999 research outputs found
Cooperation in a Repeated Public Goods Game with a Probabilistic Endpoint
In our experiment, we have a multiple-round public goods game but with a probabilistic endpoint. This changes the Nash equilibrium, such that cooperation is the new equilibrium strategy. The experiment consists of two treatments, one with a single round per session (called the intertemporal treatment), and the second with multiple rounds per session. Experimental results suggest that contribution was indeed positive and consistent provided a high enough probability of the game’s continuation, but declined when probability fell
High-throughput on-chip DNA fragmentation
free microfluidic deoxyribonucleic acid (DNA) fragmentation chip that is based on hydrodynamic shearing. Genomic DNA has been reproducibly fragmented with 2-10 kbp fragment lengths by applying hydraulic pressure ΔP across micromachined constrictions in the microfluidic channels. The utilization of a series of constrictions reduces the variance of the fragmented DNA length distribution; and parallel microfluidic channels design eliminates the device clogging
Jointly Optimal Channel Pairing and Power Allocation for Multichannel Multihop Relaying
We study the problem of channel pairing and power allocation in a
multichannel multihop relay network to enhance the end-to-end data rate. Both
amplify-and-forward (AF) and decode-and-forward (DF) relaying strategies are
considered. Given fixed power allocation to the channels, we show that channel
pairing over multiple hops can be decomposed into independent pairing problems
at each relay, and a sorted-SNR channel pairing strategy is sum-rate optimal,
where each relay pairs its incoming and outgoing channels by their SNR order.
For the joint optimization of channel pairing and power allocation under both
total and individual power constraints, we show that the problem can be
decoupled into two subproblems solved separately. This separation principle is
established by observing the equivalence between sorting SNRs and sorting
channel gains in the jointly optimal solution. It significantly reduces the
computational complexity in finding the jointly optimal solution. It follows
that the channel pairing problem in joint optimization can be again decomposed
into independent pairing problems at each relay based on sorted channel gains.
The solution for optimizing power allocation for DF relaying is also provided,
as well as an asymptotically optimal solution for AF relaying. Numerical
results are provided to demonstrate substantial performance gain of the jointly
optimal solution over some suboptimal alternatives. It is also observed that
more gain is obtained from optimal channel pairing than optimal power
allocation through judiciously exploiting the variation among multiple
channels. Impact of the variation of channel gain, the number of channels, and
the number of hops on the performance gain is also studied through numerical
examples.Comment: 15 pages. IEEE Transactions on Signal Processin
Relative entropy of entanglement for certain multipartite mixed states
We prove conjectures on the relative entropy of entanglement (REE) for two
families of multipartite qubit states. Thus, analytic expressions of REE for
these families of states can be given. The first family of states are composed
of mixture of some permutation-invariant multi-qubit states. The results
generalized to multi-qudit states are also shown to hold. The second family of
states contain D\"ur's bound entangled states. Along the way, we have discussed
the relation of REE to two other measures: robustness of entanglement and
geometric measure of entanglement, slightly extending previous results.Comment: Single column, 22 pages, 9 figures, comments welcom
Celebrating Cercignani's conjecture for the Boltzmann equation
Cercignani's conjecture assumes a linear inequality between the entropy and
entropy production functionals for Boltzmann's nonlinear integral operator in
rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities
and spectral gap inequalities, this issue has been at the core of the renewal
of the mathematical theory of convergence to thermodynamical equilibrium for
rarefied gases over the past decade. In this review paper, we survey the
various positive and negative results which were obtained since the conjecture
was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani,
powerful mind and great scientist, one of the founders of the modern theory
of the Boltzmann equation. 24 pages. V2: correction of some typos and one
ref. adde
On the stochastic mechanics of the free relativistic particle
Given a positive energy solution of the Klein-Gordon equation, the motion of
the free, spinless, relativistic particle is described in a fixed Lorentz frame
by a Markov diffusion process with non-constant diffusion coefficient. Proper
time is an increasing stochastic process and we derive a probabilistic
generalization of the equation . A
random time-change transformation provides the bridge between the and the
domain. In the domain, we obtain an \M^4-valued Markov process
with singular and constant diffusion coefficient. The square modulus of the
Klein-Gordon solution is an invariant, non integrable density for this Markov
process. It satisfies a relativistically covariant continuity equation
Complete characterization of convergence to equilibrium for an inelastic Kac model
Pulvirenti and Toscani introduced an equation which extends the Kac
caricature of a Maxwellian gas to inelastic particles. We show that the
probability distribution, solution of the relative Cauchy problem, converges
weakly to a probability distribution if and only if the symmetrized initial
distribution belongs to the standard domain of attraction of a symmetric stable
law, whose index is determined by the so-called degree of
inelasticity, , of the particles: . This result is
then used: (1) To state that the class of all stationary solutions coincides
with that of all symmetric stable laws with index . (2) To determine
the solution of a well-known stochastic functional equation in the absence of
extra-conditions usually adopted
Geometric inequalities from phase space translations
We establish a quantum version of the classical isoperimetric inequality
relating the Fisher information and the entropy power of a quantum state. The
key tool is a Fisher information inequality for a state which results from a
certain convolution operation: the latter maps a classical probability
distribution on phase space and a quantum state to a quantum state. We show
that this inequality also gives rise to several related inequalities whose
counterparts are well-known in the classical setting: in particular, it implies
an entropy power inequality for the mentioned convolution operation as well as
the isoperimetric inequality, and establishes concavity of the entropy power
along trajectories of the quantum heat diffusion semigroup. As an application,
we derive a Log-Sobolev inequality for the quantum Ornstein-Uhlenbeck
semigroup, and argue that it implies fast convergence towards the fixed point
for a large class of initial states.Comment: 37 pages; updated to match published versio
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
Consider axisymmetric strong solutions of the incompressible Navier-Stokes
equations in with non-trivial swirl. Let denote the axis of symmetry
and measure the distance to the z-axis. Suppose the solution satisfies
either or, for some \e > 0, for and
allowed to be large. We prove that is regular at time zero.Comment: More explanations and a new appendi
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