390 research outputs found
Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems
We consider a class of Ising spin systems on a set \Lambda of sites. The
sites are grouped into units with the property that each site belongs to either
one or two units, and the total internal energy of the system is the sum of the
energies of the individual units, which in turn depend only on the number of up
spins in the unit. We show that under suitable conditions on these interactions
none of the |\Lambda| Lee-Yang zeros in the complex z = exp{2\beta h} plane,
where \beta is the inverse temperature and h the uniform magnetic field, touch
the positive real axis, at least for large values of \beta. In some cases one
obtains, in an appropriately taken \beta to infinity limit, a gas of hard
objects on a set \Lambda'; the fugacity for the limiting system is a rescaling
of z and the Lee-Yang zeros of the new partition function also avoid the
positive real axis. For certain forms of the energies of the individual units
the Lee-Yang zeros of both the finite- and zero-temperature systems lie on the
negative real axis for all \beta. One zero-temperature limit of this type, for
example, is a monomer-dimer system; our results thus generalize, to finite
\beta, a well-known result of Heilmann and Lieb that the Lee-Yang zeros of
monomer-dimer systems are real and negative.Comment: Plain TeX. Seventeen pages, five figures from .eps files. Version 2
corrects minor errors in version
A New Class of Non-Linear Stability Preserving Operators
We extend Br\"and\'en's recent proof of a conjecture of Stanley and describe
a new class of non-linear operators that preserve weak Hurwitz stability and
the Laguerre-P\'olya class.Comment: Fixed typos, spelling, and updated links in reference
Sums of magnetic eigenvalues are maximal on rotationally symmetric domains
The sum of the first n energy levels of the planar Laplacian with constant
magnetic field of given total flux is shown to be maximal among triangles for
the equilateral triangle, under normalization of the ratio (moment of
inertia)/(area)^3 on the domain. The result holds for both Dirichlet and
Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary
conditions too. The square similarly maximizes the eigenvalue sum among
parallelograms, and the disk maximizes among ellipses. More generally, a domain
with rotational symmetry will maximize the magnetic eigenvalue sum among all
linear images of that domain. These results are new even for the ground state
energy (n=1).Comment: 19 pages, 1 figur
A magabiztosság-krízis skála alkalmazása idegen nyelvű megnyilatkozásoknál
Tanulmányunkban korábbi kutatásaink eredményeit kívánjuk megvizsgálni idegen nyelvű megnyilatkozásokon. 2011-ben bemutatásra került a Magyar Számítógépes Nyelvészeti Konferencián az az új narratív pszichológiai eljárás, amelyben összekapcsoltuk a narratív pszichológiai tartalomelemzést és a vokális mintázatok pszichológiai „tartalomelemzését” [12]. Ennek az eljárásnak a részeként mutattuk be a magabiztosság-krízis indexet, amely a megnyilatkozás nyelvi, tartalmi elemeit és az elhangzottak fonetikai struktúráját vizsgálva von le következtetéseket a közlő lelkiállapotára vonatkozóan. Azt a feltételezésünket igyekeztünk adatokkal is alátámasztva igazolni, hogy a krízishelyzet nyelvi-fonetikai mintázata jól körülhatárolható, és ezen jegyek alapján a közlő lelkiállapotára vonatkozóan pszichológiailag értékelhető megállapítások tehetők. Vizsgálatunk nyelvi anyagát akkor Shakespeare Lear királya első és utolsó monológjának magyar nyelvű változata alkotta. 2014-ben a Magyar Számítógépes Nyelvészeti Konferencián mutattuk be a magabiztosság-krízis skála spontán megnyilatkozásokon történő alkalmazását [11]. A mostani kutatásunk a 2011-ben elhangzott előadáshoz kíván visszanyúlni, hasznosítva az időközben szerzett tapasztalatokat, egy olasz nyelvű Lear király megnyilatkozásával gazdagítva a korábbi kutatások eredményeit
Bias reduction in traceroute sampling: towards a more accurate map of the Internet
Traceroute sampling is an important technique in exploring the internet
router graph and the autonomous system graph. Although it is one of the primary
techniques used in calculating statistics about the internet, it can introduce
bias that corrupts these estimates. This paper reports on a theoretical and
experimental investigation of a new technique to reduce the bias of traceroute
sampling when estimating the degree distribution. We develop a new estimator
for the degree of a node in a traceroute-sampled graph; validate the estimator
theoretically in Erdos-Renyi graphs and, through computer experiments, for a
wider range of graphs; and apply it to produce a new picture of the degree
distribution of the autonomous system graph.Comment: 12 pages, 3 figure
Escape rate and Hausdorff measure for entire functions
The escaping set of an entire function is the set of points that tend to
infinity under iteration. We consider subsets of the escaping set defined in
terms of escape rates and obtain upper and lower bounds for the Hausdorff
measure of these sets with respect to certain gauge functions.Comment: 24 pages; some errors corrected, proof of Theorem 2 shortene
Upper bounds for the eigenvalues of Hessian equations
We prove some upper bounds for the Dirichlet eigenvalues of a class of fully
nonlinear elliptic equations, namely the Hessian equationsComment: 15 pages, 1 figur
On the topological classification of binary trees using the Horton-Strahler index
The Horton-Strahler (HS) index has been shown to
be relevant to a number of physical (such at diffusion limited aggregation)
geological (river networks), biological (pulmonary arteries, blood vessels,
various species of trees) and computational (use of registers) applications.
Here we revisit the enumeration problem of the HS index on the rooted,
unlabeled, plane binary set of trees, and enumerate the same index on the
ambilateral set of rooted, plane binary set of trees of leaves. The
ambilateral set is a set of trees whose elements cannot be obtained from each
other via an arbitrary number of reflections with respect to vertical axes
passing through any of the nodes on the tree. For the unlabeled set we give an
alternate derivation to the existing exact solution. Extending this technique
for the ambilateral set, which is described by an infinite series of non-linear
functional equations, we are able to give a double-exponentially converging
approximant to the generating functions in a neighborhood of their convergence
circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos
correcte
Spatial Degrees of Freedom in Everett Quantum Mechanics
Stapp claims that, when spatial degrees of freedom are taken into account,
Everett quantum mechanics is ambiguous due to a "core basis problem." To
examine an aspect of this claim I generalize the ideal measurement model to
include translational degrees of freedom for both the measured system and the
measuring apparatus. Analysis of this generalized model using the Everett
interpretation in the Heisenberg picture shows that it makes unambiguous
predictions for the possible results of measurements and their respective
probabilities. The presence of translational degrees of freedom for the
measuring apparatus affects the probabilities of measurement outcomes in the
same way that a mixed state for the measured system would. Examination of a
measurement scenario involving several observers illustrates the consistency of
the model with perceived spatial localization of the measuring apparatus.Comment: 34 pp., no figs. Introduction, discussion revised. Material
tangential to main point remove
Staircase polygons: moments of diagonal lengths and column heights
We consider staircase polygons, counted by perimeter and sums of k-th powers
of their diagonal lengths, k being a positive integer. We derive limit
distributions for these parameters in the limit of large perimeter and compare
the results to Monte-Carlo simulations of self-avoiding polygons. We also
analyse staircase polygons, counted by width and sums of powers of their column
heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity:
An International Workshop On Statistical Mechanics And Combinatorics, 10-15
July 2005, Queensland, Australi
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