Sequence Space - Science topic

A probabilistic framework to study the dependence structure induced by deterministic discrete-time state-space systems between input and output processes is introduced. General sufficient conditions are formulated under which output processes exist and are unique once an input process has been fixed, a property that in the deterministic state-space...

In 2004–2006, the corresponding double sequence spaces were defined for the Pringsheim and the bounded Pringsheim convergence by Gokhan and Colak. In 2009, Colak and Mursaleen characterized some classes of matrix transformations transforming the space of bounded Pringsheim convergent (to 0) double sequences with powers and the space of uniformly bo...

This article explores two distinct function spaces: Hilbert spaces and mixed-Orlicz–Zygmund spaces with variable exponents. We first examine the relational properties of Hilbert spaces in a tensorial framework, utilizing self-adjoint operators to derive key results. Additionally, we extend a Maclaurin-type inequality to the tensorial setting using...

Transcription factors select their genomic binding sites in genomes depending on their DNA binding domain (DBD) but also on regions outside the DBD (nonDBD). However, it remains challenging to define these determinants within nonDBDs and reveal their mechanism of action. Towards this, we introduce here an in-vivo method for parallel analysis of tho...

Protein-RNA interactions are essential in gene regulation, splicing, RNA stability, and translation, making RNA a promising therapeutic agent for targeting proteins, including those considered undruggable. However, designing RNA sequences that selectively bind to proteins remains a significant challenge due to the vast sequence space and limitation...

In this article, we introduce new sequence spaces defined via an Orlicz function within the framework of a 2-normed space and incorporating the Lucas difference matrix and its associated matrix domain. The study provides a detailed examination of the topological and geometric properties of these spaces, exploring their structural characteristics an...

The outsourcing of amino acid (AA) production to the environment is relatively common across the tree of life. We recently showed that the massive loss of AA synthesis capabilities in animals is governed by selective pressure linked to the energy costs of AA production. Paradoxically, these AA auxotrophies facilitated the evolution of costlier prot...

In this paper, a novel generalized Hahn sequence space, denoted as h(C(p, q)), is introduced by utilizing the (p, q)-Cesàro matrix. Fundamental properties of this sequence space, such as its completeness and inclusion relations with other well-known sequence spaces, are explored. The duals of this newly constructed sequence space are also determine...

All animals have outsourced about half of the 20 proteinogenic amino acids (AAs). We recently demonstrated that the loss of biosynthetic pathways for these outsourced AAs is driven by energy-saving selection. Paradoxically, these metabolic simplifications enabled animals to use costly AAs more frequently in their proteomes, allowing them to explore...

Therapeutic antibody design is a complex multi-property optimization problem that traditionally relies on expensive search through sequence space. Here, we introduce "Lab-in-the-loop," a paradigm shift for antibody design that orchestrates generative machine learning models, multi-task property predictors, active learning ranking and selection, and...

Transketolases (TKs) are thiamine diphosphate (ThDP)‐dependent enzymes that catalyze the transfer of two‐carbon units in a stereoselective manner, making them valuable biocatalysts for sustainable processes. Most known TKs are about 650 amino acids long; however, a second type found in Archaea and many Bacteria consists of two proteins, each of abo...

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Regulatory sequences encode crucial gene expression signals, yet the sequence characteristics that determine their functionality across species remain obscure. Deep generative models have demonstrated considerable potential in various inverse design applications, especially in engineering genetic elements. Here, we introduce DeepCROSS, a generative...

Generalised Morrey (function) spaces enjoyed some interest recently and found applications to PDE. Here we turn our attention to their discrete counterparts. We define generalised Morrey sequence spaces $m_{\varphi,p}=m_{\varphi,p}(\mathbb{Z}^d)$. They are natural generalisations of the classical Morrey sequence spaces $m_{u,p}$, $0<p\le u<\infty$,...

Each stage of the Central Dogma contributes to proteome diversity through mechanisms such as heterozygosity, somatic mutations, transcriptional errors, and translational errors. As a result, a diverse array of protein variants can coexist within a single proteome, such as that of humans. However, until now, methods to detect, quantify, and evaluate...

Recent advances in computational biology have enabled solutions to the inverse folding problem - finding an amino acid sequence that folds into a target structure. An open question concerns the design of proteins that in addition to having the correct target structure also have precisely tuned kinetic properties, such as folding and unfolding rates...

Establishing the fundamental relationships between peptide sequences and fibril formation is critical both for understanding protein misfolding processes and for guiding biomaterial design. Here, we combine all-atom molecular dynamics (MD) simulations with artificial intelligence (AI) to investigate how subtle variations in the arrangement of a sho...

Phosphorylation site prediction based on kinase-substrate interaction plays a vital role in understanding cellular signaling pathways and disease mechanisms. Computational methods for this task can be categorized into kinase-family-focused and individual kinase-targeted approaches. Individual kinase-targeted methods have gained prominence for their...

A quenchbody (Q-body) is a fluorophore-labeled homogeneous immunosensor in which the fluorophore is quenched by tryptophan (Trp) residues in the vicinity of the antigen-binding paratope and dequenched in response to antigen binding. Developing Q-bodies against targets on demand remains challenging due to the large sequence space of the complementar...

Protein folding remains one of the most complex and fundamental problems in molecular biology. Traditional models, rooted in thermodynamics and molecular dynamics, struggle to predict protein structures due to the vast combinatorial explosion of possible conformations. However, the recent success of AlphaFold suggests that protein folding is not a...

Pyranose oxidase (POx) and C‐glycoside oxidase (CGOx) are FAD‐dependent oxidoreductases belonging to the glucose‐methanol‐choline oxidoreductase superfamily and share the same sequence space. Despite a shared structural fold, these two members possess homologous domains that enable (arm and head domain) or disable (insertion‐1 domain and barrel‐sha...

Accurate sequence-to-sequence (seq2seq) alignment is critical for applications like medical speech analysis and language learning tools relying on automatic speech recognition (ASR). State-of-the-art end-to-end (E2E) ASR systems, such as the Connectionist Temporal Classification (CTC) and transducer-based models, suffer from peaky behavior and alig...

In this article, we introduce the recurrence relation of the sequence S n obtained by the sum of the Pell numbers, and that the sequence of ratios of two consecutive S n terms is equal to the silver ratio. We construct a new triangular analogue of the Pell matrix P = P nk defined by P = P nk =    P k S n , 1 ≤ k ≤ n 0, otherwise (k, n ∈ N) Furth...

Generative artificial intelligence (AI) offers a powerful avenue for peptide design, yet this process remains challenging due to the vast sequence space, complex structure-activity relationships, and the need to balance antimicrobial potency with low toxicity. Traditional approaches often rely on trial-and-error screening and fail to efficiently na...

In the present paper, using the notion of difference sequence spaces, we introduce new kind of Cesàro summable difference sequence spaces of vector valued sequences with the aid of paranorm and modulus function. In addition, we extend the notion of statistical convergence to introduce a new sequence space SC 1 (∆, q) which coincides with C 1 1 (X,...

This article will utilize a weighted regular matrix composed of Fibonacci numbers and variable exponent sequence spaces to create a novel stochastic space with certain geometric and topological properties. This area demonstrates the new form of the Kannan contraction operator with a fixed point. In mathematical economics, we represent economic enti...

This research employs the q-Schröder matrix S q to create the sequence spaces c 0 (S q), c(S q), ℓ ∞ (S q) and ℓ p (S q) where (1 ⩽ p < ∞). We demonstrate certain topological features, derive Schauder bases, calculate the alpha, beta and gamma duals of new sequence spaces, build some matrix classes, and finally show some topological properties. In...

Studies on difference sequences was introduced in the 1980s, and since then, many mathematicians have studied this kind of sequences and obtained some generalized difference sequence spaces. In this paper, using the generalized difference operator, we introduce the concept of the deferred f-statistical convergence of generalized difference sequence...

To address the company-branch structure in data envelopment analysis (DEA), Färe and Zelenyuk (2021, Annals of Operations Research) proposed a sequential DEA (sDEA) framework, which accounts for both company-level management uniformity and the district specific influence on the production process from a branch-level perspective. To account for the...

Enzyme engineering is limited by the challenge of rapidly generating and using large datasets of sequence-function relationships for predictive design. To address this challenge, we develop a machine learning (ML)-guided platform that integrates cell-free DNA assembly, cell-free gene expression, and functional assays to rapidly map fitness landscap...

In the post-antibiotic era, antimicrobial peptides (AMPs) serve as ideal drug candidates for their lower likelihood of inducing resistance. Computational models offer an efficient way to design novel AMPs. However, current optimization and generation approaches are tailored for different application scenarios. To address this challenge, we propose...

Evolution of folded biopolymers requires effective and fast search of both the conformational space for folding and the sequence space for evolution. Molecular information theory and energy landscape theory show that the alphabet size of extant proteins and RNA is just enough to fulfill these requirements, given the constraints posed by the chemica...

The sequence spaces ru ℓ ∞ (𝒪, ∇ q ), ru ℓ p (𝒪, ∇ q ), ru c (𝒪, ∇ q ), ru c 0 (𝒪, ∇ q ), ru m ϕ (𝒪, ∇ q , p ), ru n ϕ ( 𝒪, ∇ q , p ), ru m ϕ ( 𝒪, ∇ q ), ru n ϕ ( 𝒪, ∇ q ) are defined by the Orlicz function in this article. We examine all of its characteristics, including symmetry, solidity, and completeness. A few geometric properties on convexity...

While cryo-electron microscopy (Cryo-EM) yields high-resolution density maps for complex structures, accurate determination of the corresponding three-dimensional atomic structures still necessitates significant expertise and labor-intensive manual interpretation. Recently, AI-based methods have emerged to streamline this process in the biological...

Predicting free energy changes (ΔΔG) is essential for enhancing our understanding of protein evolution and plays a pivotal role in protein engineering and pharmaceutical development. While traditional methods offer valuable insights, they are often constrained by computational speed and reliance on biased training datasets. These constraints become...

We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps.We provide a bridge between these “accessible” operators and the theory of twisted sums through the so-called quasilinear maps. Thus, for many pairs of Banach spaces X and Y...

We address a question by Henry Towsner about the possibility of representing linear operators between ultraproducts of Banach spaces by means of ultraproducts of nonlinear maps. We provide a bridge between these "accessible" operators and the theory of twisted sums through the so-called quasilinear maps. Thus, for many pairs of Banach spaces $X$ an...

First, we define a new class of fractional differential equations of order n − 1 < ϑ ≤ n, (n ≥ 2). Also, we define a new Banach double sequence space m 2 (∆ u v , φ, p) and a Hausdorff MNC on it. By using this MNC, we prove the existence of solution of infinite system of a new class of fractional differential equations of order ϑ ∈ (n − 1, n], (n ≥...

We have proposed a $ q $-analogue $ c(\mathcal{F}(q)) $ and $ c_0(\mathcal{F}(q)) $ of Fibonacci sequence spaces, where $\mathcal{F}(q) = (f^q_{km})$ denotes a $ q $-Fibonacci matrix defined in the following manner: \begin{document}$ f^q_{km} = \begin{cases} q^{m+1} \frac{f_{m+1}(q)}{f_{k+3}(q) - 1}, & \text{if } 0 \leq m \leq k, \\ 0, & \text{if }...

Neutrosophic logic, probability, and sets are all included in this discipline. The generalization of conventional sets, fuzzy sets, intuitionistic fuzzy sets, and other related ideas is the neutrosophic set theory. It is a mathematical concept that deals with situations involving inconsistent, ambiguous, and imprecise data. To fully understand sequ...

The enzymatic degradation of polyethylene terephthalate (PET) offers a sustainable solution for PET recycling. Over the past two decades, more than 100 PETases have been characterized, primarily exhibiting similar sequences and structures. Here, we report new PET-degrading α/β hydrolases, including Halo PETase1 from the marine Halopseudomonas linea...

In this article, it is obtained two new paranormed sequence spaces 0 (ℳ,) and (ℳ,) by the aid of the conservative Motzkin matrix operator ℳ and is examined some topological properties of these spaces. Also, Schauder basis and the- ,-and-duals are determined. Finally, some new matrix mappings are characterized related new paranormed sequence spaces.

Recently we have presented a unified approach to two classes of Banach spaces defined by means of variations (Waterman spaces and Chanturia classes), utilizing the concepts from the theory of ideals on the set of natural numbers. We defined correspondence between an ideal on the set of natural numbers, a certain sequence space and related space of...

In the present paper, we introduce a method of q-analogue of A r-matrix of order r. Using this method, we obtain topological properties and some inclusion relations. Additionally, the alpha dual the beta dual and the gamma dual of the newly defined sequence spaces are calculated and their basis have been determined. Finally, the necessary and suffi...

Transcription factor binding sites (TFBSs) are important sources of evolutionary innovations. Understanding how evolution navigates the sequence space of such sites can be achieved by mapping TFBS adaptive landscapes. In such a landscape, an individual location corresponds to a TFBS bound by a transcription factor. The elevation at that location co...

In this paper, the seminormed Cesàro difference sequence space ℓ(F j , q, g, r, µ, ∆ t (s) , C) is defined by using the generalized Orlicz function. Some algebraic and topological properties of the space ℓ(F j , q, g, r, µ, ∆ t (s) , C) are investigated. Various inclusion relations for this sequence space are also studied.

We will define the sequence spaces c_0 (u,∆_v^m )_p, c(u,∆_v^m )_p and l_∞ (u,∆_v^m )_p in this article. Furthermore we give some topological properties and compute their Köthe-Toeplitz duals.

The concept of fuzzy sets was introduced by Zadeh as a means of representing data that was not precise but rather fuzzy. Recently, Kočinac [19] studied some topological properties of fuzzy antinormed linear spaces. This has motivated us to introduce and study the fuzzy antinormed double sequence spaces with respect to ideal by using a bounded linea...

In this paper, we explain the sufficient conditions on a novel constructed stochastic space by weighted generalized Gamma matrix and variable exponent sequence spaces of fuzzy functions, for the Kannan contraction operator to have a unique fixed point. Finally, we discuss the numerous applications of solutions to Fuzzy Volterra-Type Non-linear Dyna...

Short linear peptide motifs play important roles in cell signaling. They can act as modification sites for enzymes and as recognition sites for peptide binding domains. SH2 domains bind specifically to tyrosine-phosphorylated proteins, with the affinity of the interaction depending strongly on the flanking sequence. Quantifying this sequence specif...

The paper aims to investigate λ -statistical convergence using modulus function and a generalized difference operator for double sequences of functions for order γ ∈ (0, 1]. Further, we prove that the statistical convergence in the newly formed sequence spaces is not well defined for γ > 1. Finally, we examine relevant inclusion relations concernin...

Navigating the protein fitness landscape is critical for understanding sequence-function relationships and improving variant effect prediction. However, the limited availability of experimentally measured functional data poses a significant bottleneck. To address this, we present a novel data augmentation strategy called fitness translocation, whic...

Protein language models (PLMs) convert amino acid sequences into the numerical representations required to train machine learning models. Many PLMs are large (>600 million parameters) and trained on a broad span of protein sequence space. However, these models have limitations in terms of predictive accuracy and computational cost. Here we use mult...

Autoregressive protein language models (pLMs) have emerged as powerful tools to efficiently design functional proteins with extraordinary diversity, as evidenced by the successful generation of diverse enzyme families, including lysozymes or carbonic anhydrases. However, a fundamental limitation of pLMs is their propensity to sample from dense regi...

We define a quasiconformal metric on the space of infinite signals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${X}^{\mathbb{N}}$$\end{document}, where X is a finite...

Reductive amination catalysed by imine reductase (IRED) and reductive aminase (RedAm) enzymes has recently been established as a powerful method for the asymmetric synthesis of chiral amines. While this biocatalytic technology has rapidly progressed from proof of concept to initial industrial applications, its scope and limitations remain to be ful...

Phylogenetic marker gene sequencing is often used as a quick and cost-effective way of evaluating microbial composition within a community. While 16S rRNA gene sequencing (16S) is commonly used for bacteria and archaea, other marker genes are preferable in certain situations, such as when 16S sequences cannot distinguish between taxa within a group...

Aberrant aggregation of the prion-like, RNA-binding protein TDP-43 underlies several debilitating neurodegenerative proteinopathies, including amyotrophic lateral sclerosis (ALS). Here, we define how short, specific RNAs antagonize TDP-43 aggregation. Short, specific RNAs engage and stabilize the TDP-43 RNA-recognition motifs, which allosterically...

This paper is a continuation of the survey “Grand Lebesgue spaces on sets of infinite measure: overview 1.”

Divergently-paired genes (DPGs) represent one of the minimal co-transcriptional units (the rest include tandemly- and convergently-paired genes) of clustered genes; the former and the latter constitute greater than 10% and 75% of the total human genes, respectively. Our previous studies have shown that vertebrate DPGs are more conserved, both organ...

In this paper, we introduce some new sequence spaces and sectional subspaces related to Rhaly matrix for an BK space and investigate some of their relations and identities among these subspaces and duals.

A key question in protein evolution and protein engineering is the prevalence of evolutionary paths between distinct proteins. An evolutionary path corresponds to a continuous path of functional sequences in sequence space leading from one protein to another. Natural selection could direct a mutating coding region in DNA along a continuous function...

Most eukaryotes possess two Rad51/RecA family DNA recombinases that are thought to have arisen from an ancient gene duplication event: Rad51, which is expressed in both mitosis and meiosis; and Dmc1, which is only expressed in meiosis. To explore the evolutionary relationship between these recombinases, here, we present high-resolution CryoEM struc...

Transformer-based architectures have achieved unprecedented success in time series analysis. However, facing the challenge of across-domain modeling, existing studies utilize statistical prior as prompt engineering fails under the huge distribution shift among various domains. In this paper, a Unified Time Series Diffusion (UTSD) model is establish...

In this paper we solve the problem of optimal recovery of the operator $A_\alpha x= (\alpha_1x_1,\alpha_2x_2,\ldots)$ on the class $W^T_q = \{(t_1h_1,t_2h_2,\ldots)\,:\,\|h\|_{\ell_q}\le 1\}$, where $1\le q < \infty$ and $t_1\ge t_2\ge \ldots \ge 0$, and $\alpha_1t_1\ge\alpha_2t_2\ge\ldots\ge 0$ are given, in the space $\ell_q$. We solve this probl...

The Cesaro sequence space , ( , which is the FK-space, has been generalized to the Cesaro-Orlicz sequence space . This prompted the study of several properties in that have been known in . In this paper, the properties of completeness and FK-properties in the Cesaro-Orlicz space are discussed. For this discussion, a modular approach is used. The re...

The purpose of this note is to obtain the discrete Hardytype variable exponent inequality for the decreasing exponent.

We develop and examine the pre-modular space of null variable exponent-weighted backward generalized difference gai sequences of fuzzy functions in this paper. These sequences of fuzzy functions are important contributions to the concept of modular spaces because they have exponent weighting. Using extended s−fuzzy functions as well as this sequenc...

In this article, we will use a weighted regular matrix formed by Leonardo numbers and variable exponent sequence spaces to build a new stochastic space. We have proposed various geometric and topological structures for this new space, as well as the multiplication operator that operates on it.

The PiggyBac transposase gene writing system has been efficiently used across biotechnological applications, however its diversity and biochemical potential remain largely unexplored. By developing a eukaryotic transposon mining pipeline, we expand the known diversity by two orders of magnitude and experimentally validate a subset of highly diverge...

Pyranose oxidase (POx) is an FAD-dependent oxidoreductase and belongs to the glucose–methanol–choline (GMC) superfamily of oxidoreductases. As recently reported, POxs and FAD-dependent C‑glycoside oxidases (CGOxs) share the same sequence space, and phylogenetic analysis of actinobacterial sequences belonging to this shared sequence space showed tha...

Unhurried conversations are necessary for careful and kind care that is responsive and responsible to both patients and clinicians. Adequate conceptual development is an important first step in being able to assess and measure this important domain of quality of care. In this article, we expand on a preliminary model to identify the key microleve...

Protein language models such as the transformer-based Evolutionary Scale Modeling 2 (ESM2) can offer deep insights into evolutionary and structural properties of proteins. While larger models, such as ESM2 15B, promise to capture more complex patterns in sequence space, they also present practical challenges due to their high dimensionality and hig...

We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When $V$ is a rooted directed tree, we show the set of hypercyclic vectors of any backward weighted shift operator on the space $c_0(V)$ or $\ell^1(V)$ is algebrable whenever it is not empty. W...

Plastic waste, particularly polyethylene terephthalate (PET), poses significant environmental challenges, prompting extensive research into enzymatic biodegradation. However, existing PET hydrolases (PETases) are constrained to a narrow sequence space and exhibited limited performance for effective biodegradation. This study introduces a protein di...

Supramolecular peptide-based materials have great potential for revolutionizing fields like nanotechnology and medicine. However, deciphering the intricate sequence-to-assembly pathway, essential for their real-life applications, remains a challenging endeavour. Their discovery relies primarily on empirical approaches that require substantial finan...

Plastic waste, particularly polyethylene terephthalate (PET), presents significant environmental challenges, prompting extensive research into enzymatic biodegradation. Existing PET hydrolases are limited to a narrow sequence space and demonstrate insufficient performance for biodegradation. This study introduces a novel discovery pipeline that com...

Proteins evolve through complex sequence spaces, with fitness landscapes serving as a conceptual framework that links sequence to function. Fitness landscapes can be smooth, where multiple similarly accessible evolutionary paths are available, or rugged, where the presence of multiple local fitness optima complicate evolution and prediction. Indeed...

The structure and function of a protein are determined by its amino acid sequence. While random mutations change a protein's sequence, evolutionary forces shape its structural fold and biological activity. Studies have shown that neutral networks can connect a local region of sequence space by single residue mutations that preserve viability. Howev...

Let $\mathcal{X} = \{ X_{\gamma} \}_{\gamma \in \Gamma}$ be a family of Banach spaces and let $\mathcal{E}$ be a Banach sequence space defined on $\Gamma$. The main aim of this work is to investigate the abstract Kadets--Klee properties, that is, the Kadets--Klee type properties in which the weak convergence of sequences is replaced by the converge...

Exploration of protein sequence space can offer insight into protein sequence-function relationships, benefitting both basic science and industrial applications. The use of sequence similarity networks (SSNs) is a standard method for exploring large sequence datasets, but is currently limited when scaling to very large datasets and when viewing mor...

The structure and function of a protein are determined by its amino acid sequence. While random mutations change a protein's sequence, evolutionary forces shape its structural fold and biological activity. Studies have shown that neutral networks can connect a local region of sequence space by single residue mutations that preserve viability. Howev...

For a nonnegative integer k, let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {T}_{k}$\end{document} denote the kth telephone number. Consider the matrix \do...

We obtain the celebrated Hardy's inequality in the context of variable exponent sequence spaces.

The aim of this research is to present the formulation of a new conservative matrix operator containing non-integer Oresme numbers, to obtain new BK-sequence spaces with the help of domains of this matrix operator on the spaces of convergent and null sequences. In the continuation of study, inclusion relations, alpha, beta and gamma duals, Schauder...

This article presents the domain of general quantum difference in Nakano sequence space. Some topological and geometric behavior, the multiplication mappings defined on it, and the spectrum of mapping ideals constructed by this space and s−numbers have been introduced. Existing results are constructed by controlling the general quantum difference a...

Designing proteins with improved functions requires a deep understanding of how sequence and function are related, a vast space that is hard to explore. The ability to efficiently compress this space by identifying functionally important features is extremely valuable. Here we establish a method called EvoScan to comprehensively segment and scan th...

In this work we define a class of injective-type norm on tensor products through the environment of sequence classes. Examples and results on this norm will be presented and the duality is studied in this context. As a byproduct, we present the definition of the associated integral-type bilinear forms and also a tensor characterization for a class...

Deep learning had succeeded in designing Cis-regulatory elements (CREs) for certain species, but necessitated training data derived from experiments. Here, we present Promoter-Factory, a protocol that leverages language models (LM) to design CREs for prokaryotes without experimental prior. Millions of sequences were drawn from thousands of prokaryo...

DNA minicircles are closed double-stranded DNA (dsDNA) fragments that have been demonstrated to be an important experimental tool to understand supercoiled, or stressed, DNA mechanics, such as nucleosome positioning and DNA-protein interactions. Specific minicircles can be simulated using Molecular Dynamics (MD) simulation. However, the enormous se...

This paper introduces the neutrosophic -statistical convergent difference sequence spaces defined through a modulus function. Additionally, we establish new topological spaces and examine various topological properties within these neutrosophic -statistical convergent difference sequence spaces.

Recent results concerning the linear dynamics and mean ergodicity of compact operators in Banach spaces, together with additional new results, are employed to investigate various spectral properties of generalized Cesàro operators acting in large classes of classical BK-sequence spaces. Of particular interest is to determine the eigenvalues and the...

We study a special type of infinite direct sums $$E({\mathcal {X}})$$ E ( X ) which can be seen as the amalgam spaces characterized by a local component given by a countable family $${\mathcal {X}}=\left( X_{\alpha }\right) _{\alpha \in I}$$ X = X α α ∈ I of quasi-normed function spaces and by a global component E , which is a quasi-normed sequence...

This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a concise overview for researchers interested in delving into the captivating theory of operator matrices.

We present a generalization of the classical Orlicz–Pettis theorem about subseries convergence in topological vector spaces. In preparation we review some aspects of the theory of locally convex cones, a generalization of locally convex topological vector spaces. We introduce conical extensions of the classical sequence spaces and a version of Schu...

We present a novel protein engineering approach to directed evolution with machine learning that integrates a new semi-supervised neural network fitness prediction model, Seq2Fitness, and an innovative optimization algorithm, b iphasic a nnealing for d iverse a daptive s equence s ampling (BADASS) to design sequences. Seq2Fitness leverages protein...

Motivation The versatile binding properties of antibodies have made them an extremely important class of biotherapeutics. However, therapeutic antibody development is a complex, expensive, and time-consuming task, with the final antibody needing to not only have strong and specific binding but also be minimally impacted by developability issues. Th...

We consider a uniqueness problem concerning the Fourier coefficients of normalized Cauchy transforms. These problems inherently involve proving a simultaneous approximation phenomenon and establishing the existence of cyclic inner functions in certain sequence spaces. Our results have several applications in different directions. First, we offer a...