New Relations for Gauge-Theory and Gravity Amplitudes at Loop Level

In this letter, we extend the tree-level Kawai--Lewellen--Tye (KLT) and Bern--Carrasco--Johansson (BCJ) amplitude relations to loop integrands of gauge theory and gravity. By rearranging the propagators of gauge and gravity loop integrands, we propose the first manifestly gauge- and diffeomorphism invariant formulation of their double-copy relations. The one-loop KLT formula expresses gravity integrands in terms of more basic gauge invariant building blocks for gauge-theory amplitudes, dubbed partial integrands. The latter obey a one-loop analogue of the BCJ relations, and both KLT and BCJ relations are universal to bosons and fermions in any number of spacetime dimensions and independent on the amount of supersymmetry. Also, one-loop integrands of Einstein--Yang--Mills (EYM) theory are related to partial integrands of pure gauge theories.Comment: 6 pages; v2: references added, minor corrections, published version with updated reference on work in progres

New BCJ representations for one-loop amplitudes in gauge theories and gravity

We explain a procedure to manifest the Bern-Carrasco-Johansson duality between color and kinematics in $n$-point one-loop amplitudes of a variety of supersymmetric gauge theories. Explicit amplitude representations are constructed through a systematic reorganization of the integrands in the Cachazo-He-Yuan formalism. Our construction holds for any nonzero number of supersymmetries and does not depend on the number of spacetime dimensions. The cancellations from supersymmetry multiplets in the loop as well as the resulting power counting of loop momenta is manifested along the lines of the corresponding superstring computations. The setup is used to derive the one-loop version of the Kawai-Lewellen-Tye formula for the loop integrands of gravitational amplitudes.Comment: 58 + 15 page

Channels of Interprovincial Consumption Risk Sharing in the People’s Republic of China

This paper analyzes consumption risk sharing among provinces in the People’s Republic of China (PRC) during 1980–2007. The analysis finds that 9.4% of shocks to gross provincial product are smoothed by the interprovincial fiscal transfer system. This system also cushions a relatively large percentage of province-specific shocks in coastal areas. Using a variety of indicators, we explored nonfiscal channels of consumption risk sharing. We found that the migration of rural labor to urban areas and the remittance of migrant wages play an important role in promoting interprovincial consumption risk sharing in inland PRC provinces. In contrast, the extent of risk sharing through financial intermediation and capital markets is very limited. These factors have resulted in a low degree of risk sharing among provinces, especially during the last decade.prc provinces; interprovincial fiscal transfers; consumption risk sharing

Ruthenium-Phenothiazine Electron Transfer Dyads with a Photoswitchable Dithienylethene Bridge

A molecular ensemble composed of a phenothiazine (PTZ) electron donor, a photoisomerizable dithienylethene (DTE) bridge, and a Ru(bpy)32+ (bpy = 2,2′-bipyridine) electron acceptor was synthesized and investigated by optical spectroscopic and electrochemical means. Our initial intention was to perform flash-quench transient absorption studies in which the Ru(bpy)32+ unit is excited selectively (“flash”) and its 3MLCT excited state is quenched oxidatively (“quench”) by excess methylviologen prior to intramolecular electron transfer from phenothiazine to Ru(III) across the dithienylethene bridge. However, after selective Ru(bpy)32+1MLCT excitation of the dyad with the DTE bridge in its open form, 1MLCT → 3MLCT intersystem crossing on the metal complex is followed by triplet–triplet energy transfer to a 3π–π* state localized on the DTE unit. This energy transfer process is faster than bimolecular oxidative quenching with methylviologen at the ruthenium site (Ru(III) is not observed); only the triplet-excited DTE then undergoes rapid (10 ns, instrumentally limited) bimolecular electron transfer with methylviologen. Subsequently, there is intramolecular electron transfer with PTZ. The time constant for formation of the phenothiazine radical cation via intramolecular electron transfer occurring over two p-xylene units is 41 ns. When the DTE bridge is photoisomerized to the closed form, PTZ+ cannot be observed any more. Irrespective of the wavelength at which the closed isomer is irradiated, most of the excitation energy appears to be funneled rapidly into a DTE-localized singlet excited state from which photoisomerization to the open form occurs within picoseconds

Time, Tense, & Rationality

In this thesis I try to advance our understanding of the nature of time. In particular I defend the idea that there is an objective difference between the past, the present, and the future; a metaphysical tense. This is in opposition to the idea that these distinctions merely mark an aspect of our perspective on entities in time. I argue that tensed beliefs – beliefs that go hand-in-hand with tensed language – are essential to our lives as rational animals. Firstly, they are essential to our practices of providing reasons for action and acting for reasons. Secondly, they are essential for our lives as emotional animals whose emotions are appropriately responsive to the world. Perry has argued that indexical – including tensed – beliefs are essential for actions. In order to attend my meeting, it is not enough that I know that it is at 2pm, I must also know that it is now 1:55pm. Examining Perry’s argument I show that its proper conclusion is that tensed and first-personal beliefs are necessary for rational actions. I argue that reasons are facts (not belief/desire complexes or intensional entities). Further, the rationality of an action derives solely from these reasons, so that when an agent is not mistaken their action is rational purely insofar as it is done for a reason that justifies it. This means that beliefs are required for rational actions only to the extent that they provide an awareness of reasons and thereby enable an action. A proper understanding of rational action thus enables me to say that if an action must involve one belief rather than another in order to be rational, this must be because the former belief involves an awareness of a reason, hence fact, that the latter does not. Combining this with the proper conclusion of Perry’s argument we can say that tensed beliefs are required in the place of any tenseless beliefs in rational actions, and therefore must involve an awareness of facts that the latter cannot capture. Given that our actions are by and large rational, it follows there are facts captured by tensed beliefs not captured by tenseless beliefs. There is a metaphysical tense. Prior has argued that some emotions involve tensed beliefs and Cockburn has furthered this to show that the appropriateness of some emotions depends upon these beliefs. It is inappropriate to grieve a future death or fear a past danger. I show that the appropriateness of emotions stems from the reasons they are felt for and that these reasons are revealed by the beliefs involved in these emotions. This enables me to argue that if an emotion must involve one belief rather than another to be appropriate, then this can only be because the former belief captures a reason that the latter does not. In combination with Prior/Cockburn’s conclusion I am thus able to argue, analogously to the case of rational actions, that if there are emotions which must involve tensed beliefs to be appropriate and there are examples of appropriate such emotions, then metaphysical tense is real. My thesis thus derives a conclusion about the nature of time from our nature as rational animals. These arguments also have implications for a proper understanding of first-personal indexicals, which must now be recognized to pick out facts not captured by non-first-personal language. The former of these conclusions has been famously attacked by McTaggart, and the latter by Wittgenstein, and so I will also say something to rebut these criticisms. My arguments also have implications for certain issues surrounding the cognitive significance of co-referring names/natural kind terms which I will show to be unproblematic

Compressive Holographic Video

Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device. In this paper we demonstrate $10\times$ temporal super resolution with multiple depths recovery from a single image. Two examples are presented for the purpose of recording subtle vibrations and tracking small particles within 5 ms.Comment: 12 pages, 6 figure

Machine learning invariants of arithmetic curves

We show that standard machine learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around 105, we demonstrate the utility of machine learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the recognition of integral points, the accuracies can reach 0.998

Machine-learning the Sato-Tate conjecture

We apply some of the latest techniques from machine-learning to the arithmetic of hyperelliptic curves. More precisely we show that, with impressive accuracy and confidence (between 99 and 100 percent precision), and in very short time (matter of seconds on an ordinary laptop), a Bayesian classifier can distinguish between Sato–Tate groups given a small number of Euler factors for the L-function. Our observations are in keeping with the Sato-Tate conjecture for curves of low genus. For elliptic curves, this amounts to distinguishing generic curves (with Sato–Tate group SU(2)) from those with complex multiplication. In genus 2, a principal component analysis is observed to separate the generic Sato–Tate group USp(4) from the non-generic groups. Furthermore in this case, for which there are many more non-generic possibilities than in the case of elliptic curves, we demonstrate an accurate characterisation of several Sato–Tate groups with the same identity component. Throughout, our observations are verified using known results from the literature and the data available in the LMFDB. The results in this paper suggest that a machine can be trained to learn the Sato–Tate distributions and may be able to classify curves efficiently