An official website of the United States government
De Sitter black holes and other non-perturbative configurations can be used to probe the holographic degrees of freedom of de Sitter space. For small black holes evidence was first given in seminal work of Banks, Fiol, and Morrise; and followups by Banks and Fischler; showing that dS is described by a form of matrix theory. For large black holes the evidence given here is new: Gravitational calculations and matrix theory calculations of the rates of exponentially rare fluctuations match one another in surprising detail. The occurrence of the Nariai geometry and the "inside-out" transition are especially interesting examples which I explain.
more »
« less
New Theory for Increasingly Tangled Banks
https://issues.org/new-theory-increasingly-tangled-banks/ Twombly, Saran, Alan Hastings, Tom Miller, Michael Cortez, Karen Abbott, Tanjona Ramiadantsoa, Julie Blackwood, and Olivia Prosper. “New Theory for Increasingly Tangled Banks.” Issues in Science and Technology 38, no. 4 (Summer 2022): 39–44. Theory has fallen out of fashion in the sciences, in favor of data collection and number crunching. But the conceptual frameworks provided by theory are essential for addressing society’s most complex and urgent problems.
more »
« less
- Award ID(s):
- 1908538
- PAR ID:
- 10397887
- Date Published:
- Journal Name:
- Issues in science and technology
- Volume:
- XXXVIII
- Issue:
- 4
- ISSN:
- 0748-5492
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean–Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves.more » « less
-
A bstract In the setting of the Berenstein-Maldacena-Nastase Matrix theory, dual to light-cone M-theory in a PP-wave background, we compute the Von Neumann entanglement entropy between a probe giant graviton and a source. We demonstrate that this entanglement entropy is directly and generally related to the local tidal acceleration experienced by the probe. This establishes a new map between local spacetime geometry and quantum entanglement, suggesting a mechanism through which geometry emerges from Matrix quantum mechanics. We extend this setting to light-cone M-theory in flat space, or the Banks-Fischler-Shenker-Susskind Matrix model, and we conjecture a new general relation between a certain measure of entanglement in Matrix theories and local spacetime geometry. The relation involves a ‘c-tensor’ that measures the evolution of local transverse area and relates to the local energy-momentum tensor measured by a probe.more » « less
-
Abstract Dispersal and dormancy are two common strategies allowing for species persistence and the maintenance of biodiversity in variable environments. However, theory and empirical tests of spatial diversity patterns tend to examine either mechanism in isolation. Here, we developed a stochastic, spatially explicit metacommunity model incorporating seed banks with varying germination and survival rates. We found that dormancy and dispersal had interactive, nonlinear effects on the maintenance and distribution of metacommunity diversity. Seed banks promoted local diversity when seed survival was high and maintained regional diversity through interactions with dispersal. The benefits of seed banks for regional diversity were largest when dispersal was high or intermediate, depending on whether local competition was equal or stabilising. Our study shows that classic predictions for how dispersal affects metacommunity diversity can be strongly influenced by dormancy. Together, these results emphasise the need to consider both temporal and spatial processes when predicting multi‐scale patterns of diversity.more » « less
-
In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the stock market and borrow money in order to raise funds. We propose a simple model to find the maximum amount of new funds the banks can raise in these ways. To do this, we incorporate market confidence of the bank together with market confidence of all the other banks in the system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of Nash equilibrium point for all these problems. Finally, using this model we investigate if banks have become safer since the crisis. We calibrate this model with market data and conduct an empirical study to assess safety of the financial system before, during after the last financial crisis.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- The DOI is not currently available.
