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 Dark and Baryonic Matter in Bright Spiral Galaxies. I. Near-Infrared and Optical Broadband Surface Photometry of 30 GalaxiesWe present photometrically calibrated images and surface photometry inthe B, V, R, J, H, and K bands of 25, and in the g, r, and K bands offive nearby bright (B0T<12.5 mag) spiralgalaxies with inclinations of 30°-65° spanning the Hubblesequence from Sa to Scd. Data are from The Ohio State University BrightSpiral Galaxy Survey, the Two Micron All Sky Survey, and the SloanDigital Sky Survey Second Data Release. Radial surface brightnessprofiles are extracted, and integrated magnitudes are measured from theprofiles. Axis ratios, position angles, and scale lengths are measuredfrom the near-infrared images. A one-dimensional bulge/diskdecomposition is performed on the near-infrared images of galaxies witha nonnegligible bulge component, and an exponential disk is fit to theradial surface brightness profiles of the remaining galaxies.Based in part on observations obtained at the Cerro TololoInter-American Observatory, operated by the Association of Universitiesfor Research in Astronomy, Inc., under a cooperative agreement with theNational Science Foundation. Dark and Baryonic Matter in Bright Spiral Galaxies. II. Radial Distributions for 34 GalaxiesWe decompose the rotation curves of 34 bright spiral galaxies intobaryonic and dark matter components. Stellar mass profiles are createdby applying color-M/L relations to near-infrared and optical photometry.We find that the radial profile of the baryonic-to-dark-matter ratio isself-similar for all galaxies, when scaled to the radius at which thecontribution of the baryonic mass to the rotation curve equals that ofthe dark matter (RX). We argue that this is due to thequasi-exponential nature of disks and rotation curves that are nearlyflat after an initial rise. The radius RX is found tocorrelate most strongly with baryonic rotation speed, such that galaxieswith RX measurements that lie further out in their disksrotate faster. This quantity also correlates very strongly with stellarmass, Hubble type, and observed rotation speed; B-band central surfacebrightness is less related to RX than these other galaxyproperties. Most of the galaxies in our sample appear to be close tomaximal disk. For these galaxies, we find that maximum observed rotationspeeds are tightly correlated with maximum rotation speeds predictedfrom the baryon distributions, such that one can create a Tully-Fisherrelation based on surface photometry and redshifts alone. Finally, wecompare our data to the NFW parameterization for dark matter profileswith and without including adiabatic contraction as it is most commonlyimplemented. Fits are generally poor, and all but two galaxies arebetter fit if adiabatic contraction is not performed. In order to havebetter fits, and especially to accommodate adiabatic contraction,baryons would need to contribute very little to the total mass in theinner parts of galaxies, seemingly in contrast with other observationalconstraints. The Hα Galaxy Survey . III. Constraints on supernova progenitors from spatial correlations with Hα emissionAims.We attempt to constrain progenitors of the different types ofsupernovae from their spatial distributions relative to star formationregions in their host galaxies, as traced by Hα + [Nii] lineemission. Methods: .We analyse 63 supernovae which have occurredwithin galaxies from our Hα survey of the local Universe. Threestatistical tests are used, based on pixel statistics, Hα radialgrowth curves, and total galaxy emission-line fluxes. Results:.Many type II supernovae come from regions of low or zero emission lineflux, and more than would be expected if the latter accurately traceshigh-mass star formation. We interpret this excess as a 40% "Runaway"fraction in the progenitor stars. Supernovae of types Ib and Ic doappear to trace star formation activity, with a much higher fractioncoming from the centres of bright star formation regions than is thecase for the type II supernovae. Type Ia supernovae overall show a weakcorrelation with locations of current star formation, but there isevidence that a significant minority, up to about 40%, may be linked tothe young stellar population. The radial distribution of allcore-collapse supernovae (types Ib, Ic and II) closely follows that ofthe line emission and hence star formation in their host galaxies, apartfrom a central deficiency which is less marked for supernovae of typesIb and Ic than for those of type II. Core-collapse supernova ratesoverall are consistent with being proportional to galaxy totalluminosities and star formation rates; however, within this total thetype Ib and Ic supernovae show a moderate bias towards more luminoushost galaxies, and type II supernovae a slight bias towardslower-luminosity hosts. The cored distribution of dark matter in spiral galaxiesWe present, for five spiral galaxies, HI data which, along with theHα rotation curves, are used to derive the distribution of darkmatter within these objects. A new method for extracting rotation curvesfrom HI data cubes is presented, which takes into account the existenceof a warp and minimizes projection effects. The rotation curves obtainedare tested by taking them as input in the construction of model datacubes that are compared with the observed ones: the agreement isexcellent. Model data cubes built using rotation curves obtained withstandard methods, such as the first-moment analysis, however, fail thetest. The HI rotation curves agree well with the Hα data, wherethey coexist. Moreover, the combined Hα + HI rotation curves aresmooth, symmetric and extend to large radii.The rotation curves are decomposed into stellar, gaseous and dark mattercontributions, and the inferred density distribution is compared withvarious mass distributions: dark haloes with a central density core,Λ cold dark matter (ΛCDM) haloes (NFW and Moore profiles),HI scaling and MOND. The observations point to haloes withconstant-density cores of size rcore ~ ropt andcentral densities scaling approximately as ρ0 ~r-2/3core. ΛCDM models (which predict acentral cusp in the density profile) are in clear conflict with thedata. HI scaling and MOND cannot account for the observed kinematics: wefind some counter-examples. The ISOPHOT 170 μm Serendipity Survey II. The catalog of optically identified galaxies%The ISOPHOT Serendipity Sky Survey strip-scanning measurements covering≈15% of the far-infrared (FIR) sky at 170 μm were searched forcompact sources associated with optically identified galaxies. CompactSerendipity Survey sources with a high signal-to-noise ratio in at leasttwo ISOPHOT C200 detector pixels were selected that have a positionalassociation with a galaxy identification in the NED and/or Simbaddatabases and a galaxy counterpart visible on the Digitized Sky Surveyplates. A catalog with 170 μm fluxes for more than 1900 galaxies hasbeen established, 200 of which were measured several times. The faintest170 μm fluxes reach values just below 0.5 Jy, while the brightest,already somewhat extended galaxies have fluxes up to ≈600 Jy. For thevast majority of listed galaxies, the 170 μm fluxes were measured forthe first time. While most of the galaxies are spirals, about 70 of thesources are classified as ellipticals or lenticulars. This is the onlycurrently available large-scale galaxy catalog containing a sufficientnumber of sources with 170 μm fluxes to allow further statisticalstudies of various FIR properties.Based on observations with ISO, an ESA project with instruments fundedby ESA Member States (especially the PI countries: France, Germany, TheNetherlands and the UK) and with the participation of ISAS and NASA.Members of the Consortium on the ISOPHOT Serendipity Survey (CISS) areMPIA Heidelberg, ESA ISO SOC Villafranca, AIP Potsdam, IPAC Pasadena,Imperial College London.Full Table 4 and Table 6 are only available in electronic form at theCDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/422/39 The Hα galaxy survey. I. The galaxy sample, Hα narrow-band observations and star formation parameters for 334 galaxiesWe discuss the selection and observations of a large sample of nearbygalaxies, which we are using to quantify the star formation activity inthe local Universe. The sample consists of 334 galaxies across allHubble types from S0/a to Im and with recession velocities of between 0and 3000 km s-1. The basic data for each galaxy are narrowband H\alpha +[NII] and R-band imaging, from which we derive starformation rates, H\alpha +[NII] equivalent widths and surfacebrightnesses, and R-band total magnitudes. A strong correlation is foundbetween total star formation rate and Hubble type, with the strongeststar formation in isolated galaxies occurring in Sc and Sbc types. Moresurprisingly, no significant trend is found between H\alpha +[NII]equivalent width and galaxy R-band luminosity. More detailed analyses ofthe data set presented here will be described in subsequent papers.Based on observations made with the Jacobus Kapteyn Telescope operatedon the island of La Palma by the Isaac Newton Group in the SpanishObservatorio del Roque de los Muchachos of the Instituto deAstrofísica de Canarias.The full version of Table \ref{tab3} is available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/414/23 Reduced image datafor this survey can be downloaded fromhttp://www.astro.livjm.ac.uk/HaGS/ A new catalogue of ISM content of normal galaxiesWe have compiled a catalogue of the gas content for a sample of 1916galaxies, considered to be a fair representation of normality''. Thedefinition of a normal'' galaxy adopted in this work implies that wehave purposely excluded from the catalogue galaxies having distortedmorphology (such as interaction bridges, tails or lopsidedness) and/orany signature of peculiar kinematics (such as polar rings,counterrotating disks or other decoupled components). In contrast, wehave included systems hosting active galactic nuclei (AGN) in thecatalogue. This catalogue revises previous compendia on the ISM contentof galaxies published by \citet{bregman} and \citet{casoli}, andcompiles data available in the literature from several small samples ofgalaxies. Masses for warm dust, atomic and molecular gas, as well asX-ray luminosities have been converted to a uniform distance scale takenfrom the Catalogue of Principal Galaxies (PGC). We have used twodifferent normalization factors to explore the variation of the gascontent along the Hubble sequence: the blue luminosity (LB)and the square of linear diameter (D225). Ourcatalogue significantly improves the statistics of previous referencecatalogues and can be used in future studies to define a template ISMcontent for normal'' galaxies along the Hubble sequence. The cataloguecan be accessed on-line and is also available at the Centre desDonnées Stellaires (CDS).The catalogue is available in electronic form athttp://dipastro.pd.astro.it/galletta/ismcat and at the CDS via anonymousftp to\ cdsarc.u-strasbg.fr (130.79.128.5) or via\http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/405/5 Bar Galaxies and Their EnvironmentsThe prints of the Palomar Sky Survey, luminosity classifications, andradial velocities were used to assign all northern Shapley-Ames galaxiesto either (1) field, (2) group, or (3) cluster environments. Thisinformation for 930 galaxies shows no evidence for a dependence of barfrequency on galaxy environment. This suggests that the formation of abar in a disk galaxy is mainly determined by the properties of theparent galaxy, rather than by the characteristics of its environment. The mass distribution in the innermost regions of spiral galaxiesWe use high-spatial resolution ( ~ 100 pc) rotation curves of 83 spiralgalaxies to investigate the mass distribution of their innermost kpc. Weshow that in this region the luminous matter completely accounts for thegravitational potential and no dark component is required. The derivedI-band disk mass-to-light ratios Y_I agree well with those obtained frompopulation synthesis models and correlate with color in a similar way.We find strict upper limits of ~ 10^7 M_Sun for the masses of compactbodies at the center of spirals ruling out that these systems host theremnants of the quasar activity. Box- and peanut-shaped bulges. I. StatisticsWe present a classification for bulges of a complete sample of ~ 1350edge-on disk galaxies derived from the RC3 (Third Reference Catalogue ofBright Galaxies, de Vaucouleurs et al. \cite{rc3}). A visualclassification of the bulges using the Digitized Sky Survey (DSS) inthree types of b/p bulges or as an elliptical type is presented andsupported by CCD images. NIR observations reveal that dust extinctiondoes almost not influence the shape of bulges. There is no substantialdifference between the shape of bulges in the optical and in the NIR.Our analysis reveals that 45% of all bulges are box- and peanut-shaped(b/p). The frequency of b/p bulges for all morphological types from S0to Sd is > 40%. In particular, this is for the first time that such alarge frequency of b/p bulges is reported for galaxies as late as Sd.The fraction of the observed b/p bulges is large enough to explain theb/p bulges by bars. Partly based on observations collected at ESO/LaSilla (Chile), DSAZ/Calar Alto (Spain), and Lowell Observatory/Flagstaff(AZ/U.S.A.). Tables 6 and 7 are only available in electronic form at CDSvia anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html Arcsecond Positions of UGC GalaxiesWe present accurate B1950 and J2000 positions for all confirmed galaxiesin the Uppsala General Catalog (UGC). The positions were measuredvisually from Digitized Sky Survey images with rms uncertaintiesσ<=[(1.2")2+(θ/100)2]1/2,where θ is the major-axis diameter. We compared each galaxymeasured with the original UGC description to ensure high reliability.The full position list is available in the electronic version only. The I-Band Tully-Fisher Relation for SC Galaxies: 21 Centimeter H I Line DataA compilation of 21 cm line spectral parameters specifically designedfor application of the Tully-Fisher (TF) distance method is presentedfor 1201 spiral galaxies, primarily field Sc galaxies, for which opticalI-band photometric imaging is also available. New H I line spectra havebeen obtained for 881 galaxies. For an additional 320 galaxies, spectraavailable in a digital archive have been reexamined to allow applicationof a single algorithm for the derivation of the TF velocity widthparameter. A velocity width algorithm is used that provides a robustmeasurement of rotational velocity and permits an estimate of the erroron that width taking into account the effects of instrumental broadeningand signal-to-noise. The digital data are used to establish regressionrelations between measurements of velocity widths using other commonprescriptions so that comparable widths can be derived throughconversion of values published in the literature. The uniform H I linewidths presented here provide the rotational velocity measurement to beused in deriving peculiar velocities via the TF method. The I-Band Tully-Fisher Relation for SC Galaxies: Optical Imaging DataProperties derived from the analysis of photometric I-band imagingobservations are presented for 1727 inclined spiral galaxies, mostly oftypes Sbc and Sc. The reduction, parameter extraction, and errorestimation procedures are discussed in detail. The asymptotic behaviorof the magnitude curve of growth and the radial variation in ellipticityand position angle are used in combination with the linearity of thesurface brightness falloff to fit the disk portion of the profile. TotalI-band magnitudes are calculated by extrapolating the detected surfacebrightness profile to a radius of eight disk scale lengths. Errors inthe magnitudes, typically ~0.04 mag, are dominated by uncertainties inthe sky subtraction and disk-fitting procedures. Comparison is made withthe similar imaging database of Mathewson, Ford, & Buchhorn, both aspresented originally by those authors and after reanalyzing theirdigital reduction files using identical disk-fitting procedures. Directcomparison is made of profile details for 292 galaxies observed incommon. Although some differences occur, good agreement is found,proving that the two data sets can be used in combination with onlyminor accommodation of those differences. The compilation of opticalproperties presented here is optimized for use in applications of theTully-Fisher relation as a secondary distance indicator in studies ofthe local peculiar velocity field. Groups of galaxies. III. Some empirical characteristics.Not Available Bulge-Disk Decomposition of 659 Spiral and Lenticular Galaxy Brightness ProfilesWe present one of the largest homogeneous sets of spiral and lenticulargalaxy brightness profile decompositions completed to date. The 659galaxies in our sample have been fitted with a de Vaucouleurs law forthe bulge component and an inner-truncated exponential for the diskcomponent. Of the 659 galaxies in the sample, 620 were successfullyfitted with the chosen fitting functions. The fits are generally welldefined, with more than 90% having rms deviations from the observedprofile of less than 0.35 mag. We find no correlations of fittingquality, as measured by these rms residuals, with either morphologicaltype or inclination. Similarly, the estimated errors of the fittedcoefficients show no significant trends with type or inclination. Thesedecompositions form a useful basis for the study of the lightdistributions of spiral and lenticular galaxies. The object base issufficiently large that well-defined samples of galaxies can be selectedfrom it. Total magnitude, radius, colour indices, colour gradients and photometric type of galaxiesWe present a catalogue of aperture photometry of galaxies, in UBVRI,assembled from three different origins: (i) an update of the catalogueof Buta et al. (1995) (ii) published photometric profiles and (iii)aperture photometry performed on CCD images. We explored different setsof growth curves to fit these data: (i) The Sersic law, (ii) The net ofgrowth curves used for the preparation of the RC3 and (iii) A linearinterpolation between the de Vaucouleurs (r(1/4) ) and exponential laws.Finally we adopted the latter solution. Fitting these growth curves, wederive (1) the total magnitude, (2) the effective radius, (3) the colourindices and (4) gradients and (5) the photometric type of 5169 galaxies.The photometric type is defined to statistically match the revisedmorphologic type and parametrizes the shape of the growth curve. It iscoded from -9, for very concentrated galaxies, to +10, for diffusegalaxies. Based in part on observations collected at the Haute-ProvenceObservatory. A catalogue of spatially resolved kinematics of galaxies: BibliographyWe present a catalogue of galaxies for which spatially resolved data ontheir internal kinematics have been published; there is no a priorirestriction regarding their morphological type. The catalogue lists thereferences to the articles where the data are published, as well as acoded description of these data: observed emission or absorption lines,velocity or velocity dispersion, radial profile or 2D field, positionangle. Tables 1, 2, and 3 are proposed in electronic form only, and areavailable from the CDS, via anonymous ftp to cdsarc.u-strasbg.fr (to130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html An Einstein X-Ray Survey of Optically Selected Galaxies. I. DataWe present the results of a complete Einstein imaging proportionalcounter X-ray survey of optically selected galaxies from theShapley-Ames Catalog, the Uppsala General Catalogue, and the EuropeanSouthern Observatory Catalog. Well-defined optical criteria are used toselect the galaxies, and X-ray fluxes are measured at the opticallydefined positions. The result is a comprehensive list of X-ray detectionand upper limit measurements for 1018 galaxies. Of these, 827 haveeither independent distance estimates or radial velocities. Associatedoptical, redshift, and distance data have been assembled for thesegalaxies, and their distances come from a combination of directlypredicted distances and those predicted from the Faber-Burstein GreatAttractor/Virgocentric infall model. The accuracy of the X-ray fluxeshas been checked in three different ways; all are consistent with thederived X-ray fluxes being of <=0.1 dex accuracy. In particular,there is agreement with previously published X-ray fluxes for galaxiesin common with a 1991 study by Roberts et al. and a 1992 study byFabbiano et al. The data presented here will be used in further studiesto characterize the X-ray output of galaxies of various morphologicaltypes and thus to enable the determination of the major sourcescontributing to the X-ray emission from galaxies. Homogeneous Velocity-Distance Data for Peculiar Velocity Analysis. III. The Mark III Catalog of Galaxy Peculiar VelocitiesThis is the third in a series of papers in which we assemble and analyzea homogeneous catalog of peculiar velocity data. In Papers I and II, wedescribed the Tully-Fisher (TF) redshift-distance samples thatconstitute the bulk of the catalog and our methodology for obtainingmutually consistent TF calibrations for these samples. In this paper, wesupply further technical details of the treatment of the data andpresent a subset of the catalog in tabular form. The full catalog, knownas the Mark III Catalog of Galaxy Peculiar Velocities, is available inaccessible on-line databases, as described herein. The electroniccatalog incorporates not only the TF samples discussed in Papers I andII but also elliptical galaxy Dn- sigma samples originally presentedelsewhere. The relative zero pointing of the elliptical and spiral datasets is discussed here. The basic elements of the Mark III Catalog arethe observables for each object (redshift, magnitude, velocity width,etc.) and inferred distances derived from the TF or Dn- sigma relations.Distances obtained from both the forward and inverse TF relations aretabulated for the spirals. Malmquist bias--corrected distances arecomputed for each catalog object using density fields obtained from theIRAS 1.2 Jy redshift survey. Distances for both individual objects andgroups are provided. A variety of auxiliary data, including distancesand local densities predicted from the IRAS redshift surveyreconstruction method, are tabulated as well. We study the distributionsof TF residuals for three of our samples and conclude that they are wellapproximated as Gaussian. However, for the Mathewson et al. sample wedemonstrate a significant decrease in TF scatter with increasingvelocity width. We test for, but find no evidence of, a correlationbetween TF residuals and galaxy morphology. Finally, we derivetransformations that map the apparent magnitude and velocity width datafor each spiral sample onto a common system. This permits theapplication of analysis methods that assume that a unique TF relationdescribes the entire sample. Optical Rotation Curves and Linewidths for Tully-Fisher ApplicationsAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1997AJ....114.2402C&db_key=AST The I band Tully-Fisher relation for cluster galaxies: data presentation.Observational parameters which can be used for redshift-independentdistance determination using the Tully-Fisher (TF) technique are givenfor \ntot spiral galaxies in the fields of 24 clusters or groups. I bandphotometry for the full sample was either obtained by us or compiledfrom published literature. Rotational velocities are derived either from21 cm spectra or optical emission line long-slit spectra, and convertedto a homogeneous scale. In addition to presenting the data, a discussionof the various sources of error on TF parameters is introduced, and thecriteria for the assignment of membership to each cluster are given. The universal rotation curve of spiral galaxies - I. The dark matter connectionWe use a homogeneous sample of about 1100 optical and radio rotationcurves (RCs) and relative surface photometry to investigate the mainmass structure properties of spirals, over a range of 6 mag and out to<~1.5 and 2 optical radii (for the optical and radio data,respectively). We confirm the strong dependence on luminosity for boththe profile and the amplitude of RCs claimed by Persic & Salucci.Spiral RCs show the striking feature that a single global parameter,e.g. luminosity, dictates the rotational velocity at any radius for anyobject, so revealing the existence of a universal RC. At highluminosities, there is a slight discrepancy between the profiles of RCsand those predicted from the luminous matter (LM) distributions: thisimplies a small, yet detectable, amount of dark matter (DM). At lowluminosities, the failure of the LM prediction is much more severe, andthe DM is the only relevant mass component. We show that the universalRC implies a number of scaling properties between dark and luminousgalactic structure parameters: (i) the DM/LM mass ratio scales inverselywith luminosity; (ii) the central halo density scales as L^-0.7 (iii)the halo core radius is comparable to the optical radius, but shrinksfor low luminosities; (iv) the total halo mass scales as L^0.5. Suchscaling properties can be represented as a curve in the(luminosity)-(DM/LM mass ratio)-(DM core radius)-(DM central density)space, which provides a geometrical description of the tight couplingbetween the dark and the luminous matter in spiral galaxies. Parameters of 2447 Southern Spiral Galaxies for Use in the Tully-Fisher RelationI-band luminosities, rotational velocities, and redshifts of 1092 spiralgalaxies have been measured by CCD photometry and Hα spectroscopyusing the 1 m and 2.3 m telescopes at Siding Spring Observatory,respectively. The results are tabulated. Luminosity profiles andHα rotation curves are given for the galaxies. When these resultsare combined with similar data for 1355 spiral galaxies publishedpreviously (Mathewson, Ford, & Buchhorn, hereafter Paper I), itprovides a large, uniform, and unique data set with which to measure,via the Tully-Fisher relation, the peculiar velocities of galaxies inthe local universe to a distance of 11,000 km s^-1^ (Mathewson &Ford). Taking advantage of the opportunity for publishing this data inmachine-readable form, in the CD-ROM, we have also included similar datafor the 1355 galaxies in Paper I. The radial distribution of supernovae in spiral galaxies.Not Available Rotation Curves of 967 Spiral GalaxiesWe present the rotation curves of 967 southern spiral galaxies, obtainedby deprojecting and folding the raw Hα data originally publishedby Mathewson, Ford, & Buchhorn (1992). For 900 objects, we alsopresent, in figures and tables, the rotation curves smoothed on scalescorresponding to 5%-20% of the optical size; of these, 80 meet objectiveexcellence criteria and are suitable for individual detailed massmodeling, while 820, individually less compelling mainly because of themoderate statistics and/or limited extension, are suitable forstatistical studies. The remaining 67 curves suffer from severeasymmetries, small statistics, and large internal scatter that maylargely limit their use in galaxy structure studies. The deprojectedfolded curves, the smoothed curves, and various related quantities areavailable via anonymous ftp at galileo.sissa.it in the directory/users/ftp/pub/psrot. Recalibration of the H-0.5 magnitudes of spiral galaxiesThe H-magnitude aperture data published by the Aaronson et al.collaboration over a 10 year period is collected into a homogeneous dataset of 1731 observations of 665 galaxies. Ninety-six percent of thesegalaxies have isophotal diameters and axial ratios determined by theThird Reference Cataloque of Bright Galaxies (RC3; de Vaucouleurs et al.1991), the most self-consistent set of optical data currently available.The precepts governing the optical data in the RC3 are systematicallydifferent from those of the Second Reference Catalogue (de Vaucouleurs,de Vaucouleurs, & Corwin 1976), which were used by Aaronson et al.for their original analyses of galaxy peculiar motions. This in turnleads to systematic differences in growth curves and fiducialH-magnitudes, prompting the present recalibration of the near-infraredTully-Fisher relationship. New optically normalized H-magnitude growthcurves are defined for galaxies of types SO to Im, from which new valuesof fiducial H-magnitudes, Hg-0.5, are measured forthe 665 galaxies. A series of internal tests show that these fourstandard growth curves are defined to an accuracy of 0.05 mag over theinterval -1.5 less than or equal to log (A/Dg) less than orequal to -0.2. Comparisons with the Aaronson et al. values of diameters,axial ratios, and fiducial H-magnitudes show the expected differences,given the different definitions of these parameters. The values ofHg-0.5 are assigned quality indices: a qualityvalue of 1 indicates an accuracy of less than 0.2 mag, quality 2indicates an accuracy of 0.2-0.35 mag, and quality 3 indicates anaccuracy of more than 0.35 mag. Revised values of corrected H I velocitywidths are also given, based on the new set of axial ratios defiend bythe RC3. A Preliminary Classification Scheme for the Central Regions of Late-Type GalaxiesThe large-scale prints in The Carnegie Atlas of Galaxies have been usedto formulate a classification scheme for the central regions oflate-type galaxies. Systems that exhibit small bright central bulges ordisks (type CB) are found to be of earlier Hubble type and of higherluminosity than galaxies that do not contain nuclei (type NN). Galaxiescontaining nuclear bars, or exhibiting central regions that are resolvedinto individual stars and knots, and galaxies with semistellar nuclei,are seen to have characteristics that are intermediate between those oftypes CB and NN. The presence or absence of a nucleus appears to be auseful criterion for distinguishing between spiral galaxies andmagellanic irregulars. Integrated photoelectric magnitudes and color indices of bright galaxies in the Johnson UBV systemThe photoelectric total magnitudes and color indices published in theThird Reference Catalogue of Bright Galaxies (RC3) are based on ananalysis of approximately equals 26,000 B, 25,000 B-V, and 17,000 U-Bmultiaperture measurements available up to mid 1987 from nearly 350sources. This paper provides the full details of the analysis andestimates of internal and external errors in the parameters. Thederivation of the parameters is based on techniques described by theVaucouleurs & Corwin (1977) whereby photoelectric multiaperture dataare fitted by mean Hubble-type-dependent curves which describe theintegral of the B-band flux and the typical B-V and U-B integrated colorgradients. A sophisticated analysis of the residuals of thesemeasurements from the curves was made to allow for the random andsystematic errors that effect such data. The result is a homogeneous setof total magnitudes BTA total colors(B-V)T and (U-B)T, and effective colors(B-V)e and (U-B)e for more than 3000 brightgalaxies in RC3. Studies of multiple supernovae in spiral galaxies.We have compiled a sample of 667 spiral galaxies selected from theSecond Reference Catalogue of Bright Galaxies (RC2) (de Vaucouleurs etal. 1976). 169 supernovae (SNe) were discovered up to 31 Dec., 1992 inthe entire galaxy sample, and two or more SNe have been found in 30galaxies. We have taken into account several selection effects,i.e. theeffects of Hubble types, luminosity, inclination and distance of thegalaxies, to check whether the frequency distribution of SNe follow aPoisson distribution, and whether the deviation from Poissondistribution are due to burst of star formation' as proposed by Ritcher& Rosa (1988, hereafter RR). It is found that after considering theeffect of luminosity and distance of the galaxies, more homogeneousgalaxy samples with the same Hubble types and inclination range havesignificantly smaller deviation from a Poisson distribution. Some of thesubsamples have acceptable Poisson distributions. The distinctionbetween the supernova(SN) frequency of SN fast producer' galaxies andnormal galaxies is found to be 4~6 times, which is significantly smallerthan that proposed by RR (70 times!), and can be regarded asfluctuations of SN frequencies of different galaxies. We suggest thatthere is no need to consider some of the galaxies as fast producers ofSNe' and that the deviation from Poisson distribution can be interpretedas joint effects of star formation, Hubble types, luminosity,inclinationand distance of the galaxies. We have also done an analysis of theradial distribution of SNe in their parent galaxies. There is anindication that multiple SNe are located farther from the nuclei oftheir parent galaxies, which is a further evidence to reject theexistence of fast producers of SNe'. Arm structure in normal spiral galaxies, 1: Multivariate data for 492 galaxiesMultivariate data have been collected as part of an effort to develop anew classification system for spiral galaxies, one which is notnecessarily based on subjective morphological properties. A sample of492 moderately bright northern Sa and Sc spirals was chosen for futurestatistical analysis. New observations were made at 20 and 21 cm; thelatter data are described in detail here. Infrared Astronomy Satellite(IRAS) fluxes were obtained from archival data. Finally, new estimatesof arm pattern radomness and of local environmental harshness werecompiled for most sample objects.
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# Can I ask competitive programming questions?

I often stuck on some competitive programming problems. I don't know a good place to ask my question. If my issue is about the algorithm to use not the implementation, can I ask my question here? How about problems that I have absolutely no idea about the solution, is it okay to ask for help in this site? If so what should I name the question? For instance is UVA 11293 an acceptable question title?

• What exactly do you mean by "competitive programming"? Questions about properties of algorithms, and comparisons between different algorithms are certainly on topic here! Yet, specific implementations are off-topic. – Ran G. Nov 13 '15 at 22:35
• Do note that we discourage posts that simply state a problem out of context, and expect the community to solve it. Generally it's better to ask some specific question about some specific aspect or concept that you're stuck on. Also, make sure to cite your sources (where the programming contest problem came from), and if the competition is currently running, I recommend you make sure that the competition allows you to ask others for help with your solution. – D.W. Nov 14 '15 at 6:03
• What is UVA 11293 supposed to mean? – muru Nov 14 '15 at 8:18
• There's an Area 51 proposal for a dedicated competitive programming site. If you're interested in that topic, please support it. – RedGreenCode Feb 5 '17 at 21:54

If my issue is about the algorithm to use not the implementation, can I ask my question here?

Depends. If you have an actual question about what you have tried, yes. If you want to post, "How to solve [UVA 11293]?", no.

How about problems that I have absolutely no idea about the solution, is it okay to ask for help in this site?

Depends. Can you formulate a specific, computer science question that makes at least a small step beyond the problem statement? Yes. If you want to post "I need an idea for [UVA 11293]!", no. You may want to try our chat instead.

If so what should I name the question? For instance is UVA 11293 an acceptable question title?

No, that is never an acceptable title. You should describe the question in the title. The name of an exercise problem, overly generic titles like "algorithm problem" or "dynamic programming" are useless. If you can not formulate a better title -- one that describes your question shortly but aptly -- you are not ready to post yet.

It all comes down to this: we expect posters to have done something before they post, and show it. Useful steps are

• understanding the problem statement (you'd be surprised...),
• trying the obvious,
• researching the literature resp. on the internet, and finally
• describing where you got stuck, that is why the above did not work.

"I don't know how to begin, help?!" is always a bad question. You want to post something like "I have tried to set up a dynamic programming recurrence, but I'm not sure about the second case. I think I have to consider X but how do I do that?".


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" /> -->

#### Important questions-Introduction To Probability Theory

11th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 50

Part A

5 x 1 = 5
1. Four persons are selected at random from a group of 3 men, 2 women, and 4 children. The probability that exactly two of them are children is

(a)

${3\over4}$

(b)

${10\over23}$

(c)

${1\over2}$

(d)

${10\over21}$

2. Two items are chosen from a lot containing twelve items of which four are defective, then the probability that at least one of the item is defective

(a)

${19\over 33}$

(b)

${17\over 33}$

(c)

${23\over 33}$

(d)

${13\over 33}$

3. A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

(a)

1:12

(b)

12:1

(c)

13:1

(d)

1:13

4. A number x is chosen at random from the first 100 natural numbers. Let A be the event of numbers which satisfies${(x-10)(x-50)\over x-30}\ge0$, then P(A) is

(a)

0.20

(b)

0.51

(c)

0.71

(d)

0.70

5. If two events A and B are independent such that P(A)=0.35 and $P(A\cup B)=0.6$ ,then P(B) is

(a)

${5\over 13}$

(b)

${1\over 13}$

(c)

${4\over 13}$

(d)

${7\over 13}$

6. Part B

5 x 2 = 10
7. If an experiment has exactly the three possible mutually exclusive outcomes A, B, and C, check in each case whether the assignment of probability is permissible
$P(A)=\frac { 4 }{ 7 } ,P(B)=\frac { 1 }{ 7 } ,P(C)=\frac { 2 }{ 7 }$

8. A factory has two Machines-I and II. Machine-I produces 60% of items and Machine-II produces 40% of the items of the total output. Further 2% of the items produced by Machine-I are defective whereas 4% produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?

9. For a sports meet, a winners’ stand comprising of three wooden blocks is in the form as shown in figure. There are six different colours available to choose from and three of the wooden blocks is to be painted such that no two of them has the same colour. Find the probability that the smallest block is to be painted in red, where red is one of the six colours.

10. An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible
P(A) = 0.15, P(B) = 0.30, P(C) = 0.43 , P(D)= 0.12

11. An experiment has the four possible mutually exclusive and exhaustive outcomes A, B, C, and D. Check whether the following assignments of probability are permissible.
P(A) =$\frac { 2 }{ 5 }$,  P(B)=$\frac { 3 }{ 5 }$,  P(C)=-$\frac { 1 }{ 5 }$,  P(D) =$\frac { 1 }{ 5 }$

12. Part C

5 x 3 = 15
13. A problem in Mathematics is given to three students whose chances of solving A problem in Mathematics is given to three students whose chances of solving $\frac { 1 }{ 3 } ,\frac { 1 }{ 4 }$ and $\frac { 1 }{ 5 }$ (i) What is the probability that the problem is solved? (ii) What is the probability that exactly one of them will solve it?

14. Suppose a fair die is rolled. Find the probability of getting
(i) an even number (ii) multiple of three

15. If and are mutually exclusive events P(A)=$\frac{3}{8}$ and P(B)=$\frac{1}{8}$ , then find
(i) P($\bar { A }$)
(ii) $P(A\cup B)$
(iii) $P(\bar { A } \cap B)$
(iv) $P(\bar { A } \cup \bar { B } )$

16. The probability of an event A occurring is 0.5 and B occurring is 0.3. If A and B are mutually exclusive events, then find the probability of
(i) $P(A\cup B)$
(ii) $P(A\cap \bar { B } )$
(iii) $P(\bar { A } \cap B)$

17. The probability that a girl, preparing for competitive examination will get a State Government service is 0.12, the probability that she will get a Central Government job is 0.25, and the probability that she will get both is 0.07. Find the probability that (i) she will get atleast one of the two jobs (ii) she will get only one of the two jobs.

18. Part D

4 x 5 = 20
19. Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.

20. An advertising executive is studying television viewing habits of married men and women during prime time hours. Based on the past viewing records he has determined that during prime time wives are watching television 60% of the time. It has also been determined that when the wife is watching television, 40% of the time the husband is also watching. When the wife is not watching the television, 30% of the time the husband is watching the television. Find the probability that
(i) the husband is watching the television during the prime time of television
(ii) if the husband is watching the television, the wife is also watching the television

21. When a pair of fair dice is rolled, what are the probabilities of getting the sum
(i)7
(ii) 7 or 9
(iii) 7 or 12?

22. A consulting firm rents car from three agencies such that 50% from agency L, 30% from agency M and 20% from agency N. If 90% of the cars from L, 70% of cars from M and 60% of the cars from N are in good conditions
(i) what is the probability that the firm will get a car in good condition?
(ii) if a car is in good condition, what is probability that it has come from agency N?


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# A static analysis for the minimization of voters in fault-tolerant circuits

Abstract : We present a formal approach to minimize the number of voters in triple-modular redundant (TMR) sequential circuits. Our technique actually works on a single copy of the TMR circuit and considers a large class of fault models of the form at most 1 SEU or SET every k clock cycles''. Verification-based voter minimization guarantees that the resulting TMR circuit (i) is fault tolerant to the soft-errors defined by the fault model and (ii) is functionally equivalent to the initial TMR circuit. Our approach operates at the logic level and takes into account the input and output interface specifications of the circuit. Its implementation makes use of graph traversal algorithms, fixed-point iterations, and binary decision diagrams (BDD). Experimental results on the ITC'99 benchmark suite indicate that our method significantly decreases the number of inserted voters, yielding a hardware reduction of up to 55% and a clock frequency increase of up to35% compared to full TMR.
Keywords :
Type de document :
Rapport
[Research Report] RR-9004, Inria - Research Centre Grenoble – Rhône-Alpes. 2016, pp.1-27
Domaine :

Littérature citée [42 références]

https://hal.inria.fr/hal-01417164
Soumis le : jeudi 15 décembre 2016 - 12:47:41
Dernière modification le : mardi 20 décembre 2016 - 11:09:56
Document(s) archivé(s) le : jeudi 16 mars 2017 - 18:44:34

### Fichier

RR-9004.pdf
Fichiers produits par l'(les) auteur(s)

### Identifiants

• HAL Id : hal-01417164, version 1

### Citation

Dmitry Burlyaev, Pascal Fradet, Alain Girault. A static analysis for the minimization of voters in fault-tolerant circuits. [Research Report] RR-9004, Inria - Research Centre Grenoble – Rhône-Alpes. 2016, pp.1-27. 〈hal-01417164〉

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# The Stone-Čech compactification of the fixed point set

Let $$G$$ be a discrete group and $$X$$ be a Tychonoff $$G$$-space. Then there exists a $$G$$-action on Stone-Čech compactification $$\beta X$$. If the fixed point set $$X^{G}\neq \emptyset$$, then the Stone-Čech compactification of the fixed point set is the fixed point set of the Stone-Čech compactification, i.e., $$\beta \left( X^{G}\right) =\left( \beta X\right) ^{G}$$?

• $\beta$ is a left adjoint functor, and taking $G$-fixed points is a limit. So I suspect this isn't true as in general left adjoint don't preserve limits. – Niall Taggart Oct 23 '18 at 10:12
• To start with, one has a canonical continuous map $\beta(X^G)\to (\beta X)^G$. Also the assumption $X^G\neq\emptyset$ is irrelevant as it can be artificially enforced by adding an isolated fixed point to $X$. – YCor Oct 23 '18 at 22:51

Not without further assumptions. First create an ordered space $$X$$ by identifying $$\langle0,\omega_1\rangle$$ and $$\langle1,\omega_1\rangle$$ in the product $$2\times(\omega_1+1)$$ to a point, $$\Omega$$ say. Then make the product $$X\times X$$ and take out $$\langle\Omega,\Omega\rangle$$. You can rotate the resulting space $$Y$$ around that hole over $$\pi$$ by mapping $$\bigl<\langle i,\alpha\rangle,\langle j,\beta\rangle\bigr>$$ to $$\bigl<\langle 1-i,\alpha\rangle,\langle 1-j,\beta\rangle\bigr>$$ and similarly for points with $$\Omega$$ as a coordinate. This map $$f:Y\to Y$$ has no fixed points but $$\beta Y=X$$ and $$\beta f$$ does have a fixed point: $$\langle\Omega,\Omega\rangle$$.

Now take the sum $$Y\cup\{0\}$$ and extend $$f$$ by $$f(0)=0$$. Then $$f$$ has one fixed point and $$\beta f$$ has two. As $$f$$ is its own inverse this gives us an action of $$\mathbb{Z}/2\mathbb{Z}$$ that is a counterexample.


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# Universal quantifiers in category theory

I’ve recently learned about the curry howard isomorphism for dependent type theory, and I’m now interested in learning about how to capture this in category theory.

I believe that I understand how to frame propositional logic in category theory: Every proposition is an object, and a proof of a proposition is a morphism from $$T$$ to that object, and we assume the category is cartesian closed. $$A$$ implies $$B$$ is assumed as an axiom by positing a morphism from $$T$$ to the exponential object $$B^A$$. A conjunction between $$A$$ and $$B$$ is true if there is a morphism from $$T$$ to $$A\times B$$, and to the coproduct for a disjunction. A negation of a proposition $$A$$ is represented by a morphism from $$A$$ to type “bottom” which is uninhabited.

But I’m not sure how to represent universal quantifiers and existential quantifiers, and I couldn’t really understand the texts I found online.

Assuming you are interested only in the Curry-Howard-Lambek type of interpretations of logic in categories then in order to interpret first-order logic in a category cartesian closed categories are not sufficient.

The problem lies in the fact that you need a category whose objects represents not only propositions, i.e. closed formulas, but predicates as well (i.e. formulas with vatiables).

In order to do this one needs some sort of fibered categories (or indexed ones if you prefer).

We assume we have a logic signature made of an algebraic signature $$\Sigma$$, containing the operation symbols, and predicate signature $$\Pi$$, containing the predicate symbols.

For start one consider the category $$T(\Sigma)$$ whose objects sets of free variables and for every pair of such sets $$X$$ and $$Y$$ we have $$T(\Sigma)[X,Y]=\mathbf{Set}[X,T_\Sigma(Y)]$$ where $$T_\Sigma(Y)$$ is the set of terms with variables in $$Y$$. So morphisms of this category are substitutions for the logic signature considered.

To each $$X \in T(\Sigma)$$ we can associate the poset $$P(X)$$ of formulas with free variables in $$X$$, with order relations given by $$\varphi \leq \psi$$ iff $$\varphi \vdash \psi$$.

Also for every morphism/substitution $$\sigma \in T(\Sigma)[X,Y]$$ we have a monotone map $$P(\sigma)\colon P(X) \to P(Y)$$ defined as $$P(\sigma)(\varphi)=\sigma(\varphi)$$, that is the formula obtained by applying the substitution $$\sigma$$ to the formula $$\varphi$$.

These assignment define a functor $$P\colon T(\Sigma) \to \mathbf{Cat}$$, where we regard posets as categories and monotone functions as functors.

In this set up we can characterize quatifiers as adjoint functors, let see how.

For every $$X$$ set of variables and a new variable $$x$$ we have a morphisms $$\pi_x^X \in T(\Sigma)[X,X\cup\{x\}]$$ given by the substitution $$\pi_x^X \colon X \longrightarrow X\cup\{x\}$$ $$\pi_x^X(x)=x$$ for every $$x \in X$$.

The induced functor/monotone map $$P(\pi_x^X)$$ sends every proposition of $$P(X)$$ into itself seen as a member of $$P(X\cup\{x\})$$.

A left adjoint to $$P(\pi_x^X)$$ would be a functor $$L_x^X \colon P(X \cup\{x\}) \to P(X)$$, that takes formulas with free variables in $$X\cup\{x\}$$ and sends them in formulas with free variables in $$X$$ (pretty much as the quantifiers that eliminate free variables).

For $$L_x^X$$ to be an adjoint we need to have a natural isomorphism $$P(X)[L_x^X(\varphi),\psi]\cong P(X\cup\{x\})[\varphi,P(\pi_x^X)(\psi)]$$ and since we are dealing with posets this amounts to require that $$L_x^X(\varphi) \leq \psi \iff \varphi \leq P(\pi_x^X)(\psi)=\psi$$

This is equivalent to require that $$L_x^X(\varphi)$$ is a proposition whose logical consequences $$\psi$$ with free variables in $$X$$ are exactly those formulas that are implied by $$\varphi$$ in the extended context of $$P(X\cup\{x\})$$.

With a little effort one can show that such $$L_x^X(\varphi)$$ must be $$\exists x \varphi$$.

Similarily a right adjoing $$R_x^X \colon P(X\cup\{x\}) \to P(X)$$ would be a functor such that there is a natural isomorphism $$P(X\cup\{x\})[P(\pi_x^X)(\varphi),\psi]\cong P(X)[\varphi,R_x^X(\psi)]$$ Again, since we are dealing with posets, this amounts to require that $$R_x^X(\psi)$$ is the formula such that $$\varphi \leq R_x^X(\psi)$$ iff and only if $$\varphi \leq \psi$$, that is $$R_x^X(\psi)$$ is a logical consequence of $$\varphi$$ if and only if $$\psi$$ is a logical consequence of $$\varphi$$.

By playing a little bit with logic one can show that the only possibility is for $$R_x^X(\psi)$$ to be $$\forall x \psi$$.

If you are interested to some pointers I suggest to read Bart Jacobs' "Categorical Type Theory" that deals in details with these subject.

Note: usually authors use a different notation form the one I used here, for instance they usually deal with the category $$T(\Sigma)$$, nevertheless if you got the general idea I think you can easily fix the difference in notations.

I hope I was able to give you the raw idea, in case you needed any additional clarification please ask.

• What is the “substitution functor”, and between which categories is it ? (I don’t know how to parse “between the categories indexed by $X$ and $Y$”, or what the functor would be). 2. A substitution is a function from variables to formulas. But in your example where you add a variable to $X$, it is a function from variables to another set of variables. This confuses me. 3. Could you give an intuition why the existential and universal quantifiers are adjoints of this functor, and what we can do with this fact? (Though as I said before, I don’t understand how the functor is constructed.) – user56834 Jun 30 at 21:17
• @user56834 I've edited the answer adding as much details as I could. Let me know if these changes address all your doubts. – Giorgio Mossa Jul 2 at 11:21


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The scripts and input files that accompany this demo can be found in the demos/public directory of the Rosetta weekly releases.

This document describes how to use the AnchoredDesign protocol, both in benchmarking and design mode. As the protocol's components AnchorFinder, AnchoredPDBCreator, and AnchoredDesign are reasonably extensively documented elsewhere, this protocol capture is meant to be used alongside that online documentation. Presented at RosettaCon2010 (in poster form) was a description of the protocol itself, plus benchmarking results, plus some early design results. The accompanying paper (Lewis SM, Kuhlman BA. Anchored design of protein-protein interfaces. PLoS One. 2011;6(6):e20872. Epub 2011 Jun 17. (pubmed link)) describes only benchmarking results, but the tools to do design are described here. A paper on design results is forthcoming.

Note that this protocol capture is somewhat focused on just the AnchorFinder portion (the least important part of the process), because the other portions are documented elsewhere but AnchorFinder largely is not.

Contained here:

• Instructions on choosing appropriate benchmarks – AnchorFinder or otherwise
• Instructions on preparing those structures – for benchmarking or via AnchoredPDBCreator
• How to benchmark AnchoredDesign against those structures
• command lines/option files, and discussion of the options

Not contained here:

• A speck of code – that lives in your Rosetta release.
• Submission scripts for running jobs. I don't know your architecture. It's all MPI compatible so it's not hard.

Sort-of contained here:

• The raw_documentation directory includes copies of the doxygen-style manual documentation for AnchorFinder, AnchoredDesign and AnchoredPDBCreator. These copies are guaranteed NOT to be up to date; look in your copy of the code or the web links above instead.

## Overview

The purpose of the AnchoredDesign protocol is to create new protein-protein interactions using information (the anchor) borrowed from a known interaction at the same interface of one partner. Because this protocol is intended to design protein-protein interactions, the obvious test is to see whether it can recover known structures of such interactions. This document is massively overconcerned with benchmarking because it accompanies the paper in which AnchoredDesign is benchmarked; unless you are actually trying to replicate the benchmarking you can ignore most of those details and skip to the design tools.

The protocol modifies a loop region around an anchor in designing binders. Selection of structures for benchmarking therefore requires interface loops with anchor regions.

The ideal anchor has several qualities:

• one or a few contiguous residues – the protocol can only have one anchor
• many interactions across an interface – this is the whole point of an anchor
• not embedded in the middle of a secondary structure element (helix/strand) – the anchor needs to be in a loop because the interface space will be sampled via loop remodeling of the anchor loop

Examples of anchors might be a phosphotyrosine inserting into an SH2 domain, a polyproline sequence binding an SH3 domain, etc.

For design, one would choose an anchor based on one's target. For benchmarking, you are free to choose anything that has an interface loop with a good anchor. To select benchmarking structures, I wrote the AnchorFinder protocol. AnchorFinder has some value in highlighting which residues might make good anchors for a given target (although computational alanine scanning, not covered here, is more likely to be useful).

After finding suitable structures with the help of AnchorFinder, the next step is to pick anchors and loops out of those structures, and in general prepare them for Rosetta's use (removing solvent atoms, etc). At this point you're ready to run AnchoredDesign.

## Compiling AnchorFinder

(This section applies to benchmarking only)

Your Rosetta code distribution should include an application called AnchorFinder. If you wish to search large numbers of PDBs for potential anchors (I searched a local copy of the entire PDB structure set), then you will wish to modify the code slightly before running it. Running any part of Rosetta against huge numbers of unprepared, straight-from-the-PDB structures is challenging because the PDB reader in Rosetta is not robust against nonstandard file formats, etc.

To compile AnchorFinder such that it will be robust, examine the manual documentation on RobustRosetta (also included in this protocol capture). Briefly, this documentation describes changes that A) make Rosetta slower (thus they aren't on by default) and B) cause it to throw C++ exceptions when it hits errors instead of crashing. The job distributor catches the errors, skips the bad structures, and continues. You must recompile after making these changes.

You do not want to use compiled executeables OTHER than AnchorFinder with these changes made – they will significantly slow the code down. AnchorFinder is quite fast so it's not a problem.

When running AnchorFinder, watch your memory usage. When I used it, there was a patch in the JobDistributor which deleted starting poses for PDBs that had already been processed. This patch was rejected by the community and since been replaced by a different patch to do the same thing; AnchorFinder is a run-once sort of thing so it has not been tested against the new method.

## Using AnchorFinder

(This section is minimally relevant if not benchmarking)

At this point you should have a compiled copy of AnchorFinder with the necessary changes to the code. You can then list your PDBs in one or many -l files (or -s) for use in Rosetta. The format for Rosetta's -l flag is one path per line:

A.pdb
B.pdb
C.pdb
...

Depending on your available architecture, it may be better to split the run up into many -l on separate processors. I don't know what's best for you.

If you want to do the whole PDB – it's a good idea to skip the largest PDB files ahead of time, particularly ribosome structures. These take a very long time to process through the PDB reader, and due to heavy nucleic acid content are skipped anyway. You can also either toss the NMR structures ahead of time or use the -obey_ENDMDL flag to only read the first model.

AnchorFinder will automatically remove nonprotein atoms from the Poses before examination. It also skips anything that is monomeric, has no protein residues, or smaller than 20 residues after processing.

It will then look through the structures searching for regions with certain command-line-defined characteristics. These characters are:

• length of windows for consideration - 4 or 5 or 6, etc, contiguous residues at a time? This flag is -window_size. I suggest 5 residue windows.
• What fraction of this window should have loop secondary structure as assigned by DSSP? -loopness controls this. It takes it as a decimal between 0-1, I suggest 0.6 (which translates to 3/5 residues for a 5 residue window) to 1 (all residues loop).
• How many cross-interface interactions per residue should the window have? I suggest a minimum of 4. This translates to 20 (redundancy included) cross-interface interactions for a 5 residue window. By redundancy, I mean residues 43 and 44 on chain A can both interact with residue 234 on chain B and it will count as two interactions. Specify this with -nbrs_per_residue.
• What file name should the good interactions be printed to? I leave it as an exercise to the reader to pick their own file name. Specified with -bestoutfile; defaults to goodfile.out.

Running AnchorFinder, while not particularly slow, is still something you only want to do once. The defaults suggested above produce lots of output, which can then be further processed quickly without reloading PDBs. To expedite this, AnchorFinder produces two levels of output. All residues have their data printed to a file named (pdbname).data – you can reprocess this to get data for differing window lengths, loopnesses, etc. Windows passing the loopness and interactions filters are printed to the specified output file.

A suggested options file for AnchorFinder is available with this document.

## Interpreting AnchorFinder Results

(This section is minimally relevant if not benchmarking)

After you've run AnchorFinder, you'll have a fairly large pile of output: pdbname.data for all pdbs, plus goodfile.out for the better windows.

pdbname.data looks like this:

Rows are residues, columns are chains, data are neighbors in that chain for each residue

residue chain   PDBdata DSSP    1       2
1       1       2 D     L       7       0
2       1       3 D     L       10      0
3       1       4 D     L       14      0
...

The columns are residue and chain in Rosetta numbering, residue/chain in PDB numbering, DSSP value, and then N columns for the N chains in the protein. The number in those columns is the number of cross-interface neighbors on that chain for that position.

goodfile.out looks like this:

PDB pdb2vk1 window 45 loopness 5 nbrs 0 28 0 0 start 46 A pymol select pdb2vk1 and chain A and resi 46-50
PDB pdb2vk1 window 108 loopness 5 nbrs 0 25 0 0 start 109 A pymol select pdb2vk1 and chain A and resi 109-113
PDB pdb2vk1 window 109 loopness 5 nbrs 0 36 0 0 start 110 A pymol select pdb2vk1 and chain A and resi 110-114
PDB pdb2vk1 window 110 loopness 5 nbrs 0 46 0 0 start 111 A pymol select pdb2vk1 and chain A and resi 111-115
PDB pdb2vk1 window 111 loopness 5 nbrs 0 46 0 0 start 112 A pymol select pdb2vk1 and chain A and resi 112-116
PDB pdb2vk1 window 112 loopness 5 nbrs 0 47 0 0 start 113 A pymol select pdb2vk1 and chain A and resi 113-117

Each line identifies the PDB, the window number, its loopness, its number of neighbors on each chain in the PDB (variable # of columns), the starting residue PDB numbering for the window, and a Pymol selection for the window.

Inputs and outputs for this stage from a convenience sample (PDBs 3cy?) are included with this protocol capture.

At this point, the data is yours to play with. I searched for windows with large numbers of neighbors on only one chain using sifter.py (included), then sorted for those with the largest number of neighbors (sort -n -k1 input). After that it was all manual filtering to choose structures for the benchmarks.

## Choosing Loop and Anchor — Benchmarking

(This section applies to benchmarking only)

OK, so you ran AnchorFinder, looked at the results, and/or picked what protein you want to run through AnchoredDesign. How do you choose a loop/anchor?

If you ran AnchorFinder, look at the AnchorFinder result lines that came up as good:

92 PDB pdb1zr0 window 526 loopness 5 nbrs 0 0 92 0 start 13 D pymol select pdb1zr0 and chain D and resi 13-17

Load this PDB into pymol (1zr0.pdb) and activate the suggested selection. You'll see that it is in a surface loop of one partner which sticks an arginine straight into its binding partner – a perfect anchor. (This is a chosen example; not all AnchorFinder hits are this nice.)

Choosing the anchor is entirely up to human effort; here the arginine 15 is an obvious choice.

For choosing loops, I just traveled up and down the chain in both directions until I hit secondary structure, significant backbone-backbone hbonding, or the protein core. Here I'd choose a loop of D10 to L17 – more N-terminal than that affects the core, and more C-terminal affects a sheet.

Anchor and loop file specifications are included in the release documentation and the examples here.

Note that for the included example, the PDB has been renumbered from 1. Scripts to do this are occasionally included with Rosetta distributions and not included here. It will be convenient to also remove waters, ligands, etc.

## Choosing a System and Anchor — Design

(This section applies to the design case only)

In the design case, you will be choosing your proteins based on what you want designed. Your target is forced by what targets:

• have crystal structures, and
• are related to your biological problem.

Choosing an anchor then requires:

• a cocrystal of your target with some partner from which to source the anchor.

You can run this cocrystal through AnchorFinder and let it suggest anchors to you, but for one structure you can just look at it yourself. Look for loops on the partner that insert into the target, or do computational alanine scanning, or examine the literature for mutations that disrupt the interface.

## Choosing a Scaffold, Design Positions, and Loops — Design

(This section applies to the design case only)

In the design case, you will be replacing your target's partner with some new scaffold to form a mostly de novo interface. Your scaffold must meet a few requirements:

• flexible, mutateable surface loops (for AnchoredDesign to modify)
• experimentally tractable (hey, your funeral if it's not)
• whatever other functionality you need for your desired design

The protocol was written with the fibronectin monobody scaffold in mind.

Choosing which loops are flexible is dependent on biological knowledge of the scaffold. In fibronectin's case, many papers have been published establishing the mutability of the BC and FG loops.

Choosing which positions are designable is similarly dependent on your scaffold. AnchoredDesign carries the assumption that the non-anchor loop positions are designable, and non-loop positions are not, but nothing in the code enforces that. Use a resfile (documented with the manual) to specify which positions are designable. The code will automatically prevent design of the anchor (you can turn that off). The code will automatically prevent design of positions that are not close to either the interface or a flexible loop (you cannot turn that off), so take care in specifying designable positions on opposite faces of your protein. Proximity is redetermined at each design opportunity so positions peripheral to the interface may not be designed regularly.

## Choosing Loop Lengths and Anchor Position

(This section applies to the design case only)

OK, so you know which scaffold to use, and which anchor, and which target. You are ready to create your starting structure for AnchoredDesign, in which the anchor will be inserted into the scaffold, and the anchor will be aligned properly to the target, dragging the scaffold and target together. The protocol used for this is called AnchoredPDBCreator; further details are below.

One important part of conformational space that AnchoredDesign cannot search is the space of loop lengths and anchor positions. You may want to try, for a loop of length N, all combinations of loops of length N-3 to N+3, or even more for long loops. As you are designing the loop to form an interface, there is no reason to believe its native length is particularly relevant. You will have to do this searching at this stage: create starting structures for all loop lengths, run them all through AnchoredDesign, and pick off the best ones later.

Loops can be shortened directly by just deleting residues mid-loop before handing the scaffold to AnchoredPDBCreator – it can insert a 3 residue anchor into a 6 residue window, and close the gap. Loop lengthening must be done externally. One way to lengthen loops is to manually modify a PDB to contain enough residues in the loop (copy-and-paste a residue, renumber as necessary), then use the loop_modeling executeable's build_initial mode to close the loop. Further instructions are included in their own folder in this packet.

A paired space is anchor placement space. Besides choosing which anchor to use (try several), exactly where it is placed within a loop can vary. For a loop of length 7, and an anchor of length 2, (assuming a flexible residue on each side), you have the following 4 choices:

X = scaffold
- = loop
A = anchor
X1234567X
X-AA----X
X--AA---X
X---AA--X
X----AA-X

Again, this space is not searched by AnchoredDesign and must be searched by trying all the inputs.

## Using AnchorPdbCreator

(This section applies to the design case only)

AnchoredPDBCreator is the protocol which assembles an anchor, scaffold, and target into a starting structure for AnchoredDesign. Its code documentation is included in this packet.

Briefly, AnchoredPDBCreator takes as input 4 files:

• The target structure, as a PDB, with the partner removed
• The anchor structure, drawn from the cocrystal with the target, containing ONLY the residues being used as an anchor, as a PDB
• The scaffold structure, as a PDB, with loop residues added/deleted as desired
• A scaffold_loop specification, which declares which residues in the scaffold are flexible and where the anchor insertion should occur.

It is ABSOLUTELY VITAL to recognize that AnchoredPDBCreator does NOT produce interfaces, it only produces starting structures for AnchoredDesign. It is entirely plausible that its structures will have the target and scaffold totally eclipsed. This is fine, AnchoredDesign will fix it.

AnchoredPDBCreator's results should be interpreted by analyzing ONLY the closure of the anchored loop. Use the result with the best loop geometry. Loop geometry can be measured by examining the LoopAnalyzerMover output tagged to the end of result PDBs:

LoopAnalyzerMover: unweighted bonded terms and angles (in degrees)

position phi_angle psi_angle omega_angle peptide_bond_C-N_distance rama_score omega_score dunbrack_score peptide_bond_score chainbreak_score
pos phi_ang psi_ang omega_ang pbnd_dst    rama  omega_sc dbrack pbnd_sc   cbreak
17  -106.8   175.8     178.2    1.322   0.998    0.0342   7.01   -2.68   0.0182
18  -82.33   64.67    -178.5    1.329   0.211    0.0217   3.11   -3.42   0.0203
19  -83.63   149.4     177.2    1.329   -1.07    0.0795      0   -3.43    0.584
20  -75.25   171.1    -178.7    1.329  -0.264    0.0161  0.348   -3.43   0.0151
21  -58.53  -42.95     174.6    1.329   -0.58     0.294      0   -3.43      2.7
22  -76.02   159.9    -179.8    1.326  -0.811  0.000404   0.97   -3.45   0.0424
23  -72.63   130.1     179.4    1.325   -1.29   0.00372   0.24   -3.46   0.0281
24  -94.91   116.5     179.8    1.323   -1.21   0.00028  0.721   -3.45   0.0694
25  -65.42   150.7     179.4    1.335   -1.58     0.004      0   -3.32     1.38
26  -64.68   147.9     179.1    1.323   -1.45    0.0079   1.61   -3.32    0.211
27  -56.44  -66.68      -180    1.329    1.34  8.08e-30   7.87   -3.43 2.37e-05
28  -124.4  -56.48     177.6    1.329    2.08    0.0568  0.608   -3.43   0.0533
29  -124.1   28.78    -177.7    1.264   0.341    0.0542   2.39    2.65     2.07
30   81.57  -134.3    -176.4    1.329      20     0.126   5.06    2.65    0.128
31  -112.9   147.2     172.7    1.318  -0.744     0.538  0.534   -3.35     1.38
total_rama 15.9674
total_omega 1.23676
total_peptide_bond -38.3223
total_chainbreak 8.70689
total rama+omega+peptide bond+chainbreak -12.4113

LAM_total -12.4113

In this particular example, position 29 is clearly problematic: the peptide bond distance is too short, as reported by the pbnd_dst, pbnd_sc, and cbreak columns.

You should be running AnchoredPDBCreator for at least 100 trajectories before choosing a starting structure.

## Running AnchorDesign

If you are benchmarking, the crystal structure of the complex is the appropriate input for AnchoredDesign. If you are designing, the best result from AnchoredPDBCreator is your starting structure.

The input files for AnchoredDesign provide an example with 1zr0 for running AnchoredDesign. It is a heterodimer so you can pretend it was AnchoredPDBCreator sourced if you want. (You can also look in the AnchoredDesign integration test at test/integration/tests/AnchoredDesign for such an input).

• The anchor file specifies which residues form anchor.
• The PDB file is the pdb.
• loopsfile_extended is for benchmarking – the extension column is true, which tells AnchoredDesign to forget the starting loop conformation before sampling
• loopsfile_native tells AnchoredDesign NOT to forget the starting loop conformation – this is probably what you would use for design, although there is no reason you can't reject the starting loop conformation for design. (This is cheating for benchmarking, but useful for making relaxed natives)
• options is the command line options file. The active options are for a simple “does it run” test; parameters for a longer running “real” test are included.
• A resfile is necessary if you wish to design, and is only active in that option set.
$> cd AnchoredDesign/input_files$> \$ROSETTA3/bin/AnchoredDesign.default.linuxclangrelease @options_design -overwrite Interpreting AnchorDesign — Benchmarking ---------------------------------------- (This section applies to the benchmarking case only)

If you are duplicating the benchmarking results, you passed the rmsd flag. AnchoredDesign will have output a lot of RMSD values allowing you to determine the performance of the protocol against the structures you chose to benchmark. The paper describes the score versus RMSD metrics used to determine quality (including the I_sup_bb_RMSD, ch2_CA_RMSD, and loop_CA_sup_RMSD. The structures themselves don't really matter; you are ensuring that the low-scoring structures have low RMSD.

## Interpreting AnchorDesign — Design

(This section applies to the design case only)

In the design case, the other fields of the AnchoredDesign output come in to play. There are three classes of output:

• scorefunction terms
• LoopAnalyzerMover output,
• InterfaceAnaylzerMover output.

Generally, you should rank your structures according to total_score (the Rosetta scorefunction). This tells you what Rosetta thinks is best.

Next, you use the LoopAnalyzerMover output (described above) and InterfaceAnalyzerMover output to determine which structures have flaws not caught by total_score. Toss structures that those filters think have problems. Pick the ones you think are best, order the DNA, and pray. When it works great, feel free to send me kudos, citations, or money!

## InterfaceAnalyzerMover

InterfaceAnalyzerMover output looks like this:

Residues missing H-bonds:
Residue      Chain   Atom
38   A   NE2
101      A   OE1
248      A   O
250      A   O
344      B   N
384      B   O
477      B   O

pymol-style selection for unstat hbond res
select start_5411_unsat, /start_5411//A/38+101+248+250+ + /start_5411//B/344+384+477+

pymol-style selection for interface res
select start_5411_interface, /start_5411//A/31+32+33+34+35+36+37+38+39+40+41+54+56+57+59+60+61+62+64+65+66+92+95+98+99+100+101+102+103+106+194+195+224+225+226+227+228+229+230+247+248+249+250+251+252+253+265+ + /start_5411//B/314+315+316+317+318+319+320+321+322+323+324+337+339+340+342+343+344+345+347+348+349+350+375+378+379+381+382+383+384+385+386+389+473+476+477+478+479+480+481+482+488+506+507+508+509+510+511+512+513+

The first section documents where Rosetta thinks there are unsatisfied hydrogen bonds at the interface. This code is known to be oversensitive to missing bonds, but it's better than nothing.

The next sections print PyMOL selections for interface residues for easier visualization.

InterfaceAnalyzerMover also includes columns into the scorefile:

dSASA_int 2396.33
dG_separated -35.3379
dG_separated/dSASAx100 -1.47467
delta_unsatHbonds 7
packstat 0
dG_cross -27.6963
dG_cross/dSASAx100 -1.15578
AllGly_dG -2.83564
cen_dG -10.3844
nres_int 96
per_residue_energy_int -1.15006
side1_score -361.478
side2_score -267.353
nres_all 520
side1_normalized -1.25513
side2_normalized -1.15238
complex_normalized -1.74616
hbond_E_fraction 0.368537

Most of these are experimental and not useful (and not part of AnchoredDesign; InterfaceAnalyzerMover has other clients). The useful ones are dG_separated/dSASAx100, which measures the Rosetta energy of binding per unit area of SASA (scaled by a factor of 100). This ensures you pick an interface that is energetic for its size, not large but sloppy.


text:
# Conditional statement problem in ODE code in Matlab

• MATLAB
I am new in matlab and recently, I have tried coding in matlab. So far, I have been getting error msg

"Warning: Failure at t=2.859413e+002. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.015868e-012) at time t."

I have referred back to my codes and realized that the problems occurs due to the conditional statement. To cut the story short, the ode doesn't seem to want to read the if, else-if statement in my codes.

e.g

if yY(1)<=Y(1)<yY(2)
hY = -0.0014*(Y(1)-yY(1))^3+ 0.0200*(Y(1)-yY(1))^2+ 0.8515*(Y(1)-yY(1));
elseif yY(2)<=Y(1)<yY(3)
hY = -0.0014*(Y(1)-yY(2))^3+ 0.0151*(Y(1)-yY(2))^2+ 0.8935*(Y(1)-yY(2))+ 1.0431;
elseif yY(3)<=Y(1)<yY(4)
hY = -0.0012*(Y(1)-yY(3))^3+ 0.0088*(Y(1)-yY(3))^2+ 0.9306*(Y(1)-yY(3))+ 2.4600;
else
hY = 1.0000*(Y(1)-yY(19))+ 510.8083;
end

It only wants to read the first highlighted piece of the code.

if((yY(1)<=Y(1)) && (Y(1)<yY(2)))


text:
# Ohio Fall 2011

#### cincyaviation

##### Member
I suppose I'd better come since I've missed the last two. I hear some nubs need me to show them up in 2x2 as well.

#### Yuxuibbs

##### Member
First competition I go to super excited
Will there be a meet or something the day/night before? It takes 3+ hours to drive there.

The one competition I can actually go to and Anthony can't go....

Last edited:

#### Hovair

##### Member
I hopefully will be going. I was really hoping that they would have 4x4. I can live. I really want to got to do megaminx and all the other events that I love.

#### FatBoyXPC

##### Member
Seth: Only if Shaden doesn't show up Why'd you skip Indiana?!?!

Trevor: Nakai Velasquez might be interested in the 5x5, let me talk to him and find out.

Ilkyoo: This is quite a drive for you! Has to be a good 5-6 hour drive. I hate driving the 3-3.5 hours it takes

#### FatBoyXPC

##### Member
KOII doesn't seem to be too big of a fan of big cubes, which I'm completely fine with

#### Evan Liu

##### Member
I also would like it if there were 4x4, and I'm actually a bit faster *cough* than the others saying it... but that's not a reason I wouldn't come.

Why doesn't the "Contact Us" on the competition web page work? After I type in the captcha and click submit, it just refreshes the page with my message still there but the captcha blank. And believe me, I am getting the captcha right. I have tried it more than 5 times already, getting the same result each time. I do not wish to ask my question here.

#### JBCM627

##### Member
KOII doesn't seem to be too big of a fan of big cubes, which I'm completely fine with
Actually until recently, KOII was really the only region in the US to frequently hold big cube (6/7) events.

#### FatBoyXPC

##### Member
Actually until recently, KOII was really the only region in the US to frequently hold big cube (6/7) events.
So what happened? Did they just get burnt out on it?

#### Mike Hughey

##### Super Moderator
Staff member
So what happened? Did they just get burnt out on it?
You don't seem to understand - Jim is saying that up until recently, we were the only region to frequently hold those events. Now what has changed is that other regions are also holding them more frequently. (Nothing in the past few months, but Berkeley and MIT have them coming up soon.) But we're still doing plenty of them - we had 7x7x7 last weekend. (and 4x4x4 and 5x5x5)

I personally love big cubes. I'd love a competition where we didn't do any cubes smaller than a 4x4x4, but I just suspect that not many people would come to it. When it comes to speedsolving, my favorite puzzles are 5x5x5, 7x7x7, and square-1, in that order.

Of course, doing big cubes takes longer, so you often have to drop two other events to hold one big cube event. That's one reason why they're relatively rare.

Edit: Oh, and I'm sad to say that we won't be able to attend this one. My daughters have a big dance presentation a little before noon that day in Indiana - it's the first time my littlest one has been in it, so she's particularly excited about it!

Last edited:

#### Yuxuibbs

##### Member
I know this is a bump.
Is anyone selling stickers? I can't order anything online and really need stickers.

Don't really care about standard/bright unless it's 3x3.
3x3: half brights, regular or F2 almost all my 3x3 stickers are chipping off (completely) and need to be replaced.
Pyraminx: stickers won't stay on cube
Megaminx: can't tell difference between blue/purple, red/orange, and the 2 purples
2x2: purple side is throwing me off
I don't have that much money but I'll bring enough to pay for stickers.

#### IMSLOW1097

##### Member
i want to buy an alpha cube at this comp....does anybody have an alpha CC, alpha V or alpha V-f they would be willing to sell or trade for a guhong (it's really good...cuts about 40, reverse cuts about 2/3 cubie, incredibly FAST)?

#### iEnjoyCubing

##### Member
I know this is a bump.
Is anyone selling stickers? I can't order anything online and really need stickers.

Don't really care about standard/bright unless it's 3x3.
3x3: half brights, regular or F2 almost all my 3x3 stickers are chipping off (completely) and need to be replaced.
Pyraminx: stickers won't stay on cube
Megaminx: can't tell difference between blue/purple, red/orange, and the 2 purples
2x2: purple side is throwing me off
I don't have that much money but I'll bring enough to pay for stickers.
I've got some Pyraminx stickers I'd be willing to sell you for like $2. i want to buy an alpha cube at this comp....does anybody have an alpha CC, alpha V or alpha V-f they would be willing to sell or trade for a guhong (it's really good...cuts about 40, reverse cuts about 2/3 cubie, incredibly FAST)? I have an Alpha CC that I'd be willing to sell, but not trade. Since it's lubed/broken in I would expect around$12. You can try it at the comp and see if you like it.

#### MovingOnUp

##### Member
Im going for sure, can't wait. Not too fussed about 4x4 though since I don't compete in big cubes really ha :/

#### iEnjoyCubing

##### Member
YAY!!!! i love alpha cc's!
Good I never really use it, so I might as well sell it. It will have the original bag/edge inserts too.

#### emolover

##### Member
I know this is a bump.
Is anyone selling stickers? I can't order anything online and really need stickers.

Don't really care about standard/bright unless it's 3x3.
3x3: half brights, regular or F2 almost all my 3x3 stickers are chipping off (completely) and need to be replaced.
Pyraminx: stickers won't stay on cube
Megaminx: can't tell difference between blue/purple, red/orange, and the 2 purples
2x2: purple side is throwing me off
I don't have that much money but I'll bring enough to pay for stickers.
Bill is selling stickers there and they are really nice!

His username is radmin and his stickers are fairly cheap. I don't think he has pyraminx stickers, I might be able to sell you some though. Keyword is MIGHT.


text:
2013
12-09

# Palindromes

A regular palindrome is a string of numbers or letters that is the same forward as backward. For example, the string “ABCDEDCBA” is a palindrome because it is the same when the string is read from left to right as when the string is read from right to left.A mirrored string is a string for which when each of the elements of the string is changed to its reverse (if it has a reverse) and the string is read backwards the result is the same as the original string. For example, the string “3AIAE” is a mirrored string because “A” and “I” are their own reverses, and “3″ and “E” are each others’ reverses.A mirrored palindrome is a string that meets the criteria of a regular palindrome and the criteria of a mirrored string. The string “ATOYOTA” is a mirrored palindrome because if the string is read backwards, the string is the same as the original and because if each of the characters is replaced by its reverse and the result is read backwards, the result is the same as the original string. Of course, “A”, “T”, “O”, and “Y” are all their own reverses.

A list of all valid characters and their reverses is as follows.

Character  Reverse  Character  Reverse  Character  Reverse

A         A         M         M         Y         Y

B                   N                   Z         5

C                   O         O         1         1

D                   P                   2         S

E         3         Q                   3         E

F                   R                   4

G                   S         2         5         Z

H         H         T         T         6

I         I         U         U         7

J         L         V         V         8         8

K                   W         W         9

L         J         X         X

Note that O (zero) and 0 (the letter) are considered the same character and therefore ONLY the letter “0″ is a valid character.

Input consists of strings (one per line) each of which will consist of one to twenty valid characters. There will be no invalid characters in any of the strings. Your program should read to the end of file.

For each input string, you should print the string starting in column 1 immediately followed by exactly one of the following strings.” — is not a palindrome.”
if the string is not a palindrome and is not a mirrored string” — is a regular palindrome.”
if the string is a palindrome and is not a mirrored string

” — is a mirrored string.”
if the string is not a palindrome and is a mirrored string

” — is a mirrored palindrome.”
if the string is a palindrome and is a mirrored string

Note that the output line is to include the -’s and spacing exactly as shown in the table above and demonstrated in the Sample Output below.

In addition, after each output line, you must print an empty line.

NOTAPALINDROME
ISAPALINILAPASI
2A3MEAS
ATOYOTA

NOTAPALINDROME -- is not a palindrome.

ISAPALINILAPASI -- is a regular palindrome.

2A3MEAS -- is a mirrored string.

ATOYOTA -- is a mirrored palindrome.

#include<stdio.h>
#include<string.h>
#define MAX 25
char str[MAX];
char tmp[MAX];
char num[200];
int Ispalindrome(char *str)
{
int len=strlen(str);
char *p,*k;
for(p=str,k=str+len-1;p<=k;p++,k--)
if(*p!=*k) return 0;
return 1;
}
int Ismirror(char *str)
{
int len=strlen(str);
char *p,*k;
strcpy(tmp,str);
for(p=tmp,k=tmp+len-1;p<=k;)
{
if(*p=='0') *p='O';
if(*k=='0') *k='O';
if(num[*p]!=1&&num[*k]!=1&&num[*p]==*k)
{
p++;
k--;
}
else return 0;
}
return 1;
}
int main()
{
memset(num,1,sizeof(num));
num['A']='A';
num['E']='3';
num['H']='H';
num['I']='I';
num['J']='L';
num['L']='J';
num['M']='M';
num['O']='O';
num['S']='2';
num['T']='T';
num['U']='U';
num['V']='V';
num['W']='W';
num['X']='X';
num['Y']='Y';
num['Z']='5';
num['1']='1';
num['2']='S';
num['3']='E';
num['5']='Z';
num['8']='8';
while(~scanf("%s",str))
{
int flag1,flag2;
flag1=Ispalindrome(str);
flag2=Ismirror(str);
if(!flag1&&!flag2)
printf("%s -- is not a palindrome.\n\n",str);
else if(flag1&&!flag2)
printf("%s -- is a regular palindrome.\n\n",str);
else if(!flag1&&flag2)
printf("%s -- is a mirrored string.\n\n",str);
else printf("%s -- is a mirrored palindrome.\n\n",str);
}
return 0;
}

1. 第一句可以忽略不计了吧。从第二句开始分析，说明这个花色下的所有牌都会在其它里面出现，那么还剩下♠和♦。第三句，可以排除2和7，因为在两种花色里有。现在是第四句，因为♠还剩下多个，只有是♦B才能知道答案。


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If (3 + a)(a/10 - 0.4) = -1, then a could be

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If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 06:14
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If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

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Joined: 02 Jul 2017
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 06:26
given (3+a)(a/10−0.4)=−1

=>(3+a)(a−4)=−10 = (-10*1)=(-2*5)

if we try to get (-10*1) => a=7 => 10* 3 ... a=5 => 8*1

try to get (-2*5) => a=2 =>(5)*(-2) answer

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Posts: 2633
Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 07:54
Top Contributor
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

Another approach is to eliminate the fractions/decimals first.

Given: (3 + a)(a/10 - 0.4) = -1
Multiply both sides by 10 to get: (3 + a)(a/10 - 0.4)(10) = (-1)(10)
Simplify: (3 + a)(a - 4) = -10
Expand and simplify: a² - a - 12 = -10
Add 10 to both sides: a² - a - 2 = 0
Factor: (a + 1)(a - 2) = 0

So, EITHER a = -1 OR a = 2

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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 07:57
Top Contributor
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

Alternatively, once you get to the point where you have the equation (3 + a)(a - 4) = -10 [see my post above for how I got there], you could easily plug in the answer choices until you found the one that satisfies the equation (3 + a)(a - 4) = -10

Cheers,
Brent
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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03 Sep 2017, 08:02
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

$$(3 + a)(\frac{a}{10} - 0.4) = -1$$

$$(3 + a)(\frac{a- 4}{10}) = -1$$

$$(3 + a)(a- 4) = -10$$

$$3a -12 + a^2 - 4a = -10$$

$$a^2 - 4a + 3a -12 +10 = 0$$

$$a^2 - a -2 = 0$$

$$(a -2)(a+1) = 0$$

$$a = 2$$ or $$-1$$

Therefore "$$a$$" could be $$2$$

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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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01 Oct 2017, 10:45
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

Hi...

if I want to do it fast and use logic..
$$\frac{a}{10}-0.4=\frac{a-4}{10}$$
so looking at the choices, 3+a should be a factor of 10...
A) so a could be -4 as $$3-4=-1$$ but then the RHS will become positive so discard
B) a as -2 would make 3+a as 1 but $$\frac{a-4}{10}$$ can never be -1
C) a as 1 gives 3+a as $$3+1=4$$.. not a factor of 10.. Discard
D) a as 2 gives 3+a as $$3+2 = 5$$, a factor of 10.. try substituting .. FITs in
E) a as 4 gives $$3+4=7$$... Discard

substitution this way would be way faster than finding solution of a
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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02 Oct 2017, 12:56
Simplifying the equation we get:
(3+a)(a/10-0.4)=-1
(3+a)(a-4)(1/10)=-1
(3+a)(a-4)=-10

Replacing a accoding to the choices:
A. -4 => (3-4)(-4-4) = -1*-8 =8 (Discard)
(...)
D. 2 => (3+2)(2-4) = 5*-2 = -10 (correct)
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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be [#permalink]

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04 Oct 2017, 16:46
Bunuel wrote:
If $$(3 + a)(\frac{a}{10} - 0.4) = -1$$, then a could be

A. -4
B. -2
C. 1
D. 2
E. 4

We can simplify the given equation:

(3 + a)(a/10 - 4/10) = -1

(3 + a)[(a-4)/10] = -1

(3 + a)(a - 4) = -10

a^2 - a - 12 = -10

a^2 - a - 2 = 0

(a - 2)(a + 1) = 0

a = 2 or a = -1

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Re: If (3 + a)(a/10 - 0.4) = -1, then a could be   [#permalink] 04 Oct 2017, 16:46
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text:
# How do you find the derivative of e^(2y)?

Nov 29, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2 x}$ Assuming: $x = {e}^{2 y}$

#### Explanation:

This queston is somewhat ambigious as is does not state the variable which we are to find the derivitive with respect to.

I will assume: $x = {e}^{2 y}$ and that we are seeking $\frac{\mathrm{dy}}{\mathrm{dx}}$

$x = {e}^{2 y}$

$\ln x = 2 y$

$y = \frac{1}{2} \ln x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{2} \cdot \frac{1}{x} = \frac{1}{2 x}$

NB: If the question was intended to be: $\frac{d}{\mathrm{dy}} \left[{e}^{2 y}\right]$ the result would have been: $2 {e}^{2 y}$


text:
## Introducing mrubymix: static require for mruby

Published on:

I've been considering a lot about the "require" problem in Webruby. We know that mruby will not have an official require function. While it is not so hard to write one, we still may not be able to get a consistent API, since all the mrbgems are directly adding modules or classes without needing a require. Personally, I think this makes require useless. What's more, when targeting an embedded system, is it possible that we will always have a dynamic library loading mechanism? I just don't have the answer.

However, we still need a way to organize the source code. Nowadays we cannot assume that anyone is interested in putting all the source code in one file! One way of solving this is to use cat to concatenate all the source files just as what we would do when compiling mruby unit tests. However, there's still one problem: you need to maintain the order of concatanation. A simple cat *.rb > rbcode.rb will not solve the problem since the order may not be what you want, just imagine if you have a zlib library named zlib.rb and many other source files depend on it.

So what we really need here is a utility that can:

1. Combine multiple Ruby source files into one giant file.
2. Maintain a dependency or an order of different files.

I'm not an enthusiast of Rails, but what came to my mind first is the Rails asset pipeline. It solves exactly the same problem, but on JavaScript or CSS files. So can we borrow the ideas from Rails and use it on Webruby, or even mruby?

Here I created a gem(Ruby gem, not mrbgem) called mrubymix. It reads a root source file, or an entrypoint file, then parses and includes all the other source files required by the entrypoint. mrubymix will automatically records the dependency of each file, and only include one source file once, even if it is required by many other file.

Here is an example, supports we have the following entrypoint file, named app.rb:

You may notice that the syntax here we use is the same as Rails asset pipeline. This app.rb file has two depencencies: aaa.rb and ./foo/bar.js. Two simple rules are used here:

• The suffix .rb can be omitted.
• The path of required file is relative to the path of current file

To demostrate how mrubymix resolves multiple dependencies of the same file, suppose aaa.rb contains the following content:

And this is the content of ./foo/bar.rb:

We can run the following command to process app.rb:

The first argument to mrubymix is the path of the entrypoint file, while the second argument is the path of output file. After running this command, the content of out.rb should be:

For each file, mrubymix will first write the full path of the file included as a Ruby comment, then the actual content of the file will be appended. Notice here that all the require lines are removed. What's more, even though the file foo/bar.rb has been required twice, only one is actually inserted, the inserted location is also the earliest one, which is ahead of all depending source files.

For now, this gem is just reinventing wheels of sprockets, which only deals with JavaScript, CoffeeScript and CSS. One idea would be change this gem to use the parsing part of sprockets, this could bring new features such as require_tree, or require_directory, etc. But for now, I can live with this simple implementation.

The build process of Webruby has also been changed to use this small library. Considering the simplicity of building process and the small size of this gem, I just added as a git submodule instead of requiring this gem to be available on your machine. This may provide another reason of maintaining an independent library instead of using sprockets.

I believe this gem is not only helpful for Webruby. Whenever you are using mruby, you need to solve the code organization problem, and this gem can provide an alternative to the regular require way:)