Dimensional reduction in manifold-like causal sets

We investigate the behavior of small subsets of causal sets that approximate Minkowski space in three, four, and five dimensions, and show that their effective dimension decreases smoothly at small distances. The details of the short distance behavior depend on a choice of dimensional estimator, but for a reasonable version of the Myrheim-Meyer dimension, the minimum dimension is $d \approx 2$, reproducing results that have been seen in other approaches to quantum gravity.Comment: 8 pages, 7 figure

Physico-chemical characterization of dietary fiber sources

The physico-chemical characteristics of several dietary fiber sources—wheat bran, corn bran, peanut hull, oatmeal, alfalfa and alpha-cell (cellulose) were studied. All samples were dried in a vacuum-oven and ground until the particles would pass a U.S. Std. Sieve No. 30 but would not pass U.S. Std. Sieve No. 80. The ground samples were analyzed for acid-detergent fiber, acid-detergent lignin, water-holding capacity, bile salt binding, cation-exchange and emulsifying capacities. Proximate analysis of all samples was performed. Based on the results of this experimental study, the following con-clusions were made: Of the six samples, alpha-cell (cellulose) had the highest and oatmeal the lowest acid-detergent fiber content. Peanut hull had the highest and oatmeal the lowest acid-detergent lignin content. There were significant differences among the means of all samples (p\u3c0.05). Among all samples, alfalfa possessed the highest water-holding capacity and oatmeal the lowest. There were significant differences among all means (p\u3c0.05). Alfalfa possessed the highest bile salt binding capacity, followed by oatmeal, but little variation among the means was observed (p\u3c0.05). For cation-exchange capacity oatmeal showed an unusually high cation-exchange capacity, followed by alfalfa. Peanut hull had the lowest cation-exchange capacity. No significant differences among the means of the five groups were observed (p\u3c0.05). As for emulsifying capacity, alfalfa possessed the highest emulsifying capacity. Peanut hull showed the least emulsifying capacity and Duncan\u27s Multiple Range test allowed partitioning of the means into three unique groups (p\u3c0.05). Acid-detergent fiber and acid-detergent lignin did not exhibit strong correlation with any of the functionalities studied. A significant linear relationship was observed between ash and bile salt binding (r = 0.84). No significant relationship was observed among different functionalities (water-holding capacity and bile salt binding, water-holding capacity and cation-exchange capacity and cation-exchange capacity and bile salt binding capacity) except for water-holding capacity and cation-exchange capacity (r = -0.83)

Measurement of the Oxidation State of Mitochondrial Cytochrome c from the Neocortex of the Mammalian Brain

Diffuse optical remission spectra from the mammalian neocortex at visible wavelengths contain spectral features originating from the mitochondria. A new algorithm is presented, based on analytically relating the first differential of the attenuation spectrum to the first differential of the chromophore spectra, that can separate and calculate the oxidation state of cytochrome c as well as the absolute concentration and saturation of hemoglobin. The algorithm is validated in phantoms and then tested on the neocortex of the rat during an anoxic challenge. Implementation of the algorithm will provide detailed information of mitochondrial oxygenation and mitochondrial function in physiological studies of the mammalian brain

Correlation Functions of Huge Operators in AdS3_3/CFT2_2: Domes, Doors and Book Pages

We describe solutions of asymptotically AdS$_3$ Einstein gravity that are sourced by the insertion of operators in the boundary CFT$_2$, whose dimension scales with the central charge of the theory. Previously, we found that the geometry corresponding to a black hole two-point function is simply related to an infinite covering of the Euclidean BTZ black hole. However, here we find that the geometry sourced by the presence of a third black hole operator turns out to be a Euclidean wormhole with two asymptotic boundaries. We construct this new geometry as a quotient of empty AdS$_3$ realized by domes and doors. The doors give access to the infinite covers that are needed to describe the insertion of the operators, while the domes describe the fundamental domains of the quotient on each cover. In particular, despite the standard fact that the Fefferman-Graham expansion is single-sided, the extended bulk geometry contains a wormhole that connects two asymptotic boundaries. We observe that the two-sided wormhole can be made single-sided by cutting off the wormhole and gluing on a "Lorentzian cap". In this way, the geometry gives the holographic description of a three-point function, up to phases. By rewriting the metric in terms of a Liouville field, we compute the on-shell action and find that the result matches with the Heavy-Heavy-Heavy three-point function predicted by the modular bootstrap. Finally, we describe the geometric transition between doors and defects, that is, when one or more dual operators describe a conical defect insertion, rather than a black hole insertion.Comment: 45 pages, 21 figure

Holography and Correlation Functions of Huge Operators: Spacetime Bananas

We initiate the study of holographic correlators for operators whose dimension scales with the central charge of the CFT. Differently from light correlators or probes, the insertion of any such maximally heavy operator changes the AdS metric, so that the correlator itself is dual to a backreacted geometry with marked points at the Poincar\'e boundary. We illustrate this new physics for two-point functions. Whereas the bulk description of light or probe operators involves Witten diagrams or extremal surfaces in an AdS background, the maximally heavy two-point functions are described by nontrivial new geometries which we refer to as "spacetime bananas". As a universal example, we discuss the two-point function of maximally heavy scalar operators described by the Schwarzschild black hole in the bulk and we show that its onshell action reproduces the expected CFT result. This computation is nonstandard, and adding boundary terms to the action on the stretched horizon is crucial. Then, we verify the conformal Ward Identity from the holographic stress tensor and discuss important aspects of the Fefferman-Graham patch. Finally we study a Heavy-Heavy-Light-Light correlator by using geodesics propagating in the banana background. Our main motivation here is to set up the formalism to explore possible universal results for three- and higher-point functions of maximally heavy operators.Comment: 45 pages, 14 figure

An Aggregate Perspective on the Geo-spatial Distribution of Residential Solar Panels

Residential solar panels in the United States (U.S.) are inefficiently distributed in terms of optimizing solar-electrical production. Controlling for local solar electricity generation potential (insolation), the residential solar share of electrical consumption is relatively higher in cloudier locales like the Pacific Northwest and Northeast than it is in sunnier areas like the Western U.S. and Florida. Rebates designed to increase residential solar adoption in places like Florida and Texas with relatively low solar-electrical shares are ineffective and may lead to net decreases in the residential solar share if housing and electrical consumption are complementary. This is because electrical consumption increases faster in response to a decline in effective residential solar prices than actual demand for panels themselves, thus driving down the solar share despite additional installations. Through the lens of a county-level structural model of demand for housing, electricity, and solar panels, we find that this phenomenon is especially prevalent in locales with high demand for cooling services (e.g., air conditioning, refrigeration, etc.) due to high numbers of cooling degree days. Inability to effectively store solar-produced electricity may be to blame. Our results thus suggest that future policies should subsidize nascent battery technologies in place of direct solar-panel installation rebates if the goal is to increase the residential solar share of electrical consumption