Rectilinear Link Diameter and Radius in a Rectilinear Polygonal Domain

We study the computation of the diameter and radius under the rectilinear link distance within a rectilinear polygonal domain of $n$ vertices and $h$ holes. We introduce a \emph{graph of oriented distances} to encode the distance between pairs of points of the domain. This helps us transform the problem so that we can search through the candidates more efficiently. Our algorithm computes both the diameter and the radius in $\min \{\,O(n^\omega), O(n^2 + nh \log h + \chi^2)\,\}$ time, where $\omega<2.373$ denotes the matrix multiplication exponent and $\chi\in \Omega(n)\cap O(n^2)$ is the number of edges of the graph of oriented distances. We also provide a faster algorithm for computing the diameter that runs in $O(n^2 \log n)$ time

Efficient calculation of electronic structure using O(N) density functional theory

We propose an efficient way to calculate the electronic structure of large systems by combining a large-scale first-principles density functional theory code, Conquest, and an efficient interior eigenproblem solver, the Sakurai-Sugiura method. The electronic Hamiltonian and charge density of large systems are obtained by \conquest and the eigenstates of the Hamiltonians are then obtained by the Sakurai-Sugiura method. Applications to a hydrated DNA system, and adsorbed P2 molecules and Ge hut clusters on large Si substrates demonstrate the applicability of this combination on systems with 10,000+ atoms with high accuracy and efficiency.Comment: Submitted to J. Chem. Theor. Compu

Interoceptive robustness through environment-mediated morphological development

Typically, AI researchers and roboticists try to realize intelligent behavior in machines by tuning parameters of a predefined structure (body plan and/or neural network architecture) using evolutionary or learning algorithms. Another but not unrelated longstanding property of these systems is their brittleness to slight aberrations, as highlighted by the growing deep learning literature on adversarial examples. Here we show robustness can be achieved by evolving the geometry of soft robots, their control systems, and how their material properties develop in response to one particular interoceptive stimulus (engineering stress) during their lifetimes. By doing so we realized robots that were equally fit but more robust to extreme material defects (such as might occur during fabrication or by damage thereafter) than robots that did not develop during their lifetimes, or developed in response to a different interoceptive stimulus (pressure). This suggests that the interplay between changes in the containing systems of agents (body plan and/or neural architecture) at different temporal scales (evolutionary and developmental) along different modalities (geometry, material properties, synaptic weights) and in response to different signals (interoceptive and external perception) all dictate those agents' abilities to evolve or learn capable and robust strategies

Generalization of the Lee-O'Sullivan List Decoding for One-Point AG Codes

We generalize the list decoding algorithm for Hermitian codes proposed by Lee and O'Sullivan based on Gr\"obner bases to general one-point AG codes, under an assumption weaker than one used by Beelen and Brander. Our generalization enables us to apply the fast algorithm to compute a Gr\"obner basis of a module proposed by Lee and O'Sullivan, which was not possible in another generalization by Lax.Comment: article.cls, 14 pages, no figure. The order of authors was changed. To appear in Journal of Symbolic Computation. This is an extended journal paper version of our earlier conference paper arXiv:1201.624

Direction Detector on an Excitable Field: Field Computation with Coincidence Detection

Living organisms process information without any central control unit and without any ruling clock. We have been studying a novel computational strategy that uses a geometrically arranged excitable field, i.e., "field computation." As an extension of this research, in the present article we report the construction of a "direction detector" on an excitable field. Using a numerical simulation, we show that the direction of a input source signal can be detected by applying the characteristic as a "coincidence detector" embedded on an excitable field. In addition, we show that this direction detection actually works in an experiment using an excitable chemical system. These results are discussed in relation to the future development of "field computation."Comment: 6 pages, 3 figure

Generalization of Calabi-Yau/Landau-Ginzburg correspondence

We discuss a possible generalization of the Calabi-Yau/Landau-Ginzburg correspondence to a more general class of manifolds. Specifically we consider the Fermat type hypersurfaces $M_N^k$: $\sum_{i=1}^N X_i^k =0$ in ${\bf CP}^{N-1}$ for various values of k and N. When k<N, the 1-loop beta function of the sigma model on $M_N^k$ is negative and we expect the theory to have a mass gap. However, the quantum cohomology relation $\sigma^{N-1}={const.}\sigma^{k-1}$ suggests that in addition to the massive vacua there exists a remaining massless sector in the theory if k>2. We assume that this massless sector is described by a Landau-Ginzburg (LG) theory of central charge $c=3N(1-2/k)$ with N chiral fields with U(1) charge $1/k$. We compute the topological invariants (elliptic genera) using LG theory and massive vacua and compare them with the geometrical data. We find that the results agree if and only if k=even and N=even. These are the cases when the hypersurfaces have a spin structure. Thus we find an evidence for the geometry/LG correspondence in the case of spin manifolds.Comment: 19 pages, Late