Holography, Unfolding and Higher-Spin Theory

Holographic duality is argued to relate classes of models that have equivalent unfolded formulation, hence exhibiting different space-time visualizations for the same theory. This general phenomenon is illustrated by the $AdS_4$ higher-spin gauge theory shown to be dual to the theory of 3d conformal currents of all spins interacting with 3d conformal higher-spin fields of Chern-Simons type. Generally, the resulting 3d boundary conformal theory is nonlinear, providing an interacting version of the 3d boundary sigma model conjectured by Klebanov and Polyakov to be dual to the $AdS_4$ HS theory in the large $N$ limit. Being a gauge theory it escapes the conditions of the theorem of Maldacena and Zhiboedov, which force a 3d boundary conformal theory to be free. Two reductions of particular higher-spin gauge theories where boundary higher-spin gauge fields decouple from the currents and which have free boundary duals are identified. Higher-spin holographic duality is also discussed for the cases of $AdS_3/CFT_2$ and duality between higher-spin theories and nonrelativistic quantum mechanics. In the latter case it is shown in particular that ($dS$) $AdS$ geometry in the higher-spin setup is dual to the (inverted) harmonic potential in the quantum-mechanical setup.Comment: 57 pages, V2: Acknowledgements, references, comments, clarifications and new section on reductions of particular HS theories associated with free boundary theories are added. Typos corrected, V3. Minor corrections: clarification in section 9 is added and typos correcte

Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula

We investigate the asymptotic behavior of the Selberg-like integral $$\frac1{N!}\int_{[0,1]^N}x_1^p\prod_{i<j}(x_i-x_j)^2\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i$$, as $N\to\infty$ for different scalings of the parameters $a$ and $b$ with $N$. Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting $N$ channels in the two attached leads. Making use of Newton's interpolation formula, we show that an asymptotic limit exists and we compute it explicitly

Maternal Diabetes and Obesity Influence the Fetal Epigenome in a Largely Hispanic Population

BACKGROUND: Obesity and diabetes mellitus are directly implicated in many adverse health consequences in adults as well as in the offspring of obese and diabetic mothers. Hispanic Americans are particularly at risk for obesity, diabetes, and end-stage renal disease. Maternal obesity and/or diabetes through prenatal programming may alter the fetal epigenome increasing the risk of metabolic disease in their offspring. The aims of this study were to determine if maternal obesity or diabetes mellitus during pregnancy results in a change in infant methylation of CpG islands adjacent to targeted genes specific for obesity or diabetes disease pathways in a largely Hispanic population. METHODS: Methylation levels in the cord blood of 69 newborns were determined using the Illumina Infinium MethylationEPIC BeadChip. Over 850,000 different probe sites were analyzed to determine whether maternal obesity and/or diabetes mellitus directly attributed to differential methylation; epigenome-wide and regional analyses were performed for significant CpG sites. RESULTS: Following quality control, agranular leukocyte samples from 69 newborns (23 normal term (NT), 14 diabetes (DM), 23 obese (OB), 9 DM/OB) were analyzed for over 850,000 different probe sites. Contrasts between the NT, DM, OB, and DM/OB were considered. After correction for multiple testing, 15 CpGs showed differential methylation from the NT, associated with 10 differentially methylated genes between the diabetic and non-diabetic subgroups, CCDC110, KALRN, PAG1, GNRH1, SLC2A9, CSRP2BP, HIVEP1, RALGDS, DHX37, and SCNN1D. The effects of diabetes were partly mediated by the altered methylation of HOOK2, LCE3C, and TMEM63B. The effects of obesity were partly mediated by the differential methylation of LTF and DUSP22. CONCLUSIONS: The presented data highlights the associated altered methylation patterns potentially mediated by maternal diabetes and/or obesity. Larger studies are warranted to investigate the role of both the identified differentially methylated loci and the effects on newborn body composition and future health risk factors for metabolic disease. Additional future consideration should be targeted to the role of Hispanic inheritance. Potential future targeting of transgenerational propagation and developmental programming may reduce population obesity and diabetes risk

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

A Note on Vectorial AdS5_5/CFT4_4 Duality for Spin-jj Boundary Theory

The vectorial holographic correspondences between higher-spin theories in AdS$_5$ and free vector models on the boundary are extended to the cases where the latter is described by free massless spin-$j$ field. The dual higher-spin theory in the bulk does not include gravity and can only be defined on rigid AdS$_5$ background with $S^4$ boundary. We discuss various properties of these rather special higher-spin theories and calculate their one-loop free energies. We show that the result is proportional to the same quantity for spin-$j$ doubleton treated as if it is a AdS$_5$ field. Finally, we consider even more special case where the boundary theory itself is given by an infinite tower of massless higher-spin fields.Comment: 27 pages, version to appear in JHE

Acarbose improves health and lifespan in aging HET3 mice

To follow‐up on our previous report that acarbose (ACA), a drug that blocks postprandial glucose spikes, increases mouse lifespan, we studied ACA at three doses: 400, 1,000 (the original dose), and 2,500 ppm, using genetically heterogeneous mice at three sites. Each dose led to a significant change (by log‐rank test) in both sexes, with larger effects in males, consistent with the original report. There were no significant differences among the three doses. The two higher doses produced 16% or 17% increases in median longevity of males, but only 4% or 5% increases in females. Age at the 90th percentile was increased significantly (8%–11%) in males at each dose, but was significantly increased (3%) in females only at 1,000 ppm. The sex effect on longevity is not explained simply by weight or fat mass, which were reduced by ACA more in females than in males. ACA at 1,000 ppm reduced lung tumors in males, diminished liver degeneration in both sexes and glomerulosclerosis in females, reduced blood glucose responses to refeeding in males, and improved rotarod performance in aging females, but not males. Three other interventions were also tested: ursolic acid, 2‐(2‐hydroxyphenyl) benzothiazole (HBX), and INT‐767; none of these affected lifespan at the doses tested. The acarbose results confirm and extend our original report, prompt further attention to the effects of transient periods of high blood glucose on aging and the diseases of aging, including cancer, and should motivate studies of acarbose and other glucose‐control drugs in humans.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148418/1/acel12898.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148418/2/acel12898_am.pd

Ground state properties of a Tonks-Girardeau Gas in a periodic potential

In this paper, we investigate the ground-state properties of a bosonic Tonks-Girardeau gas confined in a one-dimensional periodic potential. The single-particle reduced density matrix is computed numerically for systems up to $N=265$ bosons. Scaling analysis of the occupation number of the lowest orbital shows that there are no Bose-Einstein Condensation(BEC) for the periodically trapped TG gas in both commensurate and incommensurate cases. We find that, in the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, -0.5 and 1, respectively, while in the incommensurate case, they are 0.5, -0.5 and 1.5, respectively. These exponents are related to each other in a universal relation.Comment: 9 pages, 10 figure

The RNA-Binding Protein Musashi1 Affects Medulloblastoma Growth via a Network of Cancer- Related Genes and Is an Indicator of Poor Prognosis

Musashi1 (Msi1) is a highly conserved RNA-binding protein that is required during the development of the nervous system. Msi1 has been characterized as a stem cell marker, controlling the balance between self-renewal and differentiation, and has also been implicated in tumorigenesis, being highly expressed in multiple tumor types. We analyzed Msi1 expression in a large cohort of medulloblastoma samples and found that Msi1 is highly expressed in tumor tissue compared with normal cerebellum. Notably, high Msi1 expression levels proved to be a sign of poor prognosis. Msi1 expression was determined to be particularly high in molecular subgroups 3 and 4 of medulloblastoma. We determined that Msi1 is required for tumorigenesis because inhibition of Msi1 expression by small-interfering RNAs reduced the growth of Daoy medulloblastoma cells in xenografts. To characterize the participation of Msi1 in medulloblastoma, we conducted different high-throughput analyses. Ribonucleoprotein immunoprecipitation followed by microarray analysis (RIP-chip) was used to identify mRNA species preferentially associated with Msi1 protein in Daoy cells. We also used cluster analysis to identify genes with similar or opposite expression patterns to Msi1 in our medulloblastoma cohort. A network study identified RAC1, CTGF, SDCBP, SRC, PRL, and SHC1 as major nodes of an Msi1-associated network. Our results suggest that Msi1 functions as a regulator of multiple processes in medulloblastoma formation and could become an important therapeutic target

Algorithmic iteration for computational intelligence

Machine awareness is a disputed research topic, in some circles considered a crucial step in realising Artificial General Intelligence. Understanding what that is, under which conditions such feature could arise and how it can be controlled is still a matter of speculation. A more concrete object of theoretical analysis is algorithmic iteration for computational intelligence, intended as the theoretical and practical ability of algorithms to design other algorithms for actions aimed at solving well-specified tasks. We know this ability is already shown by current AIs, and understanding its limits is an essential step in qualifying claims about machine awareness and Super-AI. We propose a formal translation of algorithmic iteration in a fragment of modal logic, formulate principles of transparency and faithfulness across human and machine intelligence, and consider the relevance to theoretical research on (Super)-AI as well as the practical import of our results