40,567 research outputs found
Constant Rank Bimatrix Games are PPAD-hard
The rank of a bimatrix game (A,B) is defined as rank(A+B). Computing a Nash
equilibrium (NE) of a rank-, i.e., zero-sum game is equivalent to linear
programming (von Neumann'28, Dantzig'51). In 2005, Kannan and Theobald gave an
FPTAS for constant rank games, and asked if there exists a polynomial time
algorithm to compute an exact NE. Adsul et al. (2011) answered this question
affirmatively for rank- games, leaving rank-2 and beyond unresolved.
In this paper we show that NE computation in games with rank , is
PPAD-hard, settling a decade long open problem. Interestingly, this is the
first instance that a problem with an FPTAS turns out to be PPAD-hard. Our
reduction bypasses graphical games and game gadgets, and provides a simpler
proof of PPAD-hardness for NE computation in bimatrix games. In addition, we
get:
* An equivalence between 2D-Linear-FIXP and PPAD, improving a result by
Etessami and Yannakakis (2007) on equivalence between Linear-FIXP and PPAD.
* NE computation in a bimatrix game with convex set of Nash equilibria is as
hard as solving a simple stochastic game.
* Computing a symmetric NE of a symmetric bimatrix game with rank is
PPAD-hard.
* Computing a (1/poly(n))-approximate fixed-point of a (Linear-FIXP)
piecewise-linear function is PPAD-hard.
The status of rank- games remains unresolved
A study of the almost sequential mechanism of true ternary fission
We consider the collinear ternary fission which is a sequential ternary decay
with a very short time between the ruptures of two necks connecting the middle
cluster of the ternary nuclear system and outer fragments. In particular, we
consider the case where the Coulomb field of the first massive fragment
separated during the first step of the fission produces a lower pre-scission
barrier in the second step of the residual part of the ternary system. In this
case, we obtain a probability of about for the yield of massive
clusters such as \nuclide[70]{Ni}, \nuclide[80-82]{Ge}, \nuclide[86]{Se}, and
\nuclide[94]{Kr} in the ternary fission of \nuclide[252]{Cf}. These products
appear together with the clusters having mass numbers of --. The
results show that the yield of a heavy cluster such as \nuclide[68-70]{Ni}
would be followed by a product of -- with a large probability as
observed in the experimental data obtained with the FOBOS spectrometer at the
Joint Institute for Nuclear Research. The third product is not observed. The
landscape of the potential energy surface shows that the configuration of the
Ni + Ca + Sn decay channel is lower about 12 MeV than that of the Ca + Ni + Sn
channel. This leads to the fact, that the yield of Ni and Sn is large. The
analysis on the dependence of the velocity of the middle fragment on mass
numbers of the outer products leads to the conclusion that, in the collinear
tripartition channel of \nuclide[252]{Cf}, the middle cluster has a very small
velocity, which does not allow it to be found in experiments.Comment: 11 pages, 9 figure
Firm Investment and Monetary Policy Transmission in the Euro Area.
We present a comparable set of results on the monetary transmission channels on firm investment for the four largest euro-area countries (Germany, France, Italy and Spain). With particularly rich micro datasets for each country containing over 215,000 observations from 1985 to 1999, we ex-plore what can be learned about the interest channel and the broad credit channel. For each of those countries, we estimate neo-classical investment relationships, explaining investment by its user cost, sales and cash flow. We find investment to be sensitive to user cost changes in all those four countries. This implies an operative interest channel in these euro-area countries. We also find in-vestment in all countries to be quite sensitive to cash flow movements. However, only in Italy do smaller firms react more to cash flow movements than large firms, implying that a broad credit channel might not be equally pervasive in all countries.Investment, Monetary transmission channels, User cost of capital.
Dynamical symmetry of isobaric analog 0+ states in medium mass nuclei
An algebraic sp(4) shell model is introduced to achieve a deeper
understanding and interpretation of the properties of pairing-governed 0+
states in medium mass atomic nuclei. The theory, which embodies the simplicity
of a dynamical symmetry approach to nuclear structure, is shown to reproduce
the excitation spectra and fine structure effects driven by proton-neutron
interactions and isovector pairing correlations across a broad range of nuclei.Comment: 7 pages, 5 figure
Tunneling Anomaly in Superconductor above Paramagnetic Limit
We study the tunneling density of states (DoS) in the superconducting systems
driven by Zeeman splitting E_Z into the paramagnetic phase. We show that, even
though the BCS gap disappears, superconducting fluctuations cause a strong DoS
singularity in the vicinity of energies -E^* for electrons polarized along the
magnetic field and E^* for the opposite polarization. The position of the
singularity E^*=(1/2) (E_Z + \sqrt{E_Z^2- \Delta^2}) (where \Delta is BCS gap
at E_Z=0) is universal. We found analytically the shape of the DoS for
different dimensionality of the system. For ultrasmall grains the singularity
has the form of the hard gap, while in higher dimensions it appears as a
significant though finite dip. Our results are consistent with recent
experiments in superconducting films.Comment: 4 pages, 2 .eps figures include
First-principles investigation of spin polarized conductance in atomic carbon wire
We analyze spin-dependent energetics and conductance for one dimensional (1D)
atomic carbon wires consisting of terminal magnetic (Co) and interior
nonmagnetic (C) atoms sandwiched between gold electrodes, obtained employing
first-principles gradient corrected density functional theory and Landauer's
formalism for conductance. Wires containing an even number of interior carbon
atoms are found to be acetylenic with sigma-pi bonding patterns, while cumulene
structures are seen in wires containing odd number of interior carbon atoms, as
a result of strong pi-conjugation. Ground states of carbon wires containing up
to 13 C atoms are found to have anti-parallel spin configurations of the two
terminal Co atoms, while the 14 C wire has a parallel Co spin configuration in
the ground state. The stability of the anti-ferromagnetic state in the wires is
ascribed to a super-exchange effect. For the cumulenic wires this effect is
constant for all wire lengths. For the acetylenic wires, the super-exchange
effect diminishes as the wire length increases, going to zero for the atomic
wire containing 14 carbon atoms. Conductance calculations at the zero bias
limit show spin-valve behavior, with the parallel Co spin configuration state
giving higher conductance than the corresponding anti-parallel state, and a
non-monotonic variation of conductance with the length of the wires for both
spin configurations.Comment: revtex, 6 pages, 5 figure
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