Regime Shifts and Uncertainty in Pollution Control

We develop a simple model of managing a system subject to pollution damage under risk of an abrupt and random jump in the damage coefficient. The model allows the full dynamic characterization of the optimal emission policies under uncertainty. The results, that imply prudent behavior due to uncertainty, are compared with the ambiguous outcomes reported in the literature for similar models. The differences are explained in terms of the properties of the damage function associated with each model. The framework is used to analyze the adaptation vs. mitigation dilemma and provides a simple criterion to determine whether adaptation activities should be undertaken promptly, delayed to some future date, or avoided altogether.environmental pollution, optimal management, catastrophic transitions, uncertainty, adaptation, mitigation

Kernel-based Image Reconstruction from Scattered Radon Data

Computerized tomography requires suitable numerical methods for the approximation of a bivariate function f from a finite set of discrete Radon data, each of whose data samples represents one line integral of f . In standard reconstruction methods, specific assumptions concerning the geometry of the Radon lines are usually made. In relevant applications of image reconstruction, however, such assumptions are often too restrictive. In this case, one would rather prefer to work with reconstruction methods allowing for arbitrary distributions of scattered Radon lines. This paper proposes a novel image reconstruction method for scattered Radon data, which combines kernel-based scattered data approximation with a well-adapted regularization of the Radon transform. This results in a very flexible numerical algorithm for image reconstruction, which works for arbitrary distributions of Radon lines. This is in contrast to the classical filtered back projection, which essentially relies on a regular distribution of the Radon lines, e.g. parallel beam geometry. The good performance of the kernel-based image reconstruction method is illustrated by numerical examples and comparisons

Solution of a minimal model for many-body quantum chaos

We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a $q$-dimensional Hilbert space and time evolution for a pair of sites is generated by a $q^2\times q^2$ random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. We show how dynamical behaviour averaged over realisations of the random matrices can be evaluated using diagrammatic techniques, and how this approach leads to exact expressions in the large-$q$ limit. We give results for the spectral form factor, relaxation of local observables, bipartite entanglement growth and operator spreading.Comment: Accepted in PR

Regime shifts and uncertainty in pollution control

We develop a simple model of managing a system subject to pollution damage under risk of an abrupt and random jump in the damage coefficient. The model allows the full dynamic characterization of the optimal emission policies under uncertainty. The results, that imply prudent behavior due to uncertainty, are compared with the ambiguous outcomes reported in the literature for similar models. The differences are explained in terms of the properties of the damage function associated with each model. The framework is used to analyze the adaptation vs. mitigation dilemma and provides a simple criterion to determine whether adaptation activities should be undertaken promptly, delayed to some future date, or avoided altogether

Projected state ensemble of a generic model of many-body quantum chaos

The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the $k$-th moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension $q$, we find that all moments converge simultaneously with a time scaling linearly in the size of region $A$, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite $q$ on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times $t_k = O(\log k)$. Our results are supported with numerical simulations performed at $q=2$.Comment: 23 pages, 7 figures. Submitted for the special issue of Journal of Physics A: Mathematical and Theoretical on Quantum-Circuit Models for Many-Body Physics Out of Equilibriu

A new catalog of photometric redshifts in the Hubble Deep Field

Using the newly available infrared images of the Hubble Deep Field in the J, H, and K bands and an optimal photometric method, we have refined a technique to estimate the redshifts of 1067 galaxies. A detailed comparison of our results with the spectroscopic redshifts in those cases where the latter are available shows that this technique gives very good results for bright enough objects (AB(8140) < 26.0). From a study of the distribution of residuals (Dz(rms)/(1+z) ~ 0.1 at all redshifts) we conclude that the observed errors are mainly due to cosmic variance. This very important result allows for the assessment of errors in quantities to be directly or indirectly measured from the catalog. We present some of the statistical properties of the ensemble of galaxies in the catalog, and finish by presenting a list of bright high-redshift (z ~ 5) candidates extracted from our catalog, together with recent spectroscopic redshift determinations confirming that two of them are at z=5.34 and z=5.60.Comment: 28 pages, 12PS+4JPEG figures, aaspp style. Accepted for publication in The Astrophysical Journal. The catalog, together with a clickable map of the HDF, Tables 4 and 5 (HTML, LaTeX or ASCII format), and the figures, are available at http://bat.phys.unsw.edu.au/~fsoto/hdfcat.htm

Thermodynamics and area in Minkowski space: Heat capacity of entanglement

Tracing over the degrees of freedom inside (or outside) a sub-volume V of Minkowski space in a given quantum state |psi>, results in a statistical ensemble described by a density matrix rho. This enables one to relate quantum fluctuations in V when in the state |psi>, to statistical fluctuations in the ensemble described by rho. These fluctuations scale linearly with the surface area of V. If V is half of space, then rho is the density matrix of a canonical ensemble in Rindler space. This enables us to `derive' area scaling of thermodynamic quantities in Rindler space from area scaling of quantum fluctuations in half of Minkowski space. When considering shapes other than half of Minkowski space, even though area scaling persists, rho does not have an interpretation as a density matrix of a canonical ensemble in a curved, or geometrically non-trivial, background.Comment: 17 page

Effect of Heat Source and Imperfect Contact on Simultaneous Estimation of Thermal Properties of High-Conductivity Materials

In the current paper a novel methodology accounting for both the heater heat capacity and the imperfect thermal contact between a thin heater and a specimen is proposed. In particular, the volumetric heat capacity of the heater is considered by modelling it as a lumped capacitance body, while the imperfect thermal contact is considered by means of a contact resistance. Thus, the experimental apparatus consisting of three layers (specimen-heater-specimen) is reduced to a single finite layer (sample) subject to a "nonclassical" boundary condition at the heated surface, known as sixth kind. Once the temperature solution is derived analytically using the Laplace transform method, the scaled sensitivity coefficients are computed analytically at the interface between the heater and the sample (heater side and sample side) and at the sample backside. By applying the proposed methodology to a lab-controlled experiment available in the specialized literature, a reduction of the thermal properties values of about 1.4% is observed for a high-conductivity material (Armco iron)

Approximation orders of shift-invariant subspaces of W2s(Rd)W^s_2({\Bbb R}^d)

We extend the existing theory of approximation orders provided by shift-invariant subspaces of $L_2$ to the setting of Sobolev spaces, provide treatment of $L_2$ cases that have not been covered before, and apply our results to determine approximation order of solutions to a refinement equation with a higher-dimensional solution space.Comment: 49 page