Some aspects of pre big bang cosmology

This is a summary of a course given at the Fourth Mexican School on Gravitation and Mathematical Physics on some aspects of PBB cosmology. After introductory remarks the lectures concentrate on some amusing consequences derived from the symmetries of the string theory with respect to such classical concepts as isotropy and homogeneity. The extra dimensions and the symmetries of the M theory are further applied to show that the classical singularities might be just physically irrelevant. In the final lecture a model universe is "produced" from "almost nothing" and it is argued that initial plane waves are thermodynamically natural state for the universe to emerge from.Comment: 15 pages, a course given at the Fourth Mexican School on Gravitation and Mathematical Physics in Huatulco, Mexic

Financial Contagion and Asset Liquidation Strategies

This paper provides a framework for modeling the financial system with multiple illiquid assets during a crisis. This work generalizes the paper by Amini, Filipovic and Minca (2016) by allowing for differing liquidation strategies. The main result is a proof of sufficient conditions for the existence of an equilibrium liquidation strategy with corresponding unique clearing payments and liquidation prices. An algorithm for computing the maximal clearing payments and prices is provided.Comment: 8 page

It's a Trap: Emperor Palpatine's Poison Pill

In this paper we study the financial repercussions of the destruction of two fully armed and operational moon-sized battle stations ("Death Stars") in a 4-year period and the dissolution of the galactic government in Star Wars. The emphasis of this work is to calibrate and simulate a model of the banking and financial systems within the galaxy. Along these lines, we measure the level of systemic risk that may have been generated by the death of Emperor Palpatine and the destruction of the second Death Star. We conclude by finding the economic resources the Rebel Alliance would need to have in reserve in order to prevent a financial crisis from gripping the galaxy through an optimally allocated banking bailout.Comment: 10 pages, 4 figure

Exact Inflationary Solutions from a Superpotential

We propose a novel, potentially useful generating technique for constructing exact solutions of inflationary scalar field cosmologies with non-trivial potentials. The generating scheme uses the so-called superpotential and is inspired by recent studies of similar equations in supergravity. Some exact solutions are derived, and the physical meaning of the superpotential in these models is clarified.Comment: 6 pages, no figure

Harry Potter and the Goblin Bank of Gringotts

Gringotts Wizarding Bank is well known as the only financial institution in all of the Wizarding UK as documented in the works recounting the heroics of Harry Potter. The concentration of power and wealth in this single bank needs to be weighed against the financial stability of the entire Wizarding economy. This study will consider the impact to financial risk of breaking up Gringotts Wizarding Bank into five component pieces, along the lines of the Glass-Steagall Act in the United States. The emphasis of this work is to calibrate and simulate a model of the banking and financial systems within Wizarding UK under varying stress test scenarios simulating rumors of Lord Voldemort's return or the release of magical creatures into an unsuspecting muggle populace. We conclude by comparing the economic fallout from financial crises under the two systems: (i) Gringotts Wizarding Bank as a monopoly and (ii) the split-up financial system. We do this comparison on the level of minimal system-wide capital injections that would be needed to prevent the financial crisis from surpassing the damage caused by Lord Voldemort

Capital Regulation under Price Impacts and Dynamic Financial Contagion

We construct a continuous time model for price-mediated contagion precipitated by a common exogenous stress to the banking book of all firms in the financial system. In this setting, firms are constrained so as to satisfy a risk-weight based capital ratio requirement. We use this model to find analytical bounds on the risk-weights for assets as a function of the market liquidity. Under these appropriate risk-weights, we find existence and uniqueness for the joint system of firm behavior and the asset prices. We further consider an analytical bound on the firm liquidations, which allows us to construct exact formulas for stress testing the financial system with deterministic or random stresses. Numerical case studies are provided to demonstrate various implications of this model and analytical bounds

Puzzle: Zermelo-Fraenkel set theory is inconsistent

In this note, we present a puzzle. We prove that Zermelo-Fraenkel set theory is inconsistent by proving, using Zermelo-Fraenkel set theory, the false statement that any algorithm that determines whether any $n \times n$ matrix over $\mathbb F_2$, the finite field of order 2, is nonsingular must run in exponential time in the worst-case scenario. The object of the puzzle is to find the error in the proof.Comment: 1 pag

Complexity Science for Simpletons

In this article, we shall describe some of the most interesting topics in the subject of Complexity Science for a general audience. Anyone with a solid foundation in high school mathematics (with some calculus) and an elementary understanding of computer programming will be able to follow this article. First, we shall explain the significance of the P versus NP problem and solve it. Next, we shall describe two other famous mathematics problems, the Collatz 3n+1 Conjecture and the Riemann Hypothesis, and show how both Chaitin's incompleteness theorem and Wolfram's notion of "computational irreducibility" are important for understanding why no one has, as of yet, solved these two problems.Comment: 10 pages, made a minor correctio

Is it possible to compute the Moebius function without factoring?

It has been well known since Fermat's Little Theorem was first published that it is possible to determine that a number is composite without determining any of its nontrivial factors. It is natural to ask whether it is also possible to compute the Moebius function of a composite number without determining any of its nontrivial factors. In this note, we argue that this is impossible.Comment: 1 pag

2-State 3-Symbol Universal Turing Machines Do Not Exist

In this brief note, we give a simple information-theoretic proof that 2-state 3-symbol universal Turing machines cannot possibly exist, unless one loosens the definition of "universal".Comment: 1 pag