Related papers: A criterion for determining whether multiple shell…
Two indicators are classically used to evaluate the quality of rule-based classification systems: predictive accuracy, i.e. the system's ability to successfully reproduce learning data and coverage, i.e. the proportion of possible cases for…
This paper introduces a novel approach to multi-parameter persistence using 2-categorical structures. We develop a framework that captures hierarchical interactions between filter parameters, overcoming fundamental limitations of…
Multishape metamaterials exhibit more than one target shape change, e.g. the same metamaterial can have either a positive or negative Poisson's ratio. So far, multishape metamaterials have mostly been obtained by trial-and-error. The…
A residual design ${\cal{D}}_B$ with respect to a block $B$ of a given design $\cal{D}$ is defined to be linearly embeddable over $GF(p)$ if the $p$-ranks of the incidence matrices of ${\cal{D}}_B$ and $\cal{D}$ differ by one. A sufficient…
In a typical two-slits experiments we face the question whether it is possible or not to attain knowledge about properties incompatible with Which-Slit property together with the measurement of the final impact point. A wide family of…
After [J.Herzog, D.Popescu, Finite filtrations of modules and shellable multicomplexes, Preprint IMAR no 4/2005, Bucharest, 2005], the shellability of multicomplexes $\Gamma$ is given in terms of some special faces of $\Gamma$ called…
This paper considers the problem of constructing optimal discriminating experimental designs for competing regression models on the basis of the T-optimality criterion introduced by Atkinson and Fedorov [Biometrika 62 (1975) 57-70].…
Inspired by a recently formulated conjecture by Bannai et al. we investigate spherical codes which admit exactly three different distances and are spherical 5-designs. Computing and analyzing distance distributions we provide new proof of…
Relative $t$-designs in the $n$-dimensional hypercube $\mathcal{Q}_n$ are equivalent to weighted regular $t$-wise balanced designs, which generalize combinatorial $t$-$(n,k,\lambda)$ designs by allowing multiple block sizes as well as…
This paper studies the problem of code symbol availability: a code symbol is said to have $(r, t)$-availability if it can be reconstructed from $t$ disjoint groups of other symbols, each of size at most $r$. For example, $3$-replication…
A weaker form of the multiplicity conjecture of Herzog, Huneke, and Srinivasan is proven for two classes of monomial ideals: quadratic monomial ideals and squarefree monomial ideals with sufficiently many variables relative to the Krull…
We reconsider some fundamental problems of the thin shell model. First, we point out that the "cut and paste" construction does not guarantee a well-defined manifold because there is no overlap of coordinates across the shell. When one…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
Factorial designs with randomization restrictions are often used in industrial experiments when a complete randomization of trials is impractical. In the statistics literature, the analysis, construction and isomorphism of factorial designs…
We devise a method for designing materials that will have some desired structural characteristics. We apply it to multiblock copolymers that have two different types of monomers, A and B. We show how to determine what sequence of A's and…
Determining whether a nonlinear multi-input system is differentially flat remains challenging. One way to obtain computationally tractable sufficient conditions is to give complete characterizations of flat normal forms. We introduce a…
Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher…
For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the corresponding ruled surfaces are dual. We…
It is a classical result that an unrooted tree $T$ having positive real-valued edge lengths and no vertices of degree two can be reconstructed from the induced distance between each pair of leaves. Moreover, if each non-leaf vertex of $T$…
We present an analytical method for determining the designability of protein structures. We apply our method to the case of two-dimensional lattice structures, and give a systematic solution for the spectrum of any structure. Using this…