6 million years ago. Here using a new distance measure called the Jump distance, we calculate the number of base substitutions that might have occurred in the…

Recent psycholinguistic studies have drawn conflicting conclusions about the relationship between the quality of a language model and the ability of its surprisal estimates to predict human reading times, which has been speculated to be due…

Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…

We show that across architecture (Transformer vs. Mamba vs. RWKV), training dataset (OpenWebText vs. The Pile), and scale (14 million parameters to 12 billion parameters), autoregressive language models exhibit highly consistent patterns of…

The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…

The mean time required by a transcription factor (TF) or an enzyme to find a target in the nucleus is of prime importance for the initialization of transcription, gene activation or the start of DNA repair. We obtain new estimates for the…

To regulate a particular gene, a transcription factor (TF) needs to bind a specific genome location. How is this genome address specified amid the presence of ~10^6-10^9 decoy sites? Our analysis of 319 known TF binding motifs clearly…

We propose a model of the speech perception of individual words in the presence of mishearings. This phenomenological approach is based on concepts used in linguistics, and provides a formalism that is universal across languages. We put…

Twins in a finite word are formed by a pair of identical subwords placed at disjoint sets of positions. We investigate the maximum length of twins in a random word over a $k$-letter alphabet. The obtained lower bounds for small values of…

The regulation of a gene depends on the binding of transcription factors to specific sites located in the regulatory region of the gene. The generation of these binding sites and of cooperativity between them are essential building blocks…

In genetic systems there is a non-trivial interface between the sequence of symbols which constitutes the chromosome, or ``genotype'', and the products which this sequence encodes --- the ``phenotype''. This interface can be thought of as a…

Consider infinite random words over a finite alphabet where the letters occur as an i.i.d. sequence according to some arbitrary distribution on the alphabet. The expectation and the variance of the waiting time for the first completed…

To ensure fast gene activation, Transcription Factors (TF) use a mechanism known as facilitated diffusion to find their DNA promoter site. Here we analyze such a process where a TF alternates between 3D and 1D diffusion. In the latter (TF…

A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present an…

Recent studies have shown that as Transformer-based language models become larger and are trained on very large amounts of data, the fit of their surprisal estimates to naturalistic human reading times degrades. The current work presents a…

The time variation of the rank $k$ of words for six Indo-European languages is obtained using data from Google Books. For low ranks the distinct languages behave differently, maybe due to syntaxis rules, whereas for $k>50$ the law of large…

If life on Earth had to achieve n 'hard steps' to reach humanity's level, then the chance of this event rose as time to the n-th power. Integrating this over habitable star formation and planet lifetime distributions predicts >99% of…

A sequence of geometric random variables of length $n$ is a sequence of $n$ independent and identically distributed geometric random variables ($\Gamma_1, \Gamma_2, \dots, \Gamma_n$) where $\mathbb{P}(\Gamma_j=i)=pq^{i-1}$ for…

Consider a random word $X^n=(X_1,\ldots ,X_n)$ in an alphabet consisting of $4$ letters, with the letters viewed either as $A$, $U$, $G$ and $C$ (i.e., nucleotides in an RNA sequence) or $\alpha$, $\bar{\alpha}$, $\beta$ and $\bar{\beta}$…