Coinductive subtyping for abstract compilation of object-oriented languages into Horn formulas

In recent work we have shown how it is possible to define very precise type systems for object-oriented languages by abstractly compiling a program into a Horn formula f. Then type inference amounts to resolving a certain goal w.r.t. the coinductive (that is, the greatest) Herbrand model of f. Type systems defined in this way are idealized, since in the most interesting instantiations both the terms of the coinductive Herbrand universe and goal derivations cannot be finitely represented. However, sound and quite expressive approximations can be implemented by considering only regular terms and derivations. In doing so, it is essential to introduce a proper subtyping relation formalizing the notion of approximation between types. In this paper we study a subtyping relation on coinductive terms built on union and object type constructors. We define an interpretation of types as set of values induced by a quite intuitive relation of membership of values to types, and prove that the definition of subtyping is sound w.r.t. subset inclusion between type interpretations. The proof of soundness has allowed us to simplify the notion of contractive derivation and to discover that the previously given definition of subtyping did not cover all possible representations of the empty type

Quantum and Classical Glass Transitions in LiHoxY1−xF4Li Ho_x Y_{1-x} F_4

When performed in the proper low field, low frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in transverse field, $\text{LiHo}_x\text{Y}_{1-x}\text{F}_4$, prove the existence of a spin glass transition for $x$ = 0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields.Comment: 5 pages, 5 figures. Updated figure 3 with corrected calibration information for thermometr

Some Results on the Boundary Control of Systems of Conservation Laws

This note is concerned with the study of the initial boundary value problem for systems of conservation laws from the point of view of control theory, where the initial data is fixed and the boundary data are regarded as control functions. We first consider the problem of controllability at a fixed time for genuinely nonlinear Temple class systems, and present a description of the set of attainable configurations of the corresponding solutions in terms of suitable Oleinik-type estimates. We next present a result concerning the asymptotic stabilization near a constant state for general $n\times n$ systems. Finally we show with an example that in general one cannot achieve exact controllability to a constant state in finite time.Comment: 10 pages, 4 figures, conferenc

Leave-one-out prediction error of systolic arterial pressure time series under paced breathing

In this paper we show that different physiological states and pathological conditions may be characterized in terms of predictability of time series signals from the underlying biological system. In particular we consider systolic arterial pressure time series from healthy subjects and Chronic Heart Failure patients, undergoing paced respiration. We model time series by the regularized least squares approach and quantify predictability by the leave-one-out error. We find that the entrainment mechanism connected to paced breath, that renders the arterial blood pressure signal more regular, thus more predictable, is less effective in patients, and this effect correlates with the seriousness of the heart failure. The leave-one-out error separates controls from patients and, when all orders of nonlinearity are taken into account, alive patients from patients for which cardiac death occurred

Towards nonlinear quantum Fokker-Planck equations

It is demonstrated how the equilibrium semiclassical approach of Coffey et al. can be improved to describe more correctly the evolution. As a result a new semiclassical Klein-Kramers equation for the Wigner function is derived, which remains quantum for a free quantum Brownian particle as well. It is transformed to a semiclassical Smoluchowski equation, which leads to our semiclassical generalization of the classical Einstein law of Brownian motion derived before. A possibility is discussed how to extend these semiclassical equations to nonlinear quantum Fokker-Planck equations based on the Fisher information

A comparative study of Gaussian Graphical Model approaches for genomic data

The inference of networks of dependencies by Gaussian Graphical models on high-throughput data is an open issue in modern molecular biology. In this paper we provide a comparative study of three methods to obtain small sample and high dimension estimates of partial correlation coefficients: the Moore-Penrose pseudoinverse (PINV), residual correlation (RCM) and covariance-regularized method $(\ell_{2C})$. We first compare them on simulated datasets and we find that PINV is less stable in terms of AUC performance when the number of variables changes. The two regularized methods have comparable performances but $\ell_{2C}$ is much faster than RCM. Finally, we present the results of an application of $\ell_{2C}$ for the inference of a gene network for isoprenoid biosynthesis pathways in Arabidopsis thaliana.Comment: 7 pages, 1 figure, RevTex4, version to appear in the proceedings of 1st International Workshop on Pattern Recognition, Proteomics, Structural Biology and Bioinformatics: PR PS BB 2011, Ravenna, Italy, 13 September 201

Proof Relevant Corecursive Resolution

Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be understood coinductively. Cycle detection is a popular method to capture a small subset of such derivations. We show that in fact cycle detection is a restricted form of coinductive proof, in which the atomic formula forming the cycle plays the role of coinductive hypothesis. This paper introduces a heuristic method for obtaining richer coinductive hypotheses in the form of Horn formulas. Our approach subsumes cycle detection and gives coinductive meaning to a larger class of derivations. For this purpose we extend resolution with Horn formula resolvents and corecursive evidence generation. We illustrate our method on non-terminating type class resolution problems.Comment: 23 pages, with appendices in FLOPS 201

Dynamic rotor mode in antiferromagnetic nanoparticles

We present experimental, numerical, and theoretical evidence for a new mode of antiferromagnetic dynamics in nanoparticles. Elastic neutron scattering experiments on 8 nm particles of hematite display a loss of diffraction intensity with temperature, the intensity vanishing around 150 K. However, the signal from inelastic neutron scattering remains above that temperature, indicating a magnetic system in constant motion. In addition, the precession frequency of the inelastic magnetic signal shows an increase above 100 K. Numerical Langevin simulations of spin dynamics reproduce all measured neutron data and reveal that thermally activated spin canting gives rise to a new type of coherent magnetic precession mode. This "rotor" mode can be seen as a high-temperature version of superparamagnetism and is driven by exchange interactions between the two magnetic sublattices. The frequency of the rotor mode behaves in fair agreement with a simple analytical model, based on a high temperature approximation of the generally accepted Hamiltonian of the system. The extracted model parameters, as the magnetic interaction and the axial anisotropy, are in excellent agreement with results from Mossbauer spectroscopy