15,097 research outputs found
Existence of nodal solutions for Dirac equations with singular nonlinearities
We prove, by a shooting method, the existence of infinitely many solutions of
the form of the nonlinear Dirac
equation {equation*} i\underset{\mu=0}{\overset{3}{\sum}} \gamma^\mu
\partial_\mu \psi- m\psi - F(\bar{\psi}\psi)\psi = 0 {equation*} where
is compactly supported and \[F(x) = \{{array}{ll}
p|x|^{p-1} & \text{if} |x|>0 0 & \text{if} x=0 {array}.] with
under some restrictions on the parameters and We study also the
behavior of the solutions as tends to zero to establish the link between
these equations and the M.I.T. bag model ones
Quantum chains with a Catalan tree pattern of conserved charges: the XXZ model and the isotropic octonionic chain
A class of quantum chains possessing a family of local conserved charges with
a Catalan tree pattern is studied. Recently, we have identified such a
structure in the integrable -invariant chains. In the present work we
find sufficient conditions for the existence of a family of charges with this
structure in terms of the underlying algebra. Two additional systems with a
Catalan tree structure of conserved charges are found. One is the spin 1/2 XXZ
model with . The other is a new octonionic isotropic chain,
generalizing the Heisenberg model. This system provides an interesting example
of an infinite family of noncommuting local conserved quantities.Comment: 20 pages in plain TeX; uses macro harvma
Risk Taking of Executives under Different Incentive Contracts: Experimental Evidence
Classic financial agency theory recommends compensation through stock options rather than shares to induce risk neutrality in otherwise risk averse agents. In an experiment, we find that subjects acting as executives do also take risks that are excessive from the perspective of shareholders if compensated through options. Compensation through restricted company stock reduces the uptake
of excessive risks. Even under stock-ownership, however, experimental executives continue to take excessive risks—a result that cannot be accounted for by classic incentive theory. We develop a basic model in which such risk-taking behavior is explained based on a richer array of risk attitudes derived from Prospect Theory. We use the model to derive hypotheses on what may be driving excessive risk taking in the experiment. Testing those hypotheses, we find that most of them are indeed borne out by the data. We thus conclude that a prospect-theory-based model is more apt at
explaining risk attitudes under different compensation regimes than traditional principal-agent models grounded in expected utility theory
Structure of the conservation laws in integrable spin chains with short range interactions
We present a detailed analysis of the structure of the conservation laws in
quantum integrable chains of the XYZ-type and in the Hubbard model. With the
use of the boost operator, we establish the general form of the XYZ conserved
charges in terms of simple polynomials in spin variables and derive recursion
relations for the relative coefficients of these polynomials. For two submodels
of the XYZ chain - namely the XXX and XY cases, all the charges can be
calculated in closed form. For the XXX case, a simple description of conserved
charges is found in terms of a Catalan tree. This construction is generalized
for the su(M) invariant integrable chain. We also indicate that a quantum
recursive (ladder) operator can be traced back to the presence of a hamiltonian
mastersymmetry of degree one in the classical continuous version of the model.
We show that in the quantum continuous limits of the XYZ model, the ladder
property of the boost operator disappears. For the Hubbard model we demonstrate
the non-existence of a ladder operator. Nevertheless, the general structure of
the conserved charges is indicated, and the expression for the terms linear in
the model's free parameter for all charges is derived in closed form.Comment: 79 pages in plain TeX plus 4 uuencoded figures; (uses harvmac and
epsf
R-adaptive multisymplectic and variational integrators
Moving mesh methods (also called r-adaptive methods) are space-adaptive
strategies used for the numerical simulation of time-dependent partial
differential equations. These methods keep the total number of mesh points
fixed during the simulation, but redistribute them over time to follow the
areas where a higher mesh point density is required. There are a very limited
number of moving mesh methods designed for solving field-theoretic partial
differential equations, and the numerical analysis of the resulting schemes is
challenging. In this paper we present two ways to construct r-adaptive
variational and multisymplectic integrators for (1+1)-dimensional Lagrangian
field theories. The first method uses a variational discretization of the
physical equations and the mesh equations are then coupled in a way typical of
the existing r-adaptive schemes. The second method treats the mesh points as
pseudo-particles and incorporates their dynamics directly into the variational
principle. A user-specified adaptation strategy is then enforced through
Lagrange multipliers as a constraint on the dynamics of both the physical field
and the mesh points. We discuss the advantages and limitations of our methods.
Numerical results for the Sine-Gordon equation are also presented.Comment: 65 pages, 13 figure
Compression-aware Training of Deep Networks
In recent years, great progress has been made in a variety of application
domains thanks to the development of increasingly deeper neural networks.
Unfortunately, the huge number of units of these networks makes them expensive
both computationally and memory-wise. To overcome this, exploiting the fact
that deep networks are over-parametrized, several compression strategies have
been proposed. These methods, however, typically start from a network that has
been trained in a standard manner, without considering such a future
compression. In this paper, we propose to explicitly account for compression in
the training process. To this end, we introduce a regularizer that encourages
the parameter matrix of each layer to have low rank during training. We show
that accounting for compression during training allows us to learn much more
compact, yet at least as effective, models than state-of-the-art compression
techniques.Comment: Accepted at NIPS 201
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