33 research outputs found
Functional relations for elliptic polylogarithms
Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on considerations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formalism in turn allows for an alternative proof of the validity of the elliptic Bloch relation. While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities
Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory
Infrared equations and dual conformal constraints arise as consistency
conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions
are linear relations between leading singularities, which can be computed in
the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently.
Examples for infrared equations have been shown to be implied by global residue
theorems in the Grassmannian picture. Both dual conformal constraints and
infrared equations are mapped explicitly to global residue theorems for
one-loop next-to-maximally-helicity-violating amplitudes. In addition, the
identity relating the BCFW and its parity-conjugated form of tree-level
amplitudes, is shown to emerge from a particular combination of global residue
theorems.Comment: 21 page
Large scale analytic calculations in quantum field theories
We present a survey on the mathematical structure of zero- and single scale
quantities and the associated calculation methods and function spaces in higher
order perturbative calculations in relativistic renormalizable quantum field
theories.Comment: 25 pages Latex, 1 style fil
Intracellular directed evolution of proteins from combinatorial libraries based on conditional phage replication
Directed evolution is a powerful tool to improve the characteristics of biomolecules. Here we present a protocol for the intracellular evolution of proteins with distinct differences and advantages in comparison with established techniques. These include the ability to select for a particular function from a library of protein variants inside cells, minimizing undesired coevolution and propagation of nonfunctional library members, as well as allowing positive and negative selection logics using basally active promoters. A typical evolution experiment comprises the following stages: (i) preparation of a combinatorial M13 phagemid (PM) library expressing variants of the gene of interest (GOI) and preparation of the Escherichia coli host cells; (ii) multiple rounds of an intracellular selection process toward a desired activity; and (iii) the characterization of the evolved target proteins. The system has been developed for the selection of new orthogonal transcription factors (TFs) but is capable of evolving any gene—or gene circuit function—that can be linked to conditional M13 phage replication. Here we demonstrate our approach using as an example the directed evolution of the bacteriophage λ cI TF against two synthetic bidirectional promoters. The evolved TF variants enable simultaneous activation and repression against their engineered promoters and do not cross-react with the wild-type promoter, thus ensuring orthogonality. This protocol requires no special equipment, allowing synthetic biologists and general users to evolve improved biomolecules within ~7 weeks
Instantons and Yang-Mills Flows on Coset Spaces
We consider the Yang-Mills flow equations on a reductive coset space G/H and
the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces
G/H one can introduce geometric fluxes identified with the torsion of the spin
connection. The condition of G-equivariance imposed on the gauge fields reduces
the Yang-Mills equations to phi^4-kink equations on R. Depending on the
boundary conditions and torsion, we obtain solutions to the Yang-Mills
equations describing instantons, chains of instanton-anti-instanton pairs or
modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type
configurations are constructed as well. We also present explicit solutions to
the Yang-Mills flow equations and compare them with the Yang-Mills solutions on
R x G/H.Comment: 1+12 page
R^4 counterterm and E7(7) symmetry in maximal supergravity
The coefficient of a potential R^4 counterterm in N=8 supergravity has been
shown previously to vanish in an explicit three-loop calculation. The R^4 term
respects N=8 supersymmetry; hence this result poses the question of whether
another symmetry could be responsible for the cancellation of the three-loop
divergence. In this article we investigate possible restrictions from the coset
symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as
well as a double-soft scalar limit relation derived recently by Arkani-Hamed et
al. We implement these relations for the matrix elements of the R^4 term that
occurs in the low-energy expansion of closed-string tree-level amplitudes. We
find that the matrix elements of R^4 that we investigated all obey the
double-soft scalar limit relation, including certain
non-maximally-helicity-violating six-point amplitudes. However, the single-soft
limit does not vanish for this latter set of amplitudes, which suggests that
the E7(7) symmetry is broken by the R^4 term.Comment: 33 pages, typos corrected, published versio
Pathways to cellular supremacy in biocomputing
Synthetic biology uses living cells as the substrate for performing human-defined computations. Many current implementations of cellular computing are based on the “genetic circuit” metaphor, an approximation of the operation of silicon-based computers. Although this conceptual mapping has been relatively successful, we argue that it fundamentally limits the types of computation that may be engineered inside the cell, and fails to exploit the rich and diverse functionality available in natural living systems. We propose the notion of “cellular supremacy” to focus attention on domains in which biocomputing might offer superior performance over traditional computers. We consider potential pathways toward cellular supremacy, and suggest application areas in which it may be found.A.G.-M. was supported by the SynBio3D project of the UK Engineering and Physical Sciences Research Council (EP/R019002/1) and the European CSA on biological standardization BIOROBOOST (EU grant number 820699). T.E.G. was supported by a Royal Society University Research Fellowship (grant UF160357) and BrisSynBio, a BBSRC/ EPSRC Synthetic Biology Research Centre (grant BB/L01386X/1). P.Z. was supported by the EPSRC Portabolomics project (grant EP/N031962/1). P.C. was supported by SynBioChem, a BBSRC/EPSRC Centre for Synthetic Biology of Fine and Specialty Chemicals (grant BB/M017702/1) and the ShikiFactory100 project of the European Union’s Horizon 2020 research and innovation programme under grant agreement 814408