4,368 research outputs found
Thermodynamic analogies in economics and finance: instability of markets
Interest in thermodynamic analogies in economics is older than the idea of von Neumann to look for market entropy in liquidity, advice that was not taken in any thermodynamic analogy presented so far in the literature. In this paper we go further and use a standard strategy from trading theory to pinpoint why thermodynamic analogies necessarily fail to describe financial markets, in spite of the presence of liquidity as the underlying basis for market entropy. Market liquidity of frequently traded assets does play the role of the ‘heat bath‘, as anticipated by von Neumann, but we are able to identify the no-arbitrage condition geometrically as an assumption of translational and rotational invariance rather than (as finance theorists would claim) an equilibrium condition. We then use the empirical market distribution to introduce an asset’s entropy and discuss the underlying reason why real financial markets cannot behave thermodynamically: financial markets are unstable, they do not approach statistical equilibrium, nor are there any available topological invariants on which to base a purely formal statistical mechanics. After discussing financial markets, we finally generalize our result by proposing that the idea of Adam Smith’s Invisible Hand is a falsifiable proposition: we suggest how to test nonfinancial markets empirically for the stabilizing action of The Invisible Hand.Economics; utility; entropy and disorder; thermodynamics; financial markets; stochastic processes;
Simple Riemannian surfaces are scattering rigid
Scattering rigidity of a Riemannian manifold allows one to tell the metric of
a manifold with boundary by looking at the directions of geodesics at the
boundary. Lens rigidity allows one to tell the metric of a manifold with
boundary from the same information plus the length of geodesics. There are a
variety of results about lens rigidity but very little is known for scattering
rigidity. We will discuss the subtle difference between these two types of
rigidities and prove that they are equivalent for two-dimensional simple
manifolds with boundaries. In particular, this implies that two-dimensional
simple manifolds (such as the flat disk) are scattering rigid since they are
lens/boundary rigid (Pestov--Uhlmann, 2005).Comment: 23 page
Slopes and signatures of links
We define the slope of a colored link in an integral homology sphere,
associated to admissible characters on the link group. Away from a certain
singular locus, the slope is a rational function which can be regarded as a
multivariate generalization of the Kojima--Yamasaki -function. It is the
ratio of two Conway potentials, provided that the latter makes sense;
otherwise, it is a new invariant. The slope is responsible for an extra
correction term in the signature formula for the splice of two links, in the
previously open exceptional case where both characters are admissible. Using a
similar construction for a special class of tangles, we formulate generalized
skein relations for the signature
A Denotational Semantics for Communicating Unstructured Code
An important property of programming language semantics is that they should
be compositional. However, unstructured low-level code contains goto-like
commands making it hard to define a semantics that is compositional. In this
paper, we follow the ideas of Saabas and Uustalu to structure low-level code.
This gives us the possibility to define a compositional denotational semantics
based on least fixed points to allow for the use of inductive verification
methods. We capture the semantics of communication using finite traces similar
to the denotations of CSP. In addition, we examine properties of this semantics
and give an example that demonstrates reasoning about communication and jumps.
With this semantics, we lay the foundations for a proof calculus that captures
both, the semantics of unstructured low-level code and communication.Comment: In Proceedings FESCA 2015, arXiv:1503.0437
A theory of normed simulations
In existing simulation proof techniques, a single step in a lower-level
specification may be simulated by an extended execution fragment in a
higher-level one. As a result, it is cumbersome to mechanize these techniques
using general purpose theorem provers. Moreover, it is undecidable whether a
given relation is a simulation, even if tautology checking is decidable for the
underlying specification logic. This paper introduces various types of normed
simulations. In a normed simulation, each step in a lower-level specification
can be simulated by at most one step in the higher-level one, for any related
pair of states. In earlier work we demonstrated that normed simulations are
quite useful as a vehicle for the formalization of refinement proofs via
theorem provers. Here we show that normed simulations also have pleasant
theoretical properties: (1) under some reasonable assumptions, it is decidable
whether a given relation is a normed forward simulation, provided tautology
checking is decidable for the underlying logic; (2) at the semantic level,
normed forward and backward simulations together form a complete proof method
for establishing behavior inclusion, provided that the higher-level
specification has finite invisible nondeterminism.Comment: 31 pages, 10figure
Virtual Knot Cobordism
This paper defines a theory of cobordism for virtual knots and studies this
theory for standard and rotational virtual knots and links. Non-trivial
examples of virtual slice knots are given. Determinations of the four-ball
genus of positive virtual knots are given using the results of a companion
paper by the author and Heather Dye and Aaron Kaestner. Problems related to
band-passing are explained, and a theory of isotopy of virtual surfaces is
formulated in terms of a generalization of the Yoshikawa moves.Comment: 32 pages, 43 figures, LaTeX documen
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