Review of Noterapion Kissinger from Chile and Argentina (Coleoptera: Apionidae)

Descriptions and a key are provided for 7 South American species of Note rap ion Kissinger (2002) (type species Apion meorrhynchum Philippi and Philippi) including N. bruchi (Beguin-Billecocq), N. meorrhynchum (Philippi and Philippi), N. philippianum (Alonso-Zarazaga) and four new species described from Chile: N. chilense Kissinger, N. lwscheli Kissinger, N. nothofagi Kissinger, and N. saperion Kissinger. A lectotype designation is published for Apion meorrhynchum Philippi and Philippi and Apion uestitum Philippi and Philippi. Apion fuegianum Enderlein and A. pingue Beguin-Billecocq are synonymized with N. meorrhynchum (Philippi and Philippi), new synonymy. Noterapionini (new tribe) is erected for Noterapion Kissinger (type genus) within Apioninae. Extension of a phylogenetic analysis of Brentidae s. lato by Wanat (2001) places Noterapion near the base of Apioninae and shows the genus sharing various symplesiomorphies with primitive apionid subfamilies from Africa and not found otherwise in the New World apionids. The weevils are associated with the southern beech, Nothofagus Blume (in Nothofagaceae, see Manos, 1997), also known from the Australasian Region. Noterapion meorrhynchum develops in abandoned cynipid wasp leaf galls. The combination of a plant host with biogeographic significance and the possession of very primitive characters suggests that Noterapion may represent an ancient lineage dating back to the time of the Cretaceous and the breakup of Gondwana

A first-order logic for string diagrams

Equational reasoning with string diagrams provides an intuitive means of proving equations between morphisms in a symmetric monoidal category. This can be extended to proofs of infinite families of equations using a simple graphical syntax called !-box notation. While this does greatly increase the proving power of string diagrams, previous attempts to go beyond equational reasoning have been largely ad hoc, owing to the lack of a suitable logical framework for diagrammatic proofs involving !-boxes. In this paper, we extend equational reasoning with !-boxes to a fully-fledged first order logic called with conjunction, implication, and universal quantification over !-boxes. This logic, called !L, is then rich enough to properly formalise an induction principle for !-boxes. We then build a standard model for !L and give an example proof of a theorem for non-commutative bialgebras using !L, which is unobtainable by equational reasoning alone.Comment: 15 pages + appendi

Tensors, !-graphs, and non-commutative quantum structures

Categorical quantum mechanics (CQM) and the theory of quantum groups rely heavily on the use of structures that have both an algebraic and co-algebraic component, making them well-suited for manipulation using diagrammatic techniques. Diagrams allow us to easily form complex compositions of (co)algebraic structures, and prove their equality via graph rewriting. One of the biggest challenges in going beyond simple rewriting-based proofs is designing a graphical language that is expressive enough to prove interesting properties (e.g. normal form results) about not just single diagrams, but entire families of diagrams. One candidate is the language of !-graphs, which consist of graphs with certain subgraphs marked with boxes (called !-boxes) that can be repeated any number of times. New !-graph equations can then be proved using a powerful technique called !-box induction. However, previously this technique only applied to commutative (or cocommutative) algebraic structures, severely limiting its applications in some parts of CQM and (especially) quantum groups. In this paper, we fix this shortcoming by offering a new semantics for non-commutative !-graphs using an enriched version of Penrose's abstract tensor notation.Comment: In Proceedings QPL 2014, arXiv:1412.810

Design and layout strategies for integrated frequency synthesizers with high spectral purity

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Design guidelines for fractional-N phase-locked loops with a high spectral purity of the output signal are presented. Various causes for phase noise and spurious tones (spurs) in integer-N and fractional-N phase-locked loops (PLLs) are briefly described. These mechanisms include device noise, quantization noise folding, and noise coupling from charge pump (CP) and reference input buffer to the voltage-controlled oscillator (VCO) and vice versa through substrate and bondwires. Remedies are derived to mitigate the problems by using proper PLL parameters and a careful chip layout. They include a large CP current, sufficiently large transistors in the reference input buffer, linearization of the phase detector, a high speed of the programmable frequency divider, and minimization of the cross-coupling between the VCO and the other building blocks. Examples are given based on experimental PLLs in SiGe BiCMOS technologies for space communication and wireless base stations.BMBF, 03ZZ0512A, Zwanzig20 - Verbundvorhaben: fast-spot; TP1: Modularer Basisband- Prozessor mit extrem hohen Datenraten, sehr kurzen Latenzzeiten und SiGe-Analog-Frontend-IC-Fertigung bei >200 GHz Trägerfrequen

Synthesising Graphical Theories

In recent years, diagrammatic languages have been shown to be a powerful and expressive tool for reasoning about physical, logical, and semantic processes represented as morphisms in a monoidal category. In particular, categorical quantum mechanics, or "Quantum Picturalism", aims to turn concrete features of quantum theory into abstract structural properties, expressed in the form of diagrammatic identities. One way we search for these properties is to start with a concrete model (e.g. a set of linear maps or finite relations) and start composing generators into diagrams and looking for graphical identities. Naively, we could automate this procedure by enumerating all diagrams up to a given size and check for equalities, but this is intractable in practice because it produces far too many equations. Luckily, many of these identities are not primitive, but rather derivable from simpler ones. In 2010, Johansson, Dixon, and Bundy developed a technique called conjecture synthesis for automatically generating conjectured term equations to feed into an inductive theorem prover. In this extended abstract, we adapt this technique to diagrammatic theories, expressed as graph rewrite systems, and demonstrate its application by synthesising a graphical theory for studying entangled quantum states.Comment: 10 pages, 22 figures. Shortened and one theorem adde

PyZX: Large Scale Automated Diagrammatic Reasoning

The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a type of tensor networks that can represent arbitrary linear maps between qubits. Using the ZX-calculus, we can intuitively reason about quantum theory, and optimise and validate quantum circuits. In this paper we introduce PyZX, an open source library for automated reasoning with large ZX-diagrams. We give a brief introduction to the ZX-calculus, then show how PyZX implements methods for circuit optimisation, equality validation, and visualisation and how it can be used in tandem with other software. We end with a set of challenges that when solved would enhance the utility of automated diagrammatic reasoning.Comment: In Proceedings QPL 2019, arXiv:2004.1475

Universal MBQC with generalised parity-phase interactions and Pauli measurements

We introduce a new family of models for measurement-based quantum computation which are deterministic and approximately universal. The resource states which play the role of graph states are prepared via 2-qubit gates of the form $\exp(-i\frac{\pi}{2^{n}} Z\otimes Z)$. When $n = 2$, these are equivalent, up to local Clifford unitaries, to graph states. However, when $n > 2$, their behaviour diverges in two important ways. First, multiple applications of the entangling gate to a single pair of qubits produces non-trivial entanglement, and hence multiple parallel edges between nodes play an important role in these generalised graph states. Second, such a state can be used to realise deterministic, approximately universal computation using only Pauli $Z$ and $X$ measurements and feed-forward. Even though, for $n > 2$, the relevant resource states are no longer stabiliser states, they admit a straightforward, graphical representation using the ZX-calculus. Using this representation, we are able to provide a simple, graphical proof of universality. We furthermore show that for every $n > 2$ this family is capable of producing all Clifford gates and all diagonal gates in the $n$-th level of the Clifford hierarchy.Comment: 19 pages, accepted for publication in Quantum (quantum-journal.org). A previous version of this article had the title: "Universal MBQC with M{\o}lmer-S{\o}rensen interactions and two measurement bases

Apionidae from North and Central America : 5. Description of genus Apionion and 4 new species (Coleoptera)

Apionion (type species Apion crassum Fall) is described for 14 species formerly assigned to the Apion annulatum species group of Coelocephalapion Wagner, namely, championi Sharp, crassum Fall, derasum Sharp, dilatatum Smith, fenyesi Kissinger, howdeni Kissinger, inflatipenne Sharp, latipenne Sharp, latipes Sharp, len tum Sharp, neolentum Kissinger, samson Sharp, and subauratum Sharp from North and Central America, and annulatum Gerstaecker from South America, all originally included in Apion Herbst. Four new species are described: delion (panama), eranion (Costa Rica, Panama), humongum (Mexico, El Salvador, Honduras), and sapphirum (Mexico, Costa Rica). New records and/or supplemental descriptions are given for championi, derasum, dilatatum, fenyesi, howdeni, inflatipenne, latipenne, latipes, and neolentum