6,320 research outputs found
Trial and settlement negotiations between asymmetrically skilled parties
Parties engaged in a litigation generally enter the discovery process with different informations regarding their case and/or an unequal endowment in terms of skill and ability to produce evidence and predict the outcome of a trial. Hence, they have to bear different legal costs to assess the (equilibrium) plaintiff's win rate. The paper analyses pretrial negotiations and revisits the selection hypothesis in the case where these legal expenditures are private information. This assumption is consistent with empirical evidence (Osborne, 1999). Two alternative situations are investigated, depending on whether there exists a unilateral or a bilateral informational asymmetry.\ Our general result is that efficient pretrial negotiations select cases with the smallest legal expenditures as those going to trial, while cases with largest costs prefer to settle. Under the one-sided asymmetric information assumption, we find that the American rule yields more trials and higher aggregate legal expenditures than the French and British rules. The two-sided case leads to a higher rate of trials, but in contrast provides less clear-cut predictions regarding the influence of fee-shifting.litigation, unilateral and bilateral asymmetric information, legal expenditures
Space-time autocoding
Prior treatments of space-time communications in Rayleigh flat fading generally assume that channel coding covers either one fading interval-in which case there is a nonzero âoutage capacityâ-or multiple fading intervals-in which case there is a nonzero Shannon capacity. However, we establish conditions under which channel codes span only one fading interval and yet are arbitrarily reliable. In short, space-time signals are their own channel codes. We call this phenomenon space-time autocoding, and the accompanying capacity the space-time autocapacity. Let an M-transmitter antenna, N-receiver antenna Rayleigh flat fading channel be characterized by an MĂN matrix of independent propagation coefficients, distributed as zero-mean, unit-variance complex Gaussian random variables. This propagation matrix is unknown to the transmitter, it remains constant during a T-symbol coherence interval, and there is a fixed total transmit power. Let the coherence interval and number of transmitter antennas be related as T=ÎČM for some constant ÎČ. A TĂM matrix-valued signal, associated with R·T bits of information for some rate R is transmitted during the T-symbol coherence interval. Then there is a positive space-time autocapacity Ca such that for all R<Ca, the block probability of error goes to zero as the pair (T, M)ââ such that T/M=ÎČ. The autocoding effect occurs whether or not the propagation matrix is known to the receiver, and Ca=Nlog(1+Ï) in either case, independently of ÎČ, where Ï is the expected signal-to-noise ratio (SNR) at each receiver antenna. Lower bounds on the cutoff rate derived from random unitary space-time signals suggest that the autocoding effect manifests itself for relatively small values of T and M. For example, within a single coherence interval of duration T=16, for M=7 transmitter antennas and N=4 receiver antennas, and an 18-dB expected SNR, a total of 80 bits (corresponding to rate R=5) can theoretically be transmitted with a block probability of error less than 10^-9, all without any training or knowledge of the propagation matrix
The Kardar-Parisi-Zhang equation with spatially correlated noise: a unified picture from nonperturbative renormalization group
We investigate the scaling regimes of the Kardar-Parisi-Zhang equation in the
presence of spatially correlated noise with power law decay in Fourier space, using a nonperturbative renormalization group
approach. We determine the full phase diagram of the system as a function of
and the dimension . In addition to the weak-coupling part of the
diagram, which agrees with the results from Refs. [Europhys. Lett. 47, 14
(1999), Eur. Phys. J. B 9, 491 (1999)], we find the two fixed points describing
the short-range (SR) and long-range (LR) dominated strong-coupling phases. In
contrast with a suggestion in the references cited above, we show that, for all
values of , there exists a unique strong-coupling SR fixed point that can
be continuously followed as a function of . We show in particular that the
existence and the behavior of the LR fixed point do not provide any hint for 4
being the upper critical dimension of the KPZ equation with SR noise.Comment: 13 pages, 5 figures, final versio
When are Stochastic Transition Systems Tameable?
A decade ago, Abdulla, Ben Henda and Mayr introduced the elegant concept of
decisiveness for denumerable Markov chains [1]. Roughly speaking, decisiveness
allows one to lift most good properties from finite Markov chains to
denumerable ones, and therefore to adapt existing verification algorithms to
infinite-state models. Decisive Markov chains however do not encompass
stochastic real-time systems, and general stochastic transition systems (STSs
for short) are needed. In this article, we provide a framework to perform both
the qualitative and the quantitative analysis of STSs. First, we define various
notions of decisiveness (inherited from [1]), notions of fairness and of
attractors for STSs, and make explicit the relationships between them. Then, we
define a notion of abstraction, together with natural concepts of soundness and
completeness, and we give general transfer properties, which will be central to
several verification algorithms on STSs. We further design a generic
construction which will be useful for the analysis of {\omega}-regular
properties, when a finite attractor exists, either in the system (if it is
denumerable), or in a sound denumerable abstraction of the system. We next
provide algorithms for qualitative model-checking, and generic approximation
procedures for quantitative model-checking. Finally, we instantiate our
framework with stochastic timed automata (STA), generalized semi-Markov
processes (GSMPs) and stochastic time Petri nets (STPNs), three models
combining dense-time and probabilities. This allows us to derive decidability
and approximability results for the verification of these models. Some of these
results were known from the literature, but our generic approach permits to
view them in a unified framework, and to obtain them with less effort. We also
derive interesting new approximability results for STA, GSMPs and STPNs.Comment: 77 page
The academic and industrial embrace of space-time methods
[Guest Editors introduction to: Special issue on space-time transmission, reception, coding and signal processing]
Every episode of the classic 1966â1969 television series Star Trek begins with Captain Kirkâs (played by William Shatner) famous words : âSpace: The final frontierâŠ.â While space may not be the final frontier for the information and communication theory community, it is proving to be an important and fruitful one.
In the information theory community, the notion of space can be broadly defined as the simultaneous use of multiple, possibly coupled, channels. The notions of spaceâtime and multiple-input multiple-output (MIMO) channels are therefore often used interchangeably. The connection between space and MIMO is most transparent when we view the multiple channels as created by two or more spatially separated antennas at a wireless transmitter or receiver.
A large component of the current interest in spaceâtime methods can be attributed to discoveries in the late 1980s and early 1990s that a rich wireless scattering environment can be beneficial when multiple antennas are used on a point-to-point link. We now know that adding antennas in a rich environment provides proportional increases in point-to-point data rates, without extra transmitted power or bandwidth
Comparison of multiphase SPH and LBM approaches for the simulation of intermittent flows
Smoothed Particle Hydrodynamics (SPH) and Lattice Boltzmann Method (LBM) are
increasingly popular and attractive methods that propose efficient multiphase
formulations, each one with its own strengths and weaknesses. In this context,
when it comes to study a given multi-fluid problem, it is helpful to rely on a
quantitative comparison to decide which approach should be used and in which
context. In particular, the simulation of intermittent two-phase flows in pipes
such as slug flows is a complex problem involving moving and intersecting
interfaces for which both SPH and LBM could be considered. It is a problem of
interest in petroleum applications since the formation of slug flows that can
occur in submarine pipelines connecting the wells to the production facility
can cause undesired behaviors with hazardous consequences. In this work, we
compare SPH and LBM multiphase formulations where surface tension effects are
modeled respectively using the continuum surface force and the color gradient
approaches on a collection of standard test cases, and on the simulation of
intermittent flows in 2D. This paper aims to highlight the contributions and
limitations of SPH and LBM when applied to these problems. First, we compare
our implementations on static bubble problems with different density and
viscosity ratios. Then, we focus on gravity driven simulations of slug flows in
pipes for several Reynolds numbers. Finally, we conclude with simulations of
slug flows with inlet/outlet boundary conditions. According to the results
presented in this study, we confirm that the SPH approach is more robust and
versatile whereas the LBM formulation is more accurate and faster
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