Related papers: Combinatorial RNA Design: Designability and Struct…
In this paper, we design low correlation binary sequences favorable in wireless communication and radar applications. First, we formulate the designing problem as a nonconvex combination optimization problem with flexible correlation…
It is a classical result of Stein and Waterman that the asymptotic number of RNA secondary structures is $1.104366 \cdot n^{-3/2} \cdot 2.618034^n$. Motivated by the kinetics of RNA secondary structure formation, we are interested in…
The protein design problem involves finding polypeptide sequences folding into a given threedimensional structure. Its rigorous algorithmic solution is computationally demanding, involving a nested search in sequence and structure spaces.…
Applications in machine learning, optimization, and control require the sequential selection of a few system elements, such as sensors, data, or actuators, to optimize the system performance across multiple time steps. However, in…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Neural Architectures Search (NAS) becomes more and more popular over these years. However, NAS-generated models tends to suffer greater vulnerability to various malicious attacks. Lots of robust NAS methods leverage adversarial training to…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
For large classes of group testing problems, we derive lower bounds for the probability that all significant items are uniquely identified using specially constructed random designs. These bounds allow us to optimize parameters of the…
As transistor dimensions continue to shrink, binary devices are rapidly approaching their fundamental limits in power density. In response, multi-valued systems have attracted significant attention due to their enhanced information density.…
Designing messenger RNA (mRNA) sequences for a fixed target protein requires searching an exponentially large synonymous space while optimizing properties that affect stability and downstream performance. This is challenging because…
Questions in computational molecular biology generate various discrete optimization problems, such as DNA sequence alignment and RNA secondary structure prediction. However, the optimal solutions are fundamentally dependent on the…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
Combinatorial designs provide an interesting source of optimization problems. Among them, permutation codes are particularly interesting given their applications in powerline communications, flash memories, and block ciphers. This paper…
Motivated by the study of genome rearrangements, the NP-hard Minimum Common String Partition problems asks, given two strings, to split both strings into an identical set of blocks. We consider an extension of this problem to unbalanced…
The growing significance of RNA engineering in diverse biological applications has spurred interest in developing AI methods for structure-based RNA design. While diffusion models have excelled in protein design, adapting them for RNA…
The design space for a self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. Using a…
Consider two or more strings $\mathbf{x}^1,\mathbf{x}^2,\ldots,$ that are concatenated to form $\mathbf{x}=\langle \mathbf{x}^1,\mathbf{x}^2,\ldots \rangle$. Suppose that up to $\delta$ deletions occur in each of the concatenated strings.…
An arc-annotated string is a string of characters, called bases, augmented with a set of pairs, called arcs, each connecting two bases. Given arc-annotated strings $P$ and $Q$ the arc-preserving subsequence problem is to determine if $P$…
Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of…
In this paper we consider the problem of computing an mRNA sequence of maximal similarity for a given mRNA of secondary structure constraints, introduced by Backofen et al. in [BNS02] denoted as the MRSO problem. The problem is known to be…