Color ECE 847: Digital Image Processing Stan Birchfield

Color ECE 847: Digital Image Processing Stan Birchfield

Color ECE 847: Digital Image Processing Stan Birchfield Clemson University How it all began S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 An aside Tyrannosaurus

Titanosaurus 50 feet (L) 65 feet (L) Height: 45 feet (of course, juveniles are much smaller) Allosaurus 40 feet (L) American football field: 300 feet x 160 feet

Ark: 450 feet x 75 feet http://www.kickoffzone.com/articles/images/ClemsonMemorialStadium02.jpg http://dinodictionary.com S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Dragons and dinosaurs 1500 BC: Behemoth has tail like a cedar of Lebanon (Job 40) http://www.biblegateway.com/passage/?search=Job+40%3A15-24&version=KJV

255 BC: During First Punic War, Roman General Marcus Atilius Regulus had to kill 120-foot serpent when trying to cross River Bagrada. Its skin was displayed in Rome for 100 years. http://dragon.falbepublishing.com/carthagianserpent.html 1st cent. AD: Dragons in India are always fighting with the elephants. Pliny the Elder, History of Nature, Book 8, Ch. 11 http://penelope.uchicago.edu/holland/pliny8.html

7th cent. AD: The dragon is the largest animal on earth, found in Ethiopia and India. Isidore of Seville, Etymologies, Book 12, 4:4-5 http://pot-pourri.fltr.ucl.ac.be/files/AClassftp/TEXTES/ISIDORUS/Etymologie/B1N8PWGetQy.pdf Soft tissues (proteins) are still present in dinosaur bones http://www.smithsonianmag.com/science-nature/dinosaur.html S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 A brief look at ancient history According to the Bible, 8 people were preserved in the ark

(Noah, his 3 sons, and their wives) They left the ark in approx. 4004 1657 = 2347 B.C. http://en.wikipedia.org/wiki/Short_chronology http://www.livius.org/k/kinglist/sumerian.html Assyrian king list goes back to c. 1800 B.C.

The Babylonian chronicle, After the Flood had swept over and caused the destruction of the earth, list of kings H ET PH JA (Javan)

(Canaan) SHEM HAM (Mizraim) (Madai) (Asshur) Sumerian king list: 385,000 years of kings, Then the Flood swept over.

Then list of kings dating back to c. 2300 B.C. (Gomer) (Tubal) Estimation of absolute dates becomes possible in the 2nd half of the 3rd millennium BC. (c. 2500 B.C.) http://www.livius.org/k/kinglist/assyrian.html

http://www.livius.org/cg-cm/chronicles/cm/lagash.html Uruk chronicle goes back to c. 2100 B.C. http://www.livius.org/cg-cm/chronicles/cm/uruk.html Xia Dynasty of China (first dynasty described in ancient historical records) from c. 2100 B.C. http://en.wikipedia.org/wiki/History_of_China Indus Valley Civilization goes back to c. 2600 B.C. (mature period) http://en.wikipedia.org/wiki/Indus_Valley_Civilization

(Elam) Chinese word for boat: eight (Cush) vessel people S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Now back to color...

Outline Physics and psychology of color Trichromacy Physiology: Spectral Sensitivity Functions (SSFs) Psychology: Color Matching Functions (CMFs) Linear color space transformations Color spaces Primary colors Physics of color Spectral power distribution (SPD) amount of power in each wavelength of light

The relative SPD of two light sources nanometer Measured by spectroradiometer, typically every 5 to 20 nm To make it concrete, we will consider 31 numbers capturing the values in 10 nm bands from 400 700 nm (visible spectrum) http://en.wikipedia.org/wiki/Spectral_power_distribution S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Absorption and reflection of light The color of a surface is the light reflected

Reflection is additive (the more reflected light the brighter) Absorption is subtractive (the more pigments the darker) http://www.specialchem4coatings.com/tc/color-handbook/?id=object S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Physics of color (cont.) Illumination spectra Reflectance spectra

blue skylight tungsten bulb Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Forsyth, 2002 Visible spectrum Physically, the colors are linear: 720 nm 380 nm

electromagnetic (EM) spectrum S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Question Why then does violet look like red mixed with blue? 720 nm 380 nm Red and blue are at extreme ends of the spectrum

Should have the least in common S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Psychology of color Psychologically, the colors are circular: Newton chose 7 colors (ROYGBIV) because 7 is a perfect number 6 colors fits the data better (what is indigo anyway?) This is the famous color wheel S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Color in music De Clarios color music code http://home.vicnet.net.au/~colmusic/clario1.htm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color and moods intense royal, wealthy peaceful,

depressing http://www.infoplease.com/spot/colors1.html attention happy, optimistic calm, natural Goethes color triangle http://www.cs.brown.edu/courses/cs092/VA10/HTML/GoethesTriangleExplanation.html

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Outline Color: Physics vs. Psychology Trichromacy Physiology: Spectral Sensitivity Functions (SSFs) Psychology: Color Matching Functions (CMFs) Linear color space transformations Color spaces Primary colors Trichromacy three colors

Physiology Color sensation in human retina is result of 3 different photoreceptors SSFs Psychology Color perception in human visual system based on 3 primary colors

CMFs Rods and cones Young-Helmholtz theory (early 1800s): Color vision is the result of three different photoreceptors Experimentally confirmed (1960s) by measuring the cone response functions (absorption spectra) Three photoreceptors: S-cones M-cones L-cones (It is better not to call them red-, green-, and blue-cones)

SSFs http://en.wikipedia.org/wiki/Trichromatic_color_vision S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Tetrachromacy At low light levels, rod cells may contribute to color vision Studies suggest that some people may have four cones Some animals have many more than four cones (some shrimp have 11!)

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Tetrachromacy in action? Sharps LE810 television, the first to use RGB-Y quadpixel technology (2010) http://www.technewsdaily.com/addition-of-yellow-pixels-designed-to-make-tvs-better-0230/ S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color matching experiment In the human visual system, every color can be obtained as the linear combination of three independent primary colors

Foundations of Vision, by Brian Wandell, Sinauer Assoc., 1995 Color matching experiment 1 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 1 The primary color amounts needed for a match p1 p2 p3

http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 1 The primary color amounts needed for a match p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 1 The primary color

amounts needed for a match p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 2 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 2

p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 2 p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Color matching experiment 2 We say a negative amount of p2

was needed to make the match, because we added it to the test colors side. p1 p2 p3 The primary color amounts needed for a match: p1 p2 p3

p1 p2 p3 http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Metamer Two colors are metamers if they have different spectral distributions same visual appearance http://escience.anu.edu.au/lecture/cg/Color/Image/metamer.gif Color matching functions Select 3 primary lights For each wavelength , find the amounts e1, e2, e3 of the primaries

needed to match spectral signal t() These yield the CMFs color matching functions (CMFs) for those primaries Store in 3x31 matrix Note the negative dip S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color matching functions CMFs allow us to transform between color spaces (more later) Why is this important?

Want to paint a logo on a product with the correct shade of color Want color to look the same no matter which monitor, inkjet printer, laser printer, etc. S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Grassmans Laws Color matching is (approximately) linear Principle of superposition: If then

This makes math much simpler (later) But not true at extreme ends of measurements S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Do two people see the same color? Yes! In the following sense: They will choose the same weights for the three primaries to match the color (Modulo color-blindness) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Luminous efficiency Another color matching experiment Whether one color is brighter or darker than another Goal Obtain a luminous efficiency function (LEF) Experimental environment photopic vision: Daytime (high intensity levels), cones dominate scotopic vision: Nighttime (low-light situation), rods dominate

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Luminous efficiency (cont.) Scotopic Photopic Purkinje shift Photopic LEF (solid black) M-cone SSF (solid green) Combination of the cone SSFs (green circles) 1931 CIE XYZ space (dashed

magenta) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Luminous efficiency (cont.) The photopic LEF a weighted combination of the cone SSFs M-cones dominate weights The photopic LEF

The cone SSFs S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Outline Color: Physics vs. Psychology Trichromacy Physiology: Spectral Sensitivity Functions (SSFs) Psychology: Color Matching Functions (CMFs) Linear color space transformations Color spaces Primary colors

Sensing light Output of a single photoreceptor: wavelength SSF of the sensor (spectral sensitivity function) SPD of the incident irradiance (spectral power distribution) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Sensing light (cont.) Discrete approximation:

v = sT t SSF of the sensor (spectral sensitivity function) 311 vector SPD of the incident irradiance (spectral power distribution) 311 vector (wavelength is used to index the elements of the vectors) Recall: 31 numbers capture the values in 10 nm bands from 400 700 nm (visible spectrum) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Sensing three colors cone SSFs Three cone types: S-cones (blue) M-cones (green) L-cones (red) Projection from a point in a 31D space to a 3D space 331 matrix 311 vector

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color matching Grassmans Laws: Three primaries (independent) Test light ( )

the colors match = the SPDs are metamers Color matching is (approximately) linear! S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color matching (cont.) The linear function for modeling color matching is the SPD of the test light Intensities of the three primaries

The rows are the color matching functions (CMFs) of the three primaries Do not confuse the CMF C with the SSF S v = St are the cone values; e = Ct are the primary intensities S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color matching functions (CMFs) CMFs using RGB primaries (solid lines) Overlaid circles obtained by a 3x3 linear

transform of cone SSFs (close agreement) CMFs using 1931 CIE XYZ primaries Related exactly by a 3 x 3 transform S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Transforming between color spaces Recall: Match the same test light using two different sets of primaries: Test light 31 x 1

CMFs 3 x 31 The resulting SPDs are Intensities of the three primaries 3 x 1 and set of primaries 31 x 3 (each column is SPD of a primary light) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Transforming between color spaces From previous slide: For both cases, the resulting SPD looks identical to the test light These are metamers (could use C or C here does not matter) }

(since prev eqn is true for all t) or } 3x3 transform between color spaces (by substituting from above) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Transforming between color spaces CMFs differ according to the primaries used

One color space Another color space 33 transformation matrix between two color spaces http://groups.csail.mit.edu/graphics/classes/CompPhoto06/html/lecturenotes/Color.ppt Transforming between color spaces Given two sets of primaries, P and P Measure color matching functions C and C Solve C=FC for the 3x3 matrix F=CP

F now converts between tristimulus values: e = Fe Note that we dont need P and P once we have C and C S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Outline Color: Physics vs. Psychology Trichromacy Physiology: Spectral Sensitivity Functions (SSFs) Psychology: Color Matching Functions (CMFs) Color space transformations Color spaces

Primary colors CIE color space The most important color space of all CIE XYZ tristimulus coordinate system proposed in 1931 Advantages Non-negative everywhere The middle coordinate (Y) approximates the photopic luminous efficiency function (LEF) Note that the CIE XYZ primaries are not physically realizable

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 CIE 1931 standard colorimetric observer (2o) Commission internationale de l'clairage (CIE) Used primaries: Red: 700 nm Green: 546.1 nm Blue: 435.8 nm

2o standard observer Now considered out of date, but still widely used 1964 supplementary standard colorimetric observer (10 o) Procedure: Show pure color to observer Match using primaries weights for RGB Linear transform from RGB to XYZ (XYZ are imaginary primaries; in XYZ, all weights are positive) (using NTSC primaries) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

CIE XYZ is used as reference The CMFs of CIE XYZ are related to any other CMFs by a 3x3 matrix CMFs for CIE XYZ CMFs of any other linear color space 3x3 matrix relates the CMFs n CMFs require n2 transformations But with CIE, only require n

transformations (like Esperanto) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 CIE Chromaticity diagram Normalize: x = X / (X+Y+Z) y = Y / (X+Y+Z) z=1xy spectral locus gamut of device is convex hull

of primaries line of purples Note: It is misleading to draw colors on the chromaticity diagram (not recommended), but it makes the slide pretty S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 CIE Chromaticity diagram C Natural encoding of color for perception: hue

(dominant wavelength) saturation B G M Y R (distance from white point)

value (height out of plane) Notice similarity to color wheel S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 CIE Chromaticity diagram With 3 fixed primaries, any color can be matched (allowing negative weights)

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 CIE Chromaticity diagram But with just 2 primaries, any color can also be matched (if the primaries can be moved) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 CIE Chromaticity diagram

Complementary colors are on opposite sides S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces RGB B orthogonal axes usually 8 bits each (0 255)

natural for capture and display H/W (cameras, monitors) G R CCIR Rec. 601 was used for television (0.299 0.587 0.114) CCIR Rec. 709 defines RGB for HDTV and is used by all modern devices (0.2125 0.7154 0.0721) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces

Turn the RGB cube on its side Hexagon border is color wheel white / black are out of page C G B C

B G M Y Y M R http://viz.aset.psu.edu/gho/sem_notes/color_2d/html/primary_systems.html

S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 R Color spaces This is HLS (hue lightness saturation) C B G M

Y R http://viz.aset.psu.edu/gho/sem_notes/color_2d/html/primary_systems.html S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces Rescale HLS to get HSV (hue saturation value) Also called HSI How would you describe a color?

dominant wavelength (hue) purity (saturation) brightness (value) Transformation RGB HSV is nonlinear http://viz.aset.psu.edu/gho/sem_notes/color_2d/html/primary_systems.html S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces YCbCr color differences Y is luma component Cb is blue chroma component

Cr is red chroma component YUV is not well defined Usually YUV means scaled version of YCbCr For CCIR Rec. 601, (LumaRed, LumaGreen, LumaBlue) = (0.299 0.587 0.114) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces American analog television transmission (NTSC) uses YIQ color space: originally black-and-white television (only Y) IQ added later, modulated on top of Y for backward

compatibility European joke: Never twice the same color S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces We have already seen CIE xyz Based on a direct graph of the original X, Y and Z tristimulus functions Problem: Too much space is allocated to greens

http://www.cambridgeincolour.com/tutorials/color-spaces.htm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces Ask subject to match test color All matches fall within ellipse on chromaticity diagram These are MacAdam ellipses They capture just noticeable difference Note: Color differences dont make sense for large distances Is red more like

green or blue? http://en.wikipedia.org/wiki/MacAdam_ellipse S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces Solution: CIE Luv Perceptually uniform space Colors are distributed proportional to their perceived color difference http://www.cambridgeincolour.com/tutorials/color-spaces.htm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Color spaces CIE La*b* (1976) transforms the colors so that they extend equally on two axes Color space is now a square Each axis represents an easily recognizable property of color: red-green blend blue-red blend blue-green blend http://www.cambridgeincolour.com/tutorials/color-spaces.htm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Intl Color Consortium (ICC) ICC established in 1993 to create an open, standardized color management system Now used in most computers Systems involves three key concepts: color profiles color spaces translation between color spaces http://www.cambridgeincolour.com/tutorials/color-management1.htm S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 One final color space So far, we have been assuming

additive colors (light) Now let us consider subtractive colors (pigments) Pigments work similarly but are highly nonlinear S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color spaces CMYK is used for printers Subtractive color Black (K) is separate because it is very difficult to get good black by mixing other colors

In theory, But in practice much more complicated S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Color space Converting between RGB and CMY S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Gamut Recall: gamut is the range of colors

that a device can display Monitors gamut is triangle, because additive colors (light) follow Grassmans laws More complicated for printers, film http://www.cse.fau.edu/~maria/COURSES/COP4930-GS/ColorFigs/Mvc-061s.jpg http://www.imaging-resource.com/PRINT/PPM200/PPM200vsP400.gif S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Paint mixing This is why paint stores use many

more than three paints for mixing (~12) http://whites-autorepair.com/images/paintmixroom.jpg http://www.albert-tague.com/inc/colour-mixer2.jpg S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Additive and Subtractive Colors additive RGB subtractive

(but pigments are nonlinear) CMY Note: Order of colors is the same in both cases S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Outline Color: Physics vs. Psychology Trichromacy Physiology: Spectral Sensitivity Functions (SSFs) Psychology: Color Matching Functions (CMFs)

Linear color space transformations Color spaces Primary colors This leads us to an important question What are the primary colors? As children, we learn RYB Then were told RGB When asked about the discrepancy, were told CMY is the same as RYB S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Something about this is unsettling Yellow still appears to be pure Even when you know that green and red make yellow, It is impossible to believe In fact, red, yellow, blue, and green all appear pure So do black and white Could there be six primary colors? S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Limitations of component theories So far we have discussed component theories of color Component theories are unsatisfying because they do not describe our subjective experience well Psychologically, violet looks like a combination of red and blue yellow does not look like a combination of red and green black and white do not look like combinations of other colors S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Opponent colors http://en.wikipedia.org/wiki/Opponent_process S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Both are true Controversy raged for decades between component theory (Young-Helmholtz) opponent color theory (Hering) Both are true: three photoreceptors provide components (Experimentally confirmed by Svaetichin in 1956)

later cells transform to opponent color space (Experimentally verified by Hurvich and Jameson in 1957) (Ballard and Brown) S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847 Final thought Piet Mondrian, Composition with Yellow, Blue, and Red, 1921 http://en.wikipedia.org/wiki/Piet_Mondrian S. Birchfield, Clemson Univ., ECE 847, http://www.ces.clemson.edu/~stb/ece847

Recently Viewed Presentations

  • Health Insurance Portability and Accountability Act HIPAA 101

    Health Insurance Portability and Accountability Act HIPAA 101

    Anastasia Baker Hurn, Legal Counsel New County Officer's School January 23, 2003 Iowa State Association of Counties HIPAA - Purpose The Health Insurance Portability and Accountability Act was passed in 1996 to "improve the portability and continuity of health insurance...
  • Political Party Project - Mesa Public Schools

    Political Party Project - Mesa Public Schools

    POLITICAL PARTY PROJECT TIPS-Use the party's official website ("About Us", "History") & other reliable internet sites -When researching, created a bulleted list of important events in the party's history, major successes, important leaders, etc. **Use your research to write a...
  • 1) According to the text, a key aspect of personality is its ...

    1) According to the text, a key aspect of personality is its ...

    1) According to the text, a key aspect of personality is its _____ quality. Unique. Ever-changing. Situationally-determined. Continuous. Invariant
  • Osha hazard communication update

    Osha hazard communication update

    Major Changes. Hazard Classification. Labels. Safety Data Sheets. Information and Training. Hazard Classification. Provides specific criteria for classification of health and physical hazards, as well as classification of mixtures
  • Metabolic and Electrical Oscillations: Partners in ...

    Metabolic and Electrical Oscillations: Partners in ...

    Calcium oscillator controls fast bursting Ca2+ K(Ca) channels Metabolic oscillator controls slower oscillation ATP K(ATP) channels Metabolic Oscillations Can Occur Through Oscillations in Glycolysis Dano et al., Nature, 402:320-322, 1999 Glycolytic oscillations in yeast Modeling Approach Cells within an islet...
  • Analysis Methods for Mixed-Criticality Applications on ...

    Analysis Methods for Mixed-Criticality Applications on ...

    Analysis Methods for Mixed-Criticality Applications on TTEthernet-based Distributed Architectures. ... System model . ... Analysis Methods for Mixed-Criticality Applications on TTEthernet-based Distributed Architectures
  • WELCOME TO 5TH GRADE - Loudoun County Public Schools

    WELCOME TO 5TH GRADE - Loudoun County Public Schools

    MA from University of Missouri Kansas City. Taught in OK, FL, MO, and KS. ... Reading, Math and Science SOL assessments in May. Science will consist of 4thand 5th grade concepts. In lieu of a Writing SOL, we will have...
  • R4BP 3 - Europa

    R4BP 3 - Europa

    R4BP 3.11 and SPC editor 2.2 . Compare SPC files. Compare meta SPC and member products. e-mail notifications for authorities + Can be made by Authority user. Allows to create/edit/delete the contact. Email will be sent to concerned CA and...