Entanglement and Sources of Magnetic Anisotropy in Radical Pair-Based Avian Magnetoreceptors

One of the principal models of magnetic sensing in migratory birds rests on the quantum spin-dynamics of transient radical pairs created photochemically in ocular cryptochrome proteins. We consider here the role of electron spin entanglement and coherence in determining the sensitivity of a radical pair-based geomagnetic compass and the origins of the directional response. It emerges that the anisotropy of radical pairs formed from spin-polarized molecular triplets could form the basis of a more sensitive compass sensor than one founded on the conventional hyperfine-anisotropy model. This property offers new and more flexible opportunities for the design of biologically inspired magnetic compass sensors

ADVERTISING TO ARCHITECTS: CREATING DESIRE AND ESTABLISHING CREDIBILITY IN THE CASE OF ALUMINIUM

Media advertising, sponsorship deals and office visits are some of the main mechanisms through which manufacturers and suppliers attempt to place their materials and products before architects and find a way into professional consciousness. As scholarly interest in the promotional practices of manufacturers and their agents builds, there is a need to formulate and discuss analytical terms and tools for this research. The paper puts forward two terms through which the promotion of new materials and products to architects can be studied: desire and credibility. As a case study, it examines the introduction of aluminium as a building material in Australia in the mid-1930s and its subsequent promotion to become a major part of building construction in the 1950s

The Enhanced Principal Rank Characteristic Sequence

The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n×n matrix is a sequence ℓ1ℓ2⋯ℓn where ℓk is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give more information than the (0,1) pr-sequences previously studied (where basically the kth entry is 0 or 1 according as none or at least one of its principal minors of order k is nonzero). Various techniques including the Schur complement are introduced to establish that certain subsequences such as NAN are forbidden in epr-sequences over fields of characteristic not two. Using probabilistic methods over fields of characteristic zero, it is shown that any sequence of As and Ss ending in A is attainable, and any sequence of As and Ss followed by one or more Ns is attainable; additional families of attainable epr-sequences are constructed explicitly by other methods. For real symmetric matrices of orders 2, 3, 4, and 5, all attainable epr-sequences are listed with justifications

The ball in play demands of international rugby union

Objectives: Rugby union is a high intensity intermittent sport, typically analysed via set time periods or rolling average methods. This study reports the demands of international rugby union via global positioning system (GPS) metrics expressed as mean ball in play (BiP), maximum BiP (max BiP), and whole match outputs. Design: Single cohort cross sectional study involving 22 international players, categorised as forwards and backs. Methods: A total of 88 GPS files from eight international test matches were collected during 2016. An Opta sportscode timeline was integrated into the GPS software to split the data into BiP periods. Metres per min (m.min-1), high metabolic load per min (HML), accelerations per min (Acc), high speed running per min (HSR), and collisions per min (Coll) were expressed relative to BiP periods and over the whole match (>60min). Results: Whole match metrics were significantly lower than all BiP metrics (p < 0.001). Mean and max BiP HML, (p < 0.01) and HSR (p < 0.05) were significantly higher for backs versus forwards, whereas Coll were significantly higher for forwards (p < 0.001). In plays lasting 61s or greater, max BiP m.min-1 were higher for backs. Max BiP m.min-1, HML, HSR and Coll were all time dependant (p < 0.05) showing that both movement metrics and collision demands differ as length of play continues. Conclusions: This study uses a novel method of accurately assessing the BiP demands of rugby union. It also reports typical and maximal demands of international rugby union that can be used by practitioners and scientists to target training of worst-case scenario's equivalent to international intensity. Backs covered greater distances at higher speeds and demonstrated higher HML, in general play as well as 'worst case scenarios'; conversely forwards perform a higher number of collisions

Signatures of partition functions and their complexity reduction through the KP II equation

A statistical amoeba arises from a real-valued partition function when the positivity condition for pre-exponential terms is relaxed, and families of signatures are taken into account. This notion lets us explore special types of constraints when we focus on those signatures that preserve particular properties. Specifically, we look at sums of determinantal type, and main attention is paid to a distinguished class of soliton solutions of the Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures preserving the determinantal form, as well as the signatures compatible with the KP II equation, is provided: both of them are reduced to choices of signs for columns and rows of a coefficient matrix, and they satisfy the whole KP hierarchy. Interpretations in term of information-theoretic properties, geometric characteristics, and the relation with tropical limits are discussed.Comment: 42 pages, 11 figures. Section 7.1 has been added, the organization of the paper has been change

Algebraic inversion of the Dirac equation for the vector potential in the non-abelian case

We study the Dirac equation for spinor wavefunctions minimally coupled to an external field, from the perspective of an algebraic system of linear equations for the vector potential. By analogy with the method in electromagnetism, which has been well-studied, and leads to classical solutions of the Maxwell-Dirac equations, we set up the formalism for non-abelian gauge symmetry, with the SU(2) group and the case of four-spinor doublets. An extended isospin-charge conjugation operator is defined, enabling the hermiticity constraint on the gauge potential to be imposed in a covariant fashion, and rendering the algebraic system tractable. The outcome is an invertible linear equation for the non-abelian vector potential in terms of bispinor current densities. We show that, via application of suitable extended Fierz identities, the solution of this system for the non-abelian vector potential is a rational expression involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial vector current densities, albeit in the non-closed form of a Neumann series.Comment: 21pp, uses iopar

Orthogonal realizations of random sign patterns and other applications of the SIPP

A sign pattern is an array with entries in $\{+,-,0\}$. A matrix $Q$ is row orthogonal if $QQ^T = I$. The Strong Inner Product Property (SIPP), introduced in [B.A.~Curtis and B.L.~Shader, Sign patterns of orthogonal matrices and the strong inner product property, Linear Algebra Appl. 592: 228--259, 2020], is an important tool when determining whether a sign pattern allows row orthogonality because it guarantees there is a nearby matrix with the same property, allowing zero entries to be perturbed to nonzero entries, while preserving the sign of every nonzero entry. This paper uses the SIPP to initiate the study of conditions under which random sign patterns allow row orthogonality with high probability. Building on prior work, $5\times n$ nowhere zero sign patterns that minimally allow orthogonality are determined. Conditions on zero entries in a sign pattern are established that guarantee any row orthogonal matrix with such a sign pattern has the SIPP