The EFT-hedron

We re-examine the constraints imposed by causality and unitarity on the low-energy effective field theory expansion of four-particle scattering amplitudes, exposing a hidden “totally positive” structure strikingly similar to the positive geometries associated with grassmannians and amplituhedra. This forces the infinite tower of higher-dimension operators to lie inside a new geometry we call the “EFT-hedron”. We initiate a systematic investigation of the boundary structure of the EFT-hedron, giving infinitely many linear and non-linear inequalities that must be satisfied by the EFT expansion in any theory. We illustrate the EFT-hedron geometry and constraints in a wide variety of examples, including new consistency conditions on the scattering amplitudes of photons and gravitons in the real world.

The A/Un/grammatical Child/hood/s and Writing

This is about creating new ontologisations of sustainable child/hood/s and/as exceeding forms of contracts between generations through experimenting with bodily affects and sensing movements. Experimenting as writing that is and doing with texts to foster patterns of becomings, thus affirming the positive structure of difference: Writing as opening the self up to possible encounters with affective outsides, collapsing divides in me and simultaneously possibilizing child/hood/s as (a) matrix of becoming. This is about turning early childhood and care institutions and schools into postdiagnosis localities or places of transition, their main task becoming that of not passing on traditions but to prepare for future contingent events. Teaching children to act in disagreement that is and drivers of processes and change through creating better—as in minor—languages for being and doing differently together.

Endogenous Water System Pollution Kuznets Curve in China

Based on the data of river cross section water quality in China from 2002 to 2011, we analyze the interrelationship between economic growth and water pollution. The results reveal that water environment will deteriorate with economic growth currently. Openness has no significant effect on pollution. Pollution heaven hypothesis is not true due to environmental regulation. Positive structure effect relies heavily on the substitution of industry. Excellence in environment quality brings more tolerance of exhaustion than productivity to economic growth.

On the development and extinction of regular doubly refracting structures in the crystalline lenses of animals after death

Since the year 1816, when the author communicated to the Royal Society an account of the doubly refracting structures which exist in the crystalline lenses of fishes and other animals, he has examined a great variety of recent lenses with the view of ascertaining the origin of these structures, the order of their succession in different lenses, and the purpose which they answer in the animal economy. He had discovered in the lenses of many fishes the alternation of portions, exerting, the one a positive, and the other a negative refractive action; but in his subsequent investigations he met with the greatest discrepancy as to the regularity of their arrangement. He found that in quadrupeds the central structure is positive while in fishes, where there are three structures, it is always negative; but their positive structure in the former case sometimes exists alone, with faint traces of a negative structure, and sometimes it is followed by another positive structure separated from the first by a black neutral circle, in which the double refraction disappears; at other times various other combinations of these structures are presented, Occasionally, in the dark neutral line which separated two positive structures, he perceived a trace of an intervening structure, which seemed to be either about to disappear or about to be developed. This conjecture was satisfactorily verified by a series of observations which he made on the lenses of the sheep, the ox, and the horse, at different ages, and also on the same lens, during the spontaneous changes it undergoes when kept in distilled water. The negative structure was in these experiments gradually developed at the space intervening between the portions of the lens which had possessed the positive structure 5 and thus the same parts assumed in succession doubly refractive actions of opposite kinds. The author intimates his intention of pointing out, in a separate paper, the conclusions deducible from these facts respecting the cause and cure of cataract.

XVI. On the development and extinction of regular doubly refracting structures in the crystalline lenses of animals after death

Since the year 1816, when I communicated to the Royal Society an account of the doubly refracting structures which exist in the crystalline lenses of fishes and other animals, I have examined a great variety of recent lenses, with the view of ascertain­ing the origin of these structures, the order of their succession in different lenses, and the purpose which they answered in the animal œconomy. Although I had found that in the lenses of the cod, the salmon, the haddock, the frog-fish, the skate, and several other fishes there were three structures, the innermost of which had negative double refraction, the next positive , and the outermost negative double re­fraction, yet in the lenses of animals the greatest discrepancies presented themselves. In every case, however, excepting one, I have found the central structure in all quadrupeds to be positive, while it is always negative in fishes when there are three structures, but this positive structure sometimes existed alone, with faint traces of a negative structure; sometimes it was followed by another structure, separated from the first by a black neutral circle, in which the double refraction disappeared. Sometimes these two positive structures were succeeded by an external negative struc­ture. Sometimes the central and external positive structures were separated by a negative structure, and at other times the lens exhibited four structures, a negative and a positive one alternating. As these discrepancies appeared in the lenses of animals of the same species, I conceived that they were owing to differences of age or sex, or to some change in the health of the animal. I was therefore led to make new observations in reference to these probabilities, and to observe the phenomena with additional attention when the structure differed from that which was most common. In these observations I sometimes noticed in the dark or neutral line, which separated two positive structures, something like a trace of an intervening structure, which was either about to disappear, or about to be developed. This conjecture was confirmed by observations on the lenses of a cow eleven years old. The lenses after being carefully taken out, were freed from the adhering portions of the vitreous humour by the gentle application of blotting paper, so as not to disturb their internal structure. The lenses were elliptical. Their longest diameter was 0.774 inch, their shortest diameter 0.747 inch, and their thickness 0.513 of an inch. The first lens which I exposed to polarized light was in the highest perfection, and the symmetry of the optical figure unusually beautiful. I have represented it in Plate XV. fig. 1., in which only two structures, or two series of positive sectors, are visible. The lens was now a day old, and there seemed to be a faint light within the two black rings, especially in the outer one, which was either the remains of an old, or the germ of a new structure. If this were the case, then the anomalous combination of two positive structures would be converted into a combination of four structures, in which a negative and a positive one alternated.