A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov-Poisson Equation

Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new Particle-in-Cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509--3537]. It treats all of the stages of the standard PIC update - charge deposition, force interpolation, the field solve, and the particle push - with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. We demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve comparable accuracy to the 2nd-order method with many fewer resolution elements.Comment: 18 pages, 10 figures, submitted to SIS

Sensitivity of high-resolution satellite sensor imagery to regenerating forest age and site preparation for wildlife habitat analysis

In west-central Alberta increased landscape fragmentation has lead to increased human use, having negative effects on wildlife such as the grizzly bear (Ursus arctos L.). Recently, grizzly bears in the Foothills Model Forest were found to select clear cuts of different age ranges as habitat and selected or avoided certain clear cuts depending on the site preparation process employed. Satellite remote sensing offers a practical and cost-effective method by which cut areas, their age, and site preparation activities can be quantified. This thesis examines the utility of spectral reflectance of SPOT-5 pansharpened imagery (2.5m spatial resolution) to identify and map 44 regenerating stands sampled in August 2005. Using object based classification with the Normalized Difference Moisture Index (NDMI), green, and short wave infrared (SWIR) bands, 90% accuracy can be achieved in the detection of forest disturbance. Forest structural parameters were used to calculate the structural complexity index (SCI), the first loading of a principal components analysis. The NDMI, first-order standard deviation and second-order correlation texture measures were better able to explain differences in SCI among the 44 forest stands (R2=0.74). The best window size for the texture measures was 5x5, indicating that this is a measure only detectable at a very high spatial resolution. Age classes of these cut blocks were analysed using linear discriminant analysis and best separated (82.5%) with the SWIR and green spectral bands, second order correlation under a 25x25 window, and the predicted SCI. Site preparation was best classified (90.9%) using the NDMI and homogeneity texture under a 5x5 window. Future applications from this research include the selection of high probability grizzly habitat for high spatial resolution imagery acquisition for detailed mapping initiatives

Fluid Solver Independent Hybrid Methods for Multiscale Kinetic equations

In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I. Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G. Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM Multiscale Modeling and Simulation Vol 6., No 4,pp. 1169-1197, (2008)] we developed a general framework for the construction of hybrid algorithms which are able to face efficiently the multiscale nature of some hyperbolic and kinetic problems. Here, at variance with respect to the previous methods, we construct a method form-fitting to any type of finite volume or finite difference scheme for the reduced equilibrium system. Thanks to the coupling of Monte Carlo techniques for the solution of the kinetic equations with macroscopic methods for the limiting fluid equations, we show how it is possible to solve multiscale fluid dynamic phenomena faster with respect to traditional deterministic/stochastic methods for the full kinetic equations. In addition, due to the hybrid nature of the schemes, the numerical solution is affected by less fluctuations when compared to standard Monte Carlo schemes. Applications to the Boltzmann-BGK equation are presented to show the performance of the new methods in comparison with classical approaches used in the simulation of kinetic equations.Comment: 31 page

Tire Rubber-cement Composites: Effect Of Slag On Properties [compósites De Cimento - Borracha De Pneus: Efeito Da Escória Nas Propriedades]

Tire rubber-cement composites prepared with type I and three slag-modified cements were studied. Flexural strength, water sorption and resistance to acid attack of specimens were investigated. A decrease in modulus of rupture (MOR) is observed for all specimens containing rubber, when compared with specimens without rubber (controls). The MOR increases with the increase of the hydraulic activity of the slag upon undistinguishable from specimens prepared with type I cement. This behavior is observed for all slag-cements pastes and for mortars control specimens. For mortar specimens with rubber the MOR is independent of the cement type used. A reduction in water sorption is observed for control and with-rubber mortar specimens prepared with all slag-cements, when compared to type I cement. For mortar specimens with rubber, the lower the basicity of the slag, the lesser the water sorption of the composites. These results denote lower porosity and consequently better rubber-matrix adhesion for these specimens. Also, a smaller rate of water sorption is observed for specimens with rubber, particularly for specimens prepared with the less basic slag cements, when comparing with the controls. Results of acid attack to the slag modified mortars indicate that specimen susceptibility is governed not only by microstructural aspects, like porosity and permeability, but also by chemical aspects as the difference in alkali content or the amount of unreacted slag in the specimens.52324283292Lee, B.I., Burnett, L., Miller, T., Postage, P., Cuneo, J., (1993) J. Mater. Sci. Lett, 12, p. 967I. B. Topçu, Gem. Conor. Res. 25 (1995) 304Raghavan, D., Huynh, H., Ferraris, C.F., (1998) J. Mater. Sci, 33, p. 1745Bignozzi, M.C., Saccani, A., Sandrolini, F., (2000) Composites A, 31, p. 97Raghavan, D., (2000) J. Appl. Polym. Sci, 77, p. 934M. Nehdi, A. Khan, Cem. Concr. Aggregates 23 (2001) 3Hernandez-Olivares, F., Barluenga, G., Bollati, M., Witoszek, B., (2002) Cem. Concr. Res, 32, p. 1587N. Segre, I. Joekes, Gem. Concr. Res. 30 (2000) 1421(2001) Lea's Chemistry of Cement and Concrete, , P. C. Hewlett Ed, 4 th Ed, Butterworth Heinemann, OxfordMyers, D., (1999) Surfaces, Interfaces, and Colloids-Principles and Applications, , 2nd Ed, John Wiley & Sons, New YorkBikerman, J.J., (1961) The Science of Adhesive Joints, , Academic Press, New YorkMindess, S., Interfaces in concrete (1989) Materials Science of Concrete I, p. 163. , J.P. Skalny Ed, The Am. Ceram. Soc, Westerville, OHLuke, K., Glasser, F.P., (1987) Cem. Concr. Res, 17, p. 273M. A. Cincotto, A. F. Battagin, V. Agopyan, Bulletin 65, Ed.: Institute for Technological Research, IPT, S. Paulo, Brazil (1992)ASTM C150 - Standard specification for Portland cement, American Society for Testing and Materials (1995)- Standard specification for blended hydraulic cements (1994), ASTM C595, American Society for Testing and MaterialsMindess, S., Young, J.F., (1981) Concrete, , Prentice-Hall, Englewood Cliffs, New JerseyMehta, P.K., Monteiro, P.J.M., (1993) Concrete: Structure, Properties and Materials, , 2nd Ed, Prentice-Hall, Englewood Cliffs, New JerseyGriffith, A.A., (1920) Phil. Trans. R. Soc. Lond. A, 221, p. 163Birchall, J.D., Howard, A.J., Kendall, K., (1981) Nature, 289, p. 388Martins, M.A., Mattoso, L.H.C., (2004) J. Appl. Polym. Sci, 91, p. 670Lumley, J.S., Gollop, R.S., Moir, G.K., Taylor, H.F.W., (1996) Cem. Concr. Res, 26, p. 139Glasser, F.P., Chemical, mineralogical, and microstructural changes occurring in hydrates slag-cement blends (1991) Materials Science of Concrete II, p. 41. , J. P. Skalny, S. Mindess Eds, The Am. Ceram. Soc, Westerville, OHSegre, N., Monteiro, P.J.M., Sposito, G., (2002) J. Colloid Interface Sci, 248, p. 521Falcon, P., Adenot, F., Jacquinot, J.F., Petit, J.C., Cabrillac, R., Jordas, M., (1998) Cem. Conor. Res, 28, p. 847Israel, D., Macphee, D.E., Lachowski, E.E., (1997) J. Mater. Sci, 32, p. 4109Chandra, S., (1988) Cem. Conor. Res, 18, p. 193Zivica, V., Bajza, A., (2001) Constr. Build. Mater, 15, p. 331Pavlik, V., (1994) Cem. Conor. Res, 24, pp. 551-562Debelie, N., Verselder, H.J., Deblaere, B., Vannieuwenburg, D., Verschoore, R., (1996) Cem. Conor. Res, 26, p. 1717Shi, C., Stegemann, J.A., (2000) Cem. Conor. Res, 30, p. 803Zivica, V., Bajza, A., (2002) Constr. Build. Mater, 16, p. 215Deceukelaire, L., (1992) Cem. Conor. Res, 22, p. 903A. Macias, S. Goni, J. Madrid, Cem. Conor. Res. 29 (1999) 2005J. Hill, E. A. Byars, J. H. Sharp, C. J. Lynsdale, J. C. Cripps, Q. Zhou, Cem. Conor. Compos. 25 (2003) 997Hobbs, D.W., (2001) Int. Mater. Rev, 46, p. 11

Influence of inoculum type (ileal, caecal and faecal) on the in vitro fermentation of different sources of carbohydrates in rabbits

[EN] Two in vitro experiments were performed to analyse the fermentative potential of ileal content, caecal content, soft faeces and hard faeces from adult rabbits. Experiment 1 evaluated 3 doses (0.5, 1.0 and 2.0 g fresh digesta/g substrate dry matter [DM]) of ileal and caecal digesta as inoculum in 28 h-incubations. Two ileal and 2 caecal inocula were obtained, each by pooling the ileal or caecal digesta of 2 adult rabbits. Pectin from sugar beet pulp (SBP) and the insoluble residue obtained after a 2-step in vitro pre-digestion of SBP and wheat straw were used as substrates. The 0.5 dose produced the lowest (P0.05) between the 1.0 and 2.0 doses (44.9, 51.6 and 53.8 mL/g substrate DM, respectively; values averaged across inocula and substrates). Experiment 2 evaluated two doses of ileal inoculum (1 and 1.5 g fresh digesta/g substrate DM) and compared ileal digesta, caecal digesta, soft faeces and hard faeces as inoculum for determining in vitro gas production (144-h incubations) of the 3 substrates used in Experiment 1 and wheat starch. Three inocula of each type were obtained, each by pooling either digesta or faeces from 3 rabbits. There were no differences (P>0.05) between the 2 ileal doses tested in gas production parameters, and therefore the 1.0 dose was selected for further ileal fermentations. Starch and pectin showed similar (P>0.05) values of gas production rate and maximal gas production rate when they were fermented with caecal digesta (0.038 vs. 0.043%/h, and 13.7 vs. 15.2 mL/h, respectively), soft (0.022 vs. 0.031%/h, and 9.97 vs. 9.33 mL/h) and hard faeces (0.031 vs. 0.038%/h, and 13.6 vs. 10.8 mL/h), and values were higher than those for SBP and wheat straw; in contrast, values for starch and pectin differed with the ileal inoculum (0.046 vs. 0.024%/h, and 18.4 vs. 6.60 mL/h). Both ileal and caecal gas production parameters were well correlated with those for hard and soft faeces inocula, respectively (r≥0.77; P≤0.040). The ileal inoculum showed a relevant fermentative potential, but lower than that of caecal digesta and soft and hard faeces for all substrates except wheat starch.Funding from the Spanish Ministry of Economy and Competitiveness (Project AGL2011-22628) and the Comunidad Autónoma de Madrid (CAM; Project MEDGAN ABI-2913) is gratefully acknowledged.Abad-Guamán, R.; Larrea-Dávalos, JA.; Carabaño, R.; García, J.; Carro, MD. (2018). Influence of inoculum type (ileal, caecal and faecal) on the in vitro fermentation of different sources of carbohydrates in rabbits. World Rabbit Science. 26(3):227-240. https://doi.org/10.4995/wrs.2018.9726SWORD227240263Abad R., Ibañez M.A., Carabaño R., García J. 2013. Quantification of soluble fibre in feedstuffs for rabbits and evaluation of the interference between the determinations of soluble fibre and intestinal mucin. Anim. Feed Sci. Tech., 182: 61-70. https://doi.org/10.1016/j.anifeedsci.2013.04.001Abad-Guamán R., Carabaño R., Gómez-Conde M.S., García J. 2015. Effect of type of fiber, site of fermentation, and method of analysis on digestibility of soluble and insoluble fiber in rabbits. J. Anim. Sci., 93: 2860-2871. https://doi.org/10.2527/jas.2014-8767Association of Official Analytical Chemists International. 2000. Official Methods of Analysis 17th ed. AOAC International, Washington, DC.Bindelle J., Buldgen A., Lambotte D., Wavreille J., Leterme P. 2007. Effect of pig faecal donor and of pig diet composition on in vitro fermentation of sugar beet pulp. Anim. Feed Sci. Technol., 132: 212-226. https://doi.org/10.1016/j.anifeedsci.2006.03.010Boletín Oficial del Estado (BOE). 2013. Royal Decree 53/2013 of February 1st on the protection of animals used for experimentation or other scientific purposes. BOE nº 34, 11370-11421. https://www.boe.es/boe/dias/2013/02/08/pdfs/BOE-A-2013-1337.pdf Accessed January 2017. In Spanish.Bovera F., Calabro S., Cutrignelli M.I., Infascelli F., Piccolo G., Nizza S., Tudisco R., Nizza A. 2008. Prediction of rabbit caecal fermentation characteristics from faeces by in vitro gas production technique: roughages. J. Anim. Physiol. Anim. Nutr., 92: 260-271. https://doi.org/10.1111/j.1439-0396.2007.00748.xBovera F., D'Urso S., Di Meo C., Piccolo G., Calabro S., Nizza A. 2006. Comparison of rabbit caecal content and rabbit hard faeces as source of inoculum for the in vitro gas production technique. Asian Austral. J. Anim. Sci., 19: 1649-1657. https://doi.org/10.5713/ajas.2006.1649Bovera F., D'Urso S., Meo C.D., Tudisco R., Nizza A. 2009. A model to assess the use of caecal and faecal inocula to study fermentability of nutrients in rabbit. J. Anim. Physiol. Anim. Nutr., 93: 147-156. https://doi.org/10.1111/j.1439-0396.2007.00795.xCalabrò S., Nizza A., Pinna W., Cutrignelli M., Piccolo V. 1999. Estimation of digestibility of compound diets for rabbits using the in vitro gas production technique. World Rabbit Sci., 7: 197-201. https://doi.org/10.4995/wrs.1999.401Carabaño R., Fraga M.J., Santoma G., de Blas C. 1988. Effect of diet on composition of cecal contents and on excretion and composition of soft and hard feces of rabbits. J. Anim. Sci 66: 901-1000. https://doi.org/10.2527/jas1988.664901xCarabaño R., García J., de Blas J.C. 2001. Effect of fibre source on ileal apparent digestibility of non-starch polysaccharides in rabbits. Anim. Sci., 72: 343-350. https://doi.org/10.1017/S1357729800055843Falcão-e-Cunha L., Peres H., Freire J.P.B., Castro-Solla L. 2004. Effects of alfalfa, wheat bran or beet pulp, with or without sunflower oil, on caecal fermentation and on digestibility in the rabbit. Anim. Feed Sci. Technol., 117: 131-149. https://doi.org/10.1016/j.anifeedsci.2004.07.014García J., Carabaño R., de Blas J.C. 1999. Effect of fiber source on cell wall digestibility and rate of passage in rabbits. J. Anim. Sci., 77: 898-905. https://doi.org/10.2527/1999.774898xGarcía J., Carabaño R., Pérez-Alba L., de Blas J.C. 2000. Effect of fiber source on cecal fermentation and nitrogen recycled through cecotrophy in rabbits. J. Anim. Sci., 78: 638-646. https://doi.org/10.2527/2000.783638xGarcía J., Gidenne T., Falcão-e-Cunha L., de Blas C. 2002. Identification of the main factors that influence caecal fermentation traits in growing rabbits. Anim. Res. 51: 165-173. https://doi.org/10.1051/animres:2002011Gidenne T. 1992. Effect of fiber level, particle-size and adaptation period on digestibility and rate of passage as measured at the ileum and in the feces in the adult-rabbit. Brit. J. Nutr., 67: 133-146. https://doi.org/10.1079/BJN19920015Gidenne T. 1994. Effect of a reduction in fiber content on the rate of passage through the digestive-tract of the rabbit-comparison of models for the fecal kinetics of 2 markers. Reprod. Nutr. Dev., 34: 295-307. https://doi.org/10.1051/rnd:19940403Goering H.K., Van Soest P.J. 1970. Forage Fiber Analysis (Apparatus, Reagents, Procedures, and Some Applications). USDA Agricultural Research Service, Handbook, Washington, DC.Gouet P., Fonty G. 1979. Changes in the digestive microflora of holoxenic rabbits from birth until adulthood. Ann. Biol Anim. Bioch., 19: 553-566. https://doi.org/10.1051/rnd:19790501Littell R.C., Henry P.R., Ammerman C.B. 1998. Statistical analysis of repeated measures data using SAS procedures. J. Anim. Sci., 76: 1216-1231. https://doi.org/10.2527/1998.7641216xMarounek M., Vovk S.J., Skrivanova V. 1995. Distribution of activity of hydrolytic enzymes in the digestive-tract of rabbits. Brit. J. Nutr., 73: 463-469. https://doi.org/10.1079/BJN19950048Menke K.H., Raab L., Salewski A., Steingass H., Fritz D., Schneider W. 1979. The estimation of the digestibility and metabolizable energy of ruminant feedingstuff from the gas production when they are incubated with rumen liquor in vitro. J. Agr. Sci., 93: 217-222. https://doi.org/10.1017/S0021859600086305Mertens D.R., Allen M., Carmany J., Clegg J., Davidowicz A., Drouches M., Frank K., Gambin D., Garkie M., Gildemeister B., Jeffress D., Jeon C.S., Jones D., Kaplan D., Kim G.N., Kobata S., Main D., Moua X., Paul B., Robertson J., Taysom D., Thiex N., Williams J., Wolf M. 2002. Gravimetric determination of amylase-treated neutral detergent fiber in feeds with refluxing in beakers or crucibles: Collaborative study. J. AOAC Int., 85:1217-1240.Mould F.L., Kliem K.E., Morgan R., Mauricio R.M. 2005. In vitro microbial inoculum: A review of its function and properties. Anim. Feed Sci. Tech., 123: 31-50. https://doi.org/10.1016/j.anifeedsci.2005.04.028Murray S.M., Flickinger E.A., Patil A.R., Merchen N.R., Brent J.L., Fahey G.C. 2001. In vitro fermentation characteristics of native and processed cereal grains and potato starch using ileal chyme from dogs. J. Anim. Sci., 79: 435-444. https://doi.org/10.2527/2001.792435xOmed H.M., Lovett D.K., Axford R.F.E. 2000. Faeces as a source of microbial enzymes for estimating digestibility, In: Givens D., Owen E., Axford R., Omed H. (Eds.), Forage Evaluation in Ruminant Nutrition, CAB International, UK, pp. 135-154. https://doi.org/10.1079/9780851993447.0135Padilha M.T.S., Licois D., Gidenne T., Carre B., Fonty G. 1995. Relationships between microflora and caecal fermentation in rabbits before and after weaning. Reprod. Nutr. Dev., 35: 375-386. https://doi.org/10.1051/rnd:19950403Pascual J.J., Cervera C., Fernández-Carmona J. 2000. Comparison of different in vitro digestibility methods for nutritive evaluation of rabbit diets. World Rabbit Sci., 8: 93-97. https://doi.org/10.4995/wrs.2000.425Penney R.L., Folk G.E., Galask R.P., Petzold C.R. 1986. The microflora of the alimentary tract of rabbits in relation to pH, diet and cold. J. Appl. Rabbit Res., 9: 152-156.Piattoni F., Demeyer D., Maertens L., 1997. Fasting effects on in vitro fermentation pattern of rabbit caecal contents. World Rabbit Sci., 5: 23-26. https://doi.org/10.4995/wrs.1997.314Rodríguez-Romero N., Abecia L., Fondevila M., Balcells J. 2011. Effects of levels of insoluble and soluble fibre in diets for growing rabbits on faecal digestibility, nitrogen recycling and in vitro fermentation. World Rabbit Sci., 19: 85-94. https://doi.org/10.4995/wrs.2011.828SAS Institute Inc. 2011. Base SAS® 9.3 Procedures Guide. SAS Institute Inc. Cary, NC, USA.Schofield P., Pitt R.E., Pell A.N. 1994. Kinetics of fiber digestion from in-vitro gas-production. J. Anim. Sci., 72: 2980-2991. https://doi.org/10.2527/1994.72112980xTagliapietra F., Williams B.A., Awati A., Bonsembiante M., Schiavon S., Verstegen M.W.A. 2003. In vitro degradation kinetics of four carbohydrates using ileal and faecal inocula from suckling piglets. Ital. J. Anim. Sci., 2: 195-197.Trocino A., García J., Carabaño R., Xiccato, G. 2013. A meta-analysis on the role of soluble fibre in diets for growing rabbits. World Rabbit Sci., 21: 1-15. https://doi.org/10.4995/wrs.2013.1285Van Soest P.J., Robertson J.B., Lewis B.A. 1991. Methods for dietary fiber, neutral detergent fiber, and nonstarch polysaccharides in relation to animal nutrition. J. Dairy Sci., 74: 3583-3597. https://doi.org/10.3168/jds.S0022-0302(91)78551-2Wang D., Williams B.A., Ferruzzi M.G., D'Arcy B.R. 2013. Different concentrations of grape seed extract affect in vitro starch fermentation by porcine small and large intestinal inocula. J. Sci. Food Agr., 93: 276-283. https://doi.org/10.1002/jsfa.5753Williams B.A., Bhatia S.K., Boer H., Tamminga S. 1995. A preliminary study using the cumulative gas production technique to compare the kinetics of different fermentations by use of standard substrates. Ann. Zootech., 44: 35. https://doi.org/10.1051/animres:19950505Williams B.A., Bosch M.W., Awati A., Konstantinov S.R., Smidt H., Akkermans A.D.L., Verstegen M.W.A., Tamminga S. 2005. In vitro assessment of gastrointestinal tract (GIT) fermentation in pigs: Fermentable substrates and microbial activity. Anim. Res., 54: 191-201. https://doi.org/10.1051/animres:2005011Williams B.A., Verstegen M.W., Tamminga S. 2001. Fermentation in the large intestine of single-stomached animals and its relationship to animal health. Nutr. Res. Rev., 14: 207-228. https://doi.org/10.1079/NRR20012

Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions

We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain $D$. We prove that a smooth density exists on $D$ and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable ("tail" estimates). These results specify and extend some results by Kusuoka and Stroock [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1--76], but our approach is substantially different and based on a technique to estimate the Fourier transform inspired from Fournier [Electron. J. Probab. 13 (2008) 135--156] and Bally [Integration by parts formula for locally smooth laws and applications to equations with jumps I (2007) The Royal Swedish Academy of Sciences]. This study is motivated by existing models for financial securities which rely on SDEs with non-Lipschitz coefficients. Indeed, we apply our results to a square root-type diffusion (CIR or CEV) with coefficients depending on the state variable, that is, a situation where standard techniques for density estimation based on Malliavin calculus do not apply. We establish the existence of a smooth density, for which we give exponential estimates and study the behavior at the origin (the singular point).Comment: Published in at http://dx.doi.org/10.1214/10-AAP717 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Statistical methods in language processing

The term statistical methods here refers to a methodology that has been dominant in computational linguistics since about 1990. It is characterized by the use of stochastic models, substantial data sets, machine learning, and rigorous experimental evaluation. The shift to statistical methods in computational linguistics parallels a movement in artificial intelligence more broadly. Statistical methods have so thoroughly permeated computational linguistics that almost all work in the field draws on them in some way. There has, however, been little penetration of the methods into general linguistics. The methods themselves are largely borrowed from machine learning and information theory. We limit attention to that which has direct applicability to language processing, though the methods are quite general and have many nonlinguistic applications. Not every use of statistics in language processing falls under statistical methods as we use the term. Standard hypothesis testing and experimental design, for example, are not covered in this article. WIREs Cogni Sci 2011 2 315–322 DOI: 10.1002/wcs.111 For further resources related to this article, please visit the WIREs websitePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83468/1/111_ftp.pd