Inferring Multiple Graphical Structures

Gaussian Graphical Models provide a convenient framework for representing dependencies between variables. Recently, this tool has received a high interest for the discovery of biological networks. The literature focuses on the case where a single network is inferred from a set of measurements, but, as wetlab data is typically scarce, several assays, where the experimental conditions affect interactions, are usually merged to infer a single network. In this paper, we propose two approaches for estimating multiple related graphs, by rendering the closeness assumption into an empirical prior or group penalties. We provide quantitative results demonstrating the benefits of the proposed approaches. The methods presented in this paper are embeded in the R package 'simone' from version 1.0-0 and later

Classical generalized constant coupling model for geometrically frustrated antiferromagnets

A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found to be in very good agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of the pyrochlore specific heat correcte

Spectral Duality Between Heisenberg Chain and Gaudin Model

In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.Comment: 36 page

Novel criticality in a model with absorbing states

We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and critical exponents in this model. The exponents $\delta=0.5$ and $z=2$ follows from random-walk-type arguments. The exponents $\beta = \nu_{\perp}$ are found to be non-universal and encoded in the singular part of reactivation probability, as recently discussed by H. Hinrichsen (cond-mat/0008179). A related model with quenched randomness is also studied.Comment: 5 pages, 5 figures, generalized version with the continuously changing exponent bet

Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states

When the two-dimensional random-bond Ising model is represented as a noninteracting fermion problem, it has the same symmetries as an ensemble of random matrices known as class D. A nonlinear sigma model analysis of the latter in two dimensions has previously led to the prediction of a metallic phase, in which the fermion eigenstates at zero energy are extended. In this paper we argue that such behavior cannot occur in the random-bond Ising model, by showing that the Ising spin correlations in the metallic phase violate the bound on such correlations that results from the reality of the Ising couplings. Some types of disorder in spinless or spin-polarized p-wave superconductors and paired fractional quantum Hall states allow a mapping onto an Ising model with real but correlated bonds, and hence a metallic phase is not possible there either. It is further argued that vortex disorder, which is generic in the fractional quantum Hall applications, destroys the ordered or weak-pairing phase, in which nonabelian statistics is obtained in the pure case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure

Stringing Spins and Spinning Strings

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N =4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J,L-2J,J], interpolate smoothly between the BMN case of two impurities (J=2) and the extreme case where the number of impurities equals half the total number of fields (J=L/2). The result for this particular [J,0,J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J,L-2J,J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J,0,J] operator is consistent with the string prediction.Comment: 27 pages, 4 figures, LaTex; v2 reference added, typos fixe

Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory

We study quartic matrix models with partition function Z[E,J]=\int dM \exp(trace(JM-EM^2-(\lambda/4)M^4)). The integral is over the space of Hermitean NxN-matrices, the external matrix E encodes the dynamics, \lambda>0 is a scalar coupling constant and the matrix J is used to generate correlation functions. For E not a multiple of the identity matrix, we prove a universal algebraic recursion formula which gives all higher correlation functions in terms of the 2-point function and the distinct eigenvalues of E. The 2-point function itself satisfies a closed non-linear equation which must be solved case by case for given E. These results imply that if the 2-point function of a quartic matrix model is renormalisable by mass and wavefunction renormalisation, then the entire model is renormalisable and has vanishing \beta-function. As main application we prove that Euclidean \phi^4-quantum field theory on four-dimensional Moyal space with harmonic propagation, taken at its self-duality point and in the infinite volume limit, is exactly solvable and non-trivial. This model is a quartic matrix model, where E has for N->\infty the same spectrum as the Laplace operator in 4 dimensions. Using the theory of singular integral equations of Carleman type we compute (for N->\infty and after renormalisation of E,\lambda) the free energy density (1/volume)\log(Z[E,J]/Z[E,0]) exactly in terms of the solution of a non-linear integral equation. Existence of a solution is proved via the Schauder fixed point theorem. The derivation of the non-linear integral equation relies on an assumption which we verified numerically for coupling constants 0<\lambda\leq (1/\pi).Comment: LaTeX, 64 pages, xypic figures. v4: We prove that recursion formulae and vanishing of \beta-function hold for general quartic matrix models. v3: We add the existence proof for a solution of the non-linear integral equation. A rescaling of matrix indices was necessary. v2: We provide Schwinger-Dyson equations for all correlation functions and prove an algebraic recursion formula for their solutio

Advances in multispectral and hyperspectral imaging for archaeology and art conservation

Multispectral imaging has been applied to the field of art conservation and art history since the early 1990s. It is attractive as a noninvasive imaging technique because it is fast and hence capable of imaging large areas of an object giving both spatial and spectral information. This paper gives an overview of the different instrumental designs, image processing techniques and various applications of multispectral and hyperspectral imaging to art conservation, art history and archaeology. Recent advances in the development of remote and versatile multispectral and hyperspectral imaging as well as techniques in pigment identification will be presented. Future prospects including combination of spectral imaging with other noninvasive imaging and analytical techniques will be discussed

Targeting Potential Drivers of COVID-19: Neutrophil Extracellular Traps

Coronavirus disease 2019 (COVID-19) is a novel, viral-induced respiratory disease that in ∼10-15% of patients progresses to acute respiratory distress syndrome (ARDS) triggered by a cytokine storm. In this Perspective, autopsy results and literature are presented supporting the hypothesis that a little known yet powerful function of neutrophils-the ability to form neutrophil extracellular traps (NETs)-may contribute to organ damage and mortality in COVID-19. We show lung infiltration of neutrophils in an autopsy specimen from a patient who succumbed to COVID-19. We discuss prior reports linking aberrant NET formation to pulmonary diseases, thrombosis, mucous secretions in the airways, and cytokine production. If our hypothesis is correct, targeting NETs directly and/or indirectly with existing drugs may reduce the clinical severity of COVID-19