text:
Excitation Spectrum Of Water

It measures two fluorescence spectra excited sequentially by lasers at 263 nm and 351 nm, from single atmospheric aerosol particles in the 1-10 μm diameter size range. L11-2 Lab 11 Atomic Spectra OVERVIEW Light is an electromagnetic wave, its color is determined by its wavelength. In the field studies the fluorescence excitation spectra were measured continuously in a flow-through mode. com SpectraMax® i3 Multi-ModeDetectionPlatform withtheSpectraMax® MiniMax™ImagingCytometer UserGuide 5025027A April2013. CBD American Shaman’s ultra concentrated terpene rich hemp oil is made from industrial hemp, a type of cannabis plant. If the wavelength of the exciting light is changed and the emission from the sample plotted against the wavelength of exciting light, the result is known as the excitation spectrum. The absorption of electromagnetic radiation by water depends on the state of the water. For imidazole and imidazolium the Raman intensities observed with visible wavelength excitation derive mainly from states in the far- UV. , the diatomic hydrogen molecule H$_2$) have no permanent electric dipole moment, but many asymmetric molecules (e. In consequence, it will be interesting to assay the 2-aminobenzimidazole (2-AB) which is a photoproduct of MBC in water [7]. Previous scientific papers suggest that we can classify phytoplankton groups using the excitation spectra [3, 4]. Phosphorescence refers to the release of light that lasts longer – seconds or even hours after the excitation has stopped. The red light from a He-Ne laser has a wavelength of 632. 15 In other words, AmB exhibits a band with a vibronic structure around 400 nm (peaks at 416, 391, 372, 352 nm) and a weak CD similar in shape to the absorption spectrum. AAT Bioquest's interactive Spectrum Viewer is a powerful tool for analysis and comparison of excitation/emission spectra of commonly used fluorophores. Initially, SL gave a wide excitation band ranging from 250 to520 nm. The wavelength selector not being scanned must be removed or set to zero order. H2SO4 in a100 mL volumetric flask. Introduction. Detailed knowledge of the two-photon excitation spectra of molecular ﬂuorophores is required for de-. , the diatomic hydrogen molecule H$_2$) have no permanent electric dipole moment, but many asymmetric molecules (e. For the visible spectrum the stock solution was diluted 1: 50. excitation without contact, laser excitation efficiently measures vibrations in a high -frequency zone. excitation, since no real states are involved in this interaction mechanism. all dye families tested. Fluorescence excitation spectrum * An X,Y plot of excitation wavelength versus number of fluorescence photons generated by a fluorophore. The emission was wavelength scanned in the desired region. Generation of. 32, 3531 (1993)). Three-photon action spectra of GCaMP6f, and the absorption coefficient of water (H2O data from Kou, et. For discrete data, Riemann summation is used to quantify. A plot of emission against wavelength for any given excitation wavelength is known as the emission spectrum. Typically, earthquake excitation frequencies ofconcern will fiIll between 2 or3 Hzup to25 or 30 Hz, with the peak ranges generally between 4 and 10Hz,depending on the sub-soil conditions atthe particular site. that the presence of atmospheric water vapor and carbonic acid (referring to carbon dioxide) were the most significant contributors to the re-reflection of solar radiation. Science , this issue p. 1 at the wavelength of excitation to achieve uniform. How do the sensitivities compare?. Figure 1: White Sea sample 5 fluorescence spectrum under excitation at 270 nm. 5 ms rectangular soft pulses used in the WATERGATE blocks in order to retain some excitation of the anomeric signals close to the water. 2 ×10-2Å for the 250 nm excitation A precision of 1 cm-1 6. In fact, the Raman spectrum generally does not depend on the laser excitation. In 1881, the German plant physiologist T. spectra 13, 14) is applied for the first time to excitation spectra, in order to account for absorption effects and re-construct the excitation profiles. Of the six transitions outlined, only the two lowest energy ones (left-most, colored blue) are achieved by the energies available in the 200 to 800 nm spectrum. The PL peak shifts to longer wavelength as the excitation wavelength gradually increases (Fig. The excitation spectra of different dyes may largely overlap. Harilal,a) S. Bag Filters. Disinfection by-products Introduction A major issue of water quality management is to identify appropriate parameters for rapid and cost-effective monitor-ing of water. DC Plasma Excitation Direct current generators from TRUMPF Hüttinger are classics when it comes to DC plasma excitation. The excitation filter spectrum (Figure 4(a); red curve) exhibits a high level of transmission (approximately 80 percent) between 460 and 500 nanometers for excitation of fluorophores such as green fluorescent protein or fluorescein. The Gender Spectrum Collection is a stock photo library featuring images of trans and non-binary models that go beyond the clichés. 2 Note that the peak maximum is at λ=445 nm, which means that there is a 80 nm Stokes' shift. 55 “Principles of Radiation Interactions” Mean Excitation Energies Mean excitation energies, I, have been calculated using the quantum mechanical approach or measured in experiments. The IR spectrum is basically a plot of transmitted (or absorbed) frequencies vs. especially low in tonic water. Nile red is almost nonfluorescent in water and other polar solvents but undergoes fluorescence enhancement and large absorption and emission blue shifts in nonpolar environments (excitation/emission. It demonstrates that vinegar-water solutions contain the corresponding absorption. Conclusion: This is the largest study to date that provides major population-based data of the BEST1 mutation spectrum in China. The absorbances at the wavelength of excitation is optimally kept in between A = 0. In order to circumvent these low extinction coefficients, the luminescent metal ion can be chelated to a chromophore-containing group which functions as an 'antenna,' absorbing incident light then transferring this excitation to the metal ion, which can then deactivate by undergoing its typical luminescent emission (Figure 4). (Always add acid to water. In the field studies the fluorescence excitation spectra were measured continuously in a flow-through mode. Ultrafast anti-Stokes Raman measurements of OH stretching excitations (3000-3600 cm-1) in water show an ∼ 0. 26)Paste the spectrum below and compare the spectrum with the one provided by Invitrogen Inc. The application of 3D-EEM technology in DOM was expounded,and the mechanism of 3D-EEM technology and parallel factor analysis( PARAFAC) were introduced. The data interval was 0. water activation induces the formation of water molecular clusters similar to water molecular structures found in living cells. 5ppm from the water peak, or about -210Hz from water at 1. Always start by acquiring a one-scan 1H spectrum. frequency of water in liquid water. Carbon nanodots (CNDs) derived from a green precursor, kidney beans, was synthesized with high yield via a facile pyrolysis technique. Identifying elements in astronomical objects using their spectra. Plot b shows the excitation and emission spectra (λmax(ex)=756 nm, λmax(em)=774 nm) of Alexa Fluor 750 in water. coli has the same spectral properties , the excitation spectrum of R. photoluminescence signal disturbing the intrinsic Raman scattering spectrum of water. Conclusion: This is the largest study to date that provides major population-based data of the BEST1 mutation spectrum in China. Hassan, and A. intensity of the transmission (or absorption). saturated with water vapor. The fungicide may additionally be found as a potential pollutant of water where it can accumulate, which justifies the great interest to study its presence in natural water. The excitation spectra of the MTXPG photolytic products in patient samples compared with the excitation spectrum of MTX photolytic product in water (Fig. So GCaMP6 is a favorable candidate for longer-wavelength excitation. This signal is evidently frequency dependent and is particularly high when excited at 488 nm. emission wavelength vs. Plot a shows the excitation polarization spectrum of Alexa Fluor 750 in water with a polarization value of P = 0. Under the same conditions, the fluorescence emission spectrum is independent of the excitation wavelength, due to the partial dissipation of excitation energy during the excited state lifetime. Three-photon action spectra of GCaMP6f, and the absorption coefficient of water (H2O data from Kou, et. Science , this issue p. It demonstrates that vinegar-water solutions contain the corresponding absorption. The excitation intensity‐dependent PL and Raman spectra were obtained at room temperature by changing the laser intensity with the change of optical filters. The frequency shifts associated with different vibrations give a characteristic spectra. The backscattering geometry is used in the device for patient. Phenol Red, Reagent, ACS PH132 | 143-74-8 Phenol Red, Reagent, ACS is mostly used as a pH indicator that is commonly known due to it being used in pool water testing kits. Siemens water excitation (WE) sequences personal e-mail with P. Three-photon action spectra of GCaMP6f, and the absorption coefficient of water (H2O data from Kou, et. PL(photoluminescence) signal produced by DI water? of the peak is not double or half value of excitation wavelength and DI water is not contaminated. In the dark, a solution of ~0. Suppliers of Filtration and Water Treatment products. matic excitation x-ray beam and the imaged object. 5 nm and the integration time was 2. In flame tests salts that are dissolved in water are evaporated using a hot flame. The emission spectra of CDs diluted by 5 ml deionized water show a typical excitation-dependent feature. We are unique, in that consultants in this narrow field are very limited; and we can say with confidence that our personnel have the direct experience and knowledge to be the best overall mining-related water. 1 ×10-2nm = 0. WaterScout SM 100 Soil Moisture Sensors The key is knowing both when and how much to water! Maintaining a healthy soil moisture and water balance is essential for producing high quality plants. Fluorescence spectroscopy 45. , the carbon monoxide molecule CO) have significantly asymmetric charge distributions and are polar. Phosphorescence refers to the release of light that lasts longer – seconds or even hours after the excitation has stopped. Not for use in diagnostic procedures. UV absorbance at 254 nm, for example, has been used as a surrogate indicator for total organic carbon B. Remember to calculate and report the concentration of quinine in the orginal tonic water. The blank sample for emission and absorbance was a sealed TOC-free water sample (Starna 3Q-10) from Starna Scientiﬁc Inc. the tonic water using a least squares spreadsheet and report the appropriate uncertainties. An excitation or emission spectrum is then collected for an excitation or emission wavelength accuracy determination, respectively. 28: A typical Excitation Emission Matrix (EEM) A measurement becoming more widely used in the field of fluorescence spectroscopy is the excitation emission matrix, or EEM. The excitation spectrum provides a convenient means for selecting the best excitation wavelength for a quantitative or qualitative analysis. The emission spectra of CDs diluted by 5 ml deionized water show a typical excitation-dependent feature. M ovie of TCPO + H 2 O 2 + Diphenylanthracene Chemiluminescence Reaction. 1 Using near infrared radiation Raman shifts are independent of excitation wavelength and thus Raman spectroscopy offers the flexibility to select a suitable excitation wavelength for a specific application. IN X-RAY fluorescence spectrometry an X-ray tube is used as excitation source. 3 Arc Excitation. The fluorescence excitation spectrum is obtained by fixing the emission wavelength and by running the excitation monochromator. Introduction. An excitation spectrum is a graph of emission intensity versus excitation wavelength. , the diatomic hydrogen molecule H$_2$) have no permanent electric dipole moment, but many asymmetric molecules (e. In general, samples were prepared in 1 cm pathlength quartz cells with absorbance < 0. 3 Arc Excitation A little more sensitive, but also more complex, is the excitation of spectra with arcs. How do the sensitivities compare?. This is the absorption spectrum of water. use of the Synergy™ 4 Multi-Mode Microplate Reader to perform fluorescent excitation and emission spectrum analysis on Qdot nanocrystals. Below is a very useful table of various Fluorochromes that can be used in research requiring precise responses. Longer low power shaped pulses are used to excite specific spectral regions for selective excitation. 5, consists of dark lines or bands on top of a continuous spectrum. The excitation of the luminescent electrons is not connected with appreciable agitations of the atoms that the electrons belong to. Peak molecular brightness spectra, which can be obtained rapidly and with reduced experimental complexity, can thus serve as a ﬁrst-order approximation to cross-section spectra in determining optimal wavelengths for two-photon excitation, while providing additional information pertaining to probe photostability. Contents Scheme/Fig. Figure4-9(8) shows smoothed envelope curves which can beused for design purposes. Transition Metal Complexes When light passes through a solution containing transition metal complexes, we see those wavelengths of light that are transmitted. Spectra with Equal Excitation over a Wide Bandwidth VLADIMIR SKLENAR* AND AD BAX Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases,. Of the six transitions outlined, only the two lowest energy ones (left-most, colored blue) are achieved by the energies available in the 200 to 800 nm spectrum. Fluorescence refers to the immediate release of light, where light is emitted within a fraction of a second after excitation. The application of 3D-EEM technology in DOM was expounded,and the mechanism of 3D-EEM technology and parallel factor analysis( PARAFAC) were introduced. At a further increase of excitation wavelength the emission maximum shifts towards a longer wavelength again. The perceived color of the pigment depends upon the wavelengths of light that are not absorbed. By judicious selection of both the excitation λex and emission λem wavelengths, you should be able to avoid any significant. The excitation profile of four pulses is shown in the figure below. Data: Excitation‐Emission Matrix • Each resulting excitation‐ emission matrix (EEM) consists of hundreds of measurement combinations of a single water sample, with excitation wavelength is on one axis, emission wavelength is the second, and fluorescence intensity forms a third axis. 5 nm and the integration time was 2. 30%, no de novo mutations were identified. The excitation spectrum generally is identical to the absorption spectrum as the fluorescence intensity is proportional to the absorption. Mayo, and Richard K. emission spectroscopy of trace metals [7]. The "wiggles" in the excitation. The following approximate empirical formulas can be used to estimate the I value in eV for an element with atomic number Z: I ≈ 19. Spencer et al. The emission showed the characteristic fluorescence spectrum. According to the excitation and emission spectra of vinegar-water solutions in Figure 1, vinegar-water solutions can absorb photons of UV light at 380 nm and then emit fluorescence. With few exceptions, the fluorescence excitation spectrum of a single fluorophore species in dilute solution is identical to its absorption spectrum. The absorbances at the wavelength of excitation is optimally kept in between A = 0. excitation at 280 290 nm of their tryptophan residues. The separation of excitation and emission wavelengths is achieved by the proper selection of filters to block or pass specific wavelengths of the spectrum as presented in Figure 3. frequency of water in liquid water. fluorescence intensity. Determination of quinine in commercial soft drink by molecular fluorescence spectroscopy. Rhodamine 6G has an excitation maximum at. three-dimensional excitation-emission spectra (EEMs) of fluorescence of oil-in-water emulsion samples with various Figure 1 presents determined fluorescence spectra for various oil concentration in demineralized water for various excita- oils and oil concentrations respectively for considered crude tion wavelengths. Phosphorescence refers to the release of light that lasts longer – seconds or even hours after the excitation has stopped. So, if you have light of a given wavelength going through $x$ meters of water, the fracti. The laser intensity was fixed as P 0 for without filter (no filter). Fluorescence Spectrum8 Record the Excitation and Emission Spectra of deoxygenated (bubble N2 gas into. A basic phenomenon perhaps more familiar to chemists than to imagers, adiabatic excitation nevertheless does have several practical MRI applications. spectra of bovine bone after system response correction should have less fluorescence background. Absorption spectra were recorded using a double-beam setup with Milli-Q water in the reference channel and corrected for baseline and dark current. Frequencies appear in the x-axis in units of inverse centimeters (wavenumbers), and intensities are plotted on the y-axis in percentage units. Differences in the response shown in these graphs illustrates differences in the optical properties of water from these two sources that can potentially be used to develop field sensors for detection of wastewater. As mentioned above, it has generally been accepted that excitation energy distribution between PSII and PSI is the major determinant of the ETR under light-limited conditions. The hexane spectra were then subtracted from the olive oil sample spectra to remove the hexane Raman peaks. the tonic water using a least squares spreadsheet and report the appropriate uncertainties. 3a; the excitation wavelengths progressively increasing from 330 to 480 nm, and the emission intensity of 330–390 nm is. The dark counts were subtracted and the spectra were corrected for wavelength‐dependent variations in optical and photomultiplier sensitivity. For Research Use Only. EXCITATION-EMISSION MATRICES FOR CHARACTERIZATION OF NATURAL ORGANIC MATTER IN WATER TREATMENT Nicolás Miguel Peleato Master of Applied Science, 2013 Graduate Department of Civil Engineering University of Toronto ABSTRACT Quantification of natural organic matter (NOM) in water is limited by the complex and. excitation spot size, pulse energy, and power density to optimize spectral acquisition and to avoid or minimize sample degradation at stand-off distances of 27 and 50 m. Their new work utilizes a two-color approach with an 800-nanometer laser and its second harmonic to generate THz energy about 10 times stronger than the one-color approach. 'Fluorescence excitation and emission spectra at room temperature and at 77 K are presented. excitation at 280 290 nm of their tryptophan residues. Fluorescence excitation spectra of both FA and HA exhibited well-defined bands at 465 nm. M ovie of TCPO + H 2 O 2 + Diphenylanthracene Chemiluminescence Reaction. Solvent effects on electronic excitation spectra are considerable in many situations; therefore, we propose an efficient and reliable computational scheme that is based on the symmetry-adapted cluster-configuration interaction (SAC-CI) method and the polarizable continuum model (PCM) for describing electronic excitations in solution. cuvette holder. Under these conditions, the proton concentration in the water is 110 M (mols) while the concentration of the solute (molecules to be analyzed) is about 2 mM (millimols). Y A New Water Suppression Technique for Generating Pure-Phase Spectra with Qua1 Excitation over a Wide Bandwidth a VLADIMIR sKLENAR* AND AD BAX €. Figure 1: When passed through a prism, white light displays the color spectrum. Sketch the expected excitation spectrum shape if the emission monochromator was able. The PL peak shifts to longer wavelength as the excitation wavelength gradually increases (Fig. The diffuse reflector, scatterer or fluorescent dye is scanned with and without the Ho2O3 sample in place and the ratio of. 1 ×10-2nm = 0. It gives the absorption coefficient $\alpha$ (in inverse meters) as a function of wavelength. The spectrum of 785 nm excitation has deformation by the inﬂuence of ﬂuorescence in the high wavenumber region. Fluorescence Excitation and Emission Fundamentals Fluorescence is a member of the ubiquitous luminescence family of processes in which susceptible molecules emit light from electronically excited states created by either a physical (for example, absorption of light), mechanical (friction), or chemical mechanism. Absorption spectra were recorded using a double-beam setup with Milli-Q water in the reference channel and corrected for baseline and dark current. fluorescence intensity. Figure 9 shows Raman spectra of Shin-Etsu AQOAT (hypromellose acetate succinate). Detailed knowledge of the two-photon excitation spectra of molecular ﬂuorophores is required for de-. three-dimensional excitation-emission spectra (EEMs) of fluorescence of oil-in-water emulsion samples with various Figure 1 presents determined fluorescence spectra for various oil concentration in demineralized water for various excita- oils and oil concentrations respectively for considered crude tion wavelengths. Electrons can absorb energy from external sources, such as lasers, arc-discharge lamps, and tungsten-halogen bulbs, and be promoted to higher energy levels. The types of interaction can range from electronic excitation to molecular vibration depending on the different types of radiation, such as ultraviolet, X-rays, microwaves, and infrared radiation. We developed an in situ multi-excitation fluorometer, Multi-Exciter, which measures the excitation spectra of phytoplankton. In order to circumvent these low extinction coefficients, the luminescent metal ion can be chelated to a chromophore-containing group which functions as an 'antenna,' absorbing incident light then transferring this excitation to the metal ion, which can then deactivate by undergoing its typical luminescent emission (Figure 4). Water from 3 to 5 m depth was pumped and analysed every 2 minutes providing an. The emission maximum is chosen and only emission light at that emission wavelength is allowed to pass to the detector. Light in a typical fluorescent spectrum spikes strongly with blue, a little green and red wavelengths, with several variations based on the type of bulb. 05 in order to avoid inner filter effects and ensure. Abstract We will present a series of simulations of convective excitation of internal gravity waves (IGWs) in water. 086 - Emission and Absorption Spectra In this video Paul Andersen explains how the photons emitted from or absorbed by an atom or nuclei is directly related to electrons moving between energy level. This wavelength is also the optimal wavelength used for the excitation of rhodamine B for fluorescent emission. Sonnenschein and C. Also discuss the relationship between emission spectrum and excitation spectrum, methods for determining the limit of detection, and quenching. excitation without contact, laser excitation efficiently measures vibrations in a high -frequency zone. They are fabricated at industry-standard dimensions that make them compatible with filter cubes from all major manufacturers. multiphoton excitation. A protonated form, the predominant state, has an excitation maximum at 395 nanometers, and a less prevalent, unprotonated form that absorbs at approximately 475 nanometers. collected absorbance spectrum using. In order to convert between spectral wavelength, wavenumbers and frequency of shift in the Raman spectrum, we have developed this applet to compute Raman shifts and bandwidths. d Due to the observed similarity of the dielectric spectra of water and ice (as they show the similar graphics, only shifted along the frequency axis by six decades), the dielectric spectra has been explained using the assumption of a random-walk diffusion of protons without considering the H 2 O dipole orientations. It absorbs strongly in the microwave region by excitation of molecular rotations. PL(photoluminescence) signal produced by DI water? of the peak is not double or half value of excitation wavelength and DI water is not contaminated. The relative intensities of the lines depend on the circumstances of excitation and de-excitation of the atoms and ions and emission and possible re-absorption of the photons. FTIR spectrum of [AlL2]+NO3 in KBr disk. 005 for 349 nm excitation) were determined from the data. The active items are visually marked. However, since the observer does not use a spectroscope only one color is observed. Even after over 50 years of intensive research, accurate and cost-effective FIVN simulation and measurement techniques remain elusive. The primary objective of this work was to study the response of gravity water waves to wind excitation and, in particular, the applicability of the Miles inviscid shear-flow theory of gravity wave growth, by conducting experiments in a laboratory wind-wave channel under conditions approximating the assumptions of the mathematical model. In Figure 1, the 3D spectra of p-terphenyl, a laser dye and a component of sunscreens, has a maximum excitation of 295 nm and emission of approx. If the wavelength of the exciting light is changed and the emission from the sample plotted against the wavelength of exciting light, the result is known as the excitation spectrum. Spectra can also be created by the interference of light waves, the phenomenon that makes the brightly colored patterns seen reflected from a compact audio disc and the halos often observed next to a bright, partly clouded Moon. spectrum of the aqueously solvated anionic chromophores of green ﬂuorescent protein and photoac-tive yellow protein. Because of the high intensity, very short path lengths, usually less than 50 μm, are needed to record the spectra of aqueous solutions. The EEM is important for CDOM analysis because, in contrast to a typical two-dimensional absorbance scan of a water sample, the EEM exhibits a third dimension to provide both the absorbance and emission spectra of all fluorescent components. biological samples at multiple excitation wavelengths, creating exci-tation lambda stacks. This stable excitation state is responsible for the red absorption peak. Typically, earthquake excitation frequencies ofconcern will fiIll between 2 or3 Hzup to25 or 30 Hz, with the peak ranges generally between 4 and 10Hz,depending on the sub-soil conditions atthe particular site. use of the Synergy™ 4 Multi-Mode Microplate Reader to perform fluorescent excitation and emission spectrum analysis on Qdot nanocrystals. The dilutions were made in borate buffer of pH 9. For example, humic material ﬂuoresces over emission wavelengths of 320–350 nm when subject. Finally, an absorption spectrum, like the spectrum of sunlight shown in the bottom of Fig. The excitation spectrum generally is identical to the absorption spectrum as the fluorescence intensity is proportional to the absorption. So GCaMP6 is a favorable candidate for longer-wavelength excitation. Previous workers have reported that observation of emission at 338 nm yielded a fluorescence excitation spectrum with A. The spectrum below on the right (solid red line) is the emission spectrum of hymecromone in methanol for the excitation at λ=365 nm. Whether you're looking for solvents, ACS grade chemical reagents, analytical reference standards or chromatography supplies, Spectrum has it. The center coil is feed with the excitation voltage. So, if you have light of a given wavelength going through $x$ meters of water, the fracti. The emission spectrum shows what wavelengths are given off from the solution. The span of the absorption spectrum shown is from wavelengths on the order of a kilometer down to about the size of a proton, about 10. 76 (glycine buffer) there is a rapid drop in fluorescence stability. With few exceptions, the fluorescence excitation spectrum of a single fluorophore species in dilute solution is identical to its absorption spectrum. above hold, one would expect that the excitation spectrum will match the absorption spectrum. Abstract We will present a series of simulations of convective excitation of internal gravity waves (IGWs) in water. Operating Instructions, OpenOffice version: This is a simulation of a photodiode-array or rapid-scanning spectrofluorometer. The following approximate empirical formulas can be used to estimate the I value in eV for an element with atomic number Z: I ≈ 19. Initial EDS analysis usually involves the generation of an X-ray spectrum from the entire scan area of the SEM. The wavelength at which a molecule may be excited to emit is referred to as the excitation wavelength, and the spectrum emitted by the sample the emission spectrum (4). phytoplankton pigment excitation spectrum flow-through spectro-fluorimeter fluo-imager dynami-cal spatial map cyanobacterial bloom gotland basin temporary process shipboard laser time-consuming manual analysis large water area natural phyto-plankton analysis phytoplankton distribution phyto-plankton development line spectrofluorimetry high. the act or process of exciting or state of being excited. Excitation Spectra of quinine in 0. UV absorption spectra of polystyrene Tong Li*, Chunlin Zhou, and Ming Jiang* Department of Material Science, Fudan University, Shanghai, People's Republic of China SUMMARY Polystyrene (PSt) exhibits a new UV absorption band at around 290nm in comparison with ethylbenzene, which is attributed to. A protonated form, the predominant state, has an excitation maximum at 395 nanometers, and a less prevalent, unprotonated form that absorbs at approximately 475 nanometers. 27 For the uorescence spectra with k ex ¼ 280 nm (Fig. [275][1] The diffuse vibrational envelope displayed by water precludes direct observation of how different hydrogen-bond topologies dictate the spectral response of individual hydroxy group (OH) oscillators. XRF is based on the principle that individual atoms, when excited by an external energy source, emit X-ray photons of a characteristic energy or wavelength. 2789324 https://doi. For example, the Raman peak of water is always located approx. It was found that ﬂuorescence spectra identiﬁcation is a promising method to detect even an extremely low concentration of petroleum residues directly in the seawater. A streamlined version of the same database of spectra can now be viewed on our new website. In many cases you can visualize relevant orbitals or NTOs with ADFview by clicking on them in the window on the right. Excitation versus Emission Spectra. Precisely assigned spectral features from contributing configurations mapped well onto a bulk surface spectrum. Home; How to Determine Root Cause of Excessive Pump Vibration. 7 References 1. excitation wave: a wave of altered electrical conditions that is propagated along a muscle fiber preparatory to its contraction. same conditions, the fluorescence emission spectrum is independent of the excitation wavelength, due to the partial dissipation of excitation energy during the excited-state lifetime, as illustrated in Figure 1. In other words the acquisition time for a single Raman spectrum can be as low as 760 microseconds, 1300 Raman spectra can be acquired per second. The PL peak shifts to longer wavelength as the excitation wavelength gradually increases (Fig. An X-ray tube emits a pholychromatic continuous spectrum, on which are superimposed the characteristic lines from the anode material. The emission maximum is chosen and only emission light at that wavelength is allowed to pass to the detector. A protonated form, the predominant state, has an excitation maximum at 395 nanometers, and a less prevalent, unprotonated form that absorbs at approximately 475 nanometers. Data: Excitation‐Emission Matrix • Each resulting excitation‐ emission matrix (EEM) consists of hundreds of measurement combinations of a single water sample, with excitation wavelength is on one axis, emission wavelength is the second, and fluorescence intensity forms a third axis. The excitation spectrum of a given fluorochrome is determined in a similar manner by monitoring fluorescence emission at the wavelength of maximum intensity while the fluorophore is excited through a group consecutive wavelengths. Emission Spectrum of Hydrogen When an electric current is passed through a glass tube that contains hydrogen gas at low pressure the tube gives off blue light. DY 8 with chemical formula, C24H19N4Na05S2 and molecular structure as given in Fig. A plot of emission against wavelength for any given excitation wavelength is known as the emission spectrum. However, if fluorescence is generated, it is often much more intense than Raman scattering, hiding Raman features. excitation spot size, pulse energy, and power density to optimize spectral acquisition and to avoid or minimize sample degradation at stand-off distances of 27 and 50 m. excitation of the sample material usually takes place in an inert argon atmosphere. The moon was used as a body of relative comparable size to earth, yet. spectra 13, 14) is applied for the first time to excitation spectra, in order to account for absorption effects and re-construct the excitation profiles. This is the absorption spectrum of water. Excitation definition is - excitement; especially : the disturbed or altered condition resulting from stimulation of an individual, organ, tissue, or cell. Slipchenko,2,5 Ping Wang,2 Pu Wang,2 Jiandie D. The WS SERES spectra are correlated, both spatially and spectrally, with the corresponding localized surface plasmon resonance (LSPR) spectra of the nanoparticle arrays. HPLC determination of erythrocyte methotrexate polyglutamates after low-dose methotrexate therapy in patients with rheumatoid arthritis. For the purposes of simplicity, we will assume that fat resonates at a single peak -210Hz from water. The thermal motion of free electrons in CMEs broadens the absorption lines in the optical spectra that are produced by the Thomson scattering of visible light originating in the photosphere, which affects the intensity ratio at two different wavelengths. Previous workers have reported that observation of emission at 338 nm yielded a fluorescence excitation spectrum with A. collected absorbance spectrum using. In order to measure the absorption spectra, the excitation wavelength was changed in equidistant steps and for each step 200 single ﬂuorescence spectra were averaged. excitation spectra of SL2 in water with different concentrations (≥ 0. Indeed, below 10 mM, its absorption spectrum is representative of a monomeric form. Differences in the response shown in these graphs illustrates differences in the optical properties of water from these two sources that can potentially be used to develop field sensors for detection of wastewater. 3400-3600 cm -1 lower in energy than the excitation wavelength. In order to convert between spectral wavelength, wavenumbers and frequency of shift in the Raman spectrum, we have developed this applet to compute Raman shifts and bandwidths. Emission Spectra: Emission spectrum can be defined as a spectrum of the electromagnetic radiation emitted by a substance. Interactive Tutorials Electron Excitation and Emission. Laser excitation wavelength is 266 nm. fluorescence intensity. In summary, the excitation and emission spectra of a fluorophore contain important practical information about what wavelengths of light we need to supply and detect, in order to use that. The fungicide may additionally be found as a potential pollutant of water where it can accumulate, which justifies the great interest to study its presence in natural water. Excitation-emission matrix (EEM) fluorescence spectroscopy has been used to characterize the DOM and identify fluorescence emitting organic substances in natural water. It measures two fluorescence spectra excited sequentially by lasers at 263 nm and 351 nm, from single atmospheric aerosol particles in the 1-10 μm diameter size range. Spectra can also be created by the interference of light waves, the phenomenon that makes the brightly colored patterns seen reflected from a compact audio disc and the halos often observed next to a bright, partly clouded Moon. 1 N H 2 SO 4: Using the same solution, and an emission wavelength near the maximum found from the above step, scan the excitation wavelength from 200-340 nm. With a conventional confocal fluorescence microscope, the target molecules of pyrene arises some difficulties: excitation wavelength in deep ultraviolet forces low transmission performance of microscopic objectives and low wavelength-tunable performance of an excitation laser. insoluble in cold water. The UV-vis spectrum of tetraphenyclopentadienone is given below and should be similar to the one you obtained from lab. Welcome to the NIST Atomic Spectra Database, NIST Standard Reference Database #78. excitation spectrum by: (2) where J (J’) is the angular momentum quantum number of the initial (final) state of rare earth ion, n is the refractive index of the 65 sample, is the mean wavelength of the excitation band, N0 is rare earth ion concentration and Γ exc is the integrated excitation. Whether you're looking for solvents, ACS grade chemical reagents, analytical reference standards or chromatography supplies, Spectrum has it. The power level for each of the pulses was set such that the pulses provided a 90° flip angle for an on-resonance signal. To troubleshoot, first scan the mobile phase and verify that it is not interfering. Figure 9 shows Raman spectra of Shin-Etsu AQOAT (hypromellose acetate succinate). The peak that appears at 310 nm is due to the Raman scattering of the water used in the dilution. Absorption spectra were recorded using a double-beam setup with Milli-Q water in the reference channel and corrected for baseline and dark current. The PL peak shifts to longer wavelength as the excitation wavelength gradually increases (Fig. Note that scanning success depends on choosing a suitable excitation, as well as on emission wavelength. For discrete data, Riemann summation is used to quantify. They are suitable for both direct qualitative comparision and quantitative analysis. included an excitation/absorbance range from 250 to 600nm using 3nm for excitation intervals and 3. Water Soluble, Full Spectrum Hemp Oil (300, 600, 900 mg) quantity. The CND material was easily modified through simple oxidative treatment with nitric acid, leading to a high density "self-passivated" water soluble form (wsCNDs. From some materials, a minor portion of the absorbed light is re-emitted as fluorescence. Selective Water Excitation (WE) is different than Fat-Sat, although they are both based around the use of chemically selective RF-pulses. The thermal motion of free electrons in CMEs broadens the absorption lines in the optical spectra that are produced by the Thomson scattering of visible light originating in the photosphere, which affects the intensity ratio at two different wavelengths. Raman spectroscopy can thus be used to capture data on aqueous samples or samples with high moisture content, making it particularly useful for biological, pharmaceutical and homeland security applications. Spex Fluoromax: The excitation and emission monochromators were set at 1 mm, giving a spectral bandwidth of 4. On the spectrum, with the maximum point marked as 0dB, two points can be found at both sides with magnitude of -3dB, -6dB, or any other number you can name. a means of exciting or cause of excitement. In addition, because we are investigating a single active site, that is, an infinitely diluted system, any lateral interactions or higher-order assemblies of the INPs would be visible in the simulations. Fluorescence Excitation and Emission Fundamentals Fluorescence is a member of the ubiquitous luminescence family of processes in which susceptible molecules emit light from electronically excited states created by either a physical (for example, absorption of light), mechanical (friction), or chemical mechanism. In figure S1 we show the absorption and emission and excitation spectra of WT PYP and of several mutants thereof. 4 ps spectral evolution from the red to the blue that is similar to what is seen in the Raman spectrum of water heated to 90 °C. At a further increase of excitation wavelength the emission maximum shifts towards a longer wavelength again. Effects of laser excitation wavelength and optical mode on Raman spectra of human fresh colon, pancreas, and prostate tissues Ran Li,a Dominique Verreault,a Andrea Payne,a Charles L. Excessive vibration is a good indicator that some damaging phenomenon could be occurring within a pump, or the immediate pump system, which is why many pump users monitor pump vibration on a regular basis. The samples were pre-diluted with Milli-Q water to minimize the inner-filter effect. Differences in the response shown in these graphs illustrates differences in the optical properties of water from these two sources that can potentially be used to develop field sensors for detection of wastewater. The water content of the atmosphere varies about 100-fold between the hot and humid tropics and the cold and dry polar ice deserts. Flow induced vibration and noise (FIVN) remains a critical research topic. Many methods have been proposed to overcome the interfering scatter background x-ray photons. Laser excitation wavelength is 266 nm. Process for the excitation and acquistion of nuclear magnetic resonance signals, particularly in light water. The design of fluorescence illuminators is based on control of excitation light and emission light by readily changeable filter insertions into the light path on the. Red wavelengths are lower in energy and only boost the electron to a lower energy level than can blue light. Three-photon action spectra of GCaMP6f, and the absorption coefficient of water (H2O data from Kou, et. Lin,3 Garth Simpson,4 Bing Hu,1 and Ji-Xin Cheng2,4,6 1Hefei National Laboratory for Physical Sciences at Microscale and School of Life Science, University of Science and Technology of Science, Hefei. Optimum instrument setup should deliver excitation light as close to the peak of the excitation spectrum of the fluorophore as possible.


text:
# zbMATH — the first resource for mathematics

Hellinger integrals of diffusion processes. (English) Zbl 0598.60042
If $$\{X_ n,{\mathcal F}_ n,n\geq 1\}$$ is a sequence of measurable spaces and $$P_ n$$, $$Q_ n$$ are probability measures on $${\mathcal F}_ n$$, for each $$n\geq 1$$, then the $$\{P_ n,n\geq 1\}$$ is said to be contiguous to $$\{Q_ n,n\geq 1\}$$ if for any sequence $$\{A_ n\in {\mathcal F}_ n,n\geq 1\}$$ satisfying $$P_ n(A_ n)\to 0$$, one has $$Q_ n(A_ n)\to 0$$. This reduces to the absolutely continuous concept if all the measurable spaces and the measures are independent of n. The natural tools in this measure comparison are the Hellinger integral and the variation norm. The latter is just the variation of the signed measure $$(Q_ n-P_ n)$$ on $${\mathcal F}_ n$$, and the former is defined as: $H_ s(Q_ n-P_ n)=\int_{X_ n}f^ s_ ng_ n^{1-s}d\mu_ n,\quad 0\leq s\leq 1,$ where $$\mu_ n=(Q_ n+P_ n)$$ and $$f_ n,g_ n$$ are the Radon-Nikodým densities of $$P_ n$$ and $$Q_ n$$ relative to $$\mu_ n$$. It can be shown that $$H_ s$$ does not depend on the particular dominating measure $$\mu_ n$$, $$0\leq H_ s(P_ n,Q_ n)\leq 1$$ and $$H_ s$$ vanishes iff $$Q_ n\perp P_ n.$$
The effectiveness of the Hellinger integral in probability was shown by S. Kakutani [Ann. Math., II. Ser. 49, 214-224 (1948; Zbl 0030.02303)] and is gainfully employed in the subject ever since. [For more detail and related theory see the reviewer’s book: Foundations of stochastic analysis. (1981; Zbl 0539.60006), Sec. 4.4].
With these concepts the author’s results can be described from the introduction as follows: ”In the present paper Hellinger integrals of distribution laws $$P_{\xi_ i}$$ of diffusion processes (which are solutions of the stochastic differential equations) $d\xi_ i=a_ i(t,\xi_ i)dt+dW(t),$ i$$=1,2$$ are investigated. Here W(t), $$t\geq 0$$ is the Wiener process. Our main result is a two-sided estimate of $$H_ s(P_{\xi_ 1},P_{\xi_ 2})$$ in terms of the (drift) coefficients $$a_ i$$. These estimates are applied to obtain necessary and sufficient conditions for the convergence in variation distance (or norm) and for contiguity. Furthermore, bounds for the error probabilities in the statistical testing problem following a method due to H. Chernoff [Ann. Math. Stat. 23, 493-507 (1952; Zbl 0048.118)] are obtained. All results and proofs remain true in a slightly modified formulation if the processes $$\xi_ i$$ have a (common nonconstant) diffusion coefficient, (and different drifts $$a_ i$$ as before).”
Reviewer: M.M.Rao

##### MSC:
 60G30 Continuity and singularity of induced measures 60J60 Diffusion processes 60F05 Central limit and other weak theorems 62M07 Non-Markovian processes: hypothesis testing 62M99 Inference from stochastic processes
Full Text:
##### References:
 [1] DOI: 10.1214/aoms/1177729330 · Zbl 0048.11804 · doi:10.1214/aoms/1177729330 [2] Csiszar I., Studia Sci. Math. Hung 2 pp 299– (1967) [3] Gaixager R.G., Information Theory and Reliable Communication (1968) [4] DOI: 10.1109/TIT.1978.1055925 · doi:10.1109/TIT.1978.1055925 [5] DOI: 10.1002/mana.19750700116 · Zbl 0339.60052 · doi:10.1002/mana.19750700116 [6] DOI: 10.1080/17442508208833194 · Zbl 0476.60041 · doi:10.1080/17442508208833194 [7] Liese F., Wiss. Zeit-schrift Friedrich-S chiller-Universitat Jena 31 pp 609– (1982) [8] Liptseb R.S., Statistics of random processes (1978) [9] DOI: 10.1214/aoms/1177728422 · Zbl 0065.12101 · doi:10.1214/aoms/1177728422 [10] Nemetz T., Proc. Coll. on limit theorems of Prob. Theor. and Stat. Keszthely 26 (1974) [11] Ostebbeicheb F., Probl. Control-Inform. Theory 1978 pp 333– (1974) [12] DOI: 10.1007/BF02018663 · Zbl 0248.62001 · doi:10.1007/BF02018663 [13] Vajda I., Stud. Sci. Math. Hung 6 pp 317– (1971)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.

format: plain


text:
Article| Volume 22, ISSUE 2, P301-308, February 2020
• PDF [736 KB]PDF [736 KB]
• Top

# Inferring fetal fractions from read heterozygosity empowers the noninvasive prenatal screening

Open Access

## Abstract

### Purpose

Fetal fraction (FF) is the percent of cell-free DNA (cfDNA) in the mother’s peripheral blood that is of fetal origin, which plays a pivotal role in noninvasive prenatal screening (NIPS). We present a method that can reliably estimate FFs by examining autosome single-nucleotide polymorphisms (SNPs).

### Methods

Even at a very low sequencing depth, there are plenty of SNPs covered by more than one read. At those SNPs, we define read heterozygosity and demonstrate that the percent of read heterozygosity is a function of FF, which allows FF to be inferred.

### Results

We first demonstrated the effectiveness of our method in inferring FF. Then we used the inferred FF as an informative alternative prior to computing Bayes factors to test for aneuploidy, and observed better power than the Z-test. In analysis of clinical samples, we were able to identify female–male twins thanks to the accurate FF inference.

### Conclusion

Knowing FF improves efficacy of NIPS. It brings a powerful Bayesian method, allows “no call” for samples with small FFs, renders screening for XXY syndrome simpler, and permits an adaptive design to sequence at a higher depth for samples with small FFs.

## INTRODUCTION

Fetal fraction (FF) is the percent of cell-free DNA (cfDNA) in maternal peripheral blood that comes from the placenta of the fetus. FF plays a pivotal role in noninvasive prenatal screening (NIPS), which aims to examine whether a given chromosome is trisomy in the fetus. The American College of Medical Genetics and Genomics (ACMG) recommended in its position statement that all laboratories should include a clearly visible FF on the NIPS report, and all laboratories should establish and monitor analytical and clinical validations for FF.
• Gregg A.R.
• Skotko B.G.
• Benkendorf J.L.
• Monaghan K.G.
• Bajaj K.
• Best R.G.
• et al.
Noninvasive prenatal screening for fetal aneuploidy, 2016 update: a position statement of the American College of Medical Genetics and Genomics.
The lower limit of FF maintaining a reliable result is approximately 4%, and a low FF in maternal circulation was associated with an increased risk of fetal aneuploidies.
• Norton M.E.
• Jacobsson B.
• Swamy G.K.
• Laurent L.C.
• Ranzini A.C.
• Brar H.
• et al.
Cell-free DNA analysis for noninvasive examination of trisomy.
Thus, ACMG recommends that no call due to low FF needs to be specified in the NIPS report.
• Gregg A.R.
• Skotko B.G.
• Benkendorf J.L.
• Monaghan K.G.
• Bajaj K.
• Best R.G.
• et al.
Noninvasive prenatal screening for fetal aneuploidy, 2016 update: a position statement of the American College of Medical Genetics and Genomics.
Given the importance of the FF in NIPS, many methods have been proposed to detect FF. Early methods examined DNA sequences from the Y chromosome, either using polymerase chain reaction (PCR)
• Lo Y.M.D.
• Tein M.S.C.
• Lau T.K.
• Haines C.J.
• Leung T.N.
• Poon P.M.K.
• et al.
Quantitative analysis of fetal DNA in maternal plasma and serum: implications for noninvasive prenatal diagnosis.
or massive parallel sequencing technology.
• Chiu R.W.K.
• Akolekar R.
• Zheng Y.W.L.
• Leung T.Y.
• Sun H.
• Chan K.C.A.
• et al.
Non-invasive prenatal assessment of trisomy 21 by multiplexed maternal plasma DNA sequencing: large scale validity study.
Since methods based on the Y chromosome can only be applied to male fetuses, researchers focused efforts on developing methods that can apply to both male and female fetuses. Some used fragment size of cfDNA, where fetal cfDNA is generally shorter than maternal cfDNA;
• Yu S.C.Y.
• Chan K.C.A.
• Zheng Y.W.L.
• Jiang P.Y.
• Liao G.J.W.
• Sun H.
• et al.
Size-based molecular diagnostics using plasma DNA for noninvasive prenatal testing.
some explored the methylation differences between paternal and maternal cfDNA.
• Chan K.A.
• Ding C.
• Gerovassili A.
• Yeung S.W.
• Chiu R.W.
• Leung T.N.
• et al.
Hypermethylated RASSF1A in maternal plasma: a universal fetal DNA marker that improves the reliability of noninvasive prenatal diagnosis.
,
• Nygren A.O.H.
• Dean J.
• Jensen T.J.
• Kruse S.
• Kwong W.
• van den Boom D.
• et al.
Quantification of fetal DNA by use of methylation-based DNA discrimination.
However, these methods were not yet accurate enough for practical use. There are two very promising and elegant approaches that require no additional data. One explores the difference between DNA digestion of fetal and maternal cell-free DNA.
• Straver R.
• Oudejans C.B.M.
• Sistermans E.A.
• Reinders M.J.T.
Calculating the fetal fraction for noninvasive prenatal testing based on genome-wide nucleosome profiles.
The other explores the fact that fetal cfDNA sequences are not uniformly distributed along the genome,
• Kim S.K.
• Hannum G.
• Geis J.
• Tynan J.
• Hogg G.
• Zhao C.
• et al.
Determination of fetal DNA fraction from the plasma of pregnant women using sequence read counts.
presumably because actively expressed genomic regions were digested faster than those dormant gene regions. But these two methods present difficulties for smaller FFs.
The most successful methods are those that utilize inheritance patterns in single-nucleotide polymorphism (SNP) markers. Early methods assumed both maternal and paternal genotypes are known, and at a set of loci where the father is AA and the mother is BB, one can deduce FF by counting reads carrying As and Bs at those loci from sequencing data of maternal cfDNA.
• Lo Y.M.D.
• Chan K.C.A.
• Sun H.
• Chen E.Z.
• Jiang P.Y.
• Lun F.M.F.
• et al.
Maternal plasma DNA sequencing reveals the genome-wide genetic and mutational profile of the fetus.
,
• Liao G.J.W.
• Lun F.M.F.
• Zheng Y.W.L.
• Chan K.C.A.
• Leung T.Y.
• Lau T.K.
• et al.
Targeted massively parallel sequencing of maternal plasma DNA permits efficient and unbiased detection of fetal alleles.
A recent method only genotyped the mother.
• Jiang P.
• Peng X.
• Su X.
• Sun K.
• Yu S.C.Y.
• Chu W.I.
• et al.
FetalQuant(SD): accurate quantification of fetal DNA fraction by shallow-depth sequencing of maternal plasma DNA.
It first identified maternal homozygous loci, tallied and computed nonmaternal allele fractions at these loci from low-coverage sequencing data of maternal plasma, and used these to train a linear model to predict FF. High-depth targeted sequencing of maternal plasma was successfully used to determine FF.
• Chu T.J.
• Bunce K.
• Hogge W.A.
• Peters D.G.
A novel approach toward the challenge of accurately quantifying fetal DNA in maternal plasma.
,
• Zhang J.
• Li J.
• Saucier J.B.
• Feng Y.
• Jiang Y.
• Sinson J.
• et al.
Non-invasive prenatal sequencing for multiple Mendelian monogenic disorders using circulating cell-free fetal DNA.
Because of high sequencing depth, minor allele frequencies can be reliably estimated, the informative maternal–fetal joint genotypes can be inferred (one homozygous, one heterozygous), and based on this, FF can be determined. These methods, however, are not completely satisfactory as they are either not accurate enough, not cost-effective, or too laborious.
In this paper we introduce a statistical method that can infer FF using low depth sequencing of maternal cfDNA. The precision of the FF inference can be greatly improved if we also sequence maternal white blood cell DNA (wbcDNA) at a low depth. Our method is based on the read heterozygosity (RHet). A SNP locus is called RHet if it is covered by at least two reads carrying different alleles. RHet is determined mainly by the unobserved maternal–fetal joint genotypes and the FF. Other contributing factors include the inbreeding coefficient of the mother, the inbreeding coefficient of the fetus, the sequencing error rate, and SNP allele frequencies of the reference population. Sequencing of maternal wbcDNA contributes to the FF inference in two ways: it can be used to infer maternal inbreeding coefficient, and we can combine reads from the maternal cfDNA and wbcDNA sequencing to infer a diluted FF from a higher coverage data set and scale back.
The traditional Z-test method for NIPS first estimates chromosomal dosages for a sample (assuming a euploid mother carrying a single fetus), then it calculates the deviation of the chromosomal dosages from the mean dosage of a set of euploid controls (euploid mothers each carrying a euploid fetus), and lastly it normalizes the deviation by the sample standard deviation of the euploid controls to obtain a Z-score. Samples with Z >3 are declared trisomy positive. The cutoff of 3 is chosen such that the false positive rate is about 0.001 if the Z-score is normally distributed. If the fetus is trisomy, then the deviation is expected to be the FF. Thus, the higher the FF, the higher the power to detect true trisomy.
When FF is known (denoted by h), a more powerful test can be developed. Z-test only compares the deviation of the centered chromosomal dosage from 0. Since for a trisomy sample the chromosomal dosage is expected to be h above the mean dosage of euploid controls, we can also compare how close the centered chromosomal dosage is to h. In addition to increased power to screen for trisomy, knowing FF brings several other benefits. First, if FF is too small, which is a major source of false negatives, we can declare “no call.” Second, testing aneuploidy of sex chromosomes, such as Klinefelter syndrome (47, XXY), Turner syndrome (45, X), and XYY syndrome, becomes a much simpler problem. Third, it allows us to develop an adaptive design to sequence at a higher depth for samples with small FFs.

## Materials And Methods

### NIPS samples

Beginning 15 March 2016, we enrolled pregnant women who were undergoing routine obstetrical care at the Beijing Hospital. The institutional review board of the Beijing Hospital approved the study. All experiments were performed in accordance with relevant guidelines and regulations. Written informed consent was obtained from all patients. To be eligible for the study, pregnant women had to be at least 18 years of age and had to be carrying a fetus with a gestational age of at least 8 weeks. More information is in the Supplementary Material and Methods.

### Naive model

An ideal scenario would be no sequencing errors, and both mother and the fetus have an inbreeding coefficient of 0. Denote FF by h, and at an arbitrary biallelic SNP (A and B) denote the frequency of allele A as p. Assuming no inbreeding, the Hardy–Weinberg equilibrium holds for each genotype of one individual, such that $fAA=p2$, $fAB=2p(1−p)$, and $fBB=(1−p)2$. The distribution of the joint maternal–fetal genotypes and the A allele frequency of the mixture can be derived, as shown in Table 1.
Table 1Allele frequency in the mixture
MM-FFProbfA
AA-AAp31
AB-ABp(1 − p)1/2
BB-BB$(1−p)3$0
AA-AB$p2(1−p)$1 − h/2
BB-AB$p(1−p)2$h/2
AB-AA$p2(1−p)$1/2 + h/2
AB-BB$p(1−p)2$1/2 − h/2
Note joint genotypes AA-BB and BB-AA are Mendelian incompatible and excluded from the table.
Those SNPs covered by one read are ignored because of their likelihood containing no h. Suppose a SNP has coverage of 2, with counts of two alleles as (2, 0), (1, 1), and (0, 2). To evaluate likelihood for each count, we are conditioning on the joint genotype to obtain a weighted sum of binomial likelihood.
$Pr2,0∣p,h=1∕2p1−p(1−h+h2)+p2Pr1,1∣p,h=p1−p(1+h−h2)Pr0,2∣p,h=1∕2p1−p(1−h+h2)+1−p2$
1

The read heterozygous (1,1) has the probability of $p(1−p)(1+h−h2)$. If we assume p is uniformly distributed and integrate out p, we have the expected proportion of read heterozygosity among SNPs covered by two reads as $16(1+h−h2)$, which is a function of h.

### Full model

Let p, q be the allele frequency of the A, B allele with p + q = 1, andF be the individual’s inbreeding coefficient. The standard model to account for inbreeding coefficient as a generalization of Hardy–Weinberg equilibrium
• Vieira F.G.
• Fumagalli M.
• Albrechtsen A.
• Nielsen R.
Estimating inbreeding coefficients from NGS data: impact on genotype calling and allele frequency estimation.
is
$AA~p2+pqF,AB~2pq(1−F),BB~q2+pqF.$
2

The joint distribution of mother–fetus genotypes can be computed (Tables 2).
Table 2Probability of joint genotypes
AAABBB
AA$p(p+qF1)(p+qF2)$$p(p+qF1)q(1−F2)$0
AB$pq(1−F1)(p+qF2)$$pq(1−F1)(1−F2)$$pq(1−F1)(q+pF2)$
BB0$q(q+pF1)p(1−F2)$$q(q+pF1)(q+pF2)$
Each row is the genotype of the mother and each column is the genotype of the fetus.
The only possible errors that can occur after bi-allelic ascertainment are A to B or B to A, and the sequencing errors are different from A to B (denote eAB) and from B to A (denoteeBA). Accounting for sequencing errors, we can write the allele frequency of the mixture for each instance of joint genotype (Table 3), from which the likelihood can be obtained by modeling reads covering a given locus as binomial sampling.
Table 3Allele frequency in the mixture of maternal and fetal cell-free DNA
MM-FFProbfA
AA-AA$p(p+qF1)(p+qF2)$$1−eAB$
AB-AB$pq(1−F1)(1−F2)$$1∕2+1∕2(eBA−eAB)$
BB-BB$q(q+pF1)(q+pF2)$eBA
AA-AB$pq(p+qF1)(1−F2)$$(1−h∕2)(1−eAB)+h∕2eBA$
BB-AB$pq(q+pF1)(1−F2)$$h∕2+eAB−h∕2(eAB+eBA)$
AB-AA$pq(1−F1)(p+qF2)$$(1∕2+h∕2)(1−eBA)+(1∕2−h∕2)eAB$
AB-BB$pq(1−F1)(q+pF2)$$(1∕2−h∕2)(1−eBA)+(1∕2+h∕2)eAB$
Fetal fraction (FF) is denoted by h. The column marked “Prob” is the probability of the joint genotypes in the first column. fA denotes frequency of A allele conditioning on joint genotypes, taking into account sequencing error.
At SNP i covered by more than one read, denote $Gi=(ciA,ciB)$ the counts of reference and alternative alleles. Let x be the frequencies of A; the binomial likelihood for $Gi$ is
$B(x,Gi)=(ciA+ciB)!ciA!ciB!xciA(1−x)ciB.$
3

Denote G the collection of all $Gi$ for i in an index set ofS. For each SNP i, we write out the binomial likelihood conditioning on the joint genotypes, weighted by the probability of the joint genotype, and sum together to obtain marginal likelihood
$Mi(h,F1,F2,e)=∑j∈MMFFP(j)B(fA(j),Gi).$
4

Multiplying the marginal likelihood for each SNP to obtain a composite likelihood
$L(h;F1,F2,e)=∏i∈SMi(h,F1,F2,e).$
5

Finally, from nonpolymorphic markers covered by exactly one read, we can estimate the error spectrum used in the model (eAB and eBA for A and B in four nucleotides). We may optimize Eq. 5 to obtain ĥ.

## RESULTS

The rationale to infer FF from low depth sequencing data is detailed in the scientific facts and logic arguments in this section. First, even at a low coverage, there are sizable numbers of SNPs from the 1000 Genomes Project that are covered by more than one read. This can be deduced simply by assuming Poisson distribution at each locus and verified by real data (Supplementary Table S1). Second, at those SNPs covered by at least two reads, we can define read heterozygosity (and similarly read homozygosity). For example, at coverage of two, we may define (A, B) or (B, A) as read heterozygous, and (A, A) or (B, B) as read homozygous, where A and B are reference and alternative alleles respectively. Note that read heterozygosity, which involves sampling uncertainty, is different from the genotype heterozygosity. For example, at coverage of two, a genotype heterozygous AB has a 50% chance to produce read heterozygosity. Third, the percent of read heterozygosity is a function of FF (denoted by h). Under the naive model with ideal assumptions (see “Materials and Methods”), the percent of SNPs that are read heterozygous among SNPs covered by two reads is $16(1+h−h2)$. Thus h can be inferred. Note, however, the naive model only has theoretical value and performs poorly in real data analysis, as real data violate most of its assumptions.

### Statistical model to infer FF

For a given biallelic SNP, its allele frequency largely determines how likely we observe read heterozygosity. We identified three additional factors that affect read heterozygosity: the inbreeding coefficient of the mother F1, the inbreeding coefficient of the fetus F2, and the sequencing error ratee. Because a majority of the cfDNA comes from the mother, F1 determines the baseline of percent of read heterozygosity of a sample and is critical to the accuracy of FF inference. We therefore sequenced maternal wbcDNA and developed a statistical model to infer F1 (Supplementary Material and Methods). F2, on the other hand, contributes little to the percent of read heterozygosity, particularly when the FF is small. In practice, we can safely ignore F2 by setting it to 0. Sequencing errors produce more read heterozygosity than read homozygosity. The effect can be modeled and the sequencing error rate can be estimated for an individual sample from the nonpolymorphic part of genomes covered by a single read. At each marker covered by more than one read, we can write the single-marker likelihood, which involves parameters (h, F1, F2, and e) and data (counts of reference and alternative alleles and population allele frequencies). Multiplying all the single-marker likelihoods we obtain the composite likelihood, which is a function of h (with F1 and e inferred and plugged in and F2 set to 0). Maximizing the composite likelihood we obtain the maximum likelihood estimate of FF (see “Materials and Methods”).

### Numerical results on FF inference

To demonstrate the effectiveness of our statistical method in inferring FF, we performed (in silico) simulations to mix reads from sequences of a mother and her son, conducted (in vitro) laboratory experiments to mix DNA of mothers and their male children, and reanalyzed real data from clinical NIPS samples with putative male fetus (in natura). These study designs allow us to compare fetal fractions estimated by our method against those estimated from the sex chromosomes. The details of FF estimates from sex chromosomes can be found in Supplementary Material and Methods, Supplementary Figs. S1 and S2, and reference.
• Xu H.
• Wang S.
• Ma L.L.
• Huang S.
• Liang L.
• Liu Q.
• et al.
Informative priors on fetal fraction increase power of the noninvasive prenatal screen.
In the in silico experiments, we first mix reads from mothers and their children at different FF (Supplementary Material and Methods) to examine how F1 and F2 impact the inference of FFs. Fig. 1a, b demonstrates thatF1 has a large effect on FF and F2 has a negligible effect. We then focused on the variations of the FF estimates due to sampling. The data were simulated from mixing reads of two samples (a mother–child pair) in the 1000 Genomes Project (Supplementary Material and Methods). Figure 1c plotted the mean (of 100 replicates) with bar of the sample standard deviation of the inferred FF (y-axis) versus the true FF (x-axis). The sample standard deviation is 0.006 for FF = 0.02 and 0.008 for FF = 0.20. Lastly, we investigated how different sequencing depths affect the uncertainty of the FF estimates. Here we assume maternal wbcDNA was sequenced at the same depth as the cfDNA. We sampled and mixed reads to simulate 100 NIPS samples with FF = 0.10 at different sequencing depths. Violin plots in Fig. 1d confirmed that the higher sequencing depth, the smaller the variation of the FF estimates, and it appears that 0.5× would provide a good balance between sequencing depth and accuracy. The same simulations were done for FF = 0.04 and FF = 0.06 and similar patterns of variation were observed (Supplementary Fig. S3).
In the in vitro experiments, we used DNA from 11 mother–son pairs, mixed the DNA at different fetal proportions, sequenced the mixture at 0.5×, and inferred the FFs separately using sex chromosome dosages and read heterozygosity. Figure 2a compared the inferred FFs. The two sets of inferences are in high concordance to each other, with the coefficient of determination of $R2=0.987,$ and maximum absolute deviation being 0.014. Comparing both sets of inferences against the truth, however, showed that both estimates have slight upward biases and larger variations for large FFs (Fig. 2b, c). Experimental variation in DNA quantity measurements for mixing experiment is likely to be the explanation (Supplementary Material and Methods).
In the in natura experiments, we used samples from patients who consented to participate in an ongoing study to improve methods of NIPS (Supplementary Material and Methods). The study was approved by the Institutional Review Board of Beijing Hospital and the DNA samples were de-identified. We first retrospectively selected 69 clinical samples who carry putative male fetus with FFs (obtained from sex chromosome dosages) ranging from 0.03 to 0.15 and we intentionally collected more samples of small FFs, resequenced their cfDNA and wbcDNA at 0.5×, and inferred FFs. Figure 3a compared FFs inferred from sex chromosomes with those inferred from the read heterozygosity. The overall pattern of this plot is highly similar to that of Fig. 2a, with exception of two outliers whose FFs inferred by read heterozygosity are about twice as large as those inferred by sex chromosomes (Fig. 3b). We hypothesize these two samples are female–male twins. Following the IRB protocol, we obtained anonymized patient data and confirmed that those two samples are indeed female–male twins and both pregnancies were results of in vitro fertilization (IVF). For samples with a single male fetuses, FFs inferred by our method are in high concordance with FFs inferred from sex chromosomes (coefficient of determination $R2=0.972$) and the largest three absolute deviations are 0.017, 0.016, and 0.015.
To further evaluate our method in real data and examine the prevalence of IVF in our clinical samples, we randomly chose 443 clinical samples and performed the same data collection and statistical analysis as those 69 retrospect samples. Figure 4 demonstrated that our method works well. The 23 red dots (about 5% of 443) in Fig. 4 are IVF pregnancies with two embryos implanted. Along the blue line (y = 2x) are all red dots, indicating female–male twin pregnancies. Those vertical clusters of dots along the y-axis are female fetuses, and the dots along the diagonal line are male fetuses. For samples with a single male fetus, FFs inferred by our method are in high concordance with FFs inferred from sex chromosomes ($R2=0.971$) and the largest three absolute deviations are 0.027, 0.019, and 0.013.

### Incorporating priors on FFs to test for aneuploidy

The Z-test compares chromosomal dosages of a sample against a set of euploid controls to detect fetal trisomy.
• Chiu R.W.K.
• Chan K.C.A.
• Gao Y.
• Lau V.Y.M.
• Zheng W.
• Leung T.Y.
• et al.
Noninvasive prenatal diagnosis of fetal chromosomal aneuploidy by massively parallel genomic sequencing of DNA in maternal plasma.
Because chromosomal dosage estimates have a heavier tail than the normal distribution (Supplementary Fig. S4), the Z-test tends to produce more false positives at a fixed threshold.
• Xu H.
• Wang S.
• Ma L.L.
• Huang S.
• Liang L.
• Liu Q.
• et al.
Informative priors on fetal fraction increase power of the noninvasive prenatal screen.
By incorporating an informative null prior to account for the heavy tail, our Bayesian method can reduce false positives.
• Xu H.
• Wang S.
• Ma L.L.
• Huang S.
• Liang L.
• Liu Q.
• et al.
Informative priors on fetal fraction increase power of the noninvasive prenatal screen.
With the knowledge of the FF, we can also incorporate the informative alternative prior to compute a Bayes factor to test for the aneuploidy (Supplementary Material and Methods). Intuitively, theZ-test only examines how far a chromosomal dosage is away from the euploid dosage; with the knowledge of the FF, we can also examine how close a chromosomal dosage is to the putative dosage by assuming fetal trisomy. We may use a normal prior for FF under the alternative hypothesis to capture the uncertainty of the FF estimates, which critically depends on the sequencing depth (Supplementary Tables S2 and S3). Note that the ability to incorporate informative priors (both under the null and under the alternative) is a deciding advantage of the Bayesian approach over the Z-test method, which is oblivious to the alternative hypothesis by design.
To compare powers between the Z-test and our Bayesian method that incorporates informative priors, we simulated slightly overdispersed chromosomal dosages under the null, and used this to decide the cutoff value for both Z and Bayesian methods (Supplementary Material and Methods). Then for each target FF denoted by Θ, we simulated chromosomal dosages from N(Θ, σ) and computedZ scores and Bayes factors, where σ depends on sequencing depth and different chromosomes or regions have different σs (Supplementary Tables S2 and S3). The power can be estimated by the percent of test statistics surpassing their respective cutoff values. Table 4 demonstrates that the Bayesian method outperforms the Z-test, particularly for more difficult situations (smaller sequencing depths and smaller FFs). More power simulation results using different priors can be found in Supplementary Tables S4 and S5.
Table 4Power comparison between Bayesian method and theZ-test method
FFaMethod0.1×0.2×0.5×
0.04BF0.83060.98450.99981.00001.00001.0000
0.04Z0.81250.97790.99931.00001.00001.0000
0.06BF0.99631.00001.00001.00001.00001.0000
0.06Z0.99300.99991.00001.00001.00001.0000
0.08BF1.00001.00001.00001.00001.00001.0000
0.08Z0.99991.00001.00001.00001.00001.0000
0.12BF1.00001.00001.00001.00001.00001.0000
0.12Z1.00001.00001.00001.00001.00001.0000
FFbMethod0.1×0.2×0.5×
0.04BF0.06020.08000.36200.67100.88300.9914
0.04Z0.03960.05290.35000.65500.84360.9832
0.06BF0.17970.23650.73980.95750.99731.0000
0.06Z0.15210.22400.70390.93210.99321.0000
0.08BF0.36220.45390.93910.99811.00001.0000
0.08Z0.35400.45350.91630.99520.99991.0000
0.12BF0.70920.83480.99941.00001.00001.0000
0.12Z0.67670.79730.99841.00001.00001.0000
The comparisons were done at different FFs (row) and different coverages (column). The recorded power is at the type I error of 0.001.
BF Bayesian method,Z Z-test.
aSimulated based on empirical data of chromosomes 13, 18, and 21.
bBased on three 5-Mb regions each drawn from the three chromosomes.

## DISCUSSION

We developed a statistical method to infer FF in NIPS, extensively studied its performance, and demonstrated that incorporating the knowledge of FF improves statistical power of NIPS. Our method makes use of read heterozygosity of SNP markers on autosomes and can be applied to samples with either female or male fetuses. The use of read heterozygosity, however, makes our method sensitive to maternal inbreeding coefficient. We therefore propose to sequence maternal wbcDNA in addition to cfDNA. Sequencing maternal wbcDNA brings several benefits. First, it allows us to infer the maternal inbreeding coefficient to better estimate FF. Second, one can mix sequencing reads from wbcDNA and cfDNA to infer a diluted FF under a higher sequencing depth, and the diluted FF can be used to estimate FF after appropriate scaling. Third, although we didn’t pursue here, we would like to note that maternal wbcDNA sequencing can improve NIPS by providing individual-specific reference.
Sequencing wbcDNA in addition to cfDNA bears extra cost. Our method, however, can make do without sequencing wbcDNA. One approach is to plug in the population average inbreeding coefficient, and fit the full model to obtain fetal fraction (the plug-in method). The other is to jointly fit the full model to infer both maternal inbreeding coefficient F1 and fetal fraction h. This can be done efficiently using an iterative method by fixingF1 to update h and then fixing h to update F1 until both converge (the iterative method). The plug-in method worked well for samples with modest inbreeding coefficient (say, between −0.03 and 0.03), but suffered significant bias for samples with extreme inbreeding coefficient. Such an example can be found in Supplementary Fig. S5 (left), in which the outlying sample has an inbreeding coefficient of 0.085. The iterative method, on the other hand, worked well for samples with extreme inbreeding coefficients, but produced a larger variation for samples with modest coefficients (Supplementary Fig. S5, middle). Naturally we combined the plug-in method and the iterative method via thresholding F1 (estimated from the iterative method), such that if $F1>0.03$ we used the iterative method to estimate h and otherwise we used the plug-in method. Supplementary Fig. S5 (right) demonstrated the strength of the combined approach. More extensive numerical studies are warranted.
Our method is designed for nonadmixed samples, but it can be extended to work with admixed samples such as African Americans and Mexicans. The trick is to select a subset of SNPs to make the inference. The natural weight goes into the likelihood calculation for each SNP is p(1 − p) where p is the reference allele frequency. Taking African Americans as an example, we defined $logr=log2p1(1−p1)p2(1−p2)$ for each SNP where p1 and p2 are reference allele frequencies of a SNP in European and African populations respectively. We select SNPs whose logr are in a small range, e.g., (−1, 1), to make inferences. Since these SNPs are less ancestry informative, our Hardy–Weinberg assumption is arguably applicable to these SNPs. Supplementary Fig. S6 showed such SNPs are plenty (more than 60%) among SNPs whose minor allele frequencies are >0.01 between any pair of ancestral populations. We simulated cfDNA from African American samples with different fetal fractions (Supplementary Material and Methods), and used selected SNPs to infer their fetal fractions, using either European allele frequencies or African allele frequencies. Supplementary Fig. S7 showed that this approach works well, particularly when the two sets of estimates were averaged.
The knowledge of FF is critical to increase the efficacy of NIPS. One study suggests that samples with smaller FFs may have increased risk of fetal aneuploidy.
• Norton M.E.
• Jacobsson B.
• Swamy G.K.
• Laurent L.C.
• Ranzini A.C.
• Brar H.
• et al.
Cell-free DNA analysis for noninvasive examination of trisomy.
Reporting a “no call" and referring the subject to an invasive test is an effective way to reduce false negatives among these samples. Alternatively, we can perform additional sequencing to increase the sequencing depth to a level that has sufficient power for a given FF. The similar adaptive design can be applied to screen microduplications and microdeletions, where the power tends to be much smaller than the whole chromosome trisomy screening (Table 4).
Because of the widespread practice of drastically reducing costs, NIPS is usually done at the raw sequencing depth of 0.1× in China. When the FF is as large as 6%, 0.1× appears to have sufficient power to screen for trisomy of whole chromosomes. When the FF is at 4%, however, the power is 83% at the type I error of 0.001, which is unsatisfactory given the high social and economic cost of false negatives (Table 4). The situation is much worse for using NIPS to screen for microdeletion and microduplication (NIPS+). Such screenings are done at the raw sequencing depth of 0.5× in China. At such a sequencing depth, our power simulation suggested that for a 5M region, the power is merely 36% at FF of 4%, and 74% at FF of 6% (Table 4). On the other hand, our data suggested that there are 2.2% clinical samples whose FF is <4% and 12.9% clinical samples whose FF is <6% (Supplementary Fig. S8). Therefore, it is imperative to increase sequencing depths for both NIPS and NIPS+ to guarantee the efficacy of the screening.

## Ethics declarations

### Disclosure

Yongtao Guan is a consultant for Beijing USCI Medical Laboratory serving as its Chief Scientific Officer and owns its stocks and options. Beijing USCI Medical Laboratory contributed to fund the study, but played no role in designing experiment, analyzing data, and interpreting results.

## Acknowledgements

This work was supported by the National Key Research and Development Program of China under contract number 2016YFC100707 awarded to USCI Medical Diagnostic Laboratory Inc. The majority of the work was done when Y.G. was a faculty member at Baylor College of Medicine and was supported in part by the US Department of Agriculture/Agriculture Research Service under contract number 6250-51000-057.

### Author Contributions

These authors contributed equally: Minghao Dang, Hanli Xu

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## References

• Gregg A.R.
• Skotko B.G.
• Benkendorf J.L.
• Monaghan K.G.
• Bajaj K.
• Best R.G.
• et al.
Noninvasive prenatal screening for fetal aneuploidy, 2016 update: a position statement of the American College of Medical Genetics and Genomics.
1:CAS:528:DC%2BC28Xhs1aks77L
10.1038/gim.2016.97
Genet Med. 2016; 18: 1056-1065
• Norton M.E.
• Jacobsson B.
• Swamy G.K.
• Laurent L.C.
• Ranzini A.C.
• Brar H.
• et al.
Cell-free DNA analysis for noninvasive examination of trisomy.
1:CAS:528:DC%2BC2MXhtFOls7fJ
10.1056/NEJMoa1407349
N Engl J Med. 2015; 372: 1589-1597
• Lo Y.M.D.
• Tein M.S.C.
• Lau T.K.
• Haines C.J.
• Leung T.N.
• Poon P.M.K.
• et al.
Quantitative analysis of fetal DNA in maternal plasma and serum: implications for noninvasive prenatal diagnosis.
1:CAS:528:DyaK1cXlvVaiurc%3D
10.1086/301800
Am J Hum Genet. 1998; 62: 768-775
• Chiu R.W.K.
• Akolekar R.
• Zheng Y.W.L.
• Leung T.Y.
• Sun H.
• Chan K.C.A.
• et al.
Non-invasive prenatal assessment of trisomy 21 by multiplexed maternal plasma DNA sequencing: large scale validity study.
10.1136/bmj.c7401
BMJ. 2011; 342
• Yu S.C.Y.
• Chan K.C.A.
• Zheng Y.W.L.
• Jiang P.Y.
• Liao G.J.W.
• Sun H.
• et al.
Size-based molecular diagnostics using plasma DNA for noninvasive prenatal testing.
1:CAS:528:DC%2BC2cXotlyrtr8%3D
10.1073/pnas.1406103111
Proc Natl Acad Sci U S A. 2014; 111: 8583-8588
• Chan K.A.
• Ding C.
• Gerovassili A.
• Yeung S.W.
• Chiu R.W.
• Leung T.N.
• et al.
Hypermethylated RASSF1A in maternal plasma: a universal fetal DNA marker that improves the reliability of noninvasive prenatal diagnosis.
1:CAS:528:DC%2BD2sXhtw%3D%3D
10.1373/clinchem.2006.074997
Clin Chem. 2006; 52: 2211-2218
• Nygren A.O.H.
• Dean J.
• Jensen T.J.
• Kruse S.
• Kwong W.
• van den Boom D.
• et al.
Quantification of fetal DNA by use of methylation-based DNA discrimination.
1:CAS:528:DC%2BC3cXht12is73O
10.1373/clinchem.2010.146290
Clin Chem. 2010; 56: 1627-1635
• Straver R.
• Oudejans C.B.M.
• Sistermans E.A.
• Reinders M.J.T.
Calculating the fetal fraction for noninvasive prenatal testing based on genome-wide nucleosome profiles.
1:CAS:528:DC%2BC28XhtFSru7%2FP
10.1002/pd.4816
Prenat Diagn. 2016; 36: 614-621
• Kim S.K.
• Hannum G.
• Geis J.
• Tynan J.
• Hogg G.
• Zhao C.
• et al.
Determination of fetal DNA fraction from the plasma of pregnant women using sequence read counts.
1:CAS:528:DC%2BC2MXht1yqt7%2FM
10.1002/pd.4615
Prenat Diagn. 2015; 35: 810-815
• Lo Y.M.D.
• Chan K.C.A.
• Sun H.
• Chen E.Z.
• Jiang P.Y.
• Lun F.M.F.
• et al.
Maternal plasma DNA sequencing reveals the genome-wide genetic and mutational profile of the fetus.
10.1126/scitranslmed.3001720
Sci Transl Med. 2010; 2
• Liao G.J.W.
• Lun F.M.F.
• Zheng Y.W.L.
• Chan K.C.A.
• Leung T.Y.
• Lau T.K.
• et al.
Targeted massively parallel sequencing of maternal plasma DNA permits efficient and unbiased detection of fetal alleles.
1:CAS:528:DC%2BC3MXitFSksr4%3D
10.1373/clinchem.2010.154336
Clin Chem. 2011; 57: 92-101
• Jiang P.
• Peng X.
• Su X.
• Sun K.
• Yu S.C.Y.
• Chu W.I.
• et al.
FetalQuant(SD): accurate quantification of fetal DNA fraction by shallow-depth sequencing of maternal plasma DNA.
10.1038/npjgenmed.2016.13
NPJ Genom Med. 2016; 1: 16013
• Chu T.J.
• Bunce K.
• Hogge W.A.
• Peters D.G.
A novel approach toward the challenge of accurately quantifying fetal DNA in maternal plasma.
10.1002/pd.2656
Prenat Diagn. 2010; 30: 1226-1229
• Zhang J.
• Li J.
• Saucier J.B.
• Feng Y.
• Jiang Y.
• Sinson J.
• et al.
Non-invasive prenatal sequencing for multiple Mendelian monogenic disorders using circulating cell-free fetal DNA.
1:CAS:528:DC%2BC1MXmtFKjsLg%3D
10.1038/s41591-018-0334-x
Nat Med. 2019; 25: 439-447
• Vieira F.G.
• Fumagalli M.
• Albrechtsen A.
• Nielsen R.
Estimating inbreeding coefficients from NGS data: impact on genotype calling and allele frequency estimation.
1:CAS:528:DC%2BC3sXhslKksbfP
10.1101/gr.157388.113
Genome Res. 2013; 23: 1852-1861
• Xu H.
• Wang S.
• Ma L.L.
• Huang S.
• Liang L.
• Liu Q.
• et al.
Informative priors on fetal fraction increase power of the noninvasive prenatal screen.
1:CAS:528:DC%2BC1cXhs1CgtrvE
10.1038/gim.2017.186
Genet Med. 2018; 20: 817-824
• Chiu R.W.K.
• Chan K.C.A.
• Gao Y.
• Lau V.Y.M.
• Zheng W.
• Leung T.Y.
• et al.
Noninvasive prenatal diagnosis of fetal chromosomal aneuploidy by massively parallel genomic sequencing of DNA in maternal plasma.
1:CAS:528:DC%2BD1MXhtlemuw%3D%3D
10.1073/pnas.0810641105
Proc Natl Acad Sci U S A. 2008; 105: 20458-20463


text:
# Figure 3

 Nuclear modification factor of electrons from semileptonic heavy-flavour hadron decays as a function of $\pT$ in Xe--Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV for the 0--20\% (left panel) and 20--40\% (right panel) centrality intervals. Statistical uncertainties (vertical bars) and systematic uncertainties (open boxes) are shown. The filled boxes at $\RAA$ = 1 represent the normalisation uncertainty. Comparisons with the PHSD~, MC@sHQ+EPOS2~ and Djordjevic~ models are displayed.


text:
Krishna
0

Step 1: Measure the distance between the points. to know the lengths of the three sides of the triangle.

FORMULA: d\ =\ \sqrt{\left(x_{2\ }-\ x_1\right)^2\ +\ \left(y_{2\ }\ -\ y_1\right)^2}\

EXAMPLE: Given points (2, 1)(10, 7),

length=\ \sqrt{\left(10\ -\ 2\right)^2\ +\ \left(7-1\right)^2}

length=\sqrt{64\ +\ 36}

Side\ length=\sqrt{100}

Step 2; Compare the given lengths of the sides and angles.

Step 3: Conclude that the given triangle is an Equilateral triangle. If you find either all lengths or all angles are equal. (Otherwise go to the next step.)

EXAMPLE:  Lengths  36 cm, 36 cm and 36 cm   \degree

Angles : 60 \degree , 60 \degree and  60 \degree

Step 4:  Conclude that the given triangle is an Isosceles triangle. If you find either two equal. (Otherwise go to the next step.)

EXAMPLE:  Lengths: 36 cm, 36 cm and 57 cm

Angles: 50 \degree , 50 \degree and 80 \degree

Step 5: Conclude that the given triangle is a Scalene Triangle. If you find either sides or angles are not equal.

EXAMPLE: Lengths: 4.6 cm, 3.4 cm and 4.3 cm

Angles: 70 \degree , 30 \degree and 80 \degree


text:
# Resonance

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The phenomenon of increasing amplitudes of forced oscillations when the frequency of the external action approximates one of the frequencies of the eigenoscillations (cf. Eigen oscillation) of a dynamical system. Resonance is simplest in a linear dynamical system. The differential equation of motion of a linear system with one degree of freedom in an environment with viscous friction and with harmonic external action takes the form:

$$a\ddot q+b\dot q+cq=H\sin(pt+\delta),$$

where $q$ is a generalized coordinate, $a,b,c$ are constant parameters characterizing the system, and $H$, $p$, $\delta$ are the amplitude, the frequency and the initial phase of the external action, respectively. The stationary forced oscillations occur in accordance with the harmonic law with frequency $p$ and amplitude

$$D=\frac{H}{a\sqrt{(k^2-p^2)^2+b^2p^2/a^2}}$$

where $k=\sqrt{c/a}$ is the frequency of the eigenoscillations in the absence of energy dissipation $(b=0)$. The amplitude $D$ has a maximum value when $p/k=\sqrt{1-b^2/2ac}$, and with low energy dissipation it is close to this value when $p=k$. Sometimes by resonance is meant that case where $p=k$. If $b=0$ then, when $p=k$, the amplitude of the forced oscillations increases proportional to time. If a linear system has $n$ degrees of freedom, then resonance begins when the frequency of the external force coincides with one of the eigenfrequencies of the system. With non-harmonic action, resonance may occur only when the frequencies of its harmonic spectrum coincide with the frequencies of eigenoscillations.

#### References

 [1] S.P. Strelkov, "Introduction to oscillation theory" , Moscow (1951) (In Russian)


text:
# State the Condition and Give Balanced Equation for the Conversion of Water Gas to Hydrogen – in the Bosch Process. - Chemistry

Short Note

State the condition and give balanced equation for the conversion of water gas to hydrogen – in the Bosch process.

#### Solution

Conditions and balance equations for conversion of water gas to hydrogen

Water gas should be mixed with excess of steam, catalyst → Fe2O3 promoter → Cr2O3 at 450°C

$\ce{[Co + H2] + \underset{\text{steam}}{H2O}->[Fe2O3 450°C][Cr2O3] CO2 + 2H2 +\triangle}$

Concept: Hydrogen from Water
Is there an error in this question or solution?

#### APPEARS IN

Viraf J. Dalal Class 9 Simplified ICSE Chemistry
Chapter 6 Study Of The First Element — Hydrogen


text:
An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Gromov-Witten Theory of Spin Curves and Orbifolds

Edited by: Tyler J. Jarvis Brigham Young University, Provo, UT
Takashi Kimura Boston University, Boston, MA
Arkady Vaintrob University of Oregon, Eugene, OR
Available Formats:
Electronic ISBN: 978-0-8218-7993-1
Product Code: CONM/403.E
List Price: $65.00 MAA Member Price:$58.50
AMS Member Price: $52.00 Click above image for expanded view Gromov-Witten Theory of Spin Curves and Orbifolds Edited by: Tyler J. Jarvis Brigham Young University, Provo, UT Takashi Kimura Boston University, Boston, MA Arkady Vaintrob University of Oregon, Eugene, OR Available Formats:  Electronic ISBN: 978-0-8218-7993-1 Product Code: CONM/403.E  List Price:$65.00 MAA Member Price: $58.50 AMS Member Price:$52.00
• Book Details

Contemporary Mathematics
Volume: 4032006; 189 pp
MSC: Primary 14; 53;

This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies.

A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.

Graduate students and research mathematicians interested in algebraic geometry, topology, and mathematical physics.

• Articles
• A. Polishchuk - Moduli spaces of curves with effective $r$-spin structures [ MR 2234882 ]
• Alessandro Chiodo - A construction of Witten’s top Chern class in $K$-theory [ MR 2238814 ]
• Y.-P. Lee - Witten’s conjecture and the Virasoro conjecture for genus up to two [ MR 2234883 ]
• Xiaobo Liu - Idempotents on the big phase space [ MR 2234884 ]
• Ralph M. Kaufmann - Singularities with symmetries, orbifold Frobenius algebras and mirror symmetry [ MR 2234885 ]
• Yongbin Ruan - The cohomology ring of crepant resolutions of orbifolds [ MR 2234886 ]
• Ernesto Lupercio and Bernardo Uribe - Differential characters on orbifolds and string connections. I. Global quotients [ MR 2234887 ]
• Jack Morava - HKR characters and higher twisted sectors [ MR 2234888 ]
• S. V. Shadrin - Combinatorics of binomial decompositions of the simplest Hodge integrals [ MR 2234889 ]
• James Spencer - The orbifold cohomology of the moduli of genus-two curves [ MR 2234890 ]

• Request Review Copy
• Get Permissions
Volume: 4032006; 189 pp
MSC: Primary 14; 53;

This volume is a collection of articles on orbifolds, algebraic curves with higher spin structures, and related invariants of Gromov-Witten type. Orbifold Gromov-Witten theory generalizes quantum cohomology for orbifolds, whereas spin cohomological field theory is based on the moduli spaces of higher spin curves and is related by Witten's conjecture to the Gelfand-Dickey integrable hierarchies.

A common feature of these two very different looking theories is the central role played by orbicurves in both of them. Insights in one theory can often yield insights into the other. This book brings together for the first time papers related to both sides of this interaction. The articles in the collection cover diverse topics, such as geometry and topology of orbifolds, cohomological field theories, orbifold Gromov-Witten theory, $G$-Frobenius algebra and singularities, Frobenius manifolds and Givental's quantization formalism, moduli of higher spin curves and spin cohomological field theory.

Graduate students and research mathematicians interested in algebraic geometry, topology, and mathematical physics.

• Articles
• A. Polishchuk - Moduli spaces of curves with effective $r$-spin structures [ MR 2234882 ]
• Alessandro Chiodo - A construction of Witten’s top Chern class in $K$-theory [ MR 2238814 ]
• Y.-P. Lee - Witten’s conjecture and the Virasoro conjecture for genus up to two [ MR 2234883 ]
• Xiaobo Liu - Idempotents on the big phase space [ MR 2234884 ]
• Ralph M. Kaufmann - Singularities with symmetries, orbifold Frobenius algebras and mirror symmetry [ MR 2234885 ]
• Yongbin Ruan - The cohomology ring of crepant resolutions of orbifolds [ MR 2234886 ]
• Ernesto Lupercio and Bernardo Uribe - Differential characters on orbifolds and string connections. I. Global quotients [ MR 2234887 ]
• Jack Morava - HKR characters and higher twisted sectors [ MR 2234888 ]
• S. V. Shadrin - Combinatorics of binomial decompositions of the simplest Hodge integrals [ MR 2234889 ]
• James Spencer - The orbifold cohomology of the moduli of genus-two curves [ MR 2234890 ]
Please select which format for which you are requesting permissions.


text:
Challenge “Simple text editing with Vim” at VimGolf: How does the #1 solution work?

Simple text editing with Vim: http://vimgolf.com/challenges/4d1a34ccfa85f32065000004

I find it difficult to understand the #1 solution (Score 13).

Sorry, no solution is pasted in this post, because I don't know if it's appropriate to do that.

-
There is a problem with this question: nobody can even see the #1 solution (unless they're registered at vimgolf, like me). Meanwhile, why don't you TRY it step by step – sehe Jul 13 '11 at 13:09

The solution is centered on the :g command. From the help:

:g   :global   E147   E148
:[range]g[lobal]/{pattern}/[cmd]
Execute the Ex command [cmd] (default ":p") on the
lines within [range] where {pattern} matches.

So basically, the solution executes some ex commands on lines that have a "V", which are exactly the ones that need editing. You probably noticed that earlier solutions rely on duplicating the lines, rather than really changing them. This solution specially shows an interesting pattern:

3jYjVp3jYjVp3jYjVpZZ
^     ^     ^

Which could be reduced with a macro:

qa3jYjVpq3@aZZ

The solution using the :g command does basically the same thing. The first command executed is t.. From the help:

:t
:t                  Synonym for copy.

Copy the lines given by [range] to below the line

The address given was ., which means current line:

Line numbers may be specified with:          :range   E14   {address}
{number}            an absolute line number
.                   the current line                           :.
$the last line in the file :$
%                   equal to 1,$(the entire file) :% 't position of mark t (lowercase) :' 'T position of mark T (uppercase); when the mark is in another file it cannot be used in a range /{pattern}[/] the next line where {pattern} matches :/ ?{pattern}[?] the previous line where {pattern} matches :? \/ the next line where the previously used search pattern matches \? the previous line where the previously used search pattern matches \& the next line where the previously used substitute pattern matches So the ex command t. means "copy current line to below the current line". Then, there is a bar which: :bar :\bar '|' can be used to separate commands, so you can give multiple commands in one line. If you want to use '|' in an argument, precede it with '\'. And the d command, which obviously deletes the line. It was given a range of +, meaning the "current line + 1". You could pass .+1 but + for short. These info can be read surrounding the help for :range: The default line specifier for most commands is the cursor position, but the commands ":write" and ":global" have the whole file (1,$) as default.

Each may be followed (several times) by '+' or '-' and an optional number.
This number is added or subtracted from the preceding line number.  If the
number is omitted, 1 is used.

And that's it.

:g/V/t.|+d<CR>ZZ

On every line that has a "V", copy it down and delete the next line. Write and quit.

One thing that I didn't mention is why the :g commands are executed three times instead of 6 or even more (lines are duplicated along the process). The :g command starts positioning the cursor on line one, and goes down to \$. But if the commands change the current line, :g continues from there. So:

:g/V/

Current line is 4. Now:

t.

This moves the cursor to line 5. And then:

+d

Deletes line 6, the cursor remain in 5. So the next :g match will be in line 8.

-
+1 Nice explanation even if I can't read the problem. :) – Xavier T. Jul 13 '11 at 13:59
Thanks @Xavier T. The problem should be visible to every one, just follow the link provided in the question. – sidyll Jul 13 '11 at 14:06
You're right, I can actually see the starting/ending condition ! – Xavier T. Jul 13 '11 at 14:17
@sidyll It requires registration, and registration is in twitter. I am not ever going to do this. – ZyX Jul 13 '11 at 14:26
Another good solution is to use this: :g/#/ norm jYjVp – Magnun Leno Jul 13 '11 at 21:02


text:
Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

Topics - Vedant Shah

Pages: [1]
1
MAT334--Misc / Class Participation
« on: October 08, 2018, 04:30:27 PM »
How is the Class and Tutorial participation calculated for the bonus component of the final grade?

2
MAT334--Lectures & Home Assignments / Section 1.2 Question 18
« on: September 23, 2018, 05:19:33 PM »

Show that two lines $\Re(a+ib)=0$ and $\Re(c+id)=0$ are perpendicular  $\iff \Re(a \bar{c}) = 0$
From section 1.2: Let $a = A+iB$ and $c= C+iD$. Then the lines are $Ax-By+\Re(b)=0$ and $Cx-Dy+\Re(d)=0$
Setting the slope of the first equal to the negative reciprocal of the other I get: $\frac{A}{B} = - \frac{D}{C} \iff AC=-BD$
Finally, $\Re(a \bar{c}) = AC-BD= 2AC$

How do I proceed?

Thanks!

Pages: [1]