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 $d+i\, d$ 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 ($\mathbb{Z}_2$) 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 $D=3$ 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 $d+is$ pairing symmetry whose pair amplitude grows as the square-root of the doping. The relative weight between $s$-wave and $d$-wave components can be controlled by a single variational parameter $c$. We optimize our ansatz w.r.t. $c$ for the frustrated $t-J_1-J_2$ model (including both nearest and next-nearest neighbor antiferromagnetic interactions $J_1$ and $J_2$, respectively) for $J_2\simeq J_1/2$ 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