Stringy KLT relations, global symmetries, and E_7(7) violation

We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi) R^4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'^3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R^4 is incompatible with continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R^4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.Comment: 23 pages, published versio

A minK-HERG complex regulates the cardiac potassium current I(Kr).

MinK is a widely expressed protein of relative molecular mass approximately 15K that forms potassium channels by aggregation with other membrane proteins. MinK governs ion channel activation, regulation by second messengers, and the function and structure of the ion conduction pathway. Association of minK with a channel protein known as KvLQT1 produces a voltage-gated outward K+ current (I[sK]) resembling the slow cardiac repolarization current (I[Ks]). HERG, a human homologue of the ether-a-go-go gene of the fruitfly Drosophila melanogaster, encodes a protein that produces the rapidly activating cardiac delayed rectifier (I[Kr]). These two potassium currents, I(Ks) and I(Kr), provide the principal repolarizing currents in cardiac myocytes for the termination of action potentials. Although heterologously expressed HERG channels are largely indistinguishable from native cardiac I(Kr), a role for minK in this current is suggested by the diminished I(Kr) in an atrial tumour line subjected to minK antisense suppression. Here we show that HERG and minK form a stable complex, and that this heteromultimerization regulates I(Kr) activity. MinK, through the formation of heteromeric channel complexes, is thus central to the control of the heart rate and rhythm

The D^{2k} R^4 Invariants of N=8 Supergravity

The existence of a linearized SUSY invariant for N=8 supergravity whose gravitational components are usually called R^4 was established long ago by on-shell superspace arguments. Superspace and string theory methods have also established analogous higher dimensional D^{2k} R^4 invariants. However, very little is known about the SUSY completions of these operators which involve other fields of the theory. In this paper we find the detailed component expansion of the linearized R^4 invariant starting from the corresponding superamplitude which generates all component matrix elements of the operator. It is then quite straightforward to extend results to the entire set of D^{2k} R^4 operators.Comment: 17 page

Modification of the National Weather Service Distributed Hydrologic Model for subsurface water exchanges between grids

To account for spatial variability of precipitation, as well as basin physiographic properties, the National Weather Service (NWS) has developed a distributed version of its hydrologic component, termed the Hydrology Laboratory-Research Distributed Hydrologic Model (HL-RDHM). Because channels are the only source of water exchange between neighboring computational elements, the absence of such exchange has been identified as a weakness in the model. The primary objective of this paper is to modify the model structure to account for subsurface water exchanges without dramatically altering the conceptual framework of the water balance module. The subsurface exchanges are established by partitioning the slow response components released from the lower layer storages into two parts: the first part involves the grid's conceptual channel, while the second is added to the lower layer storages of the downstream pixel. Realizing the deficiency of the water balance module to locate the lower zone layers in sufficient depths, a complementary study is conducted to test the feasibility of further improvement in the modified model by equally shifting downward the lower zone layers of all pixels over the basin. The Baron Fork at Eldon, Oklahoma, is chosen as the test basin. Ten years of grid-based multisensor precipitation data are used to investigate the effects of the modification, plus shifting the lower zone layers on model performance. The results show that the modified-shifted HL-RDHM can markedly improve the streamflow simulations at the interior point, as well as very high peak-flow simulations at the basin's outlet. Copyright 2011 by the American Geophysical Union

A simple approach to counterterms in N=8 supergravity

We present a simple systematic method to study candidate counterterms in N=8 supergravity. Complicated details of the counterterm operators are avoided because we work with the on-shell matrix elements they produce. All n-point matrix elements of an independent SUSY invariant operator of the form D^{2k} R^n +... must be local and satisfy SUSY Ward identities. These are strong constraints, and we test directly whether or not matrix elements with these properties can be constructed. If not, then the operator does not have a supersymmetrization, and it is excluded as a potential counterterm. For n>4, we find that R^n, D^2 R^n, D^4 R^n, and D^6 R^n are excluded as counterterms of MHV amplitudes, while only R^n and D^2 R^n are excluded at the NMHV level. As a consequence, for loop order L<7, there are no independent D^{2k}R^n counterterms with n>4. If an operator is not ruled out, our method constructs an explicit superamplitude for its matrix elements. This is done for the 7-loop D^4 R^6 operator at the NMHV level and in other cases. We also initiate the study of counterterms without leading pure-graviton matrix elements, which can occur beyond the MHV level. The landscape of excluded/allowed candidate counterterms is summarized in a colorful chart.Comment: 25 pages, 1 figure, published versio

Memory Aware Synapses: Learning what (not) to forget

Humans can learn in a continuous manner. Old rarely utilized knowledge can be overwritten by new incoming information while important, frequently used knowledge is prevented from being erased. In artificial learning systems, lifelong learning so far has focused mainly on accumulating knowledge over tasks and overcoming catastrophic forgetting. In this paper, we argue that, given the limited model capacity and the unlimited new information to be learned, knowledge has to be preserved or erased selectively. Inspired by neuroplasticity, we propose a novel approach for lifelong learning, coined Memory Aware Synapses (MAS). It computes the importance of the parameters of a neural network in an unsupervised and online manner. Given a new sample which is fed to the network, MAS accumulates an importance measure for each parameter of the network, based on how sensitive the predicted output function is to a change in this parameter. When learning a new task, changes to important parameters can then be penalized, effectively preventing important knowledge related to previous tasks from being overwritten. Further, we show an interesting connection between a local version of our method and Hebb's rule,which is a model for the learning process in the brain. We test our method on a sequence of object recognition tasks and on the challenging problem of learning an embedding for predicting $$ triplets. We show state-of-the-art performance and, for the first time, the ability to adapt the importance of the parameters based on unlabeled data towards what the network needs (not) to forget, which may vary depending on test conditions.Comment: ECCV 201

Assessing the Role of Compaction in the Formation of Adcumulates: a Microstructural Perspective

The formation of adcumulates necessitates the continued growth of primocrysts down to low porosities. Gravitationally driven viscous compaction at the base of a crystal mushy layer on the magma chamber floor, driven by the weight of the mushy layer itself, is commonly suggested as a significant process acting to drive out interstitial liquid and promote adcumulate formation. Compaction necessitates viscous deformation, by either dislocation creep or diffusion-controlled processes such as pressure-solution: many studies suggest that the foliations preserved in cumulates are a consequence of recrystallization during compaction, completely overprinting primary magmatic fabrics. We test the compaction hypothesis by looking for microstructural evidence of viscous deformation. A detailed examination of cumulates from the Skaergaard intrusion, East Greenland, demonstrates only limited crystal plastic deformation, with no correlation between the extent of dislocation creep and the calculated volume fraction of trapped liquid left in the cumulates. Although the evidence for diffusion-controlled deformation is often cryptic, there is an anti-correlation between apparent aspect ratio of plagioclase and the extent of adcumulate crystallization, contradicting previous hypotheses involving transposition of original magmatic fabrics by dissolution–reprecipitation. This is supported by the spatial distribution of compositional zoning in plagioclase, which demonstrates that pressure-solution or related diffusion-controlled processes were insufficient to obscure primary magmatic fabrics. The Skaergaard adcumulates did not form by viscous compaction. Instead we suggest that they formed by primary processes involving mass transport in a thin mushy layer. Compaction is most likely to occur in slowly cooled intrusions in which the bulk magma crystallizes abundant dense minerals. We present preliminary observations of microstructures in norites from the lower Main Zone of the Bushveld Intrusion, South Africa, and in plagioclase-rich cumulates from the Fe–Ti oxide-rich Baima Intrusion, SW China. The evidence for dislocation creep in both intrusions is unambiguous, although deformation was insuffi- cient to obliterate all traces of the primary magmatic fabrics and unlikely to have been sufficient to significantly reduce the volume of interstitial liquid.This work was supported by the Natural Environment Research Council [grant numbers NE/J021520/1 and NE/M000060/1] and a Royal Society International Joint Project grant. Z.V. is supported by a Marie SkłodowskaCurie Individual European Fellow grant

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

The Structure of n-Point One-Loop Open Superstring Amplitudes

In this article we present the worldsheet integrand for one-loop amplitudes in maximally supersymmetric superstring theory involving any number n of massless open string states. The polarization dependence is organized into the same BRST invariant kinematic combinations which also govern the leading string correction to tree level amplitudes. The dimensions of the bases for both the kinematics and the associated worldsheet integrals is found to be the unsigned Stirling number S_3^{n-1} of first kind. We explain why the same combinatorial structures govern on the one hand finite one-loop amplitudes of equal helicity states in pure Yang Mills theory and on the other hand the color tensors at quadratic alpha prime order of the color dressed tree amplitude.Comment: 75 pp, 8 figs, harvmac TeX, v2: published versio

The Skaergaard trough layering: sedimentation in a convecting magma chamber.

The upper parts of the floor cumulates of the Skaergaard Intrusion, East Greenland, contain abundant features known as troughs. The troughs are gently plunging synformal structures comprising stacks of crescentic modally graded layers with a sharply defined mafic base that grades upward into plagioclase-rich material. The origin of the troughs and layering is contentious, attributed variously to deposition of mineral grains by magmatic currents descending from the nearby walls, or to in situ development by localised recrystallisation during gravitationally-driven compaction. They are characterised by outcrop-scale features such as mineral lineations parallel to the trough axis, evidence of erosion and layer truncation associated with migration of the trough axis, and disruption of layering by syn-magmatic slumping. A detailed microstructural study of the modal trough layers, using electron backscatter diffraction together with geochemical mapping, demonstrates that these rocks do not record evidence for deformation by either dislocation creep or dissolution-reprecipitation. Instead, the troughs are characterised by the alignment of euhedral plagioclase crystals with unmodified primary igneous compositional zoning. We argue that the lineations and foliations are, therefore, a consequence of grain alignment during magmatic flow. Post-accumulation amplification of the modal layering occurred as a result of differential migration of an unmixed immiscible interstitial liquid, with upwards migration of the Si-rich conjugate into the plagioclase-rich upper part of the layers, whereas the Fe-rich immiscible conjugate remained in the mafic base. Both field and microstructure evidence support the origin of the troughs as the sites of repeated deposition from crystal-rich currents descending from the nearby chamber walls