501 research outputs found
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
On the functions counting walks with small steps in the quarter plane
Models of spatially homogeneous walks in the quarter plane
with steps taken from a subset of the set of jumps to the eight
nearest neighbors are considered. The generating function of the numbers of such walks starting at the origin and
ending at after steps is studied. For all
non-singular models of walks, the functions and are continued as multi-valued functions on having
infinitely many meromorphic branches, of which the set of poles is identified.
The nature of these functions is derived from this result: namely, for all the
51 walks which admit a certain infinite group of birational transformations of
, the interval of variation of splits into
two dense subsets such that the functions and are shown to be holonomic for any from the one of them and
non-holonomic for any from the other. This entails the non-holonomy of
, and therefore proves a conjecture of
Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure
Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals
Lattice statistical mechanics, often provides a natural (holonomic) framework
to perform singularity analysis with several complex variables that would, in a
general mathematical framework, be too complex, or could not be defined.
Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau
ODEs, associated with double hypergeometric series, we show that holonomic
functions are actually a good framework for actually finding the singular
manifolds. We, then, analyse the singular algebraic varieties of the n-fold
integrals , corresponding to the decomposition of the magnetic
susceptibility of the anisotropic square Ising model. We revisit a set of
Nickelian singularities that turns out to be a two-parameter family of elliptic
curves. We then find a first set of non-Nickelian singularities for and , that also turns out to be rational or ellipic
curves. We underline the fact that these singular curves depend on the
anisotropy of the Ising model. We address, from a birational viewpoint, the
emergence of families of elliptic curves, and of Calabi-Yau manifolds on such
problems. We discuss the accumulation of these singular curves for the
non-holonomic anisotropic full susceptibility.Comment: 36 page
The Beta Ansatz: A Tale of Two Complex Structures
Brane tilings, sometimes called dimer models, are a class of bipartite graphs on a torus which encode the gauge theory data of four-dimensional SCFTs dual to D3-branes probing toric Calabi-Yau threefolds. An efficient way of encoding this information exploits the theory of dessin d’enfants, expressing the structure in terms of a permutation triple, which is in turn related to a Belyi pair, namely a holomorphic map from a torus to a P1 with three marked points. The procedure of a-maximization, in the context of isoradial embeddings of the dimer, also associates a complex structure to the torus, determined by the R-charges in the SCFT, which can be compared with the Belyi complex structure. Algorithms for the explicit construction of the Belyi pairs are described in detail. In the case of orbifolds, these algorithms are related to the construction of covers of elliptic curves, which exploits the properties of Weierstraß elliptic functions. We present a counter example to a previous conjecture identifying the complex structure of the Belyi curve to the complex structure associated with R-charges
Prospects for progress on health inequalities in England in the post-primary care trust era : professional views on challenges, risks and opportunities
Background - Addressing health inequalities remains a prominent policy objective of the current UK government, but current NHS reforms involve a significant shift in roles and responsibilities. Clinicians are now placed at the heart of healthcare commissioning through which significant inequalities in access, uptake and impact of healthcare services must be addressed. Questions arise as to whether these new arrangements will help or hinder progress on health inequalities. This paper explores the perspectives of experienced healthcare professionals working within the commissioning arena; many of whom are likely to remain key actors in this unfolding scenario.
Methods - Semi-structured interviews were conducted with 42 professionals involved with health and social care commissioning at national and local levels. These included representatives from the Department of Health, Primary Care Trusts, Strategic Health Authorities, Local Authorities, and third sector organisations.
Results - In general, respondents lamented the lack of progress on health inequalities during the PCT commissioning era, where strong policy had not resulted in measurable improvements. However, there was concern that GP-led commissioning will fare little better, particularly in a time of reduced spending. Specific concerns centred on: reduced commitment to a health inequalities agenda; inadequate skills and loss of expertise; and weakened partnership working and engagement. There were more mixed opinions as to whether GP commissioners would be better able than their predecessors to challenge large provider trusts and shift spend towards prevention and early intervention, and whether GPs’ clinical experience would support commissioning action on inequalities. Though largely pessimistic, respondents highlighted some opportunities, including the potential for greater accountability of healthcare commissioners to the public and more influential needs assessments via emergent Health & Wellbeing Boards.
Conclusions - There is doubt about the ability of GP commissioners to take clearer action on health inequalities than PCTs have historically achieved. Key actors expect the contribution from commissioning to address health inequalities to become even more piecemeal in the new arrangements, as it will be dependent upon the interest and agency of particular individuals within the new commissioning groups to engage and influence a wider range of stakeholders.</p
High-spin States in \u3csup\u3e191, 193\u3c/sup\u3eAu and \u3csup\u3e192\u3c/sup\u3ePt: Evidence for Oblate Deformation and Triaxial Shapes
High-spin states of 191, 193Au and 192Pt have been populated in the 186W(11B, xn) and 186W(11B, p4n) reactions, respectively, at a beam energy of 68 MeV and their γ decay was studied using the YRAST Ball detector array at the Wright Nuclear Structure Laboratory at Yale University. The level scheme of 193Au has been extended up to Iπ = 55/2+. New transitions were observed also in 191Au and 192Pt. Particle-plus-Triaxial-Rotor (PTR) and Total Routhian Surface (TRS) calculations were performed to determine the equilibrium deformations of the Au isotopes. The predictions for oblate deformations in these nuclei are in agreement with the experimental data. Development of nonaxial shapes is discussed within the framework of the PTR model
Solving Phase Retrieval with a Learned Reference
Fourier phase retrieval is a classical problem that deals with the recovery
of an image from the amplitude measurements of its Fourier coefficients.
Conventional methods solve this problem via iterative (alternating)
minimization by leveraging some prior knowledge about the structure of the
unknown image. The inherent ambiguities about shift and flip in the Fourier
measurements make this problem especially difficult; and most of the existing
methods use several random restarts with different permutations. In this paper,
we assume that a known (learned) reference is added to the signal before
capturing the Fourier amplitude measurements. Our method is inspired by the
principle of adding a reference signal in holography. To recover the signal, we
implement an iterative phase retrieval method as an unrolled network. Then we
use back propagation to learn the reference that provides us the best
reconstruction for a fixed number of phase retrieval iterations. We performed a
number of simulations on a variety of datasets under different conditions and
found that our proposed method for phase retrieval via unrolled network and
learned reference provides near-perfect recovery at fixed (small) computational
cost. We compared our method with standard Fourier phase retrieval methods and
observed significant performance enhancement using the learned reference.Comment: Accepted to ECCV 2020. Code is available at
https://github.com/CSIPlab/learnPR_referenc
New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
In this paper we show how an infinite system of coupled Toda-type nonlinear
differential equations derived by one of us can be used efficiently to
calculate the time-dependent pair-correlations in the Ising chain in a
transverse field. The results are seen to match extremely well long large-time
asymptotic expansions newly derived here. For our initial conditions we use new
long asymptotic expansions for the equal-time pair correlation functions of the
transverse Ising chain, extending an old result of T.T. Wu for the 2d Ising
model. Using this one can also study the equal-time wavevector-dependent
correlation function of the quantum chain, a.k.a. the q-dependent diagonal
susceptibility in the 2d Ising model, in great detail with very little
computational effort.Comment: LaTeX 2e, 31 pages, 8 figures (16 eps files). vs2: Two references
added and minor changes of style. vs3: Corrections made and reference adde
Cerebral activations related to ballistic, stepwise interrupted and gradually modulated movements in parkinson patients
Patients with Parkinson's disease (PD) experience impaired initiation and inhibition of movements such as difficulty to start/stop walking. At single-joint level this is accompanied by reduced inhibition of antagonist muscle activity. While normal basal ganglia (BG) contributions to motor control include selecting appropriate muscles by inhibiting others, it is unclear how PD-related changes in BG function cause impaired movement initiation and inhibition at single-joint level. To further elucidate these changes we studied 4 right-hand movement tasks with fMRI, by dissociating activations related to abrupt movement initiation, inhibition and gradual movement modulation. Initiation and inhibition were inferred from ballistic and stepwise interrupted movement, respectively, while smooth wrist circumduction enabled the assessment of gradually modulated movement. Task-related activations were compared between PD patients (N = 12) and healthy subjects (N = 18). In healthy subjects, movement initiation was characterized by antero-ventral striatum, substantia nigra (SN) and premotor activations while inhibition was dominated by subthalamic nucleus (STN) and pallidal activations, in line with the known role of these areas in simple movement. Gradual movement mainly involved antero-dorsal putamen and pallidum. Compared to healthy subjects, patients showed reduced striatal/SN and increased pallidal activation for initiation, whereas for inhibition STN activation was reduced and striatal-thalamo-cortical activation increased. For gradual movement patients showed reduced pallidal and increased thalamo-cortical activation. We conclude that PD-related changes during movement initiation fit the (rather static) model of alterations in direct and indirect BG pathways. Reduced STN activation and regional cortical increased activation in PD during inhibition and gradual movement modulation are better explained by a dynamic model that also takes into account enhanced responsiveness to external stimuli in this disease and the effects of hyper-fluctuating cortical inputs to the striatum and STN in particular
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