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Reticulate evolutionary processes result in phylogenetic histories that cannot be modeled using a tree topology. Here, we apply methods from topological data analysis to molecular sequence data with reticulations. Using a simple example, we…
Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by…
The present study is focused on the superscaling behavior of electron-nucleus cross sections in the region lying above the quasielastic peak, especially the region dominated by electroexcitation of the Delta. Non-quasielastic cross sections…
Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple…
In this paper, we consider a concatenated coding based class of DNA storage codes in which the selected molecules are constrained to be taken from an ``inner'' codebook associated with the sequencing channel. This codebook is used in a…
Generative models have the ability to synthesize data points drawn from the data distribution, however, not all generated samples are high quality. In this paper, we propose using a combination of coresets selection methods and ``entropic…
This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous…
In this paper, we study the equilibrium behavior of Eigen's quasispecies equations for an arbitrary gene network. We consider a genome consisting of $ N $ genes, so that each gene sequence $ \sigma $ may be written as $ \sigma = \sigma_1…
The field of deep learning has witnessed significant breakthroughs, spanning various applications, and fundamentally transforming current software capabilities. However, alongside these advancements, there have been increasing concerns…
A variety of recent imaging techniques are able to beat the diffraction limit in fluorescence microcopy by activating and localizing subsets of the fluorescent molecules in the specimen, and repeating this process until all of the molecules…
New advances in nano sciences open the door for scientists to study biological processes on a microscopic molecule-by-molecule basis. Recent single-molecule biophysical experiments on enzyme systems, in particular, reveal that enzyme…
Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the known molecules seen in training. We find that a key limitation is…
In this study, we explore the potential of machine learning for modeling molecular electronic spectral intensities as a continuous function in a given wavelength range. Since presently available chemical space datasets provide excitation…
High read depth can be used to assemble short sequence repeats. The existing genome assemblers fail in repetitive regions of longer than average read. I propose a new algorithm for a DNA assembly which uses the relative frequency of reads…
Templated copying is the central operation by which biology produces complex molecules. Cells copy sequence information from DNA to RNA and on into proteins, which are the molecules responsible for the function and regulation of cellular…
The origin of life can be understood mathematically to be the origin of information that can replicate. The likelihood that entropy spontaneously becomes information can be calculated from first principles, and depends exponentially on the…
Recent research shows that a faulty or sub-optimally operating metabolic network can often be rescued by the targeted removal of enzyme-coding genes--the exact opposite of what traditional gene therapy would suggest. Predictions go as far…
In this paper, we consider the problem of column subset selection. We present a novel analysis of the spectral norm reconstruction for a simple randomized algorithm and establish a new bound that depends explicitly on the sampling…
Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…