01). The temperature measurements showed that both irradiation conditions caused intrapulpal temperature increase below 2 °C. The highest temperature increase and the time after which the temperature returned to its initial values were respectively 0.3 °C and 12 s for the irradiation with 8 J/cm2 and 1.8 °C and 93 s for the irradiation with 11 J/cm2 (Fig. 1). The results of the present study showed that the irradiation of dentine with a CO2 laser (λ = 10.6 μm) at 11 J/cm2 and 10 ms pulse duration, after fluoride application was indeed able to cause a decrease in the loss of calcium and phosphorous in the demineralization solution. The Selleckchem Antidiabetic Compound Library calcium loss in this group

was even statistically significant lower than the

observed in the fluoride-treated group. Thus, the possibility of enhancing the effects of fluoride through CO2 laser irradiation has been demonstrated. Especially interesting to note is that these results were obtained with a clinical CO2 laser and using parameters which did not cause any visible thermal damage to the tooth surfaces. Similar findings have been observed by other authors measuring calcium and phosphorous dissolution14, 15 and 16 and lesion depth19 in CO2 laser-irradiated dentine. Nonetheless decrease in calcium and phosphorous Ivacaftor datasheet losses after irradiation with the set of parameters used in the present study has not been demonstrated before. Moreover, most of the previous studies were conducted with a CO2 laser emitting in the continuous-wave mode, which is not the safest condition for irradiating vital teeth.18 The lowest energy density tested in this study (8 J/cm2) did not cause any significant reduction in mineral loss either alone or in combination with fluoride.

This was initially not expected, because according to the literature and the characteristics of the laser–tissue interaction for the 10.6 μm wavelength, this energy density could already be sufficient to promote the necessary changes in the tissue. For example, in a study conducted with the same pulse duration (10 ms) as used in the present study, but in enamel, a 67%-inhibition of demineralization was observed with 10 J/cm2.24 Thus, knowing that for similar irradiation intensities the temperatures produced in dentine are two times higher than they ASK1 are in enamel, theoretically only half of the amount of an energy density, successfully tested in enamel, would be necessary to cause the same effects in dentine.18 Therefore, we expected to obtain a reduction in calcium loss already with the lowest energy density tested in the present study, but this was not confirmed. These results are probably explained by the fact that the energy applied to the tissue is not the only factor influencing the temperature excursions. The number of pulses applied to the same spot and the repetition rate also play an important role in the gradients of temperature formed.

The value of τa for xenon atoms on glass surfaces at 300 K can be estimated to be ∼10−10 s from the expression τa = τ0exp(−E/kBT), where E = 0.12 eV is the desorption activation energy xenon on borosilicate glasses [34] and assuming τ0 = 10−12 s. Although none of the correlation times associated with these events are long enough to cause biexponential relaxation, it is possible however that strong xenon adsorption sites are present on the Pyrex surface. The prolonged

correlation INK 128 datasheet times at these locations may lead to a violation of the extreme narrowing condition and thus to differential line broadening. An additional hint for surface interactions as the source for the satellite broadening is the differential

broadening between the two satellite transitions. Such differential broadening may be the result of paramagnetic – quadrupolar cross correlation that was observed recently by Jerschow and co-workers by 23Na NMR in the presence of paramagnetic contrast agents [74]. The only source for paramagnetism in the sample used for the spectra in Fig. 2 was on the Pyrex surface [75]. Other causes for differential line broadening may be CSA-quadrupolar cross-correlation effects during prolonged surface adsorption. Bleomycin manufacturer Alternatively, the lineshape may be inhomogeneously broadened by differences in EFG experienced by the xenon atoms in various parts of the container that were not averaged by gas diffusion at the gas pressures used. Although the precise mechanism of the satellite broadening remains speculative thus far, it likely originated from interactions with the Pyrex surface that were scaled down by exchange with the gas phase where the NMR signal was observed. A ‘scaling down’ of

surface effects also takes place for quadrupolar splitting that is on the order of 6 MHz on a Pyrex surface [35] but that is observed as a few Hz splitting Teicoplanin in the gas phase. Another distinctive feature shown in Fig. 2 is that thermally polarized 131Xe and hyperpolarized 131Xe signals were 180° out of phase with respect to each other while both 129Xe spectra possessed the same phase. This observation warrants a more detailed explanation. 131Xe is unique among the stable (i.e., non-radioactive) noble gas isotopes because it is the only isotope with a positive gyromagnetic ratio γ  . Therefore, according to Em   = −γmz  ℏB  0, the energy level Em   with the highest possible positive z-  quantum number, mz   = +3/2, constitutes the ground state for 131Xe. Vice versa, 3He, 21Ne, 83Kr and 129Xe have negative gyromagnetic ratios, and the respective ground state is the one with the most negative mz   quantum number. The sign of γ   determines the sign of the coherence generated by a 90° pulse ( H^rf-pulse,x=-γB0I^x) and thus can be important in magnetization transfer or coherence transfer NMR experiments.

These results are the first demonstration both of a pathological spatiotemporal AB in patients with right hemisphere damage and of the perceptual results of a decline find more in attention capacity

during healthy ageing. The paradigm developed here has revealed itself to be robust and adaptable to different participant groups for the exploration of interactions between spatial and temporal attentional processes. Here, we have been able to show that patients with right hemisphere damage are severely impaired at identifying letters appearing away from a central task. In fact they detect and discriminate only around 50% of these letters at both levels of central task difficulty when they appear simultaneously. This poor performance for letters appearing simultaneously with the diamond task is not simply for those on the contralesional side but also for those presented ipsilesionally (only 60% of these are detected during the high load task, see Fig. 3c). However, the critical aim of this study was to examine whether difficulties in discriminating the letters extended temporally. That is, if the peripheral letters appear after the central diamonds, is there a protracted period over which discrimination remains poor? Further, is this posited lag period affected by

the attentional demand of the central task? Our results demonstrate that, when there was a high attention demand in the central task, patients were impaired in accurately CH5424802 responding to these letters for a lag period that lasted for up to 850 msec. They failed to accurately discriminate significantly more letters at an SOA of 850 msec than when these letters were simultaneously presented with the diamonds. Critically, although patients and controls demonstrate very different performance in their perception away from fixation, performance of both groups for the central task, at both levels of attentional demand, was equivalent. Therefore, there was not a generalized loss of ability but rather specific buy 5-Fluoracil failures, revealed both spatially and temporally,

in secondary task completion when a large amount of attention was required in a central task. There is effectively less visual field available and so fewer letters are correctly identified away from fixation; we did not find a near versus far effect. The results of Experiment 1 align well with previous research on similar patients who have shown that increasing the amount of attention required in a central task increases the ipsilesional bias (e.g., Peers et al., 2006) and decreases neural activity for contralesional stimuli (e.g., Vuilleumier et al., 2008). Here we extend this to examine the temporal dynamics of these phenomena, revealing that the increased ipsilesional bias and loss of perception on the contralesional side extends forward in time. The patients tested here all had suffered from right hemisphere lesions. The majority of them had cortical damage, involving parietal cortex (4/5 patients).

, 2013). In the same general location, Silliman et al.’s (2012) comparative observations of abnormal levels of total polyaromatic hydrocarbons (PAHs) in sediment samples collected in October 2010 at 3 m and 15 m from the waters’ edge indicated that MC-252 oil from the DWH spill had reached some nearshore marshes. The implication of the previous reported results is that all observational sources including visual, optical, and PolSAR identified heavily oiled and structurally damaged shoreline marshes. In contrast, only the L-band PolSAR enabled detection of low oil contamination in nearshore and interior marsh canopies

that did not exhibit visual structural PI3K Inhibitor Library nmr damage or manifest health impairment at canopy top. However, the lack of direct observational evidence prevents an absolute determination of whether UAVSAR-derived products detected oil exposure in interior marshes. The objective of the research described herein was to confirm whether the spatial distribution of MC-252 oil determined from ground validation corroborated the PolSAR backscatter indicator of oil extent; mainly, did MC-252 oil reach further into the marshlands, as indicated by PolSAR backscatter, than the shoreline check details oiling detected in visual and optical

surveys? It is important to note that the marshlands of Barataria Bay, as with all the southern Louisiana marshes, are subject to historic oiling from other sources. PolSAR is not sensitive to the type of oil that is being detected; thus, to merely show that there was oil in the near-shore and interior marshes, although necessary, would not be sufficient to prove that oil was likely to have been present when the PolSAR data were collected not after the DWH spill in 2010.

In order to confirm that MC-252 oil reached the interior marshes in northeastern Barataria Bay, Louisiana where substantial changes in the 2010 PolSAR backscatter occurred, it was imperative that the oil detected be unambiguously linked to MC-252 oil from the DWH. We accomplished this through oil source-fingerprinting of sediment samples collected in June 2011 at focused locations of observed shoreline oiling and nearshore and interior marsh sites that exhibited substantial change in the 2009 pre-spill and 2010 post-spill backscatter mechanism. Samples were also collected from sites with no substantial change for comparison. Tying the oil to the 2010 spill was critical to showing that L-band PolSAR is a legitimate method for detecting subcanopy oiling. A total of 29 sediment samples were collected at locations selected based on the UAVSAR data and in-situ field observations made in June 2011. No similar conditions of extensive oil slicks and elevated sea levels occurred after the 2010 UAVSAR PolSAR collection to the time of the marsh sediment collections one year later.

) and on a vegetation-free bottom at a depth of 5.5 m. P. elegans was found at five stations and R. harrisii at nine. In addition, Platorchestia platensis (Krøyer, 1845) was present at one station on a beach reinforced by a stony embankment near Kuźnica ( Figure 1). The most important indigenous taxa forming benthic communities selleck chemicals llc in Puck Bay both in terms of abundance and biomass were Cerastoderma glaucum (Bruguière, 1789), Hydrobia ulvae (Pennant, 1777), Hydrobia ventrosa (Montagu, 1803), Hediste diversicolor (Müller, 1776) and chironomid larvae. The total

number of taxa on the soft bottom varied from locality to locality, from three in a post-dredging pit in the northern part of Puck Bay (depth 6.9 m) to 26 www.selleckchem.com/products/Vincristine-Sulfate.html in the southern part of the bay on a bottom overgrown with vascular plants (depth 1.5 m) (Figure 2). At least one non-native species was present at all but two stations. The maximum number of alien taxa – five – was found at only one station; at most stations (34%) three alien taxa were present. At all the stations where non-indigenous species were present they made up from 6 to 33% of all the taxa recorded at a station (mean = 17%). The abundance of macrofauna at the various stations ranged from 2033 indiv. m− 2 in the post-dredging pit to 34 152 indiv. m− 2 off the Hel Peninsula at 1.4 m depth (Figure 3).

The percentage of alien species in the total abundance varied from 0 to 46% (mean 6%). The proportions of these species in the abundance were largest in small, sheltered bays. The proportion of alien species in the total macrofaunal biomass reached 65% (mean 10%) (Figure 4). The percentage fantofarone of Gammaridae juveniles in the total macrofaunal abundance was below 8.6% (mean 0.5%), but in the total biomass was no greater than 1%. There was a significant positive correlation between the number of indigenous and

non-indigenous taxa in the samples (Cramer V = 0.36, P = 0.0001)( Figure 5a). In samples containing no more than two indigenous taxa, there was one alien species at most. The largest numbers of alien species (max 4) were found in samples where numbers of native taxa were also high (from 8 to 17). There was a weak positive correlation between the number of indigenous taxa and the abundance of non-indigenous species inhabiting the same area (Cramer V = 0.29, P = 0.057) ( Figure 5b). The abundance of nonindigenous species (> 7000 indiv. m− 2) was greatest in localities with the highest number of native species (16–17). Analysis of the number of indigenous and non-indigenous taxa with respect to habitat revealed a significantly higher number of the former on a bottom dominated by vascular plants than on a vegetation-free bottom; likewise, the former were present in significantly greater numbers on a bottom covered by both vascular plants and Chara spp. than on one covered by a mat of filamentous algae (in both cases, P < 0.05) ( Figure 6a).

5) for 1 h at 37 °C and the cleavage of caspase-3 substrate was measured at an excitation wavelength of 390 nm and an emission wavelength of 460 nm. The activity was expressed as relative fluorescence unit (RFU). To investigate the internucleosomal DNA fragmentation caused by both silver and gold nanoparticles, DNA laddering assay was performed according to the standard procedure described by Su et al. (2005) with little modification [38]. A total of 1 × 106 cells was treated with silver and gold nanoparticles (100 μg/ml) Selleck H 89 for 48 h and then collected by centrifugation. Further, the DNA was isolated using commercially available

kit (Genei, Bangalore, India) following the manufacturer’s instructions. DNA was resolved on 1.5% agarose gel (containing 3 μg/ml of ethidium bromide in 1 × TAE buffer of pH 8.5) at 90 V for 1.5 h and the bands were visualized using UV transilluminator. In this present study, gold nanoparticles were rapidly synthesized using A. indica leaves extract as bio-reductants. Similar to silver nanoparticles formation, the bio-reduction of HAuCl4 into gold nanoparticles was completed within 30 min of

incubation. The very first indication for nanoparticles formation is colour change. A clear pinkish violet colour was formed within 30 min when 1 mM Alectinib HAuCl4 was added into the aqueous leaves extract of A. indica, which indicates the biogenic synthesis of gold nanoparticles ( Fig. 1). The intensity of pinkish violet colour was increased with the incubation period and it was due

to the excitation of Etomidate surface plasmon vibrations. On the other hand, control (leaf extract alone) showed no change of colour ( Fig. 1). Very recently, Karuppaiya et al. (2013) have reported that the aqueous extract of Dysosma pleiantha rhizome rapidly biosynthesized gold nanoparticles within 20 min [25]. A characteristic absorption peak at 540 nm further confirmed the formation of nano-sized gold particles ( Fig. 2). The formation of gold nanoparticles was started at 15 min and was completed at 30 min. Interestingly, the peak was found to be stable at the same wave length for up to 1 h, indicating that phytochemicals may have stabilized the synthesized gold nanoparticles ( Fig. 2). Fig. 3a and b depict digitalized FE–SEM and TEM images of biosynthesized gold nanoparticles, respectively. These two images showed spherical shaped gold nanoparticles with a size of less than 30 nm. XRD analysis showed three distinct diffraction peaks at 38.1°, 44.1° and 64.1° which indexed the planes 1 1 1, 2 0 0 and 2 2 0 of the cubic face-centred gold. The obtained data was matched well with the Joint Committee on Powder Diffraction Standards (JCPDS) file no. 04–0784, which suggest the crystalline nature of gold nanoparticles ( Fig. 4).

gov/home.jsp) where the Functional Annotation Clustering tool was applied to generate clusters of overrepresented Gene Ontology (GO) terms (Huang et al., 2009). The data were check details analyzed in GraphPad Prism 5.00® software (GraphPad Software, Inc., San Diego, CA) using one-way analysis of variance (ANOVA) followed by Dunnett’s test for multiple comparisons or Student’s t-tests to compare two groups. Non-parametric data were compared using the Kruskal–Wallis test followed by Dunn’s test, and percent data from two groups were compared using the Mann–Whitney test. Data are expressed as the mean ± SD,

or as the median with range, and differences were considered statistically significant at p < 0.05. We performed transcriptome analysis on isolated splenic NK cells from 20 mice (5 mice/group) that were treated daily by gavage

for 14 days with ptaquiloside and/or selenium to identify transcripts that were associated with ptaquiloside-induced immunosuppression. The gene expression profiles from the Pt, PtSe and Se experimental groups, compared with the control group, showed 872, 302 and 489 altered genes, Daporinad respectively (Table 1). Of the up-regulated gene transcripts from all experimental groups, 123 were mapped to biological processes, from which we highlighted five, although, as shown in Fig. 2, none had high enrichment scores (≥1.3). The Pt and Se groups showed a very different pattern of distribution of differentially expressed genes in these 5 biological processes, whereas no particular biological process was favored in the PtSe group. The corresponding genes for each enriched GO term are listed in Table 2 and in Supplementary Table 1. When considering

gene transcripts that could be related to the immunosuppressive effects of ptaquiloside, we did not find genes directly related to this effect, but selected the genes metallothionein Nintedanib (BIBF 1120) 1 (Mt1) and metallothionein 2 (Mt2), which are involved in cellular ion homeostasis and act as zinc regulator that is essential to normal immune function. Ptaquiloside treatment increased the expression of these gene transcripts 2.9-fold (p < 0.001758) and 3.0-fold (p < 0.025148) compared with the control group, respectively. Supplementary Table S1.   The GO terms are over-represented among the genes whose expression was up regulated in the experimental groups vs. the control group. Each category biological process (GOTERM_BP_FAT) is represented by at least 3 genes. Of the down-regulated gene transcripts, 1174 were mapped to a wide range of biological processes. Transcripts with enrichment scores ≥1.3 for at least one of these groups are presented in Fig. 3. These data showed no specific biological process that was associated with ptaquiloside-induced immunosuppression in NK cells. The corresponding genes for each enriched GO term are listed in Supplementary Table 2. Supplementary Table S2.   The GO terms are over-represented among the genes whose expression was up regulated in the experimental groups vs. the control group.

Benchmarks are typically public reports that apply a standard methodology and estimate risk-stratified or risk-adjusted HAIs and/or their preventive processes across a large network of healthcare facilities. Recognized benchmarks for HAI include the NHSN [23], INICC [24], European Centre for Disease Prevention and Control (ECDC), and World Health Organization (WHO) estimates [1]. The characteristics of these four benchmarks, including the advantages and limitations, are shown in Table 1. (1) NHSN reports: NHSN is a secure, internet-based surveillance system at the US Centers for Disease

Control and Prevention (CDC) [23]. It was established in 2005 to integrate and replace three different surveillance systems at the CDC, including the NNIS, and NHSN is by far the most important and well-established surveillance NVP-BKM120 manufacturer system worldwide. One of its main stated purposes is to provide enrolled facilities with risk-adjusted metrics that can be used for inter-facility comparisons and local quality improvement Belnacasan activities. Starting in 2007, NHSN published a yearly report to estimate the magnitude of HAI, mainly in regards

to risk-stratified pooled means and percentiles of device-associated and procedure-associated HAIs [14] and [16]. However, ignoring non-device-associated pneumonia, bloodstream infections, and urinary tract infections as well as some surgeries limits the comprehensiveness of the NHSN surveillance system [25]. The last antimicrobial resistance report was published by NNIS in 2004 [26], pointing to the infrequency of reporting Isotretinoin for some NHSN modules. NHSN is widely used as a benchmark even outside of the US because its surveillance methodology is implemented in many hospitals worldwide. However, frequent changes in NHSN definitions, especially for catheter-associated urinary tract infection (CAUTI),

dialysis events, antimicrobial use, and neonatal central line associated bloodstream infection (CLABSI), make it difficult for any healthcare facility outside the NHSN to interpret the results of their benchmarking if they do not incorporate these changes into their own surveillance system on a timely basis [27], [28] and [29]. Approximately 90% of enrolled hospitals are general hospitals, including acute, trauma, and teaching facilities, although the number of enrolled hospitals has increased sharply during the last few years and now includes a larger representation of smaller hospitals. The recent availability of benchmark reports from different parts of the world has widened the benchmarking options for new hospitals in GCC states.

.. , |ββββ〉},

and which satisfy the following eigenvalue equation: equation(1) H^Z|m1m2m3m4〉=(m1+m2+m3+m4)ℏωH|m1m2m3m4 The symmetry-operations within the Td point group are those of one E (identity operator), eight C3 axes (proper rotations), three C2 axes (proper rotations), six S4 axes (improper rotations), and six σd planes (dihedral symmetry planes) [24]. Thus, the order of the Td group, h, is 24, and the Td point-group is isomorphic to the S4 symmetric group of permutations of four elements. It is noted that the 24 symmetry operations cannot mix states with different eigenvalues to the Zeeman Hamiltonian; that is, the matrix representations of the symmetry elements http://www.selleckchem.com/products/PD-0332991.html are block-diagonal. The function |αααα〉 is the only function with eigenvalue +2ℏωH+2ℏωH and since this function is total-symmetric it is already an irreducible representation with symmetry A  1. The four functions αααβ〉, are the only functions with eigenvalue of +ℏωH+ℏωH and these functions are therefore considered separately. The number of symmetry-adapted basis functions within each

of the irreducible representations of the Td   group is determined using Schur’s orthogonality theorems [24] and [25] that leads to equation(2) al=1h∑cg(c)χ(l)(c)∗χ(c)where al   is the number of functions with representation l  , the sum is over the classes c   of symmetry operations, g  (c  ) is the number of operations within the class, and χ(l)(c)χ(l)(c) www.selleckchem.com/products/SP600125.html and χ(c)χ(c) are the characters of the representation l   and of the set of functions MycoClean Mycoplasma Removal Kit in question, respectively. The characters χ(l)(c)χ(l)(c) are available from standard character-tables while χ(c)χ(c) is simply the number of basis functions that do not change under the

given symmetry operation. Thus, equation(3) aA1=124(1×1×4+8×1×1+3×1×0+6×1×0+6×1×2)=1 equation(4) aA2=124(1×1×4+8×1×1+3×1×0+6×(-1)×0+6×(-1)×2)=0 equation(5) aE=aT1=0aE=aT1=0 equation(6) aT2=124(1×3×4+8×0×1+3×(-1)×0+6×(-1)×0+6×1×2)=1 The four basis functions, ααβα〉, , therefore span one function with A1 symmetry and three functions with T2 symmetry (the order of the T2 symmetry is three). The full set of symmetry-adapted functions are now generated from the original set by applying the 24 symmetry operations and multiplying by the character of the symmetry operation in question as detailed elsewhere [24] and [25]. Thus, generation from |αααβ〉 gives, equation(7) Three additional functions with T  2 symmetry can be constructed in a similar manner by applying the procedure detailed in Eq. (7) to the other three functions that have an eigenvalue of +ℏωH+ℏωH, that is |ααβα〉, |αβαα〉 and |βααα〉. Finally, a basis set of functions with T2 symmetry, which consists of three orthonormal functions, can be constructed from linear combinations of the four functions generated above.

(52): equation(54) R2∞=R2G+PEΔR21+ΔR2/kEXWhich is identical to the relaxation rate expected for the R1ρ experiment in the strong Palbociclib field limit (Ref. [44], ω1 ≫ δG, δE, kEX, ΔR2, Eqs. (5), (6), (7) and (8)). Thus the fast pulsing limit of the CPMG experiment, and the strong field limit of the R1ρ experiment

lead to identical relaxation rates, as would be expected. Eq. (54) is similar, but not identical to similarly reported results [2] and [6]. Going further, when kEX ≫ ΔR2 > 0, both the CPMG and R1ρ (in the strong field limit) experiments converge on the intuitive population averaged relaxation rate [42]: equation(55) limPE→0kex>ΔR2R2∞=PGR2G+PER2E Finally, in the limit ΔR2 = 0, the CPMG propagator (Eq. (46)) in the limit of fast pulsing (Eq. (80) using the results in Supplementary Section 1) becomes: equation(56) MΔR2=0∞=e-TrelR2GPGPGPEPEWhich is identical to the evolution matrix for free precession in the limit of fast exchange (Eq. (17) and using the results in Supplementary Section 1). High pulse frequency CPMG experiments only act to make the system appear to be formally in fast exchange limit when ΔR2 = 0. Physical insight into the CPMG experiment is obtained by considering the overall propagator for the CPMG experiment (Eq. (42)), raised to the power Ncyc. equation(57) M=e-2τcpNcyc(2R2G+f00R+f11R)(F0eτcpE0-F2eτcpE2)B00N+(F0e-τcpE0-F2e-τcpE2)B11N+(e-τcpE1-eτcpE1)B01NNcyc

Akt cancer The CPMG experiment can be considered in terms of a series expansion. The propagator initially contains six unequally weighted evolution frequencies, ±E0, Calpain ±E1 and ±E2, where the cofactors are the product of an Fx (x = 0, 2) constant, (Eq. (36)), and a Bxx (xx = 00, 11, 01) matrix (Eqs. (18) and (40)). Raising these terms to the power Ncyc will result in new terms that can be represented in terms of sums and differences of the six frequencies, and weighting coefficients. Temporarily ignoring the coefficients, the frequencies that can be involved in the expansion can be revealed using Eq. (41), noting that ε0

is real and ε1 is imaginary: equation(58) (etcp2∊0+etcp2∊1+e-tcp2∊0+e-tcp2∊1+e-tcp(∊0+∊1)+etcp(∊0+∊1))Ncyc=(etcp(∊0+∊1)+e-tcp(∊0+∊1))Ncyc(etcp(∊0-∊1)+1+e-tcp(∊0-∊1))Ncyc(etcp2∊0+etcp2∊1+e-tcp2∊0+e-tcp2∊1+e-tcp(∊0+∊1)+etcp(∊0+∊1))Ncyc=(etcp(∊0+∊1)+e-tcp(∊0+∊1))Ncyc(etcp(∊0-∊1)+1+e-tcp(∊0-∊1))Ncyc The expansion results therefore in the product of a binomial expansion over τcp(ε0 + ε1), and a trinomial expansion over τcp(ε0 − ε1). The expansion in Eq. (57) will therefore result in 3Ncyc2Ncyc individual terms, arranged over (1 + Ncyc)(1 + 2Ncyc) possible frequencies ( Fig. 4A). Including the average relaxation rate factor at the front of Eq. (57), 2τcpNcyc(f00R + f11R), the real part of the frequencies will fall between 4Ncycτcpf00R and 4Ncycτcpf11R, or Trelf00R to Trelf11R.