Related papers: A criterion for determining whether multiple shell…
We examined what determines the designability of 2-letter codes (H and P) lattice proteins from three points of view. First, whether the native structure is searched within all possible structures or within maximally compact structures.…
We present a method to derive separability criteria for the different classes of multiparticle entanglement, especially genuine multiparticle entanglement. The resulting criteria are necessary and sufficient for certain families of states.…
The hull of linear codes have promising utilization in coding theory and quantum coding theory. In this paper, we study the hull of generalized Reed-Solomon codes and extended generalized Reed-Solomon codes over finite fields with respect…
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight of this code supporting 2-designs. In this paper, we study this family of…
With shell model codes being able to encompassing larger and larger spaces we find that the percentage occupancy of the leading spaces becomes smaller and smaller. How can the shell model survive in such circumstances? We will not solve…
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are…
Linear code with complementary dual($LCD$) are those codes which meet their duals trivially. In this paper we will give rather alternative proof of Massey's theorem\cite{Massey2}, which is one of the most important characterization of $LCD$…
In the present paper, we give proofs of the existence of a 3-design in the extended ternary quadratic residue code of length 14 and the extended quaternary quadratic residue code of length 18.
Discussion of the designation of multiple-star components leads to a conclusion that, apart from components, we need to designate systems and centers-of-mass. The hierarchy is coded then by simple links to parent. This system is adopted in…
In computerized adaptive testing (CAT), items (questions) are selected in real time based on the already observed responses, so that the ability of the examinee can be estimated as accurately as possible. This is typically formulated as a…
The two basic equations satisfied by the parameters of a block design define a three-dimensional affine variety $\mathcal{D}$ in $\mathbb{R}^{5}$. A point of $\mathcal{D}$ that is not in some sense trivial lies on four lines lying in…
PCR testing is an invaluable diagnostic tool that has most recently seen widespread use during the COVID-19 pandemic. A recent work by Wang, Gabrys and Vardy proposed tropical codes as a model for group PCR testing. For a known but…
In this paper, we report our ongoing investigations of the inherent non-determinism in contemporary execution environments that can potentially lead to divergence in state of a multi-channel hardware/software system. Our approach involved…
Among an infinite number of possible folds, nature has chosen only about 1000 distinct folds to form protein structures. Theoretical studies suggest that selected folds are intrinsically more designable than others; these selected folds are…
We introduce Textile IR, a bidirectional intermediate representation that connects manufacturing-valid CAD, physics-based simulation, and lifecycle assessment for fashion design. Unlike existing siloed tools where pattern software…
Investigation of the reliability of technical systems is one of the application areas of stochastic processes. The reliability of a technical system is based on two main elements. The first is the connection type of the system, and the…
Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…
A computer code can simulate a system's propagation of variation from random inputs to output measures of quality. Our aim here is to estimate a critical output tail probability or quantile without a large Monte Carlo experiment. Instead,…
This paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix. This representation turns…
Reliability is a serious concern for future extreme-scale high-performance computing (HPC) systems. While the HPC community has developed various resilience solutions, the solution space remains fragmented. There are no formal methods and…