431 research outputs found
High order Fuchsian equations for the square lattice Ising model:
This paper deals with , the six-particle contribution to
the magnetic susceptibility of the square lattice Ising model. We have
generated, modulo a prime, series coefficients for . The
length of the series is sufficient to produce the corresponding Fuchsian linear
differential equation (modulo a prime). We obtain the Fuchsian linear
differential equation that annihilates the "depleted" series
. The factorization of the corresponding differential
operator is performed using a method of factorization modulo a prime introduced
in a previous paper. The "depleted" differential operator is shown to have a
structure similar to the corresponding operator for . It
splits into factors of smaller orders, with the left-most factor of order six
being equivalent to the symmetric fifth power of the linear differential
operator corresponding to the elliptic integral . The right-most factor has
a direct sum structure, and using series calculated modulo several primes, all
the factors in the direct sum have been reconstructed in exact arithmetics.Comment: 23 page
The Ising model and Special Geometries
We show that the globally nilpotent G-operators corresponding to the factors
of the linear differential operators annihilating the multifold integrals
of the magnetic susceptibility of the Ising model () are
homomorphic to their adjoint. This property of being self-adjoint up to
operator homomorphisms, is equivalent to the fact that their symmetric square,
or their exterior square, have rational solutions. The differential Galois
groups are in the special orthogonal, or symplectic, groups. This self-adjoint
(up to operator equivalence) property means that the factor operators we
already know to be Derived from Geometry, are special globally nilpotent
operators: they correspond to "Special Geometries".
Beyond the small order factor operators (occurring in the linear differential
operators associated with and ), and, in particular,
those associated with modular forms, we focus on the quite large order-twelve
and order-23 operators. We show that the order-twelve operator has an exterior
square which annihilates a rational solution. Then, its differential Galois
group is in the symplectic group . The order-23 operator
is shown to factorize in an order-two operator and an order-21 operator. The
symmetric square of this order-21 operator has a rational solution. Its
differential Galois group is, thus, in the orthogonal group
.Comment: 33 page
Renormalization, isogenies and rational symmetries of differential equations
We give an example of infinite order rational transformation that leaves a
linear differential equation covariant. This example can be seen as a
non-trivial but still simple illustration of an exact representation of the
renormalization group.Comment: 36 page
Globally nilpotent differential operators and the square Ising model
We recall various multiple integrals related to the isotropic square Ising
model, and corresponding, respectively, to the n-particle contributions of the
magnetic susceptibility, to the (lattice) form factors, to the two-point
correlation functions and to their lambda-extensions. These integrals are
holonomic and even G-functions: they satisfy Fuchsian linear differential
equations with polynomial coefficients and have some arithmetic properties. We
recall the explicit forms, found in previous work, of these Fuchsian equations.
These differential operators are very selected Fuchsian linear differential
operators, and their remarkable properties have a deep geometrical origin: they
are all globally nilpotent, or, sometimes, even have zero p-curvature. Focusing
on the factorised parts of all these operators, we find out that the global
nilpotence of the factors corresponds to a set of selected structures of
algebraic geometry: elliptic curves, modular curves, and even a remarkable
weight-1 modular form emerging in the three-particle contribution
of the magnetic susceptibility of the square Ising model. In the case where we
do not have G-functions, but Hamburger functions (one irregular singularity at
0 or ) that correspond to the confluence of singularities in the
scaling limit, the p-curvature is also found to verify new structures
associated with simple deformations of the nilpotent property.Comment: 55 page
Unrolled primal-dual networks for lensless cameras
Conventional models for lensless imaging assume that each measurement results from convolving a given scene with a single experimentally measured point-spread function. These models fail to simulate lensless cameras truthfully, as these models do not account for optical aberrations or scenes with depth variations. Our work shows that learning a supervised primal-dual reconstruction method results in image quality matching state of the art in the literature without demanding a large network capacity. We show that embedding learnable forward and adjoint models improves the reconstruction quality of lensless images (+5dB PSNR) compared to works that assume a fixed point-spread function
Difference system for Selberg correlation integrals
The Selberg correlation integrals are averages of the products
with respect to the Selberg
density. Our interest is in the case , , when this
corresponds to the -th moment of the corresponding characteristic
polynomial. We give the explicit form of a matrix linear
difference system in the variable which determines the average, and we
give the Gauss decomposition of the corresponding matrix.
For a positive integer the difference system can be used to efficiently
compute the power series defined by this average.Comment: 21 page
Mining remittances corresponding to metalliferous ores: regulation and budget impact
Economic statistics and forecasting show that Romania has a very favourable potential as far as the metalliferous ores are concerned. As these are owned by the state, once they are allowed to be exploited, they generate considerable amounts for the consolidated public budget. The present paper is meant to conduct a synthetic analysis on the topic of mining remittances from an economic perspective, by considering the juridical framework of capitalizing deposits of ferrous and non-ferrous ores, correlated with the general regulations concerning property and the specific existing regulations of the EU and of the countries that have experience and potential in the mining sector
NuMI Beam Monitoring Simulation and Data Analysis Status and Progress
With the Main Injector Neutrino Oscillation Search (MINOS) experiment decommissioned, muon and hadron monitors became an important diagnostic tool for the NuMI Off-axis v Appearance (NOvA) experiment at Fermilab to monitor the Neutrinos at the Main Injector (NuMI) beam. The goal of this study is to maintain the quality of the monitor signals and to establish correlations with the neutrino beam profile. And we carry out a systematic study of the response of the muon monitors to the changes in the parameters of the proton beam and lattice parameters. We report here on the progress of the beam data analysis and comparison with the simulation results
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