Computing elements of certain form in ideals to prove properties of operators

Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this by examples coming from actual operator statements and discuss relevant algorithmic methods for finding such polynomials based on noncommutative Gr\"obner bases. In particular, we present algorithms for computing the intersection of a two-sided ideal with a one-sided ideal as well as for computing homogeneous polynomials in two-sided ideals and monomials in one-sided ideals. All methods presented in this work are implemented in the Mathematica package OperatorGB.Comment: 26 page

Compatible rewriting of noncommutative polynomials for proving operator identities

The goal of this paper is to prove operator identities using equalities between noncommutative polynomials. In general, a polynomial expression is not valid in terms of operators, since it may not be compatible with domains and codomains of the corresponding operators. Recently, some of the authors introduced a framework based on labelled quivers to rigorously translate polynomial identities to operator identities. In the present paper, we extend and adapt the framework to the context of rewriting and polynomial reduction. We give a sufficient condition on the polynomials used for rewriting to ensure that standard polynomial reduction automatically respects domains and codomains of operators. Finally, we adapt the noncommutative Buchberger procedure to compute additional compatible polynomials for rewriting. In the package OperatorGB, we also provide an implementation of the concepts developed.Comment: 17 page

Algebraic proof methods for identities of matrices and operators: improvements of Hartwig's triple reverse order law

When improving results about generalized inverses, the aim often is to do this in the most general setting possible by eliminating superfluous assumptions and by simplifying some of the conditions in statements. In this paper, we use Hartwig's well-known triple reverse order law as an example for showing how this can be done using a recent framework for algebraic proofs and the software package OperatorGB. Our improvements of Hartwig's result are proven in rings with involution and we discuss computer-assisted proofs that show these results in other settings based on the framework and a single computation with noncommutative polynomials

Constructing living buildings: a review of relevant technologies for a novel application of biohybrid robotics

Biohybrid robotics takes an engineering approach to the expansion and exploitation of biological behaviours for application to automated tasks. Here, we identify the construction of living buildings and infrastructure as a high-potential application domain for biohybrid robotics, and review technological advances relevant to its future development. Construction, civil infrastructure maintenance and building occupancy in the last decades have comprised a major portion of economic production, energy consumption and carbon emissions. Integrating biological organisms into automated construction tasks and permanent building components therefore has high potential for impact. Live materials can provide several advantages over standard synthetic construction materials, including self-repair of damage, increase rather than degradation of structural performance over time, resilience to corrosive environments, support of biodiversity, and mitigation of urban heat islands. Here, we review relevant technologies, which are currently disparate. They span robotics, self-organizing systems, artificial life, construction automation, structural engineering, architecture, bioengineering, biomaterials, and molecular and cellular biology. In these disciplines, developments relevant to biohybrid construction and living buildings are in the early stages, and typically are not exchanged between disciplines. We, therefore, consider this review useful to the future development of biohybrid engineering for this highly interdisciplinary application.publishe

Rapid and High-Throughput Detection of Highly Pathogenic Bacteria by Ibis PLEX-ID Technology

In this manuscript, we describe the identification of highly pathogenic bacteria using an assay coupling biothreat group-specific PCR with electrospray ionization mass spectrometry (PCR/ESI-MS) run on an Ibis PLEX-ID high-throughput platform. The biothreat cluster assay identifies most of the potential bioterrorism-relevant microorganisms including Bacillus anthracis, Francisella tularensis, Yersinia pestis, Burkholderia mallei and pseudomallei, Brucella species, and Coxiella burnetii. DNA from 45 different reference materials with different formulations and different concentrations were chosen and sent to a service screening laboratory that uses the PCR/ESI-MS platform to provide a microbial identification service. The standard reference materials were produced out of a repository built up in the framework of the EU funded project “Establishment of Quality Assurances for Detection of Highly Pathogenic Bacteria of Potential Bioterrorism Risk” (EQADeBa). All samples were correctly identified at least to the genus level

Interaction-Dependent PCR: Identification of Ligand−Target Pairs from Libraries of Ligands and Libraries of Targets in a Single Solution-Phase Experiment

Interaction-dependent PCR (IDPCR) is a solution-phase method to identify binding partners from combined libraries of small-molecule ligands and targets in a single experiment. Binding between DNA-linked targets and DNA-linked ligands induces formation of an extendable duplex. Extension links codes that identify the ligand and target into one selectively amplifiable DNA molecule. In a model selection, IDPCR resulted in the enrichment of DNA encoding all five known protein−ligand pairs out of 67 599 possible sequences.Chemistry and Chemical Biolog