An assessment of PenSim2

The Department for Work and Pensions (DWP)’s Pensim2 model is a dynamic microsimulation model. The principal purpose of this model is to estimate the future distribution of pensioner incomes, thus enabling analysis of the distributional effects of proposed changes to pension policy. This paper presents the results of an assessment of Pensim2 by researchers at the IFS. We start by looking at the overall structure of the model, and how it compares with other dynamic policy analysis models across the world. We make recommendations at this stage as to how the overall modelling strategy could be improved. We then go on to analyse the characteristics of most of the individual modules which make up Pensim2, examining the data used and the regression and predictions used in each step. The results from this examination are used to formulate a set of short and medium-term recommendations for developing and improving the model. Finally, we look at what might become possible for the model over a much longer time frame – looking towards developing a ‘Pensim3’ model over the next decade or so

Zero energy resonance and the logarithmically slow decay of unstable multilevel systems

The long time behavior of the reduced time evolution operator for unstable multilevel systems is studied based on the N-level Friedrichs model in the presence of a zero energy resonance.The latter means the divergence of the resolvent at zero energy. Resorting to the technique developed by Jensen and Kato [Duke Math. J. 46, 583 (1979)], the zero energy resonance of this model is characterized by the zero energy eigenstate that does not belong to the Hilbert space. It is then shown that for some kinds of the rational form factors the logarithmically slow decay of the reduced time evolution operator can be realized.Comment: 31 pages, no figure

The last glacial-interglacial cycle in Lake Ohrid (Macedonia/Albania): testing diatom response to climate

Lake Ohrid is a site of global importance for palaeoclimate research. This study presents results of diatom analysis of a ca. 136 ka sequence, Co1202, from the northeast of the lake basin. It offers the opportunity to test diatom response across two glacial-interglacial transitions and within the Last Glacial, while setting up taxonomic protocols for future research. The results are outstanding in demonstrating the sensitivity of diatoms to climate change, providing proxy evidence for temperature change marked by glacial-interglacial shifts between the dominant planktonic taxa, Cyclotella fottii and C. ocellata, and exact correlation with geochemical proxies to mark the start of the Last Interglacial at ca. 130 ka. Importantly, diatoms show much stronger evidence in this site for warming during MIS3 than recorded in other productivity-related proxies, peaking at ca. 39 ka, prior to the extreme conditions of the Last Glacial maximum. In the light of the observed patterns, and from the results of analysis of early Holocene sediments from a second core, Lz1120, the lack of a response to Late Glacial and early Holocene warming from ca. 15-7.4 ka suggests the Co1202 sequence may be compromised during this phase. After ca. 7.4 ka, there is evidence for enhanced nutrient enrichment compared to the Last Interglacial, following by a post-Medieval cooling trend. Taxonomically, morphological variability in C. fottii shows no clear trends linked to climate, but an intriguing change in central area morphology occurs after ca. 48.7 ka, coincident with a tephra layer. In contrast, C. ocellata shows morphological variation in the number of ocelli between interglacials, suggesting climatically-forced variation or evolutionary selection pressure. The application of a simple dissolution index does not track preservation quality very effectively, underlining the importance of diatom concentration data in future studies

Automatic mapping of strip mine operations from spacecraft data

The author has identified the following significant results. Computer techniques were applied to process ERTS tapes acquired over coal mining operations in southeastern Ohio on 21 August 1972 and 3 September 1973. ERTS products obtained included geometrically-correct map overlays, at scales from 1:24,000 to 1:250,000, showing stripped earth, partially reclaimed earth, water, and natural vegetation. Computer-generated tables listing the area covered by each land-water category in square kilometers were also produced. By comparing these mapping products, the study demonstrates the capability of ERTS to monitor changes in the extent of stripping and reclamation. NASA C-130 photography acquired on 7 September 1973 when compared with the ERTS products generated from the 3 September 1973 tape established the categorization accuracy to be better than 90%. It is estimated that the stripping and reclamation maps and data were produced from the ERTS CCTs at a tenth of the cost of conventional techniques

Automated strip-mine and reclamation mapping from ERTS

The author has identified the following significant results. Computer processing techniques were applied to ERTS-1 computer-compatible tape (CCT) data acquired in August 1972 on the Ohio Power Company's coal mining operation in Muskingum County, Ohio. Processing results succeeded in automatically classifying, with an accuracy greater than 90%: (1) stripped earth and major sources of erosion; (2) partially reclaimed areas and minor sources of erosion; (3) water with sedimentation; (4) water without sedimentation; and (5) vegetation. Computer-generated tables listing the area in acres and square kilometers were produced for each target category. Processing results also included geometrically corrected map overlays, one for each target category, drawn on a transparent material by a pen under computer control. Each target category is assigned a distinctive color on the overlay to facilitate interpretation. The overlays, drawn at a scale of 1:250,000 when placed over an AMS map of the same area, immediately provided map locations for each target. These mapping products were generated at a tenth of the cost of conventional mapping techniques

Magnetic transport in a straight parabolic channel

We study a charged two-dimensional particle confined to a straight parabolic-potential channel and exposed to a homogeneous magnetic field under influence of a potential perturbation $W$. If $W$ is bounded and periodic along the channel, a perturbative argument yields the absolute continuity of the bottom of the spectrum. We show it can have any finite number of open gaps provided the confining potential is sufficiently strong. However, if $W$ depends on the periodic variable only, we prove by Thomas argument that the whole spectrum is absolutely continuous, irrespectively of the size of the perturbation. On the other hand, if $W$ is small and satisfies a weak localization condition in the the longitudinal direction, we prove by Mourre method that a part of the absolutely continuous spectrum persists

Self-adjoint extensions and SUSY breaking in Supersymmetric Quantum Mechanics

We consider the self-adjoint extensions (SAE) of the symmetric supercharges and Hamiltonian for a model of SUSY Quantum Mechanics in $\mathbb{R}^+$ with a singular superpotential. We show that only for two particular SAE, whose domains are scale invariant, the algebra of N=2 SUSY is realized, one with manifest SUSY and the other with spontaneously broken SUSY. Otherwise, only the N=1 SUSY algebra is obtained, with spontaneously broken SUSY and non degenerate energy spectrum.Comment: LaTeX. 23 pages and 1 figure (minor changes). Version to appear in the Journal of Physics A: Mat. and Ge

Time-Dependent Models for Dark Matter at the Galactic Center

The prospects of indirect detection of dark matter at the galactic center depend sensitively on the mass profile within the inner parsec. We calculate the distribution of dark matter on sub-parsec scales by integrating the time-dependent Fokker-Planck equation, including the effects of self-annihilations, scattering of dark matter particles by stars, and capture in the supermassive black hole. We consider a variety of initial dark matter distributions, including models with very high densities ("spikes") near the black hole, and models with "adiabatic compression" of the baryons. The annihilation signal after 10 Gyr is found to be substantially reduced from its initial value, but in dark matter models with an initial spike, order-of-magnitude enhancements can persist compared with the rate in spike-free models, with important implications for indirect dark matter searches with GLAST and Air Cherenkov Telescopes like HESS and CANGAROO.Comment: Four page

Restricted three-body problem in effective-field-theory models of gravity

One of the outstanding problems of classical celestial mechanics was the restricted 3-body prob- lem, in which a planetoid of small mass is subject to the Newtonian attraction of two celestial bodies of large mass, as it occurs, for example, in the sun-earth-moon system. On the other hand, over the last decades, a systematic investigation of quantum corrections to the Newtonian potential has been carried out in the literature on quantum gravity. The present paper studies the effect of these tiny quantum corrections on the evaluation of equilibrium points. It is shown that, despite the extreme smallness of the corrections, there exists no choice of sign of these corrections for which all qualitative features of the restricted 3-body problem in Newtonian theory remain unaffected. Moreover, first-order stability of equilibrium points is characterized by solving a pair of algebraic equations of fifth degree, where some coefficients depend on the Planck length. The coordinates of stable equilibrium points are slightly changed with respect to Newtonian theory, because the planetoid is no longer at equal distance from the two bodies of large mass. The effect is conceptually interesting but too small to be observed, at least for the restricted 3-body problems available in the solar system.Comment: 20 pages, latex, 8 figure