Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity

Holographic entanglement entropy was recently recast in terms of Riemannian flows or 'bit threads'. We consider the Lorentzian analog to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. By the nesting of Lorentzian flows, holographic complexity is shown to obey a number of properties. Particularly, the rate of complexity is bounded below by conditional complexity, describing a multi-step optimization with intermediate and final target states. We provide multiple explicit geometric realizations of Lorentzian flows in AdS backgrounds, including their time-dependence and behavior near the singularity in a black hole interior. Conceptually, discretized flows are interpreted as Lorentzian threads or 'gatelines'. Upon selecting a reference state, complexity thence counts the minimum number of gatelines needed to prepare a target state described by a tensor network discretizing the maximal volume slice, matching its quantum information theoretic definition. We point out that suboptimal tensor networks are important to fully characterize the state, leading us to propose a refined notion of complexity as an ensemble average. The bulk symplectic potential provides a specific 'canonical' thread configuration characterizing perturbations around arbitrary CFT states. Consistency of this solution requires the bulk satisfy the linearized Einstein's equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating for a principle of 'spacetime complexity'. Lastly, we argue Lorentzian threads provide a notion of emergent time. This article is an expanded and detailed version of [arXiv:2105.12735], including several new results.Comment: 95 pages +appendices, 25 pretty figures. Comments welcom

Lorentzian Threads as Gatelines and Holographic Complexity

The continuous min flow-max cut principle is used to reformulate the "complexity=volume" conjecture using Lorentzian flows-divergenceless norm-bounded timelike vector fields whose minimum flux through a boundary subregion is equal to the volume of the homologous maximal bulk Cauchy slice. The nesting property is used to show the rate of complexity is bounded below by "conditional complexity," describing a multistep optimization with intermediate and final target states. Conceptually, discretized Lorentzian flows are interpreted in terms of threads or gatelines such that complexity is equal to the minimum number of gatelines used to prepare a conformal field theory (CFT) state by an optimal tensor network (TN) discretizing the state. We propose a refined measure of complexity, capturing the role of suboptimal TNs, as an ensemble average. The bulk symplectic potential provides a "canonical" thread configuration characterizing perturbations around arbitrary CFT states. Its consistency requires the bulk to obey linearized Einstein's equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating a notion of "spacetime complexity.

Computing spacetime

Inspired by the universality of computation, we advocate for a principle of spacetime complexity, where gravity arises as a consequence of spacetime optimizing the computational cost of its own quantum dynamics. This principle is explicitly realized in the context of the Anti-de Sitter/Conformal Field Theory correspondence, where complexity is naturally understood in terms of state preparation via Euclidean path integrals, and Einstein's equations emerge from the laws of quantum complexity. We visualize spacetime complexity using Lorentzian threads which, conceptually, represent the operations needed to prepare a quantum state in a tensor network discretizing spacetime. Thus, spacetime itself evolves via optimized computation.Comment: 9 pages, 2 figures, Received honorable mention for the 2022 Essay Competition of the Gravity Research Foundation; References added, to appear in the October 2022 Special Issue of the International Journal of Modern Physics

Current understanding of trigeminal ganglion structure and function in headache

Introduction The trigeminal ganglion is unique among the somatosensory ganglia regarding its topography, structure, composition and possibly some functional properties of its cellular components. Being mainly responsible for the sensory innervation of the anterior regions of the head, it is a major target for headache research. One intriguing question is if the trigeminal ganglion is merely a transition site for sensory information from the periphery to the central nervous system, or if intracellular modulatory mechanisms and intercellular signaling are capable of controlling sensory information relevant for the pathophysiology of headaches. Methods An online search based on PubMed was made using the keyword “trigeminal ganglion” in combination with “anatomy”, “headache”, “migraine”, “neuropeptides”, “receptors” and “signaling”. From the relevant literature, further references were selected in view of their relevance for headache mechanisms. The essential information was organized based on location and cell types of the trigeminal ganglion, neuropeptides, receptors for signaling molecules, signaling mechanisms, and their possible relevance for headache generation. Results The trigeminal ganglion consists of clusters of sensory neurons and their peripheral and central axon processes, which are arranged according to the three trigeminal partitions V1–V3. The neurons are surrounded by satellite glial cells, the axons by Schwann cells. In addition, macrophage-like cells can be found in the trigeminal ganglion. Neurons express various neuropeptides, among which calcitonin gene-related peptide is the most prominent in terms of its prevalence and its role in primary headaches. The classical calcitonin gene-related peptide receptors are expressed in non-calcitonin gene-related peptide neurons and satellite glial cells, although the possibility of a second calcitonin gene-related peptide receptor in calcitonin gene-related peptide neurons remains to be investigated. A variety of other signal molecules like adenosine triphosphate, nitric oxide, cytokines, and neurotrophic factors are released from trigeminal ganglion cells and may act at receptors on adjacent neurons or satellite glial cells. Conclusions The trigeminal ganglion may act as an integrative organ. The morphological and functional arrangement of trigeminal ganglion cells suggests that intercellular and possibly also autocrine signaling mechanisms interact with intracellular mechanisms, including gene expression, to modulate sensory information. Receptors and neurotrophic factors delivered to the periphery or the trigeminal brainstem can contribute to peripheral and central sensitization, as in the case of primary headaches. The trigeminal ganglion as a target of drug action outside the blood-brain barrier should therefore be taken into account

PP-Wave / CFT_2 Duality

We investigate the pp-wave limit of the AdS_3\times S^3\times K3 compactification of Type IIB string theory from the point of view of the dual Sym_N(K3) CFT. It is proposed that a fundamental string in this pp-wave geometry is dual to the c=6 effective string of the Sym_N(K3) CFT, with the string bits of the latter being composed of twist operators. The massive fundamental string oscillators correspond to certain twisted Virasoro generators in the effective string. It is shown that both the ground states and the genus expansion parameter (at least in the orbifold limit of the CFT) coincide. Surprisingly the latter scales like J^2/N rather than the J^4/N^2 which might have been expected. We demonstrate a leading-order agreement between the pp-wave and CFT particle spectra. For a degenerate special case (one NS 5-brane) an intriguing complete agreement is found.Comment: JHEP3 LaTeX, 20 pages; discussion of WZW levels clarified, reference adde

Cross-talk signaling in the trigeminal ganglion: role of neuropeptides and other mediators

Abstract The trigeminal ganglion with its three trigeminal nerve tracts consists mainly of clusters of sensory neurons with their peripheral and central processes. Most neurons are surrounded by satellite glial cells and the axons are wrapped by myelinating and non-myelinating Schwann cells. Trigeminal neurons express various neuropeptides, most notably, calcitonin gene-related peptide (CGRP), substance P, and pituitary adenylate cyclase-activating polypeptide (PACAP). Two types of CGRP receptors are expressed in neurons and satellite glia. A variety of other signal molecules like ATP, nitric oxide, cytokines, and neurotrophic factors are released from trigeminal ganglion neurons and signal to neighboring neurons or satellite glial cells, which can signal back to neurons with same or other mediators. This potential cross-talk of signals involves intracellular mechanisms, including gene expression, that can modulate mediators of sensory information, such as neuropeptides, receptors, and neurotrophic factors. From the ganglia cell bodies, which are outside the blood–brain barrier, the mediators are further distributed to peripheral sites and/or to the spinal trigeminal nucleus in the brainstem, where they can affect neural transmission. A major question is how the sensory neurons in the trigeminal ganglion differ from those in the dorsal root ganglion. Despite their functional overlap, there are distinct differences in their ontogeny, gene expression, signaling pathways, and responses to anti-migraine drugs. Consequently, drugs that modulate cross-talk in the trigeminal ganglion can modulate both peripheral and central sensitization, which may potentially be distinct from sensitization mediated in the dorsal root ganglion

NCS-1 Inhibits insulin stimulated GLUT4 translocation in 3T3L1 adipocytes through a phosphatidylinositol 4-kinase dependent pathway

Expression of NCS-1 (neuronal calcium sensor-1, also termed frequenin) in 3T3L1 adipocytes strongly inhibited insulin-stimulated translocation of GLUT4 and insulin-responsive aminopeptidase. The effect of NCS-1 was specific for GLUT4 and the insulin-responsive aminopeptidase translocation as there was no effect on the trafficking of the cation-independent mannose 6-phosphate receptor or the GLUT1 glucose transporter isoform. Moreover, NCS-1 showed partial colocalization with GLUT4-EGFP in the perinuclear region. The inhibitory action of NCS-1 was independent of calcium sequestration since neither treatment with ionomycin nor endothelin-1, both of which elevated the intracellular calcium concentration, restored insulin-stimulated GLUT4 translocation. Furthermore, NCS-1 did not alter the insulin-stimulated protein kinase B (PKB/Akt) phosphorylation or the recruitment of Cbl to the plasma membrane. In contrast, expression of the NCS-1 effector phosphatidylinositol 4-kinase (PI 4-kinase) inhibited insulin-stimulated GLUT4 translocation, whereas co-transfection with an inactive PI 4-kinase mutant prevented the NCS-1-induced inhibition. These data demonstrate that PI 4-kinase functions to negatively regulate GLUT4 translocation through its interaction with NCS-1

Fabular: regression formulas as probabilistic programming

Regression formulas are a domain-specific language adopted by several R packages for describing an important and useful class of statistical models: hierarchical linear regressions. Formulas are succinct, expressive, and clearly popular, so are they a useful addition to probabilistic programming languages? And what do they mean? We propose a core calculus of hierarchical linear regression, in which regression coefficients are themselves defined by nested regressions (unlike in R). We explain how our calculus captures the essence of the formula DSL found in R. We describe the design and implementation of Fabular, a version of the Tabular schema-driven probabilistic programming language, enriched with formulas based on our regression calculus. To the best of our knowledge, this is the first formal description of the core ideas of R's formula notation, the first development of a calculus of regression formulas, and the first demonstration of the benefits of composing regression formulas and latent variables in a probabilistic programming language.Adam Ścibior received travel support from the DARPA PPAML programme. Marcin Szymczak was supported by Microsoft Research through its PhD Scholarship Programme.This is the author accepted manuscript. The final version is available from the Association of Computer Machinery via http://dx.doi.org/10.1145/2837614.283765

Characterization of Antibodies against Receptor Activity-Modifying Protein 1 (RAMP1): A Cautionary Tale

Calcitonin gene-related peptide (CGRP) is a key component of migraine pathophysiology, yielding effective migraine therapeutics. CGRP receptors contain a core accessory protein subunit: receptor activity-modifying protein 1 (RAMP1). Understanding of RAMP1 expression is incomplete, partly due to the challenges in identifying specific and validated antibody tools. We profiled antibodies for immunodetection of RAMP1 using Western blotting, immunocytochemistry and immunohistochemistry, including using RAMP1 knockout mouse tissue. Most antibodies could detect RAMP1 in Western blotting and immunocytochemistry using transfected cells. Two antibodies (844, ab256575) could detect a RAMP1-like band in Western blots of rodent brain but not RAMP1 knockout mice. However, cross-reactivity with other proteins was evident for all antibodies. This cross-reactivity prevented clear conclusions about RAMP1 anatomical localization, as each antibody detected a distinct pattern of immunoreactivity in rodent brain. We cannot confidently attribute immunoreactivity produced by RAMP1 antibodies (including 844) to the presence of RAMP1 protein in immunohistochemical applications in brain tissue. RAMP1 expression in brain and other tissues therefore needs to be revisited using RAMP1 antibodies that have been comprehensively validated using multiple strategies to establish multiple lines of convincing evidence. As RAMP1 is important for other GPCR/ligand pairings, our results have broader significance beyond the CGRP field