10,322 research outputs found
Gauge theory of Finance?
Some problems with the recent stimulating proposal of a ``Gauge Theory of
Finance'' by Ilinski and collaborators are outlined. First, the derivation of
the log-normal distribution is shown equivalent both in information and
mathematical content to the simpler and well-known derivation, dating back from
Bachelier and Samuelson. Similarly, the re-derivation of Black-Scholes equation
is shown equivalent to the standard one because the limit of no uncertainty is
equivalent to the standard risk-free replication argument. Both re-derivations
of the log-normality and Black-Scholes result do not provide a test of the
theory because it is degenerate in the limits where these results apply. Third,
the choice of the exponential form a la Boltzmann, of the weight of a given
market configuration, is a key postulate that requires justification. In
addition, the ``Gauge Theory of Finance'' seems to lead to ``virtual''
arbitrage opportunities for pure Markov random walk market when there should be
none. These remarks are offered in the hope to improve the formulation of the
``Gauge Theory of Finance'' into a coherent and useful framework.Comment: 4 page
Chiral topological spin liquids with projected entangled pair states
Topological chiral phases are ubiquitous in the physics of the Fractional
Quantum Hall Effect. Non-chiral topological spin liquids are also well known.
Here, using the framework of projected entangled pair states (PEPS), we
construct a family of chiral spin liquids on the square lattice which are
generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from
deformed local tensors with symmetry. On a cylinder, we construct
four topological sectors with even or odd number of spinons on the boundary and
even or odd number of () fluxes penetrating the cylinder which,
we argue, remain orthogonal in the limit of infinite perimeter. The analysis of
the transfer matrix provides evidence of short-range (long-range) triplet
(singlet) correlations as for the critical (non-chiral) RVB state. The
Entanglement Spectrum exhibits chiral edge modes, which we confront to
predictions of Conformal Field Theory, and the corresponding Entanglement
Hamiltonian is shown to be long ranged.Comment: 7 pages, 6 figures, Final version (small changes
Field-induced superfluids and Bose liquids in Projected Entangled Pair States
In two-dimensional incompressible quantum spin liquids, a large enough
magnetic field generically induces "doping" of polarized S=1 triplons or S=1/2
spinons. We review a number of cases such as spin-3/2 AKLT or spin-1/2
Resonating Valence Bond (RVB) liquids where the Projected Entangled Pair States
(PEPS) framework provides very simple and comprehensive pictures. On the
bipartite honeycomb lattice, simple PEPS can describe Bose condensed triplons
(AKLT) or spinons (RVB) superfluids with transverse staggered (N\'eel) magnetic
order. On the Kagome lattice, doping the RVB state with deconfined spinons or
triplons (i.e. spinon bound pairs) yields uncondensed Bose liquids preserving
U(1) spin-rotation symmetry. We find that spinon (triplon) doping destroys
(preserves) the topological Z_2 symmetry of the underlying RVB state. We also
find that spinon doping induces longer range interactions in the entanglement
Hamiltonian, suggesting the emergence of (additive) log-corrections to the
entanglement entropy.Comment: 7 pages, 7 figures Improved final version (as published
RVB superconductors with fermionic projected entangled pair states
We construct a family of simple fermionic projected entangled pair states
(fPEPS) on the square lattice with bond dimension which are exactly
hole-doped resonating valence bond (RVB) wavefunctions with short-range singlet
bonds. Under doping the insulating RVB spin liquid evolves immediately into a
superconductor with mixed pairing symmetry whose pair amplitude grows as
the square-root of the doping. The relative weight between -wave and
-wave components can be controlled by a single variational parameter . We
optimize our ansatz w.r.t. for the frustrated model (including
both nearest and next-nearest neighbor antiferromagnetic interactions and
, respectively) for and obtain an energy very close to
the infinite-PEPS state (using full update optimization and same bond
dimension). The orbital symmetry of the optimized RVB superconductor has
predominant d-wave character, although we argue a residual (complex s-wave)
time reversal symmetry breaking component should always be present. Connections
of the results to the physics of superconducting cuprates and pnictides are
outlined.Comment: 6 pages, 4 figures and Supplemental Material (3 pages, 2 figures).
Updated version including new iPEPS results using full update optimization
scheme, showing excellent agreement with RVB wave functio
Energy efficiency analysis of next-generation passive optical network (NG-PON) technologies in a major city network
Ever-increasing bandwidth demands associated with mobile backhaul, content-rich services and the convergence of residential and business access will drive the need for next-generation passive optical networks (NG-PONs) in the long term. At the same time, there is a growing interest in reducing the energy consumption and the associated cost of the access network. In this paper, we consider a deployment scenario in a major city to assess the energy efficiency of various PON solutions from a telecom operator's perspective. We compare five next-generation technologies to a baseline GPON deployment offering similar bandwidths and Quality of Service (QoS) for best-effort high speed connectivity services. We follow two approaches:first, we consider a fixed split ratio (1:64) in an existing Optical Distribution Network (ODN); next, we consider an upgraded ODN with an optimized split ratio for the specific bandwidth and QoS values. For medium bandwidth demands, our results show that legacy PONs can be upgraded to 10G PON without any ODN modification. For future applications that may require access rates up to 1 Gb/s, NG-PON2 technologies with higher split ratios and increased reach become more interesting systems, offering the potential for both increased energy efficiency and node consolidation
Advertising and the rise of the free daily newspapers
We analyze the competition between two newspapers in a vertical differentiation model where the qualities of the journals are determined endogenously in the first stage of the game. We show that when the advertising revenues per reader increase there is a critical value above which the quality of the low quality newspaper discontinuously falls while it become similtaneously a free newspaper. This is beneficial to the high quality journal and detrimental to the readers.Advertising, Newspaper quality
To acquire or to compete ? An entry dilemna
In this paper we address the following question : is it more profitable, for an entrant in a differentiated market, to acquire an existing firm than to compete ? We illustrate the answer by considering competition in the banking sectorvertical differentiation; entry; banking competition
The TV news scheduling game when the newscaster’s face matters
The present note first provides an alternative formulation of the Cancian, Bills and Bergström (1995) - problem which discards the non-existence difficulty and consequently allows to consider some extensions of the TV-newscast scheduling game. The extension we consider consists in assuming that viewers’ preferences between the competing channels do not depend only on the timing of their broadcast, but also on some other characteristics, like the content of the show or the identity of the newscaster. Then we identify a sufficient condition on the dispersion of these preferences over the viewers’ population guaranteeing the existence of a unique Nash equilibrium. It turns out that, at this equilibrium, both networks broadcast their news at the same instant.advertising; newspaper quality
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