Fractional oxyhemoglobin is the oxyhemoglobin concentration divided by the concentration of all measured hemoglobin species in the same blood sample. With $H_O,H_D,H_C,H_M$ denoting oxyhemoglobin, deoxyhemoglobin, carboxyhemoglobin and methemoglobin concentrations, respectively,Additional measured hemoglobin species belong in the denominator when present. Functional oxygen saturation instead uses $H_O/(H_O+H_D)$. The distinction is the denominator, not whether the result is written as a fraction or a percentage.^[ref]

For a constructed mixture with concentrations proportional to $85,5,10,0$, respectively, fractional oxyhemoglobin is $85\%$, while functional oxygen saturation is $85/90\approx 94.4\%$. The second number excludes the carboxyhemoglobin from its denominator; it has not created additional oxygen-carrying oxyhemoglobin.

This distinction matters when converting hemoglobin measurements into arterial oxygen content. If $H$ is total hemoglobin concentration and $\beta$ is a stipulated oxygen-binding capacity per unit hemoglobin mass, the bound-oxygen term is $\beta H{F}_{{\mathrm{O}}_2\mathrm{Hb}}$. Choosing $H=15$ g/dL and $\beta =1.34$ mL/g in the example gives $17.085$ mL of bound oxygen per dL of blood. Substituting $85/90$ instead would give about $18.98$ mL/dL. This calculation isolates the denominator error; dissolved oxygen is a separate contribution. A measurement of oxygen saturation alone therefore does not determine total blood oxygen content.

Functional oxygen saturation is the fraction of the sum of oxyhemoglobin and deoxyhemoglobin that is present as oxyhemoglobin:Here $H_O$ and $H_D$ are the corresponding concentrations in the same blood sample. Carboxyhemoglobin and methemoglobin are excluded from this denominator. Fractional oxyhemoglobin instead divides by the total concentration of measured hemoglobin species.^[ref]

A constructed example shows what the exclusion does. If a sample contains 90 concentration units of oxyhemoglobin, 10 of deoxyhemoglobin and 25 of carboxyhemoglobin, its functional oxygen saturation is $90/(90+10)=0.90$. Its fractional oxyhemoglobin is $90/125=0.72$. Both values describe the same mixture, with different reference populations.

If $d$ denotes the fraction of total hemoglobin excluded from the functional denominator, thenThus knowing only $s_{{\mathrm{O}}_2}$ does not determine the oxygenated fraction of total hemoglobin unless $d$ is also known or negligible. In the example, $d=25/125=0.20$ and $0.90(1-0.20)=0.72$.

The distinction has an experimental consequence for co-oximetry. Optical analysis must distinguish the absorbing hemoglobin derivatives before calculating the desired ratio; changing the denominator of the displayed result does not change the blood sample. Total oxygen content additionally requires hemoglobin concentration and the dissolved oxygen contribution. Hemoglobin-concentration and saturation separation therefore remains necessary even when functional oxygen saturation has been measured accurately.

Hemoglobin-concentration and saturation separation is the distinction between how much hemoglobin a volume of blood contains and what fraction of its available oxygen-binding capacity is occupied. Oxygen saturation is a ratio; hemoglobin concentration is an amount per volume. Neither quantity alone specifies arterial oxygen content.

Let $H$ be total hemoglobin concentration, $F$ the fractional oxyhemoglobin and $\beta$ a chosen oxygen capacity per unit hemoglobin mass. A simple content model iswhere the final term represents dissolved oxygen using a solubility coefficient $\alpha$ and oxygen partial pressure $p_{{\mathrm{O}}_2}$. The model separates carrier amount, carrier occupancy and dissolved gas. Functional oxygen saturation can replace $F$ only when the excluded hemoglobin species are negligible or separately accounted for.^[ref][ref]

For an original comparison, neglect dissolved oxygen and stipulate $\beta =1.34$ mL/g and $F=0.98$. Samples with $H=15$ and $H=8$ g/dL then carry about $19.70$ and $10.51$ mL of bound oxygen per dL, respectively. The equal oxygen saturation does not imply equal oxygen content. Conversely, halving $H$ and doubling $F$ preserves the product $HF$ only while the new fraction remains physically attainable.

A primary instrument illustrates how the distinction can be measured rather than merely defined. In 1989, a capillary-tube oximeter used red and infrared light, a detector and digitized processing to derive hemoglobin concentration and oxygen saturation separately.^[ref] Measurements sensitive to different optical features supply information that one saturation number cannot contain. At fixed blood flow, oxygen delivery scales with content; equal saturation readings alone cannot establish equal delivery.

A total synthesis constructs a target compound from simpler starting materials through a planned sequence of chemical reactions. For a complex target, success includes the required connectivity and stereochemistry, not merely the elemental formula or an approximate mass.

Tropinone provides a classic strategic example: compatible small precursors can assemble a bridged framework through a coordinated sequence, rather than making every ring separately.^[ref] A route's value also depends on selectivity, yield, operational reliability and how easily structural identity can be established. “Total” does not require that every carbon atom begin as an element.

A gonad is an organ producing germ cells and usually reproductive hormones. The testis and ovary are familiar examples. Gamete production, hormone secretion and transport through accessory ducts are related functions but need not occur in the same cell population.

Angular resampling converts a signal recorded at known times into values at equally spaced shaft angles. It is a change of sampling coordinate, used in order tracking and time-synchronous averaging. The signal must be accompanied by a reliable monotonic angle history over the interval being transformed.^[ref]

For positive speed $r(t)$ in revolutions per minute, an unwrapped reference angle isChoose ${\theta }_j={\theta }_0+j\Delta \theta$, find times $t_j$ satisfying $\theta (t_j)={\theta }_j$, and estimate $x(t_j)$ by interpolation from the original samples. Uniform time samples generally produce nonuniform angle samples; evaluating at the new $t_j$ is the resampling step. A modulo-$2\pi$ angle must first be unwrapped, rather than inverted as if each revolution restarted time.

An original acceleration model has $r(t)=600+600t$ revolutions per minute, with $t$ in seconds. Taking ${\theta }_0=0$ givesSampling every quarter revolution requires $10t_j+5t_j^2=j/4$, henceThe first quarter-turn intervals are about 0.02470 and 0.02411 seconds: angular spacing stays fixed while time spacing decreases. A third-order sinusoid becomes a fixed sinusoid of three cycles per revolution on the resampled coordinate.

With $N$ equally spaced samples per revolution, the angular Nyquist limit is $N/2$ cycles per revolution. Thus representing a maximum order $q_{\max }$ requires more than $2q_{\max }$ angular samples per turn, with practical margin and appropriate filtering. This does not repair aliasing already present in the original time record. Its sampling rate, anti-aliasing filter and the fastest physical signal frequency also matter.

A once-per-revolution tachometer constrains completed turns but does not directly measure every speed fluctuation within a turn. Inferring the intermediate angle introduces a model; a higher-resolution rotary encoder can supply more information. Stops, reversals, missing pulses and timing offsets need explicit handling. Resampling an uncertain angle history can produce a sharp-looking spectrum without making that angle history accurate.

A rotational order expresses a signal’s frequency relative to a specified reference shaft’s rotational frequency:Thus $q=1$ means one oscillation per reference revolution and $q=1/2$ means one oscillation per two reference revolutions. A rotational order is dimensionless and need not be an integer. It is especially useful when a machine changes speed: a shaft-synchronous feature can keep the same rotational order while moving through many frequencies in an ordinary frequency spectrum.^[ref]

The reference is essential. Suppose shaft A turns at $600\mathrm{rpm}=10\mathrm{Hz}$ and shaft B at $1500\mathrm{rpm}=25\mathrm{Hz}$. The same $100\mathrm{Hz}$ signal has rotational order $10$ relative to A and $4$ relative to B. Changing the reference has changed the dimensionless label, not the measured vibration. Likewise, a 24-tooth gear turning at $900\mathrm{rpm}$ has a gear mesh frequency of $24\times 15=360\mathrm{Hz}$. Its mating 8-tooth gear turns at $2700\mathrm{rpm}$, giving the same gear mesh frequency but rotational orders $24$ and $8$ relative to the two shafts.

For a component with unwrapped phase $\varphi (t)$ and reference angle $\theta (t)$, the instantaneous version iswhere the reference angular velocity is nonzero and both angles use the same units. A constant rotational order gives $\varphi (t)=q\theta (t)+{\varphi }_0$. This explains why angular resampling makes a speed-following component periodic as a function of shaft angle. A vibration fixed at $100\mathrm{Hz}$ instead changes from rotational order $10$ to $5$ when the reference shaft accelerates from $600$ to $1200\mathrm{rpm}$.

An order tracking measurement therefore pairs a vibration sensor, such as an accelerometer, with a shaft-angle or speed reference, such as a tachometer. An order peak identifies a speed relationship; it does not by itself establish which part is damaged. A resonance can greatly change the amplitude as speed changes even when the excitation’s rotational order stays fixed.

Image contrast measures how distinguishable image intensities are under a stated definition. For a periodic bright-dark pattern, Michelson contrast is $(I_{\max }-I_{\min })/(I_{\max }+I_{\min })$. For a small feature on a uniform background, a relative difference from that background is often more informative.

A high-contrast image can still have poor spatial resolution, and a finely resolved feature can be difficult to detect if noise masks its intensity difference. Illumination, background, optical blur, detector response and display scaling all affect measured contrast. Choosing a formula should follow the imaging task.

Photonics studies and engineers the generation, transport, manipulation and detection of light. A photonic system may combine a laser, optical waveguides, modulators and photodetectors to carry information or measure a physical quantity.

An optical communication link illustrates the chain: a source produces light, a modulator encodes a signal, a waveguide transports it, and a detector converts received photons into an electrical response. Wavelength, polarization and phase can provide different information channels. Loss and detector noise determine how much of the encoded information is recoverable, so moving a signal optically does not remove the need for a quantitative signal model.

Plasmonics studies and uses the coupling of electromagnetic waves with collective electron motion, especially at material surfaces and in small metallic structures. A surface plasmon polariton propagates along an interface while its field decays away from it; a localized surface plasmon resonance confines an oscillating response near a finite structure. Such modes can concentrate fields on scales smaller than the free-space wavelength.

For an ideal flat interface between a lossless metal of relative permittivity ${\epsilon }_m$ and a dielectric of relative permittivity ${\epsilon }_d$, the bound transverse-magnetic mode hasWith ${\epsilon }_d>0$ and ${\epsilon }_m<-{\epsilon }_d$, its parallel wave number exceeds that of a propagating wave in the dielectric. This explains why direct illumination of a perfectly flat interface needs additional momentum coupling. A grating or nearby optical field can supply that coupling. Real metals have loss: stronger confinement does not automatically imply long propagation distances.

A striking experiment used periodic arrays of tiny holes in metal films. In 1998, T. W. Ebbesen and colleagues reported transmission peaks at wavelengths much larger than individual hole diameters. One silver sample had 150-nanometre holes, 900-nanometre spacing and 200-nanometre film thickness. A spectrophotometer measured the transmitted beam, and angle-dependent spectra supported coupling to surface electronic excitations. Efficiency normalized to hole area could exceed one; this compares with the small open area, not with all incident power.^[ref]

Optical heterodyne detection combines a signal field with a reference field at a different frequency, producing an electrical beat within a receiver's bandwidth. The reference is a local oscillator. A photodetector responds to the squared sum of the fields; averaging over optical carrier cycles removes the fast sum-frequency term but can retain the difference-frequency interference.

For constant powers $P_s,P_{\mathrm{LO}}$ incident on a linear detector of responsivity $R$, a useful model isThe mode-overlap factor in optical heterodyne detection satisfies $|\gamma |\le 1$ and includes spatial and polarization matching. The beat frequency is $|{\nu }_s-{\nu }_{\mathrm{LO}}|$, while its phase carries a relative optical wave phase. Orthogonal polarizations can give $\gamma =0$ and no beat despite nonzero power from both sources.

For an original chosen $P_s=1\mathrm{nW}$, $P_{\mathrm{LO}}=1\mathrm{mW}$, $R=0.50A/W$ and $|\gamma |=1$, the beat's peak current is $1.0\mu \mathrm{A}$. The signal alone produces only $0.50\mathrm{nA}$ of current, but the mixed DC level is about $0.50\mathrm{mA}$. A chosen frequency difference of $10\mathrm{MHz}$ is measurable electronically even though each carrier has an optical frequency. Increasing the reference also increases its noise and can overload the receiver; beat amplitude is not an unlimited sensitivity gain.

NIST's physical receiver-characterization experiment combined an external-cavity semiconductor laser and a Nd:YAG laser near $1319\mathrm{nm}$. Variable attenuators, a beam splitter, a polarizer and single-mode fibre controlled the powers and matched the modes before the receiver. Sweeping the optical frequency difference generated a tunable test modulation.^[ref]

The receiver must pass the beat frequency and preserve the intended overlap. A single real beat frequency supplies the magnitude of the frequency difference; identifying which optical frequency is higher needs additional information. At zero difference, the corresponding fixed-phase measurement is optical homodyne detection.

Tesseract is an open-source engine for optical character recognition. It combines image analysis with trained recognition data to extract text from images. Its documentation describes a command-line interface and a programming interface, with recognition data for different writing systems. A language choice affects the model used; it does not translate the recognized text.^[ref]

For example, the documented command tesseract scan.png result -l eng reads an image, selects English recognition data and writes text to result.txt. The output basename is result, so the filename extension is supplied by the selected output format. Adding pdf requests a PDF containing the page image and a searchable text layer. If recognition confuses a letter in the image, searching that text layer can still miss the intended word.^[ref]

The architecture has changed over its history. Ray Smith's 2007 paper describes an engine that groups connected image outlines into lines and words, then recognizes them in successive passes. Version 4 introduced recognition based on long short-term memory neural networks; the 5.x manual documents this engine alongside the legacy option.^[ref][ref]

A useful test compares output with a checked transcription using character error rate, while also inspecting omitted regions and reading order. Recognition accuracy depends on image quality, layout and matching language data. Installing the engine alone does not establish the accuracy of a particular scanned collection.

The character error rate measures disagreement between recognized text and a reference transcription using edit distance. With unit-cost insertions $I$, deletions $D$ and substitutions $S$ in a minimum-cost alignment, and $N$ reference characters, the reference-length convention isThe alignment matters: counting mismatched positions without allowing edits can exaggerate the effect of one omitted character. This convention is used to evaluate optical character recognition against a specified transcription.^[ref]

For reference cat and recognized cut, one substitution gives $\mathrm{CER}=1/3$. For reference a and recognized aaaa, three insertions give $\mathrm{CER}=3$, or $300\%$. The second result is valid: under this denominator, character error rate is not bounded by one. Clipping the result or using the longer string as denominator defines a different metric.^[ref]

Aggregation also changes the question. Suppose one one-character sample has one error and a hundred-character sample has none. The unweighted mean of their two rates is $50\%$, while pooling edits and reference lengths gives $1/101\approx 0.99\%$. Reporting the aggregation rule prevents a short, difficult sample from being confused with a large fraction of the complete text.

The definition of character must be fixed too. Unicode code points and user-perceived grapheme clusters can give different lengths; Unicode normalization, spaces and punctuation can change both the alignment and its denominator. An empty reference needs an explicit convention because the displayed formula divides by zero. A score is meaningful only together with these evaluation choices.

An adaptive classifier updates its decision rule or parameters using information acquired while processing further data. In statistical classification, this can specialize an initially broad model to the conditions of a particular stream or document. The update may use supplied labels or examples accepted under a stated trust rule; adaptation is not evidence that every accepted label is correct.

In the 2007 description of Tesseract, satisfactory first-pass words provide examples for a more document-sensitive classifier. The paper motivates this by the limited collection of fonts within a document and describes normalization differences between static and adaptive classification. It explicitly does not describe the adaptive classifier as a simple template matcher.^[ref]

A separate toy calculation illustrates parameter adaptation without claiming to reproduce that implementation. Suppose a class is represented by the mean $\mu$ of one measured feature from $n$ trusted examples. Accepting another value $x$ givesWith $n=4$, $\mu =10$ and $x=12$, the updated mean is $10.4$. A classifier using that class mean can change its later decisions as a result.

The trust rule matters as much as the arithmetic. If a wrong prediction is accepted as a label, its update can make related wrong predictions more likely. A confidence score can help select examples, but a numerical score is not automatically a calibrated probability of correctness. A useful evaluation compares a frozen baseline and the adaptive system on checked data, including the possibility of degradation as well as improvement.

Character segmentation separates an image of text into regions or hypotheses associated with individual characters. It is a specialized image segmentation problem within optical character recognition. The useful boundaries depend on the writing and imaging process: visible connected ink regions need not correspond one-to-one with characters.^[ref]

For example, the dot and stem of a lowercase i can be disconnected regions belonging to one character. Two touching characters can instead form a single connected region. Connected-component labeling can locate connected regions, but counting those regions alone therefore cannot reliably count the characters.

A recognizer can compare alternative splits and merges. A degraded image of rn may admit one merged-region interpretation as m and a two-character interpretation as r followed by n. The choice depends on shape evidence, spacing and recognition context. Incorrectly committing to one region per character too early can make the correct word unavailable to later stages.

The historical Tesseract engine described by Ray Smith tests cuts when word recognition is unsatisfactory and can also associate broken pieces. Recognition thus supplies feedback about segmentation hypotheses, rather than merely accepting a fixed partition.^[ref]

Character segmentation should be evaluated separately from simply matching the final text. A boundary error can cause several character edits, while a correct boundary can still receive the wrong label. Character error rate measures the resulting transcription disagreement; it does not by itself identify which stage caused it.

Pamela M. Pollock and colleagues, Nature Genetics 33(1), 19–20, January 2003; first online 25 November 2002. DOI 10.1038/ng1054. Abstract: mutation analysis of microdissected samples found the substitution labeled V599E in the original paper in 63 of 77 nevi; the authors distinguish an initiating pathway alteration from sufficient evidence for melanoma tumorigenesis.

Original byline: Judah Folkman, Ezio Merler, Charles Abernathy and Gretchen Williams. Journal of Experimental Medicine 133(2), 275–288 (1971), DOI 10.1084/jem.133.2.275; PMID 4332371. Printed p. 275 describes new-vessel outgrowth near membrane chambers containing tumor cells in rat dorsal air sacs, motivating a diffusible-factor interpretation; the abstract reports an angiogenic tumor-derived fraction. Publisher PDF: rupress.org/jem/article-pdf/133/2/275/1084025/275.pdf . The historical fraction is not equated with a single modern chemically defined growth factor.

Additional verified locator: printed p. 279, Biological Assay of TAF and Reading the Air Sac Assay; Figures 1–4. The modified rat dorsal air sac assay used a membrane wick over holes in silicone tubing to deliver tumour fractions, read after 48 hours under a stereoscope at 20×, followed by histological sections. Vascular proliferation was graded 0–5+. Figure 2 shows a negative wick control; Figures 3–4 show positive responses. This biological activity scale is not an absolute endothelial cell count. Primary full-text indexed view: pmc.ncbi.nlm.nih.gov/articles/PMC2138906/ .

Primary article by Judah Folkman, New England Journal of Medicine 285, 1182–1186, November 18, 1971; DOI 10.1056/NEJM197111182852108. Publisher preview identifies the author and Department of Surgery, Children’s Hospital Medical Center and Harvard Medical School. The article frames tumor cells and capillary endothelial cells as interacting populations and proposes therapeutic implications of angiogenesis dependence.