Folding a Paper Strip to Minimize Thickness

In this paper, we study how to fold a specified origami crease pattern in order to minimize the impact of paper thickness. Specifically, origami designs are often expressed by a mountain-valley pattern (plane graph of creases with relative fold orientations), but in general this specification is consistent with exponentially many possible folded states. We analyze the complexity of finding the best consistent folded state according to two metrics: minimizing the total number of layers in the folded state (so that a "flat folding" is indeed close to flat), and minimizing the total amount of paper required to execute the folding (where "thicker" creases consume more paper). We prove both problems strongly NP-complete even for 1D folding. On the other hand, we prove the first problem fixed-parameter tractable in 1D with respect to the number of layers.Comment: 9 pages, 7 figure

The X-ray Spectrum and Light Curve of Supernova 1995N

We report on multi-epoch X-ray observations of the Type IIn (narrow emission line) supernova SN 1995N with the ROSAT and ASCA satellites. The January 1998 ASCA X-ray spectrum is well fitted by a thermal bremsstrahlung (kT~10 keV, N_H~6e20 cm^-2) or power-law (alpha~1.7, N_H~1e21 cm^-2) model. The X-ray light curve shows evidence for significant flux evolution between August 1996 and January 1998: the count rate from the source decreased by 30% between our August 1996 and August 1997 ROSAT observations, and the X-ray luminosity most likely increased by a factor of ~2 between our August 1997 ROSAT and January 1998 ASCA observations, although evolution of the spectral shape over this interval is not ruled out. The high X-ray luminosity, L_X~1e41 erg/sec, places SN 1995N in a small group of Type IIn supernovae with strong circumstellar interaction, and the evolving X-ray luminosity suggests that the circumstellar medium is distributed inhomogeneously.Comment: MNRAS accepted. 6 pages, 2 figures; uses mn.sty and psfi

Symmetric Assembly Puzzles are Hard, Beyond a Few Pieces

We study the complexity of symmetric assembly puzzles: given a collection of simple polygons, can we translate, rotate, and possibly flip them so that their interior-disjoint union is line symmetric? On the negative side, we show that the problem is strongly NP-complete even if the pieces are all polyominos. On the positive side, we show that the problem can be solved in polynomial time if the number of pieces is a fixed constant

Adjoint inversion modeling of Asian dust emission using lidar observations

International audienceA four-dimensional variational (4D-Var) data assimilation system for a regional dust model (RAMS/CFORS-4DVAR; RC4) is applied to an adjoint inversion of a heavy dust event over eastern Asia during 20 March?4 April 2007. The vertical profiles of the dust extinction coefficients derived from NIES Lidar network are directly assimilated, with validation using observation data. Two experiments assess impacts of observation site selection: Experiment A uses five Japanese observation sites located downwind of dust source regions; Experiment B uses these and two other sites near source regions. Assimilation improves the modeled dust extinction coefficients. Experiment A and Experiment B assimilation results are mutually consistent, indicating that observations of Experiment A distributed over Japan can provide comprehensive information related to dust emission inversion. Time series data of dust AOT calculated using modeled and Lidar dust extinction coefficients improve the model results. At Seoul, Matsue, and Toyama, assimilation reduces the root mean square differences of dust AOT by 35?40%. However, at Beijing and Tsukuba, the RMS differences degrade because of fewer observations during the heavy dust event. Vertical profiles of the dust layer observed by CALIPSO are compared with assimilation results. The dense dust layer was trapped at potential temperatures (?) of 280?300 K and was higher toward the north; the model reproduces those characteristics well. Latitudinal distributions of modeled dust AOT along the CALIPSO orbit paths agree well with those of CALIPSO dust AOT, OMI AI, and MODIS coarse-mode AOT, capturing the latitude at which AOTs and AI have high values. Assimilation results show increased dust emissions over the Gobi Desert and Mongolia; especially for 29?30 March, emission flux is about 10 times greater. Strong dust uplift fluxes over the Gobi Desert and Mongolia cause the heavy dust event. Total optimized dust emissions are 57.9 Tg (Experiment A; 57.8% larger than before assimilation) and 56.3 Tg (Experiment B; 53.4% larger)