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At least 325 records · Page 18

Habitat specialization and edge effects of soil microbial communities in a fragmented landscape

Abstract Soil microorganisms play outsized roles in nutrient cycling, plant health, and climate regulation. Despite their importance, we have a limited understanding of how soil microbes are affected by habitat fragmentation, including their responses to conditions at fragment edges, or “edge effects.” To understand the responses of soil communities to edge effects, we analyzed the distributions of soil bacteria, archaea, and fungi in an experimentally fragmented system of open patches embedded within a forest matrix. In addition, we identified taxa that consistently differed among patch, edge, or matrix habitats (“specialists”) and taxa that showed no habitat preference (“nonspecialists”). We hypothesized that microbial community turnover would be most pronounced at the edge between habitats. We also hypothesized that specialist fungi would be more likely to be mycorrhizal than nonspecialist fungi because mycorrhizae should be affected more by different plant hosts among habitats, whereas specialist prokaryotes would have smaller genomes (indicating reduced metabolic versatility) and be less likely to be able to sporulate than nonspecialist prokaryotes. Across all replicate sites, the matrix and patch soils harbored distinct microbial communities. However, sites where the contrasts in vegetation and pH between the patch and matrix were most pronounced exhibited larger differences between patch and matrix communities and tended to have edge communities that differed from those in the patch and forest. There were similar numbers of patch and matrix specialists, but very few edge specialist taxa. Acidobacteria and ectomycorrhizae were more likely to be forest specialists, while Chloroflexi, Ascomycota, and Glomeromycota (i.e., arbuscular mycorrhizae) were more likely to be patch specialists. Contrary to our hypotheses, nonspecialist bacteria were not more likely than specialist bacteria to have larger genomes or to be spore‐formers. We found partial support for our mycorrhizal hypothesis: arbuscular mycorrhizae, but not ectomycorrhizae, were more likely to be specialists. Overall, our results indicate that soil microbial communities are sensitive to edges, but not all taxa are equally affected, with arbuscular mycorrhizae in particular showing a strong response to habitat edges. In the context of increasing habitat fragmentation worldwide, our results can help inform efforts to maintain the structure and functioning of the soil microbiome.

Winfrey, Claire C. [Department of Ecology and Evol↗

Deprotection of N ‐ tert ‐Butoxycarbonyl (Boc) Protected Functionalized Heteroarenes via Addition–Elimination with 3‐Methoxypropylamine

Continued pursuit of functionalized soft‐N‐donor complexant scaffolds with favorable solubility and kinetics profiles applicable for the separation of the trivalent minor actinides from the lanthanides has attracted significant interest over the last three decades. Recent work from this laboratory resulted in the production of various N ‐Boc protected [1,2,4]triazinyl‐pyridin‐2‐yl indole Lewis basic procomplexants which necessitated the removal of the indole N ‐Boc protecting group prior to evaluation of complexant efficacy in separations assays. Traditional deprotection strategies involving trifluoroacetic and other protic and Lewis acids proved unsuccessful in removal of the recalcitrant indole‐ N ‐Boc protecting group necessitating the development of a new strategy for deprotection of this complexant class. A serendipitous result facilitated utilization of 3‐methoxypropylamine as a mild deprotecting agent for various N ‐Boc protected heteroarenes via a proposed addition–elimination mechanism. Method development, application to various heteroarenes including indoles, 1,2‐indazoles, 1,2‐pyrazoles, and related derivatives, a ten‐fold scale‐up reaction, and experimental evaluation of a preliminary mechanistic hypothesis are reported herein.

Gulledge, Zachary Z.↗

Through the interface: New insights of the hydrogen evolution and oxidation reactions in aqueous solutions

Abstract Hydrogen evolution and oxidation reactions (HER/HOR) are the most fundamental reactions in electrocatalysis. Despite the practical significance, the mechanisms of HER/HOR in aqueous solutions are still elusive. Various theories have been proposed to rationalize the pH effect, cation effect, and structure effect of HER/HOR but none of them can explain all observations. In this review, we discuss four schools of thought for the HER/HOR, focusing on the strengths and shortcomings of each hypothesis and highlighting the magnitude of electrochemical interface structure in hydrogen electrocatalysis.

Liu, Ershuai↗

Association of female reproductive and hormonal factors with gallbladder cancer risk in Asia: A pooled analysis of the Asia Cohort Consortium

Abstract The female predominance of gallbladder cancer (GBC) has led to a hypothesis regarding the hormone‐related aetiology of GBC. We aimed to investigate the association between female reproductive factors and GBC risk, considering birth cohorts of Asian women. We conducted a pooled analysis of 331,323 women from 12 cohorts across 4 countries (China, Japan, Korea, and Singapore) in the Asia Cohort Consortium. Cox proportional hazard models were used to estimate the hazard ratios (HRs) and corresponding 95% confidence intervals (CIs) to assess the association between reproductive factors (age at menarche, parity, age at first delivery, breastfeeding, and age at menopause) and GBC risk. We observed that a later age at menarche was associated with an increased risk of GBC (HR 1.4, 95% CI 1.16–1.70 for 17 years and older vs. 13–14 years), especially among the cohort born in 1940 and later (HR 2.5, 95% CI 1.50–4.35). Among the cohort born before 1940, women with a later age at first delivery showed an increased risk of GBC (HR 1.56, 95% CI 1.08–2.24 for 31 years of age and older vs. 20 years of age and younger). Other reproductive factors did not show a clear association with GBC risk. Later ages at menarche and at first delivery were associated with a higher risk of GBC, and these associations varied by birth cohort.

Shin, Aesun↗

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A synthetic strategy for the preparation of alkoxy‐functionalized bis‐1,2,4‐triazinyl‐2,6‐pyridines

Heteroaryl-1,2,4-triazine complexants are commonly utilized in separation science for the selective chelation of minor An from Ln in simulated high-level waste. Furthermore, to facilitate access to relevant chemical entities for hypothesis-driven inquiry toward improved separations performance, a synthetic method to construct various alkoxy-complexant derivatives was required. In this work, a convergent synthetic strategy for the production of 3,3′- and 4,4′-tetraalkoxy-bis-1,2,4-triazinyl-2,6-pyridines from readily available starting materials via a dealkylation/alkylation/condensation approach is described. Synthetic method development, substrate scope, preliminary solubility, and hydrolytic stability data in various process-relevant diluents are reported herein.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Demonstrating Hierarchical System Development With the Common Community Physics Package Single‐Column Model: A Case Study Over the Southern Great Plains

This study demonstrates a specific application of the hierarchical system development (HSD) approach to investigate, analyze, and attribute model issues within the Unified Forecast System (UFS), with a focus on process isolation. By evaluating a non‐precipitating, shallow cumulus case at the Atmospheric Radiation Measurement Southern Great Plains site in the UFS global forecast against the observation, the investigation identifies a warmer and deeper daytime convective planetary boundary layer (PBL) and misrepresented nocturnal PBL transition. Hypothesis testing, which employs the Common Community Physics Package (CCPP) single‐column model (SCM) and uses the same physics as the UFS global model, confirms that these issues are attributed to the model physics and initialization. Specifically, misrepresented PBL processes are linked to problematic surface condition and a lack of cloud formation, which may stem from deficiencies in PBL and cloud microphysics parameterizations and their interactions. The UFS initial condition contributes to an earlier, excessively collapsed daytime convective boundary layer and a lack of decoupling between the stable boundary layer and residual layer late in the afternoon. This work introduces an avenue for the community to engage with the application of HSD, along with the CCPP and CCPP SCM, to understand the interplay of model physics, disentangle the roles of model components, as well as facilitate model and forecast improvement.

54 ENVIRONMENTAL SCIENCES↗

Screening a knowledge‐based library of low molecular weight compounds against the proline biosynthetic enzyme 1‐pyrroline‐5‐carboxylate 1 ( PYCR1)

Abstract Δ 1 ‐pyrroline‐5‐carboxylate reductase isoform 1 (PYCR1) is the last enzyme of proline biosynthesis and catalyzes the NAD(P)H‐dependent reduction of Δ 1 ‐pyrroline‐5‐carboxylate toL‐proline. High PYCR1 gene expression is observed in many cancers and linked to poor patient outcomes and tumor aggressiveness. The knockdown of thePYCR1gene or the inhibition of PYCR1 enzyme has been shown to inhibit tumorigenesis in cancer cells and animal models of cancer, motivating inhibitor discovery. We screened a library of 71 low molecular weight compounds (average MW of 131 Da) against PYCR1 using an enzyme activity assay. Hit compounds were validated with X‐ray crystallography and kinetic assays to determine affinity parameters. The library was counter‐screened against human Δ 1 ‐pyrroline‐5‐carboxylate reductase isoform 3 and proline dehydrogenase (PRODH) to assess specificity/promiscuity. Twelve PYCR1 and one PRODH inhibitor crystal structures were determined. Three compounds inhibit PYCR1 with competitive inhibition parameter of 100 μM or lower. Among these, (S)‐tetrahydro‐2H‐pyran‐2‐carboxylic acid (70 μM) has higher affinity than the current best tool compoundN‐formyl‐l‐proline, is 30 times more specific for PYCR1 over human Δ 1 ‐pyrroline‐5‐carboxylate reductase isoform 3, and negligibly inhibits PRODH. Structure‐affinity relationships suggest that hydrogen bonding of the heteroatom of this compound is important for binding to PYCR1. The structures of PYCR1 and PRODH complexed with 1‐hydroxyethane‐1‐sulfonate demonstrate that the sulfonate group is a suitable replacement for the carboxylate anchor. This result suggests that the exploration of carboxylic acid isosteres may be a promising strategy for discovering new classes of PYCR1 and PRODH inhibitors. The structure of PYCR1 complexed withl‐pipecolate and NADH supports the hypothesis that PYCR1 has an alternative function in lysine metabolism.

Biochemistry & Molecular Biology↗

Position-specific carbon isotope analysis of serine by gas chromatography/Orbitrap mass spectrometry, and an application to plant metabolism

Position-specific 13 C/ 12 C ratios within amino acids remain largely unexplored in environmental samples due to methodological limitations. We hypothesized that natural-abundance isotope patterns in serine may serve as a proxy for plant metabolic fluxes including photorespiration. Here we describe an Orbitrap method optimized for the position-specific carbon isotope analysis of serine to test our hypothesis and discuss the generalizability of this method to other amino acids. Position-specific carbon isotope ratios of serine were measured using a Thermo Scientific™ Q Exactive™ GC Orbitrap™. Amino acids were hydrolyzed from Arabidopsis biomass, purified from potential matrix interferences, and derivatized alongside standards. Derivatized serine (N,O-bis(trifluoroacetyl)methyl ester) was isolated using gas chromatography, trapped in a reservoir, and purged into the electron ionization source over tens of minutes, producing fragment ions containing different combinations of atoms from the serine-derivative molecule. The 13 C/ 12 C ratios of fragments with monoisotopic masses of 110.0217, 138.0166, and 165.0037 Da were monitored in the mass analyzer and used to calculate position-specific δ 13 C values relative to a working standard. This methodology constrains position-specific δ 13 C values for nanomole amounts of serine isolated from chemically complex mixtures. The δ 13 C values of fragment ions of serine were characterized with ≤1‰ precisions, leading to propagated standard errors of 0.7–5‰ for each carbon position. Position-specific δ 13 C values differed by up to ca 28 ± 5‰ between serine molecules hydrolyzed from plants grown under contrasting pCO 2 , selected to promote different fluxes through photosynthesis and photorespiration. The method was validated using pure serine standards characterized offline. Here this study presents the first Orbitrap-based measurements of natural-abundance, position-specific carbon isotope variation in an amino acid isolated from a biological matrix. We present a method for the precise characterization of isotope ratios in serine and propose applications probing metabolism in plants. We discuss the potential for extending these approaches to other amino acids, paving the way for novel applications.

59 BASIC BIOLOGICAL SCIENCES↗

Land management effects on wet aggregate stability and carbon content

Land management affects soil structure and many other soil properties and processes. Our objectives were to evaluate soil organic C (SOC), aggregate size distribution, aggregate-associated C, and soil structure as affected by long-term land management and slope. A chronosequence of 38 on-farm sites with low to high (5–18%) slopes was selected to evaluate 5–40 yr of management. The sites were classified as business as usual (BAU) cropland (BAU-Crop), BAU pasture (BAU-Past), newly established conservation reserve program (CRP) areas (CRP-New), and established CRP (CRP-Old). Soil samples were collected from the 0-to-5- and 5-to-15-cm depth increments and processed for soil property measurements including fractionation by wet sieving into five aggregate size classes (>2,000, 1,000–2,000, 500–1,000, 250–500, and 53–250 μm). Within the surface 5 cm, mean weight diameter (MWD) and geometric mean diameter (GMD) were used to characterize soil structural stability. The BAU-Past and CRP-Old sites had 79% more macroaggregates (>2,000, 1,000–2,000, and 500–1,000 μm), 123% higher MWD, 38% higher GMD, and 47% higher SOC than BAU-Crop or CRP-New sites. The 5-to-15-cm depth increment showed a similar but lower magnitude response. Aggregate-associated C was quantified using a constant soil mass that reflected aggregate size distribution to prevent overestimating C content. Lower-slope locations had more SOC, more macroaggregates, more C associated with macroaggregates, and higher GMD and MWD compared with high-slope locations across all management classifications and soil depths. The results support our hypothesis that the high-slop soils may benefits from specific management decisions than the lower-sloping soils as a function of landscape property. We recommend reestablishing grassland on sloping land that is susceptible to excessive soil erosion, although those practices will likely take a long time to restore soil structural stability and SOC content to precultivation levels.

54 ENVIRONMENTAL SCIENCES↗

Synthesis of Pyrimidine Modified Seleno–DNA as a Novel Approach to Antisense Candidate

Chemically modified antisense oligonucleotides (ASO) currently in pre–clinical and clinical experiments mainly focus on the 2’–position derivatizations to enhance stability and targeting affinity. Considering the possible incompatibility of 2’–modifications with RNase H stimulation and activity, we have hypothesized that the atom specific modifications on nucleobases can retain the complex structure and RNase H activity, while enhancing ASO's binding affinity, specificity, and stability against nucleases. Herein we report a novel strategy to explore our hypothesis by synthesizing the deoxynucleoside phosphoramidite building block with the seleno–modification at 5–position of thymidine, as well as its Se–oligonucleotides. Via X–ray crystal structural study, we found that the Se–modification was located in the major groove of nucleic acid duplex and didn't cause the thermal and structural perturbations. Surprisingly, our nucleobase–modified Se–DNAs were exceptionally resistant to nuclease digestion, while compatible with RNase H activity. In conclusion, this affords a novel avenue for potential anti–sense modification in the form of Se–antisense oligonucleotides (Se–ASO).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Persistent Structure and Frustrated Magnetism in High Entropy Rare-Earth Zirconates

The configurational complexity and distinct local atomic environments of high entropy oxides remain largely unexplored, leaving structure-property relationships and the hypothesis that the family offers rich tunability for applications ambiguous. This work investigates the influence of cation size and materials synthesis in determining the resulting structure and magnetic properties of a family of high entropy rare-earth zirconates (HEREZs, nominal composition RE 2 Zr 2 O 7 with RE = rare-earth element combinations including Eu, Gd, Tb, Dy, Ho, La, or Sc). Here, the structural characterization of the series is examined through synchrotron X-ray diffraction and pair distribution function analysis, and electron microscopy, demonstrating average defect-fluorite structures with considerable local disorder, in all samples. The surface morphology and particle sizes are found to vary significantly with preparation method, with irregular micron-sized particles formed by high temperature sintering routes, spherical nanoparticles resulting from chemical co-precipitation methods, and porous nanoparticle agglomerates resulting from polymer steric entrapment synthesis. In agreement with the disordered cation distribution found across all samples, magnetic measurements indicate that all synthesized HEREZs show frustrated magnetic behavior, as seen in a number of single-component RE 2 Zr 2 O 7 pyrochlore oxides. These findings advance the understanding of the local structure of high entropy oxides and demonstrate strategies for designing nanostructured morphologies in the class.

36 MATERIALS SCIENCE↗

Hierarchically Structured Vitrimer Biocomposites for Sustainable Manufacturing

Polymers containing dynamic covalent bonds (DCBs) exhibit thermoplastic-like flow above their topology freezing temperature (T v ) while maintaining thermoset-like properties below it, making them promising for sustainable manufacturing. However, their large-scale adoption remains limited due to challenges in accurately determining T v and achieving efficient fiber-matrix bonding in composite applications. Here, hierarchically structured epoxy-anhydride-based polyester vitrimer composites reinforced with cellulosic filaments is demonstrated, where hydroxyl groups on fiber surfaces participate directly in transesterification with the matrix. Further, this dynamic interfacial bonding delivers exceptional mechanical properties, including ≈70 MPa shear strength and >10% strain-to-failure, while enabling thermal malleability. Using a combination of nuclear magnetic resonance and nano-infrared spectroscopies, direct evidence is provided that chemical bond exchange begins well below the conventionally measured T v , supporting the hypothesis that rheologically determined T v reflects a combination of chemical exchange and frictional dynamics rather than a discrete transition. The composites demonstrate excellent processability through vacuum-assisted resin transfer molding and maintain >90% of their mechanical properties after multiple thermal reforming cycles. These findings advance both the fundamental understanding of vitrimeric transitions and the practical development of sustainable, high-performance composite materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigations of water/oxide interfaces by molecular dynamics simulations

Water/oxide interfaces are ubiquitous on earth and show significant influence on many chemical processes. For example, understanding water and solute adsorption as well as catalytic water splitting can help build better fuel cells and solar cells to overcome our looming energy crisis; the interaction between biomolecules and water/oxide interfaces is one hypothesis to explain the origin of life. However, knowledge in this area is still limited due to the difficulty of studying water/solid interfaces. As a result, research using increasingly sophisticated experimental techniques and computational simulations has been carried out in recent years. Although it is difficult for experimental techniques to provide detailed microscopic structural information, molecular dynamics (MD) simulations have satisfactory performance. In this report, we discuss classical and ab initio MD simulations of water/oxide interfaces. Generally, we are interested in the following questions: How do solid surfaces perturb interfacial water structure? How do interfacial water molecules and adsorbed solutes affect solid surfaces and how do interfacial environments affect solvent and solute behavior? Finally, we discuss progress in the application of neural network potential based MD simulations, which offer a promising future because this approach has already enabled ab initio level accuracy for very large systems and long trajectories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Factors Affecting Bait Site Visitation: Area of Influence of Baits

Baiting is a fundamental strategy for the global management of wild pigs (Sus scrofa); however, little information exists on how anthropogenic bait affects wild pig movements on a landscape. We investigated factors that are important in determining the spatial area of attraction for wild pigs to bait (‘area of influence’ of a bait site) using data from Global Positioning System (GPS) collars and locations of bait sites. We monitored movements of wild pigs in 2 distinct study areas in the United States from February to September 2016 and used locational data using GPS collars to analyze the influence of habitat quality (dependent on site), home range size, number of bait sites in the home range, distance to a bait site, and sex in relation to movement in time and space. We determined the average area of influence by calculating the area of a circle with the radius as the average maximum distance travelled by wild pigs to reach a bait site. The average area of influence for our bait sites was 6.7 km 2 (or a radius of approximately 1.5 km), suggesting a bait spacing of approximately 1.5 km would be adequate to capture visitation by most wild pigs and a spacing of 3 km could allow substantial visitation while minimizing redundant effort depending on the spatial structure of the populations. Eighty percent of wild pigs first visited bait sites within 8.9 days after bait deployment; and they visited earlier when their home range size was larger. As the number of bait sites in an individual's home range increased, individual pigs visited more bait sites, and the probability of a visit increased dramatically up to approximately 5 bait sites and much less thereafter. Wild pigs travelled farther distances to visit bait sites in lower quality habitat. Our results support the hypothesis that habitat quality can mediate the efficacy of baiting programs for wildlife by influencing their movement patterns and motivation to use anthropogenic resources. Our results suggest wild pigs will travel extensively within their home range to visit bait sites, and that in lower quality habitat, most animals will find bait sites more quickly. Determining the area of influence of bait sites can increase the efficacy of planning and monitoring management programs. Overall, our study provides new information to help managers plan baiting designs to attract the greatest number of pigs.

59 BASIC BIOLOGICAL SCIENCES↗

Stochastic Fault Detection

This entry describes the state-of-the-art and future perspectives on stochastic fault detection, namely, stochastic fault detection and diagnosis (FDD). Both model-based and data-driven FDD methods for stochastic signals and systems have been included, where the use of hypothesis testing, Kalman filtering, system estimation, principal component analysis (PCA), and stochastic distribution control has been discussed for the construction of effective FDD algorithms. Indeed, stochastic FDD constitute an important and integrated part in developing fault-tolerant controls (FTC) for guaranteed safe operation of control systems, of which increased penetration of random factors is inevitable nowadays.

Wang, Aiping↗

Quantum complexity of time evolution with chaotic Hamiltonians

We study the quantum complexity of time evolution in large-N chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator e -iHt whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion — the Eigenstate Complexity Hypothesis (ECH) — which bounds the overlap between offdiagonal energy eigenstate projectors and the k-local operators of the theory, and use it to argue that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-N SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with N = 2 fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE * BQP/poly and PSPACE * BQSUBEXP/subexp, and the “fast-forwarding” of quantum Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A principle of maximum ignorance for semiclassical gravity

The principle of maximum ignorance posits that the coarse-grained description of a system is maximally agnostic about its underlying microscopic structure. We briefly review this principle for random matrix theory and for the eigenstate thermalization hypothesis. We then apply this principle in holography to construct ensembles of random mixed states. This leads to an ensemble of microstates which models our microscopic ignorance, and which on average reproduces the effective semiclassical physics of a given bulk state. We call this ensemble the state-averaging ansatz. The output of our model is a prediction for semiclassical contributions to variances and higher statistical moments over the ensemble of microstates. The statistical moments provide coarse-grained — yet gravitationally non-perturbative — information about the microstructure of the individual states of the ensemble. We show that these contributions exactly match the on-shell action of known wormhole configurations of the gravitational path integral. These results strengthen the view that wormholes simply parametrize the ignorance of the microstructure of a fundamental state, given a fixed semiclassical bulk description.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗