We examine how to construct a spatial manifold and its geometry from the entanglement structure of an abstract quantum state in Hilbert space. Given a decomposition of Hilbert space H into a tensor ...product of factors, we consider a class of “redundancy-constrained states” in H that generalize the area-law behavior for entanglement entropy usually found in condensed-matter systems with gapped local Hamiltonians. Using mutual information to define a distance measure on the graph, we employ classical multidimensional scaling to extract the best-fit spatial dimensionality of the emergent geometry. We then show that entanglement perturbations on such emergent geometries naturally give rise to local modifications of spatial curvature which obey a (spatial) analog of Einstein’s equation. The Hilbert space corresponding to a region of flat space is finite-dimensional and scales as the volume, though the entropy (and the maximum change thereof) scales like the area of the boundary. A version of the ER=EPR conjecture is recovered, in that perturbations that entangle distant parts of the emergent geometry generate a configuration that may be considered as a highly quantum wormhole.
Evolutionary changes in traits that affect both ecological divergence and mating signals could lead to reproductive isolation and the formation of new species. Insect cuticular hydrocarbons (CHCs) ...are potential examples of such dual traits. They form a waxy layer on the cuticle of the insect to maintain water balance and prevent desiccation, while also acting as signaling molecules in mate recognition and chemical communication. Because the synthesis of these hydrocarbons in insect oenocytes occurs through a common biochemical pathway, natural or sexual selection on one role may affect the other. In this review, we explore how ecological divergence in insect CHCs can lead to divergence in mating signals and reproductive isolation. We suggest that the evolution of insect CHCs may be ripe models for understanding ecological speciation.
Biologists have long sought to understand which genes and what kinds of changes in their sequences are responsible for the evolution of morphological diversity. Here, I outline eight principles ...derived from molecular and evolutionary developmental biology and review recent studies of species divergence that have led to a genetic theory of morphological evolution, which states that (1) form evolves largely by altering the expression of functionally conserved proteins, and (2) such changes largely occur through mutations in the cis-regulatory sequences of pleiotropic developmental regulatory loci and of the target genes within the vast networks they control.
We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can ...be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson’s “entanglement equilibrium” that the geometry should obey Einstein’s equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.
...because it extrapolated from molecular data to make inferences about the evolution of form, it may also be considered a pioneering study in evolutionary developmental biology. While standard ...population genetic tests have been used to search human protein sequences for statistical evidence of positive selection 63,69, several examples of positive selection on cis-regulatory sequences of physiological genes are documented 70-72.
Bushes in the tree of life Rokas, Antonis; Carroll, Sean B
PLoS biology,
11/2006, Volume:
4, Issue:
11
Journal Article
Peer reviewed
Open access
Here we examine how the combination of the spacing of cladogenetic events and the high frequency of independently evolved characters (homoplasy) limit the resolution of ancient divergences. Because ...some histories may not be resolvable by even vast increases in amounts of conventional data, the identification of new molecular characters will be crucial to future progress. "... there is, after all, one true tree of life, the unique pattern of evolutionary branchings that actually happened. ...molecular systematics must now move beyond conventional characters and mine genomic data for new, less-homoplastic characters such as RGCs 62.
I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a ...closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schrödinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.
In a wide class of cosmological models, a positive cosmological constant drives cosmological evolution toward an asymptotically de Sitter phase. Here we connect this behavior to the increase of ...entropy over time, based on the idea that de Sitter spacetime is a maximum-entropy state. We prove a cosmic no-hair theorem for Robertson-Walker and Bianchi I spacetimes that admit a Q-screen (“quantum” holographic screen) with certain entropic properties: If generalized entropy, in the sense of the cosmological version of the generalized second law conjectured by Bousso and Engelhardt, increases up to a finite maximum value along the screen, then the spacetime is asymptotically de Sitter in the future. Moreover, the limiting value of generalized entropy coincides with the de Sitter horizon entropy. We do not use the Einstein field equations in our proof, nor do we assume the existence of a positive cosmological constant. As such, asymptotic relaxation to a de Sitter phase can, in a precise sense, be thought of as cosmological equilibration.
We investigate the proposed connection between de Sitter spacetime and the multiscale entanglement renormalization ansatz (MERA) tensor network, and ask what can be learned via such a construction. ...We show that the quantum state obeys a cosmic no-hair theorem: the reduced density operator describing a causal patch of the MERA asymptotes to a fixed point of a quantum channel, just as spacetimes with a positive cosmological constant asymptote to de Sitter space. The MERA is potentially compatible with a weak form of complementarity (local physics only describes single patches at a time, but the overall Hilbert space is infinite dimensional) or, with certain specific modifications to the tensor structure, a strong form (the entire theory describes only a single patch plus its horizon, in a finite-dimensional Hilbert space). We also suggest that de Sitter evolution has an interpretation in terms of circuit complexity, as has been conjectured for anti–de Sitter space.
Tandem gene duplication is an important mutational process in evolutionary adaptation and human disease. Hypothetically, two tandem gene copies should produce twice the output of a single gene, but ...this expectation has not been rigorously investigated. Here, we show that tandem duplication often results in more than double the gene activity. A naturally occurring tandem duplication of the Alcohol dehydrogenase (Adh) gene exhibits 2.6-fold greater expression than the single-copy gene in transgenic Drosophila. This tandem duplication also exhibits greater activity than two copies of the gene in trans, demonstrating that it is the tandem arrangement and not copy number that is the cause of overactivity. We also show that tandem duplication of an unrelated synthetic reporter gene is overactive (2.3- to 5.1-fold) at all sites in the genome that we tested, suggesting that overactivity could be a general property of tandem gene duplicates. Overactivity occurs at the level of RNA transcription, and therefore tandem duplicate overactivity appears to be a previously unidentified form of position effect. The increment of surplus gene expression observed is comparable to many regulatory mutations fixed in nature and, if typical of other genomes, would shape the fate of tandem duplicates in evolution.
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