115,287 research outputs found

### On Iterated Dominance, Matrix Elimination, and Matched Paths

We study computational problems arising from the iterated removal of weakly
dominated actions in anonymous games. Our main result shows that it is
NP-complete to decide whether an anonymous game with three actions can be
solved via iterated weak dominance. The two-action case can be reformulated as
a natural elimination problem on a matrix, the complexity of which turns out to
be surprisingly difficult to characterize and ultimately remains open. We
however establish connections to a matching problem along paths in a directed
graph, which is computationally hard in general but can also be used to
identify tractable cases of matrix elimination. We finally identify different
classes of anonymous games where iterated dominance is in P and NP-complete,
respectively.Comment: 12 pages, 3 figures, 27th International Symposium on Theoretical
Aspects of Computer Science (STACS

### Simplicial blowups and discrete normal surfaces in simpcomp

simpcomp is an extension to GAP, the well known system for computational
discrete algebra. It allows the user to work with simplicial complexes. In the
latest version, support for simplicial blowups and discrete normal surfaces was
added, both features unique to simpcomp. Furthermore, new functions for
constructing certain infinite series of triangulations have been implemented
and interfaces to other software packages have been improved to previous
versions.Comment: 10 page

### On annealed elliptic Green function estimates

We consider a random, uniformly elliptic coefficient field $a$ on the lattice
$\mathbb{Z}^d$. The distribution $\langle \cdot \rangle$ of the coefficient
field is assumed to be stationary. Delmotte and Deuschel showed that the
gradient and second mixed derivative of the parabolic Green function $G(t,x,y)$
satisfy optimal annealed estimates which are $L^2$ resp. $L^1$ in probability,
i.e. they obtained bounds on $\langle |\nabla_x G(t,x,y)|^2
\rangle^{\frac{1}{2}}$ and $\langle |\nabla_x \nabla_y G(t,x,y)| \rangle$, see
T. Delmotte and J.-D. Deuschel: On estimating the derivatives of symmetric
diffusions in stationary random environments, with applications to the
$\nabla\phi$ interface model, Probab. Theory Relat. Fields 133 (2005),
358--390. In particular, the elliptic Green function $G(x,y)$ satisfies optimal
annealed bounds. In a recent work, the authors extended these elliptic bounds
to higher moments, i.e. $L^p$ in probability for all $p<\infty$, see D.
Marahrens and F. Otto: {Annealed estimates on the Green function},
arXiv:1304.4408 (2013). In this note, we present a new argument that relies
purely on elliptic theory to derive the elliptic estimates (see Proposition 1.2
below) for $\langle |\nabla_x G(x,y)|^2 \rangle^{\frac{1}{2}}$ and $\langle
|\nabla_x \nabla_y G(x,y)| \rangle$.Comment: 15 page

### Stacked polytopes and tight triangulations of manifolds

Tightness of a triangulated manifold is a topological condition, roughly
meaning that any simplexwise linear embedding of the triangulation into
euclidean space is "as convex as possible". It can thus be understood as a
generalization of the concept of convexity. In even dimensions,
super-neighborliness is known to be a purely combinatorial condition which
implies the tightness of a triangulation.
Here we present other sufficient and purely combinatorial conditions which
can be applied to the odd-dimensional case as well. One of the conditions is
that all vertex links are stacked spheres, which implies that the triangulation
is in Walkup's class $\mathcal{K}(d)$. We show that in any dimension $d\geq 4$
\emph{tight-neighborly} triangulations as defined by Lutz, Sulanke and Swartz
are tight.
Furthermore, triangulations with $k$-stacked vertex links and the centrally
symmetric case are discussed.Comment: 28 pages, 2 figure

### Time Quasilattices in Dissipative Dynamical Systems

We establish the existence of `time quasilattices' as stable trajectories in
dissipative dynamical systems. These tilings of the time axis, with two unit
cells of different durations, can be generated as cuts through a periodic
lattice spanned by two orthogonal directions of time. We show that there are
precisely two admissible time quasilattices, which we term the infinite Pell
and Clapeyron words, reached by a generalization of the period-doubling
cascade. Finite Pell and Clapeyron words of increasing length provide
systematic periodic approximations to time quasilattices which can be verified
experimentally. The results apply to all systems featuring the universal
sequence of periodic windows. We provide examples of discrete-time maps, and
periodically-driven continuous-time dynamical systems. We identify quantum
many-body systems in which time quasilattices develop rigidity via the
interaction of many degrees of freedom, thus constituting dissipative discrete
`time quasicrystals'.Comment: 38 pages, 14 figures. This version incorporates "Pell and Clapeyron
Words as Stable Trajectories in Dynamical Systems", arXiv:1707.09333.
Submission to SciPos

### The photon polarization tensor in a homogeneous magnetic or electric field

We revisit the photon polarization tensor in a homogeneous external magnetic
or electric field. The starting point of our considerations is the momentum
space representation of the one-loop photon polarization tensor in the presence
of a homogeneous electromagnetic field, known in terms of a double parameter
integral. Our focus is on explicit analytical insights for both on- and
off-the-light-cone dynamics in a wide range of well-specified physical
parameter regimes, ranging from the perturbative to the manifestly
nonperturbative strong field regime. The basic ideas underlying
well-established approximations to the photon polarization tensor are carefully
examined and critically reviewed. In particular, we systematically keep track
of all contributions, both the ones to be neglected and those to be taken into
account explicitly, to all orders. This allows us to study their ranges of
applicability in a much more systematic and rigorous way. We point out the
limitations of such approximations and manage to go beyond at several
instances.Comment: 43 pages, 2 figures; two misprints in Eqs. (118) and (142) corrected
(a factor 2^(-2/3) was missing

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