Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Density curves of β-values of Infinium I/II probes are plotted with different colors. and SQN can correct the type bias efficiently on this sampleFull size image Identify DMPs/DMRs by preprocessed results of different methodsWe used the dmpFinder function in minfi R package to evaluate the result of identifying DMPs obtained by the five methods. We selected the probes with p-value of the results obtained after dmpFinder less than 0. 05 as DMPs. The number of DMPs of five methods is listed in Table 2. Then the Venn diagram of the detected probes was plotted, shown in Fig. 6. As shown in Fig. 6, BMIQ and RCP methods show larger overlap with other methods, where the ratio of common probes is 43. 41% (7370/16977 in BMIQ) and 39. 42% (7370/18696 in RCP). Moreover, the most probes identified after BMIQ have intersections with others and only 311 probes (311/16977=1. 83%) are identified uniquely. But it is also shown that there are differences among results of different methods, which maybe caused by the models they applying to normalization. Then the GO term enrichment analysis were analyzed with gometh function in missMethyl package. The GO terms of FDR ≤0. 05 of five methods were got (see Table 2) and the Venn diagram of GO terms obtained after normalization is shown in Fig. 7. RCP got the highest rate of common (42/76=55. 26%) GO terms among the five methods and SQN got the most number (n=199) of GO terms of which 33. 67% (67/199) identified by only this method. Fig. 6Venn diagram of DMPs obtained by five methods. After filtering probes with p-value <0. 01, we use dmpfinder in minfi to identify DMPs with p-value <0. 05. BMIQ and RCP can lead to better results than other three methodsFull size imageFig. 7Venn diagram of GO terms obtained by five methods. There are 42 common GO terms identified by five methods. RCP has the highest rate of common terms (42/76=55. 26%). SQN discovers most terms but 33.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Moreover, if p < N MathType@MTEF@5@5@+=feaafiart1ev1aaat9MDH5MBPbIqV92AaeXatLxBI9g6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaae@2F82@ the computational complexity is smaller than O ( N N ) MathType@MTEF@5@5@+=feaafiart1ev1aaat9MDH5MBPbIqV92AaeXatLxBI9g6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGaem4ta8@311D@ which is the computational complexity for the fast MDS method proposed by Morrison et al. [12]. When p is very large (say p2 > N), SC-MDS has no advantage in computational speed, but it makes the computation feasible even when the computer memory does not afford the MDS computation. Furthermore, if we do not use CMDS as our default MDS method but use the linear time algorithm [8] instead, then we can further reduce the complexity of the SC-MDS method to O(pN). This improvement makes application of the MDS to large data sets feasible. Hence, data analysis using SC-MDS can guarantee better accuracy than existing non-metric MDS methods. Results and DiscussionSimulation experimentsWe simulate a spiral in two dimensions:r = 2θ, 2π ≤ θ ≤ 5π. First, let us construct the reference coordinates X.

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: Please find our replies to your comments in the attached PDF. Citation: RC2: 'Outstanding achievement; a few points require further clarification and improved presentation', Jed Kaplan, 06 Apr 2024 Review of Holocene land cover change in North America: continental trends, regional drivers, and implications for vegetation-atmosphere feedbacksDawson, et al. This manuscript describes a study to reconstruct land cover for the Holocene over North America. As part of the LandCover6k initiative, the methodology follows a standardized procedure: first pollen records from sedimentary archives are synthesized and samples are assigned ages using up-to-date age-depth models. Then, pollen spectra are simplified and decimated to include specific taxa, and relative abundances of these taxa are passed to the pollen-landscape model. generates quantitative estimates of land cover for specific taxa that can be further generalized into broad groups of plant functional cover, e. g. , broadleaf deciduous or needleleaf evergreen trees. These point-based data are then interpolated to a continuous 1-degree grid covering the study area. The work presented here complements similar activities undertaken for other parts of the and ongoing work in the tropics and elsewhere. The authors present the results of the synthesis in the form of gridded maps and synthetic timeseries covering the entire spatial domain, and for specific regions that they analyze in further detail. Overall, this is an excellent study that is rigorous in its methodology, interesting and in some ways novel in terms of results, and honest about shortcomings. The authors helpfully provide a roadmap for future research including on improving the land cover reconstructions and recommendations for research that could employ the maps and other datasets produced here. There are a few issues that should be clarified before publication, and ultimately this paper and the associated datasets will make a valuable contribution to the journal and support range of fields in further study. General comments While changes in ice cover were considered, it appears that sea level changes (and proglacial lakes) were ignored in this study. This is a major limitation of the spatial analyses and at the very least should be justified. It’s a bit strange because these paleogeographic changes are considered in previous, similar studies by some of the same authors (e. g. , Williams, 2003; Williams et al. , 2004).

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Different components will exit the column at the same or nearly the same time, a problem known as coelution. This results in partial or full overlap of peaks in the mass spectral domain. To help overcome this problem, two-dimensional gas chromatography-mass spectrometry (GCxGC-MS) has become a common chemical analysis tool. There are two columns in the two-dimensional gas chromatography-mass spectrometry. Rather than going to a detector, the output of the first column goes into a modulator that collects the sample and periodically injects it into a second column with different chemical properties. Due to the different properties of this second column, compounds will have a different retention time in the second column, resulting in two levels of chemical separation. The detector is positioned at the output of the second column. This process results in a four-dimensional dataset with two time axes (retention time one (RT1) from the first column and retention time two (RT2) from the second column), mass, and intensity. For each RT1/RT2 coordinate pair, the mass and intensity form a mass spectrum. An understanding of the structure, strengths, and shortcomings of GCxGC-MS data is essential in order to effectively apply visualization techniques. GCxGC-MS is known for its large peak capacity, an order of magnitude increase in chemical separation ability compared to GC-MS [4], and its improved speed [3]. However, GCxGC-MS still has several complexities that make it a challenging process to use effectively. Inconsistencies in sample amounts will lead to differences in peak intensities. Peak retention times and shapes experience slight differences that are uncontrollable, but are not related to actual chemical differences in the samples [4]. Data samples exhibit background noise that can vary from sample to sample, and make accurate peak quantification difficult. Finally, despite the improved separation ability over one-dimensional GC--MS still exhibits some peak overlap due to coelution. Algorithms that attempt to correct these deficiencies have been developed with promising results, but this is still an active area of research. To correct for differences in sample amounts, normalization can be performed. As GCxGC intensities are fairly linear with respect to sample amounts, a multiplicative scaling factor can be used to normalize samples as long as at least one consistent peak can be found to normalize against [4].

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: So we use SC-MDS to randomly separate the 16,502 genes into 6 overlapping subsets, where N I = 2200 and N g = 4500. Although the essential dimension should be smaller then 2168, we still use N I = 2200 to ensure accurate reconstruction. The QR operation and SVD operation are available for this size. In each subset, we compute the 4500 × 4500 distance matrix and then compute the 3D MDS layout. Figure 4 is the 3D layout of SC-MDS results on these 16,502 genes. In this figure, two genes located closely have similar GO descriptions. We use the Euclidian distance in this 3D layout to measure the relationship between genes. For example, gene probe IDs 220259_at, 220815_at, 221980_at, 201015_s_at, 209880_s_at, 219765_at, 203018_s_at, 205523_at, 209879_at, 218796_at refer to the same GO description and they have the same coordinates in Figure 4. This gene correlation map is useful for many gene selection problems. Although we could not validate this result by comparing it with CMDS, we can repeat the SC-MDS procedure to see if we get consistent results among repeats. We find that the values of between different repeats are all small. This suggests that our method is stable for this large data set. Figure 4The 3D layout of SC-MDS on 16,502 human genes. (N I = 2200, N g = 4500) In this correlation map, genes with similar biological functions or in the same biological pathway tend to be located in the same neighborhood. Full size imageAnother way to check our method is to sample a subset of genes to create the correlation map, for example, 4000 sampled genes. Then we can compare the performance between CMDS and SC-MDS. We randomly sampled 4000 genes from the 16,502 genes, and then compute the distance matrix corresponding to these genes. The CMDS layout showed that there are 1106 dimensions in this gene set. Then we applied SC-MDS to this distance matrix with three different pairs (N I = 2200, N g = 2500), (N I = 1110, N g = 2000) and (N I = 500, N g = 1000).

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: Figure 2As noted in the supplement the three interpolated surfaces sum across to 100% in each row, and there is no “missing” fraction that represents bare ground. In the Arctic and in desert areas, the landscape is not 100% vegetated. This information should not be buried in the supplement, and needs to be clearly noted when the main figures are presented in the figure caption and body text. It should further be noted as a limitation and explained why this is not the case in the main manuscript text. Line 311Given that there are only 3 sites in Mexico, is the spatial domain of the study justified? Wouldn't a maximum distance buffer around nearest site be better - e. g. , up to 100 km apart (corresponding to the indicative catchment area)? As noted above there is a distance filter on the grid based on the CR value, but it would be interesting to see how this translates into distance from a site. Some statistics, such as the max distance from any site in the interpolation, would be helpful, even if only in the supplementary materials. Line 320The number of gridcells contributing to the curves presented in Figure 3 changes based on ice area, apparently not sea level, but also CR value. Can we see an additional curve on this figure showing the total area in the spatial domain contributing to the cover estimate? Lines 435-436In this sentence, and others, please just choose one form of plant nomenclature or the other, and stick with it. Lines 541-543“… desert, steppe, and other open-land arid ecosystems are likely to be underrepresented in these reconstructions, due to a scarcity of dryland sites” yet the interpolated maps and timeseries curves imply continuous vegetation cover (without bare ground), if I understand correctly. This limitation of the methodology should be further described and justified. Line 566Is there really nothing to say here about sea level dynamics over the period? Line 625I suggest a small rewording of this sentence to: “During the late Holocene, the growth of Indigenous populations and intensification of land use in the Americas had increasing effects on land cover. Understanding the interactions among…” Line 632Evidence for dense populations and land use in are dismissed here, yet a number of examples of this are provided in the following paragraph. This sentence could be reworded to better tie to what is coming next.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: While fairly straightforward, background levels and peak co-elution can hinder the accuracy. Several peak alignment techniques have been developed to correct the problem of peak shift in chromatography, such as the piecewise automated beam search algorithm developed by Yao et al. [5], or the registration technique described by Hollingsworth et al. [4]. Reichenbach et al. [6] found that the background level was mainly the sum of two slowly changing functions: a steady-state standing-current offset and a temperature-induced column bleed. They found that this background level varies slowly compared to the characteristic peak widths, and has the statistical characteristics of random white noise. With this knowledge they were able to develop an efficient algorithm for removing the background from a total ion count image, resulting in a near-zero mean background level. Very often one would like to identify, or search for, a particular analyte of interest within a GCxGC-MS sample. These identification algorithms generally involve and correlation with samples from a known mass spectral library, such as in [7]. These algorithms, however, are complicated by coelution. In order to remove the overlap in the mass spectral domain that results when multiple components elute at the same time, spectral peak deconvolution algorithms have been developed, such as [8]. In general, however, these algorithms are dependent on there being at least some separation between the centers of the overlapping peaks. Due to such issues, the visual inspection and explorations of samples plays a vital role in the analysis process. GCxGC-MS visualization techniquesSeveral visualization techniques have been developed for exploring GCxGC-MS data and are used almost universally. Typical methods include: two-dimensional total ion count rendering [3, 4], two-dimensional contour plots, three-dimensional height rendering, or displaying the data in tabular form [3]. Additionally, subsets of the data can be displayed, such as mass-spectrum views for a given retention time coordinate pair, or visualizing a single mass or range of masses using any of the previously mentioned methods. The scientific community has recently begun taking advantage of modern graphics hardware for more detailed, complex and realistic visualizations for all sorts of complex datasets, and mass spectrometry is no exception. Corral et al.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: We repeated SC-MDS 10 times for each pair. Figure 5a is the 2D CMDS layout. between the original data and CMDS is 1. 796 × 10-15. Figure 5b is the 2D SC-MDS layout with (N I = 2200, N g = 2500), and its average compared with the original data is 0. 0138. Figure 5c is the 2D SC-MDS layout with (N I = 1110, N g = 2000), its average is 0. 0140. Figure 5d is 2D SC-MDS layout with (N I = 500, N g = 1000), and its average is 0. 0282. We can see that all the 2D structures are preserved, though less well in Figure 5d where there is a substantial dimension loss. Figure 52D MDS comparison of 4000 GO samples. a The 2D CMDS projection of 4000 sampled genes of Affy U133A GeneChip. b The 2D layout of an approximate solution by SC-MDS with no dimension loss (N I = 2200, N g = 2500). The points in a group are chosen g randomly. c The 2D layout of the approximate solution by SC-MDS with loss of 1058 dimensions (N I = 1110, N g = 2000). The points in a group are chosen randomly. d The 2D layout of the approximate solution by SC-MDS with loss of 1668 dimensions (N I = 500, N g = 1000). The points in a group are chosen randomly. Full size imageGene expression clusteringThe goal of gene expression clustering is to subdivide a set of gene expressing profiles into clusters such that genes in the same cluster share the same or similar patterns of expression profiles. In the situation with high dimensional data, researchers tend to obtain a manifold, which is defined by the regression of the data. Because gene expression data is typically noisy, by clustering the projection of data in this manifold, which is in a lower dimensional space in comparison to the original data, a better result can be obtained. In this section, we show that the SC-MDS method can successfully transform a high dimensional gene expression data set to a much lower dimension and preserve the intrinsic information of the original data. This transformation makes the clustering algorithm faster to get a converged solution.

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: Paragraph starting on line 660What is the purpose of this paragraph? Can it be tied back to the data presented in the current study? Section starting on line 668 (4. 1. 1)This section needs to be tied back more clearly to the findings in the current study, at least speculatively. The section reads like a review paper now and there is nothing new in here. Line 675-676The full name of the “TEMPO” acronym could be removed here and just put in the 4. 1. 1 could be improved. Line 715“Great Plains” Line 728-731It is not clear from this section or from the maps or timeseries how large, in absolute terms, the coverage of T. Canadensis could have ever been. The paragraph seems to insinuate that it could have been abundant enough to make a majority proportion of forest cover, therefore having a strong influence on, e. g. , albedo. But… (see next comment) Lines 731-732missing something because I don't see a shift in the dominance in Fig. 4, which is always more than 50% summergreen trees and shrubs, with evergreen less than 30% cover fraction throughout the Holocene. Are you arguing that ETS forests were conifer-dominated? Otherwise, the albedo changes would have been very subtle, especially since T. Canadensis can persist in the understory for a century or longer and so while it is there and producing pollen, it will have no influence on summer albedo and relatively little on winter. Lines 741-743Looking at the summary figures, these changes must have all be very subtle. If not, then some further quantitative information should be highlighted here. Line 747Broadleaf summergreen trees have greater maximum evapotranspiration rates than needleleaf evergreens and this effect should also be mentioned here as it is probably more important than the summertime albedo differences. Line 753I am not convinced that there is anything more than “relatively subtle shifts in the proportions of summergreen and evergreen trees and shrubs” shown in the data presented here. Line 775-776If “… estimates are sensitive to parameter choices…” then why didn't you not just explore a larger parameter space and make a range of reconstructions? Instead of just one?

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: [9] develop some basic hardware-accelerated rendering techniques for very large Liquid Chromatography-(LCMS) datasets, adapting terrain-rendering techniques to suit the LCMS data. This height rendering technique is also used by Linsen et al. for differential protein expression analysis [10]. Their work also includes data resampling, as well interactive modification of the color scheme and material properties. Other research combines mathematical and statistical methods with visualization in order to provide more insight into data. Recent work by Wiklund et al. [11] makes use of an orthogonal partial least-square (OPLS) model-based approach for definition of statistically and potentially biochemically significant compounds. Wiklund et al. present the S-plot, visualizing both the covariance and correlation between metabolites and class designation, and an extension dubbed the SUS-plot (shared and unique structure) to compare the outcome of multiple classification models compared to a common reference. However, little research has gone into interactive comparative visualization techniques for this type of data. Hollingsworth et al. utilized image processing based techniques based on the total ion count image [4]. This basically amounts to a flattening of the data from four dimensions to three by aggregating the individual intensities at each retention time coordinate in order to obtain the total ion count. Prior to visualization and comparison each image must undergo background removal and peak detection. Peak alignment is performed on the reference image in order to remove incidental differences with the analyzed image. Finally, normalization is performed so that differences in sample amounts will not result in false positives. Once this pre-processing is complete, a difference image is computed. This difference can be visualized using tabular data, a 2D image, or 3D height field visualization in either grayscale or color. Their main contribution, however, is the calculation of a fuzzy difference that compares each pixel value in one image with a small neighborhood of pixels in the other, rather than doing a pixel-by-pixel comparison. This technique helps to reduce the incidental differences in peak shape and retention time that may still exist even after alignment. While these techniques represent a good first step, they are ill-suited for biomarker detection as they rely solely on images produced from the total ion count image. Additionally, since only the magnitude of the difference is considered, the results obtained can be misleading.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Moreover, the representation of these gene expression data in this lower dimensional space reveals a better clustering result in biological validation. We use the α38-synchronized yeast cell cycle dataset [5]. There were 5006 genes in the data set, and each gene has a 25 point-time-course expression profile. However, this expression profile contained missing values, and we input these missing values by the KNN imputation method [13]. To avoid the synchronized block effect, we remove the first two points of the time course data, so that the expression profiles for each gene are left with 23 time-course points. We then (1) compute the pair-wise dissimilarity of genes from each subset that are randomly chosen by the sufficient condition of SC-MDS; (2) apply SC-MDS to the subsets to reconstruct the new coordinate in the feature space; and (3) cluster genes in this feature space. Because CMDS cannot handle large samples and thus cannot be used to reduce the dimension when the sample size is large, we do not consider the clustering results in the reduced dimension space derived from CMDS. Instead, we compare the clustering results in the reduced dimension space derived from SC-MDS with the results obtained in the original (non-reduced) space. Using the standard Euclidean distance to measure the pair-wise dissimilarity of genes, we process the SC-MDS method such that the data points are split into 61 groups, N I = 100 and N g = 200. Note that instead of computing the pair-wise dissimilarity for every pair, we need to compute only the pair-wise dissimilarity in each group. This reduces the computational complexity of all processing to O(N). We choose N I to be greater than the length of original time course data points to satisfy the sufficient condition for an accurate layout. Using a PC with CPU 1. 67 GHz, 2G memory and Matlab R14 as the testing software, we complete the analysis with the CPU time of ~46 seconds. From the degradation rate of the distribution of standard deviations of output coordinates (Figure 6) the derived from the average of 30 repeats with different randomly grouping the elements of each subgroup, there are turning points at the 4th, 7th and 11th coordinates; after the 11th coordinate, the degradation is very small.

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: Log in or new issue alertsGet alerts Submit a your Email address: Subscribe to e4. 0 Unported, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Research 19(5):p 945-946, May 2024. | DOI: 10. 4103/1673-5374. 385290 A main requirement for cells to function normally is the availability of glucose. Glucose, available either direct from circulation or storage, is converted to the essential energy that cells need to drive critical intrinsic functions. If cells are deprived of glucose, they become dysfunctional and suffer distress. Photobiomodulation, the use of specific wavelengths of light on body tissues, has been shown to promote, through small organelles called mitochondria, the metabolism of glucose to make energy for cells; this energy can be used to improve cell function and survival. In this perspective, we hypothesize that the availability of glucose is central to the core mechanism of photobiomodulation; that photobiomodulation is at its most efficient in stimulating mitochondrial activity and improving cell function when there is glucose readily available. Glucose is the key metabolic substrate for energy consumption. Carbohydrates, lipids, and proteins all ultimately break down into glucose, which then serves as the primary metabolic fuel of all mammalian cells. Indeed, glucose is the final substrate that enters the cells and converts to adenosine triphosphate (ATP), the key energy source that drives many cell functions, for example, the active transport of molecules across cell membranes, the contraction of muscles, the generation of hormones and cell membranes, nerve impulse conduction, together with cell division and growth. Hence, a constant supply of glucose must be available to cells and this supply comes mainly from two sources; either directly from the circulation or storage (Figure 1A; Nakrani et al. , 2021). Figure 1: Mechanism of glucose metabolism and the impact of photobiomodulation. (A) Schematic diagram of glucose metabolism. Within the cell (large grey circle), glucose (small green circles) is converted to pyruvate. If there is oxygen available (aerobic respiration), the mitochondria will convert the pyruvate into CO2 and H2O giving off a high yield of 36 molecules of adenosine triphosphate (ATP) using oxidative phosphorylation.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Large, yet statistically insignificant differences may be emphasized while small, yet significant differences may not be noticeable. Visual analysis systemWe present and handle mass spectral data as both two and three-dimensional distributions through the use of novel interactive techniques. We allow users to explore their data using coordinated multiple views as shown in our previous work [2]. Furthermore, we have also expanded these tools to include dynamic filtering and selection, as well as three dimensional volume rendering of the data. In this section, we illustrate various components of our visual analysis system. Count (TIC) visualizationThe first component that we show is the TIC visualization. The total ion count is a reduction of the data set from four dimensions down to three. For each retention time coordinate, the intensities of the entire mass spectrum at that point are summed together to obtain the total intensity, or total ion count. Once the TIC data has been computed, it can be visualized either in 2D, or as a 3D height rendering. 2D TICThe two-dimensional total ion count image is one of the most common visualization techniques for GCxGC-MS data. Ion count values are mapped to a color using the specified transfer function and rendered to the screen as a flat, two-dimensional image, as in Figure 1. Figure 1GCxGC-MS data sets. GCxGC-MS data sets rendered as 2D TIC images (top). Our system provides visual analytic tools to help researchers identify meaningful differences (bottom). Here we show a canine cancer sample (left) compared with a healthy canine sample (right). Full size image3D TICA total ion count height rendering is nearly identical to the two-dimensional total ion count image. For the height rendering, the intensity is used as the z-coordinate in a polygonal mesh, and can be scaled linearly or logarithmically to fit within a reasonable dimension. The x and y coordinates are evenly spaced points corresponding to retention time 1 and retention time 2. When used in conjunction with a normal color mapping, this does not actually convey any more information than a two-dimensional TIC image (Figure 2, left). However, this is still a useful technique as data can often be portrayed more effectively by mapping the data values to multiple display parameters, in this case color and height. Not only do the two parameters serve to reinforce each other, but one may overcome deficiencies in the other. Figure 2A color Field.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: By examining the second order difference of Figure 6, a local extremum occurs at 4th, 7th and 11th coordinates. Because the standard deviation decreases smoothly after the 7th coordinate, and because the variation of the concavity in the 7th coordinate is larger than those at the 4th and 11th coordinates, we assume that the variables after dimension 7 are noisy and can be removed for dimension reduction. Hence, we lay out these 5006 genes on a 7-dimensional space. In this space, two genes located nearby will have similar expression profiles in this dataset. Then we perform the K-means clustering method to compare the clustering result between the original expression data and our low dimensional layout. Figure 6The standard deviation of each coordinate of the layout representation. The first turning point occurs at dimension 4, the second turning point occurs at dimension 7, and after dimension 11 the standard deviation decays smoothly. Full size imageNote that K-means usually get a local optimal solution. When we want to obtain a reliable solution, we need to repeat K-means several times and choose the best solution. Or we can define a function to measure the quality of K-means solutions, and then apply the simulated annealing to get the optimal solution. Thus, obtaining a reliable K-means solution will take time. Fortunately, applying K-means in the reduced dimension space are more stable than applying K-means in the high dimension space. That is, the iteration of K-means in the reduced dimension space converges faster than in the high dimension space. To demonstrate how dimension affects the stability of K-means, we repeat K-means on the yeast cell cycle data in the SC-MDS space with different restricted dimensions, until K-means obtain 50 converged solutions. Figure 7 shows that the CPU times are inversely proportional to the data dimension. The time K-means requires in a seven dimensional space is ~1/3 of a 23 dimensional space. Hence dimension reduction accelerates the K-means solution. However, although applying K-means in a low dimension space is faster than in a high dimension space, loss of too many dimensions will distort the distance relationship between data points, thus distorting the clustering result. Hence, the dimension of reduced space should be determined carefully. Figure 7K-means convergence time vs. data dimension.

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: Precisely how photobiomodulation may offer these beneficial outcomes are not entirely clear, although a primary mechanism of action has been shown to lie within the mitochondria (Hamblin, 2016). In particular, the mitochondria have photoacceptors, for example, cytochrome c oxidase and/or interfacial nanowater, that absorb light across the red-to-near-infrared range (Figure 1B and C). For cytochrome c oxidase, the most well-known of the photoacceptors, the absorption of photon energy results in an increase in electron transport, more oxygen consumption, higher mitochondrial membrane potential, and an increase in ATP production. Signaling molecules are produced, including a brief burst of ROS, promoting nitric oxide release and an increase in the expression of genes related to protein synthesis, cell migration and proliferation, anti-inflammatory signaling, anti-apoptotic proteins, and antioxidant enzymes. But cytochrome c oxidase is not the only photoacceptor. In recent years, it has become clear that other photoacceptors must also be present in the cell and interfacial nanowater has been suggested to be a likely candidate. Layers of nanowater are found within the mitochondria and these tend to get viscous; this increase in viscosity impedes the function of ATP synthase and this can lead to cell distress and pathology. Photobiomodulation has been related to a decrease in the viscosity of nanowater, leading to an increase in the efficiency of the ATP synthase and higher levels of ATP. This mitochondrial stimulation after a photobiomodulation-induced change in the composition of water molecules, can then presumably lead to the activation of the signaling pathways and gene expression that result in beneficial cellular outcomes (see above). Hence, photobiomodulation can improve energy metabolism within body cells, principally through activation of the mitochondria that leads to an increase in ATP levels. But in order to stimulate the mitochondria to produce the ATP, there needs to be glucose available to fuel the process. We hypothesize that photobiomodulation is most effective in stimulating mitochondrial function when there is glucose readily available for use (Figure 1B and C). The glucose may be available directly from the circulation or from glycogen stores in muscle, liver, or within the astrocytes in the brain (see above).

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: A color mapped height field (left). Using the high contrast option for height field rendering (right), small peaks and background noise, which might otherwise be hidden, are easily seen. Full size imageAdditionally, as a new application, the height field can be used with alternative color mapping schemes, similar to work done by Linsen et al. with LC-MS data [12]. In this case, the height of the peaks is a useful method for communicating peak intensity compared with the color mapped attribute. As an alternative to color mapping, we also provide a 'high contrast' rendering option for the height field. For this technique we enable OpenGL lighting and create a single light source positioned along the positive z-axis with ambient, diffuse, and specular components. We apply diffuse, specular, and shininess material properties to the polygons. Vertex normals are calculated at each vertex in the mesh, corresponding to each RT1/RT2 coordinate. The end result is a high-gloss, metallic looking rendering with high contrast. With this technique, even small peaks are highlighted and readily noticeable, as seen in Figure 2 (right). Background noise is also highly visible in this view, as it produces a large number of small peaks and valleys. TIC color mapsThe total ion count visualizations both support color mapping based on intensity, difference, and standard deviations away from a mean. Each of these methods can be configured to use either a continuous or discrete color scheme. For the continuous color scheme, the system uses a set of three curves that allow independent control of the hue, saturation, and brightness. For the discrete color scheme, the system presents the user with a histogram that displays bin colors and data distribution. The user can modify the number of bins, data range for the bins, and bin colors interactively. The color for each bin can be specified by the user, or the system can automatically generate a color mapping. In each case, values are initially mapped to a logarithmic scale where a larger color range is used to represent small intensities, and the scale of large peaks is greatly reduced. We provide three different types of visualization modes for the TIC color maps: intensity, difference and standard deviation. IntensityThe intensity mode is a simple mapping of the peak intensity to color. This technique is useful for providing a high-level view of the data.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: 5% genes are indicated to have cell cycle function in the cluster obtained in the reduced space, and its p-value is 1. 1 × 10-9. In Fig. 9(b), 40% genes are indicated to have cell cycle function in the cluster obtained in the original space, and its p-value is 1. 4 × 10-8. There are, however, another 37 genes that are included in the corresponding cluster in the original space. Nine of them have significant functions in DNA processing. Conversely, there are another 17 genes that are included in the corresponding cluster in the reduced space. Six of them have significant function in mitotic cell cycle and cell cycle control. In Fig. 10, 51. 8% of the genes in the 32th cluster are annotated to have cell cycle functions in the cluster of K-means in the reduced space, while the genes in the corresponding cluster in the original space, the 29th cluster, 42. 3% are annotated to have cell cycle function. Compare the difference between Fig. 10(a) and 10(b). Five genes included in the cluster of the original space have no significant in the cell cycle function. Conversely, 7 genes included in the cluster of the reduced space include 3 genes (YHR152w, YML128c and YOR265w) that are significant in meiosis. In Fig. 11, 45. 8% of the genes in the 54 cluster of the reduced space are annotated to have cell cycle, its p-value = 7. 27 × 1014; 48% of the genes in the 58 cluster of the original space are annotated to cell cycle function, its p-value = 2. 03 × 10-7. We can see that in this pair, the cluster in the reduced space is worse than that in the original space. The other comparisons between the clusters from the reduced 7-dimensional space data and from the original space data are shown in Additional file 1 and file 2. Combine the above three cases and twenty pairs that are almost matched, we can see that applying K-means to the SC-MDS reduced space performs at least as well as in the original data set. SC-MDS did not distort the pairwise relationship between data points, and it speeds up the analysis with accuracy preserved. Figure 9Comparison of the clustering results in the reduced space and in the original space (I).

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: If using a motor vehicle analogy; no matter how well the car engine (i. e. , mitochondria) is tuned-up and serviced, cleaned, and polished (i. e. , with photobiomodulation treatment), it will not work without the necessary fuel (i. e. , glucose). We have several lines of evidence in support of our hypothesis. First, there has been a report in drosophila that, under normal physiological conditions when food is readily available, photobiomodulation increases survival rate and body metabolism. By contrast, during fasting, when glucose levels are low, photobiomodulation has little or no effect on both these parameters (Weinrich et al. , 2017). This result suggests that for photobiomodulation to work effectively, there must be a readily available source of glucose for the mitochondria to work with. There are also some indications for a similar effect in mice. When diabetic mice have been fasted for eight hours, photobiomodulation has no effect on their low blood glucose levels compared to controls. However, when these diabetic mice are administered an intraperitoneal injection of glucose, photobiomodulation treatment is effective in reducing the subsequent increase in blood glucose levels (Bonifacio et al. , 2022), see their Figure 6B). Although the metabolic pathways in drosophila are highly conserved to mammals (Cho et al. , 2011), this result in mice requires further exploration, given the more complex and tighter regulation of glucose metabolism in mammals during fasting. Second, photobiomodulation has been shown to prompt glucose metabolism within body cells. Several recent studies have shown that photobiomodulation can reduce blood glucose levels, together with insulin resistance, in both non-diabetic (Castro et al. , 2020) and diabetic (Gong et al. , 2021) animal models, as well as in patients (Pacheco et al. , 2018). This phenomenon arises presumably after a photobiomodulation-induced stimulation of mitochondrial activity in body cells, which utilizes the available glucose in blood circulation.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: The z-value is simply how many standard deviations different a value is than the calculated mean. We then use that difference to determine the appropriate color. z = μ A - b σ A (2) This can help a user to determine whether an observed difference is truly meaningful. Additionally, this technique may effectively reveal areas of difference in smaller peaks that are significant in terms of standard deviations, but were not previously noticed simply because the peaks themselves are smaller. An example is shown in Figure 3 (right), note the green streaks that are not seen in Figure 3 (middle). This helps the user explore regions in the image that are statistically different in a sample when compared to a group of samples. Mass spectrum visualizationA mass spectrum view is simply a plot of intensity on the y-axis vs. the mass-to-charge ratio on the x-axis, as seen in Figure 4 (bottom). The user is given the option to plot this spectrum as a bar graph, or as a connected line. In order to help a user form a hypothesis about particular mass values that constitute an observed difference, this system provides a novel technique for visualizing the mass spectral difference between two samples. The technique is similar to rendering a normal mass spectrum. In this case, the zero intensity baseline is drawn across the middle of the viewing window, with bars for positive differences rising upward, and bars for negative differences falling downward from the baseline as demonstrated in Figure 5. Figure 4The OmicsVis tool. OmicsVis provides users with the ability to crop data sets, enabling them to remove solvent-saturated areas and reduce file size for ease of use. Full size imageFigure 5Spectrum. Visualizing the mass spectral difference between two samples. Full size imageCroppingDatasets created by GCxGC-MS can quickly become extremely large. A typical experiment setup for datasets used in this thesis involve collecting data over a time duration of 40 minutes or more, taking one reading every 10 milliseconds, with each reading containing an intensity value for 900 or more m/z values. Such a setup creates over 850MB of raw data per sample, with experiments containing from 10 to 40 samples. Cropping the datasets not only makes them faster and easier to store and work with, but also allows uninteresting or problematic areas to be removed. Typically, a large amount of solvent will elute near the beginning of the data collection.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: (a) The 20th cluster of K-means in the 7-dimensional space from the SC-MDS method. 45. 5% of the genes in this cluster are annotated cell cycle functions. (b) The 59th cluster of K-means in the original 23-dimensional space. 40% of the genes in this cluster are annotated cell cycle functions. The blue lines are gene expression profiles and the red line indicates the average of these expression profiles. Full size imageFigure 10Comparison of the clustering results in the reduced space and in the original space (II). (a) The 32th cluster of K-means in the 7-dimensional space from SC-MDS method. 51. 8% of genes in this cluster are annotated cell cycle functions. (b) The 29th cluster of K-means in the original 23-dimensional space. 42. 3% of genes in this cluster are annotated cell cycle functions. Full size imageFigure 11Comparison of the clustering results on the reduced space and on the original space (III). (a) The 54th cluster of K-means in the 7-dimensional space from the SC-MDS method. 45. 8% of genes in this cluster are annotated cell cycle functions. (b) The 58th cluster of K-means in the original 23-dimensional space. 48% of genes in this cluster are annotated cell cycle functions. Full size imageConclusionOur new method reduces the computational complexity from O(N3) to O(N) when the dimension of the feature space is far less than the number of genes N, and it successfully reconstructs the low dimensional representation as does the classical MDS. Its performance depends on the grouping method and the minimal number of the intersection points between groups. Feasible methods for grouping methods are suggested; each group must contain both neighboring and far apart data points. Our method can represent a high dimensional large data set in a low dimensional space not only efficiently but also effectively. This Split-and-Combine method makes the parallel computation of MDS feasible. If samples increase to the level that one computer could not handle, we can split data to several subgroups, assign them to different computers to compute the MDS, and then collect the results and combine them into one.

Output: corroborate


Input: Claim: Astrobiology is fully understood and does not require further research. [SEP] Text: Our hypothesis, if correct, has considerable experimental and clinical implications; for optimal beneficial outcomes for the treatment of ailments across the body, from the brain to the musculoskeletal system and from the microbiome to the heart, scientists in the laboratory and medical and allied health professionals in the clinic should apply photobiomodulation soon after meals. Our hypothesis awaits experimental and clinical validation. We thank Fonds de dotation Clinatec and for supporting our work. We also thank (Wellred Inc. , Australia), (UCL, UK), and (London, UK) for proofreading the first version of the manuscript. C-Editors: T-Editor: Jia Y1. (2014) Metabolic determinants of cancer cell sensitivity to glucose limitation and biguanides. Nature 508:108–112. 2. Bonifacio M, Benfato ID, de M, de de F, de (2022) Effects of photobiomodulation on glucose homeostasis and morphometric parameters in pancreatic islets of diabetic mice. Sci 37:1799–1809. 3. Castro KMR, de (2020) Can photobiomodulation therapy (PBMT) control blood glucose levels and alter muscle glycogen synthesis? . J B 207:111877. 4. (2011) The role of mitochondria in Drosophila aging. 46:331–334. 5. (2004) Why do cancers have high aerobic glycolysis? . Cancer 4:891–899. 6. (2021) Photobiomodulation therapy ameliorates hyperglycemia and insulin resistance by activating cytochrome c oxidase-mediated protein kinase B in muscle. Aging (Albany NY) 13:10015–10033. 7. Hamblin MR (2016) Shining light on the head:photobiomodulation for brain disorders. BBA Clin 6:113–124. 8. (2016) Turning on lights to stop neurodegeneration:the potential of near infrared light therapy in Alzheimer's and Parkinson's disease. 9:500. 9. Judge A, Dodd MS (2020) Metabolism. 64:607–647. 10. (2021) Physiology glucose metabolism. In:StatPearls [Internet] (FL) StatPearls Publishing. 11. (2018).

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: The high intensities and large variation in this area can skew the scaling and data mapping schemes employed in analysis algorithms. This area can be graphically selected, and cropping can be performed across a group of samples based on those parameters. Figure 4 depicts the use of the cropping tool. Mass filterWhen a user is looking for bio-markers and meaningful differences between samples, the user will often identify a few mass values that make up some interesting compound. The mass filter tool allows users to select a unique mass or set of masses from the mass spectrum display. Total ion count data for active TIC visualizations is then re-acquired using only the selected masses. The color mapping is then rescaled to match the new range of values across all of the TIC displays, and the TIC displays are refreshed. This allows a user to quickly determine differences among samples for a selected set of mass values. While other applications provide mass filtering via dialog options, none currently support real-time updating of the mass filter in an interactive manner. Mass values can quickly be added to or removed from the filter as the data sets are being interactively explored for differences in a unique set of mass values. Volume visualizationVolume rendering is a well-established method for depicting the embedded structures in a three-dimensional scalar field. The most interesting feature of volume rendering is that important regions can be enhanced while distracting details can be hidden by adjusting their transparency. By incorporating non-photorealistic rendering into volume visualization, volume illustration [13] has proven to be very effective in feature-oriented visualization. The exploration of the mass spectral data can benefit from applying volume visualization in three ways. First, visualizing one dataset with the assistance of a multi-dimensional transfer function gives the user a global picture on the intensity distribution and possible peak patterns. Second, the user can freely select subregions to investigate the local mass spectra. The determination is either interactively specified, or automatically found by comparing the mass spectra in a small-sized window with the mass spectra of known metabolites stored in a database. It also facilitates comparing the spectra of different potential bio-markers. Figure 6 compares a selected region of four samples. Third, by globally or locally comparing the mass spectra of a set of sample data with volume visualization techniques, the user's attention can be quickly directed towards the most interesting features, easing the task of finding or verifying the differences among samplesFigure 6Volume visualization.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: in through your institution and BioinformaticsThis issuesearch term and Applied to Genomics Editor's -and Journals on Books on and Applied to Genomics Editor's -and and and BioinformaticsThis issuesearch term Menu 10. 1093/nargab/lqaa101 Published: 11 December 2020 10. 1093/nargab/lqaa101 Select format. ris (Mendeley, Papers, Zotero). enw (EndNote). bibtex (BibTex). txt (Medlars, RefWorks) Download citation and BioinformaticsThis issuesearch term and BioinformaticsThis issuesearch term important goal in molecular biology is to quantify both the patterns across a genomic sequence and the relationship between phenotype and underlying sequence. We propose a multivariate tensor-based orthogonal polynomial approach to characterize nucleotides or amino acids in a given sequence and map corresponding phenotypes onto the sequence space. We have applied this method to a previously published case of small transcription activating RNAs. Covariance patterns along the sequence showcased strong correlations between nucleotides at the ends of the sequence. However, when the phenotype is projected onto the sequence space, this pattern does not emerge. When doing second order analysis and quantifying the functional relationship between the phenotype and pairs of sites along the sequence, we identified sites with high regressions spread across the sequence, indicating potential intramolecular binding. In addition to quantifying interactions between different parts of a sequence, the method quantifies sequence–phenotype interactions at first and higher order levels. We discuss the strengths and constraints of the method and compare it to computational methods such as machine learning approaches. An accompanying command line tool to compute these polynomials is provided. We show proof of concept of this approach and demonstrate its potential application to other biological systems. to the inherent complexity in biological systems, much of the analysis that aims to study systems, such as sequence structure and function in genomics, has been largely based on computational methods. Advancements in sequencing technology and the rise in the availability of genomic data has led to the development of novel computational tools that seek to determine the relationship between underlying sequence and the resulting function or phenotype. These methods aim to predict protein function given sequence and structure information, identify novel and potential DNA binding motifs, including transcription factor binding sites and determine RNA secondary structure based on the underlying sequence (1–4).

Output: corroborate


Input: Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: That problem seemed resolved with the advent of Einstein’s Theory (SRT). SRT was believed to capture the true meaning of MED concerning the behavior of light signals, and SRT was certainly an endorsement of Lorentz transformation, so SRT was believed to offer the one possible revision of NM that could make mechanics fully consistent with MED. But meanwhile, new phenomena were being discovered at the micro scale of physics, and they often seemed inexplicable with any known theory, whether NM, SRT, or MED. These were phenomena suggesting quantization of light, quantized atomic states, atomic, molecular and crystal structures, radioactivity, etc. So at almost the same time as one problem seemed to be resolved, other problems were emerging. Since the earlier situation between NM and MED had demanded that Physics allow two seemingly discordant theories to co-exist until some good argument could replace one of them, the situation then presented by the new phenomena being discovered naturally invited the development of another potentially discordant theory: (QM). The discovery of the photoelectric effect, and the introduction of the idea of the photon, initiated QM. Almost immediately, QM was developed to handle the Hydrogen atom, and the ground state thereof, the stability of which was thought to be impossible with MED. Accepting that apparent incompatibility with MED, and even embracing it, researchers moved on to excited states, to other atoms, then to molecules, and reactions, and to all the rest of the complexity that today makes up modern (QC). Also, experimenters got into sub-atomic elementary p2. Maxwell’s electrodynamics and QM’s photons It often seems that MED, a theory largely about spatially extended EM fields, has little in common with QM, a theory largely about discrete material systems and the discrete photons that they emit and absorb. Photons are imagined to be the opposite of spatially extended; i. e. , localized, like the matter p2. 1. Waveform development The first step in the life history of a photon is its development from a spatially localized energy bundle that is emitted from a source into a spatially extended waveform that travels through space. To help think about this problem, it is useful to recall some phenomenology familiar from physics at a more macroscopic scale.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: This set of samples consists of twenty-nine samples obtained from mice. Ten each were extracted from the body and yolk, while nine were extracted from the head. In each case, half of the samples were exposed to alcohol and half were not. Because alcohol is a depressant and slows down metabolic processes, it is expected that differences between the two samples should show up in the metabolomics data. The first step taken is to convert the cdf files into raw data files. Since these particular files have very high background levels, the file size drops from about 1. 3GB down to 677MB. Compressing the files further reduced the size down to about 245MB. Finally, the samples were cropped to remove regions that were empty or oversaturated with solvent. It was also shown that background level alone occupies mass values above 600, so this area was cropped. The resulting files averaged about 60MB, which can be read from networked file servers in a reasonable amount of time. The first step after converting the data sets is to view the total ion count image from each one. Since each is displayed using a global color scale, quick visual comparison can identify unusual data samples. At this point, one is basically trying to obtain an overview of the data, and look for obvious outliers. For each pair of alcohol and control means, a difference volume was calculated. Mean/standard deviation color mappings were created to help visualize the samples. There is a single red peak that indicates an area of higher concentration in the alcohol samples, but several green peaks can be noticed, standing out against the green hued background that is caused by the higher background level present in the control samples. These areas are also indicated by the mean/standard deviation color mapping in Figure 7. A researcher searching for bio-markers could then target these areas specifically for further analysis. Figure 7Alcohol mean colorized by comparing with the mean and standard deviation of the control samples. The red area indicates an unusual concentration in the alcohol samples. Full size imageThe linked views included in the system allow a user to investigate the mass spectra in real time. This form of focus+context can be used to form hypothesis about what masses or compounds are contributing the observed differences. Figure 8 demonstrates this feature. Without spending too much time working with these samples, a quick effort can be made using this system to look for meaningful differences between the groups. Using visual inspection, samples with missing or blurry peaks can be eliminated.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: While computational methods, such as machine learning (ML) models, provide powerful ways to extract patterns in complex data, they lack the clarity of interpretation that comes with purely mathematical approaches. In this work, we present a method to do analytical mathematics with sequences that integrates well with computational methods and that has the potential to reveal new results and complement those given by purely computational or ML approaches. Current methods that aim to connect sequence information to output phenotype largely utilize ML tools, such as deep learning, to quantify the role of each site in a sequence in the resulting phenotypes. Some examples of this include deep learning tools that aim to predict protein structure given the underlying amino acid sequence and others that are designed to predict the effect of each site in a pre-mRNA sequence on mRNA splicing (5,6). Although these methods seem promising and do reveal substantial biological insights, they come with caveats such as the requirement of large training datasets and ‘the incorporation of irrelevant features’ into the deep learning model as in the case of SpliceAI (6). Here, we describe a mathematical method using multivariate tensor-based orthogonal polynomials to convert sequence information into vectors and build orthogonal polynomials with the aim of quantifying the effect of the sequence states on the resulting phenotype (7). Our method proposes an entirely novel way to work with nucleotides in a genomic sequence. Elements in a sequence (nucleotides, amino acids, etc. ) are not meaningfully described by scalar values (i. e. by a single number) because they are distinct types of things that are not well-characterized in this way (7). In general, instead of representing nucleotides with individual numbers, current methods utilize kmers, or words of length k, to represent a set of nucleotide bases. Here, a 1-mer is the same as a single site in a sequence. The use of kmers is ubiquitous as a bioinformatics tool and they’re used widely in many bioinformatics applications such as genome assembly and compressing genomic sequence data (8,9). In addition, kmers can be utilized to look for associations between different sequences and any associated traits in GWAS studies (10). Another widely used representation is encoding each nucleotide as a one-hot encoded array that is fed into ML algorithms.

Output: corroborate


Input: Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: One phenomenon very well known for light modeled as EM waves is the spreading transverse to the propagation direction known as of ‘diffraction’. Diffraction is the result of some sort of limitation transverse to the propagation direction. Historically, the limitation has been due to a finite aperture through which the light propagates. The light spreads out from the aperture, more-so the smaller the aperture is. In the photon model discussed here, the limitation is softer than an aperture edge, but a limitation nevertheless: it is the finite spread of the Gaussian waveform in the two directions transverse to the propagation direction. The more narrow the Gaussian peak is, the more spread there will be. The closest familiar analog for longitudinal spreading is known as ‘dispersion’. This word refers to the ‘blurring’ effect that any frequency dependence the propagation speed through the medium entails. For example, a signal pulse in a medium looses its sharp edges because those sharp edges imply superposition of many different wavelengths, and hence different frequencies, which the medium may affect differently. In Earth’s atmosphere, or ocean, square waves can turn to blob waves because of dispersion. Let us begin a scenario with a single pulse in E. Let it have a Gaussian profile along the propagation direction, say x with E ∝ exp ( − x 2 ). We can apply Maxwell’s equations, and watch what happens. is the so-called ‘generating function’ for the infinite set of Hermite polynomials, all of which have very regularly spaced zero crossings. What happens is that the single pulse in E (an even function) generates a double pulse in B (an odd function), which in turn generates a triple pulse in E (another even function), and so on; that is, all the derivatives in play generate successively higher-order Hermite polynomials multiplying the Gaussian. Meanwhile, all the E × B Poynting vectors in play support general spreading of the Gaussian. With each step, the emergent functions look more and more like wavelets, and the individual peaks in the wavelets stay about the same width as more of them accrue, so the wavelength for the emergent wavelet becomes more and more defined. Figure 1 illustrates this behavior at the stage where E has developed five peaks (four zero crossings).

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Averages for the remaining samples in each group can then be computed. From the healthy group,multiple samples can be chosen and used for computation of the mean. While the variations present in these samples make conclusions hard to draw, researchers found such visual exploration techniques to be valuable. Particularly, researchers were able to visually inspect data and rule it out quickly, rather than spending days of analysis time trying to detect features and differences that may be completely obscured. Figure 8Linked views allow the mass spectra to be explored in real-time as the user interacts with the TIC image. Full size imageThree-dimensional mass spectrum explorationWe can also explore data in a three-dimensional visual representation to depict its properties such as the location, the uncertainty and the weight. This representation uses the (RT1, RT2, MS) triple coordinate space, and is modeled with a cylinder whose height and radius are proportional to the weight and uncertainty respectively, and whose appearance is encoded as a color-mapped texture representing its mass spectrum, as seen in Figure 9. The visual pattern of each peak is fixed during the exploration. The user can freely navigate in this three-dimensional space, visually check the mass spectrum of specific bio-marker candidates, and locate, explore and compare the properties of the selected metabolites of interest. Figure 9Exploring differences in canine samples. Interactive exploration of the 3500 detected peaks in two samples. The user interactively filters the bio-markers by adjusting parameters, (a) is the result (1300 peaks) by changing the thresholds from (0. 01, 0. 001) to (0. 008,0. 004) respectively (see the left top snapshot). (b) is the result (198 peaks) by interactively specifying a region in the region operating characteristics plane (see the left top snapshot). (c-d) Comparative exploration of 198 peaks in two samples. For instance, the bio-markers indicated with red arrows exhibit different mass spectra, which can be inspected by comparing their numerical values, color map views, and plot views provided in our system (see the views in the dashed red rectangle). Full size imageOur visualization technique compactly displays the mass spectra in a three-dimensional space, thereby easing the understanding and comparison.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Thus, the study of both the positive and negative impacts of covariation on molecular function can provide insight into the nucleotides involved in important intra- and intermolecular interactions. Importantly, while the Watson-Crick base pairing interactions depicted in Figure 2 are rather easy to computationally predict, there are many other types of interactions occurring within structured RNAs that are less simple to predict. Studies providing insight into the functional importance of sequence covariation may assist in improving the predictions of these other types of structural elements in the future. Figure 2. Importance of covariation for secondary structure. (A) It shows a case where there exists favorable intramolecular interaction (top panel) and an unfavorable intermolecular interaction with another transcript (bottom panel). (B) Here, the same original sequence has 3 nt mutated which gives rise to an unfavorable intramolecular interaction (top panel) but a favorable intermolecular interaction with the other transcript (bottom panel). (C) It shows mutually exclusive structures with competing intramolecular and intermolecular interactions when there is a mutation (denoted in blue) that covaries with the nucleotides denoted in red. Open in new tabDownload slide of orthogonal polynomials Given a set of or protein sequences, along with corresponding phenotypic data, our method consists of building tensor-valued first and higher order polynomials and projecting the phenotypic data onto this polynomial space (see for detailed explanation and proofs). Note that we assume that the sequences we are working with are of good sequencing quality and depth. Thus, before applying this method to sequence data, the user will have to perform general bioinformatic pre-processing steps to produce the final set of sequences to be analyzed. To apply our methods to the STAR system, we first converted each site in each sequence of the 99 sequences of STAR and target RNAs into a vector as depicted in Figure 3. This is similar to one-hot encoding an array which is a first step when feeding sequence data to an ML algorithm (11). For each type of RNA, each sequence had a corresponding experimentally derived OFF/ON fluorescence value which served as the numerical phenotype that we later project onto the polynomial space. Figure 3. Example sequences with corresponding phenotypic values. Example sequences with corresponding phenotypic values.

Output: corroborate


Input: Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: Series 1 is the original input Gaussian function, Series 2 is the Gaussian after the overall spreading has developed to this point, and Series 3 is the wavelet that has emerged in the process; i. e. the spread-out Gaussian times the fourth-order Hermit polynomial generated. Figure 1. A wavelet develops when an EM pulse is acted upon by Maxwell’s equations. What we have so far is only one eighth of the story needed to fully represent a photon: development from a pulse into a waveform. We have told the story for one pulse in E. If we would match that with another pulse in B we would have overall propagation along with waveform development. That would bring us to one quarter of the whole story of the photon. If we would match that with two more pulses, E and B pointing at 90 ° in space from the first pair and coming ‘alive’ a quarter cycle out of phase with the first pair, we would have the circular polarization characteristic of photons, but we would still have just half the story. So let us move on, and seek the other half. 2. 2. Waveform regression The remaining half of the story of the photon is about waveform regression. How does this complex structure of four Hermite polynomials multiplied by their generating Gaussian unwind, and go back to being a set of four pulses, so that it can be absorbed into a receiver? Again, let us refer to some similar but more familiar phenomenology: A third phenomenon possible for light modeled as EM waves is ‘focusing’. This is what we have optical lenses and shaped mirrors for. It works somewhat contrary to transverse spreading, gathering incident energy into a smaller area transverse to the propagation direction. Of course we don’t have any lenses or mirrors in the photon model, but we shall find a mechanism that produces a similar effect. A fourth phenomenon possible for light modeled as EM waves is ‘pulse restoration’. This is what transmission lines have ‘repeater stations’ for. A communication signal degraded by dispersion can be reconstituted when passed through an intelligent filter. Of course we don’t have any filters in a photon model, but we shall find a mechanism that produces a similar effect. The ‘similar effect’ comes from the imposition of boundary conditions in the longitudinal direction.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Skip to main content Explore journals Get published About BMC My account Search all BMC 1. the interacting proteins have homologs that interact, 2. the interacting proteins each have a Pfam domain found to interact with the other in PDB and, 3. the interacting proteins have at least one identical GO annotation. We used protein-protein interaction data from the Database of (DIP) [27] (July 2004 release) and IntAct [28] (September 2004 release). We prove our hypothesis first in yeast by estimating likelihood ratios for high-throughput interactions based on the number of known true positives and false positives using Bayesian network approaches. Based on these results, we estimate the number of true positives in the high-throughput data sets of S. cerevisiae, C. elegans, D. melanogaster and H. sapiens. The results can be searched at and downloaded from our website [29]. ResultsCalculating the reliability of each genomic featureWe used protein-protein interactions from high-throughput data sets for yeast as our test set to calculate the reliability of each genomic feature (see Methods). Of these 12,674 interactions, we chose a set of 3464 interactions as our gold standard – 1479 as the positive gold standard and 1985 interactions as the negative gold standard (see Methods). Our goal was to maximize the interactions identified in the gold positive set (high sensitivity) and at the same time minimize the number of interactions identified in the gold negative set (high specificity). In these interactions, we identified all those that had homologous interactions. The true positives (TP) were those interactions with homologs that were in the gold positive set, and the false positives (FP) were those that were in the gold negative set. Using these values, we calculated the likelihood ratio (L) for the genomic feature of 'homologous interactions' (see Methods). Similarly, we calculated the likelihood ratios for the other two genomic features – interacting proteins with at least one identical GO annotation and interacting proteins having one of 2 Pfam domains known to interact in PDB. We also calculated the likelihood ratio for the absence of genomic features. Figure 1 shows the likelihood ratios calculated. Likelihood ratio (L) expresses the reliability of each genomic feature. > 1 indicates the ability of the genomic feature to identify more true positives than false positives. As seen in Figure 1, all the genomic features have L values greater than 1.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: (A) It shows the sampling distribution of absolute values of the largest regressions of the phenotype onto combination of two sites. Notable regressions are those at the tail end of the distribution, and are shown in red (>35 000). (B) Relationship between distances across STAR sites and absolute values of the largest regressions with 14 site pairs with high regressions shown in red. (C) To further zoom into the 14 pairs of sites with notable regressions, as depicted in (A) and (B), curves are drawn between the interacting nucleotide at one site and the corresponding nucleotide at another site. This indicates a more global structure across the STAR sequence, instead of a case in which regressions of the phenotype onto pairs of sites in the 5′ region of the sequence are greater than those in the 3′ region. Open in new tabDownload slideOut of the 14 site pairs shown in Figure 9, there are four pairs that are between sites in the 5′ and 3′ regions. This potentially supports the hypothesis mentioned earlier which states that possible binding between these parts of the sequence would allow the hairpin region of the RNA to stay intact (by not binding with the hairpin) and pursue its function of transcription termination of the downstream gene. However, in addition to this long-range interaction, there are a cluster of strongly interacting sites in the middle portion of the sequence, between sites 11 and 20. This includes site 17 which has the most interactions (a ‘C’ at site 17 interacting with five other sites). There exists large values for regressions of the phenotype onto these site pairs (see S2 for values). This suggests that there might exist some level of potential intramolecular binding in the middle section of the sequence that was not picked up by the software when the initial sequences were being designed. this work, we propose a novel mathematical tool to describe sites along biological sequences as vectors and quantify sequence–function relationships by projecting phenotypes onto the sequence space. Given a set of sequences and corresponding phenotypic data for each sequence, tensor-based orthogonal polynomials can be constructed based on the actual variation in sequences. The regression of phenotypes onto these polynomials can quantify not only the effects of different nucleotides at individual sites, but also the effect on phenotype of combinations of nucleotides at different sites.

Output: corroborate


Input: Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: pulse that was used to describe the waveform development part of the scenario was somewhat unrealistic in that its tails extended to infinity. There is no way that a localized source could emit an energy pulse whose tails would extend to infinity. It is somewhat more realistic to imagine the equivalent of a mirror at the source, and another mirror at the eventual receiver, to confine the waveform like a wave in a box, with zero amplitude at the surface of each mirror and everywhere beyond. With such boundary conditions imposed, the analytic functions involved in the model are no longer the simple Gaussian and the simple Hermite polynomials that it generates. Now we have not one, but three, Gaussians, the extra two being needed to cancel the first one at the two boundaries. Correspondingly, we always have at least three (actually six) Hermite polynomials alive at any given time. That is a loss of mathematical simplicity. But there is a gain of conceptual simplicity. It is easy to envision that the propagation scenario has some symmetry about its mid point. The waveform will spread until its central peak is halfway between the source and the receiver. After that, the mirror at the receiver will be more significant than the mirror at the source, causing the waveform to start ‘piling up’ near the receiver, and eventually end up as a pulse near the receiver, similar to the pulse originally launched near the source. This ‘regressing waveform’ is somewhat reminiscent of ‘advanced’ solutions to Maxwell’s equations going backwards in time. These were introduced many times in the early 20th century, but particularly popularized in the mid 20th century by Wheeler and Feynman (1945 and 1949). Wheeler and Feynman were looking to time symmetry as the basis for an electromagnetic generalization of instantaneous (Newtonian) gravitational interaction. There are important differences between the regressing waveforms introduced above and the Wheeler-Feynman advanced solutions: 1) Wheeler and Feynman were looking at interactions between essentially point sources and receivers, and so had to be looking at spherically expanding retarded solutions and spherically contracting advanced solutions, not at essentially one-dimensional expanding and contracting wavelets. 2) The Wheeler-Feynman expansion or contraction is related to the spherical area of a wave front, not the waveform in the radial propagation direction.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Thus, including the interactions supported by the presence of all 3 genomic features (d+g+h) in the results gives a sensitivity of 12. 3% and a specificity of 99. 4%. On further including interactions supported by interacting Pfam domains and similar GO annotations (d+g), the sensitivity rises to 14. 5% and the specificity marginally decreases to 99. 3%. As interactions supported by each individual feature or other combinations of features that have an L > 1, are included in the results, the sensitivity increases at the cost of specificity. Thus our method predicts interactions, which are supported by at least one of the 3 genomic features, to be true with a sensitivity of 89. 7% and a specificity of 62. 8%. Figure 2ROC curve for the combination of genomic features using 10-fold cross validations. The dotted line shows the empirical ROC curve, while the solid line shows the fitted ROC curve (obtained using ). Each point on the ROC curve corresponds to sensitivity and specificity for one or a combination of more than one genomic features. d: interacting Pfam domains; g: similar GO annotations; h: homologous interactions; none: no genomic features. More than one genomic features are indicated by listing the features separated by a '+' sign. Full size imagePredicting true interactions in all high-throughput data setsWe used our method to assign L values to all interactions in three other high-throughput data sets for C. elegans, D. melanogaster and H. sapiens [7–9]. We also assigned L values to the interactions in yeast high-throughput data sets [3–6] that were not part of the gold standard. We predicted all interactions with L > 1 as true interactions. Table 5 shows the distribution of the predicted true interactions across different L values for each species. Figure 3 shows the percentage of interactions predicted as true in the high-throughput data sets of each species. Table 5 Number of interactions in different ranges of likelihood ratios for high-throughput data sets of various speciesFull size tableFigure 3Percentage of interactions predicted true across different high-throughput data sets. Full size imageAuthors of the high-throughput data sets usually assign a confidence level to interactions.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: To show proof of concept, this method was applied to a case of synthetic RNA regulatory sequences, described in previously published work (19), that were experimentally constructed with the goal of identifying how sequence structure and design motifs affect RNA regulatory activity. This method has some fundamental parallels with ML methods, such as neural networks, in that they share the very first step of one-hot encoding nucleotides and converting them to vectors/arrays. Figure 10 shows the similarities and differences between the two approaches. In the ML approach, sequence and corresponding phenotype data are fed into an algorithm (such as a deep neural net) after which the algorithm is trained to learn the relationship between the phenotype and the sequence (see (25) for example). In the mathematical approach, the sequence data is used to build a space within which we can conduct further mathematical analysis such as mapping phenotypes onto the sequence space. We argue that doing such mathematical analysis has some advantages because, here, the meaning of the values produced through this approach is clear because they were derived through the mathematics whereas when these results are derived from black box approaches, it is more difficult to interpret them. For example, in the analytical approach, we have a clear understanding of what a projection of a variable onto the polynomial space is, whereas this would be difficult to grasp in the traditional deep learning approaches. Figure 10. Comparison of analytical and ML approaches. Overview of similarities and differences between an ML approach and an analytical mathematics approach such as the method described here. The two share similar first steps and are ultimately aiming to understand sequence–phenotype relationships. Open in new tabDownload slideOne other advantage that this approach has over other ML approaches is that once the sequence space is constructed (which is the part that requires most of the computational resources), one can easily project any corresponding phenotypes onto this space. In the ML approach, on the other hand, the algorithm would have to be re-trained entirely if one wanted to map a different phenotype to the underlying sequence. Furthermore, these two mappings would not be easily comparable as each phenotype and underlying sequence would have been trained differently. However, a hybrid approach that combines the two methods could be implemented. For example, it is possible to approximate some types of orthogonal polynomials using neural networks as has been done before (26,27).

Output: corroborate


Input: Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: 3) A lengthy discussion of the paradox of advanced actions is necessitated in the Wheeler-Feynman work, whereas the ‘regressing’ solutions introduced here are not in fact ‘advanced’ at all; they are just regressing, in real time, in the propagation direction. What we have here is quite different though. There are no differential equations running backwards in time; there is just ‘piling up’ of a solution to differential equations in response to a boundary condition. 2. 3. The photon model in terms of EM fields Taken together, the waveform development followed by the waveform regression suggest a photon model in terms of EM fields that exhibits continuous evolution: it goes from a state of pulse-like localization near its source, to a state of wave-like extension in space during its travel, and then back to a state of pulse-like localization near its receiver. Observe that with this photon model, ‘light in flight’ develops its wavelength only during its flight. It doesn’t have it to start with, and it gives it up at the end. So light at emission, or reception, has a position, but no wavelength, whereas light in flight has a wavelength, but no position. Thus the model expresses a ‘wave-p3. EM signals as photons Every neutral atom contains at least two p3. 1. Standard formulae for scalar and vector potentials Expressed in Gaussian units, the Liénard-Wiechert (LW) scalar and vector potentials at position r and time t are Φ ( r t ) = e [ 1 κ R ] retarded and A ( r t ) = e [ β → κ R ] retarded E1 where κ = 1 − n ⋅ β → β → is source velocity normalized by c and n = R R (a unit vector), and R = r source ( t − R c ) − r (an implicit definition for the terminology ‘retarded’).

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Surprisingly, evidence from interacting Pfam domains (d) performs better than that of the combination of the other two features (g+h), highlighting the importance of the incorporation of structural evidence. Due to the absence of information about non-interacting proteins, we prepared our gold negative set from proteins that have different subcellular localizations. However, some interactions are transient with interacting proteins residing in the same sub-cellular compartment for only a small fraction of their life time. As a result, some of the interactions in the gold negative set are actually true. Thus, the specificity of our method is probably higher than 62. 9%. Using the evidence of the three genomic features, we predicted the number of true interactions in various high-throughput data sets. Our prediction of 56. 3% true interactions in yeast high-throughput data sets is in conformance with the previous estimates of the number of false positives in these data sets [1, 11]. However, yeast Y2H [3, 4] and Co-IP data sets [5, 6] show very different numbers of true positives independently – 37% and 73% respectively (data not shown). The D. melanogaster data set [8] shows a very low rate of true positives. One reason could be that this experiment was performed using most of the predicted transcripts in the D. melanogaster genome, including biologically irrelevant ones. The C. elegans data set [7] includes a higher percentage of true positives than D. melanogaster, perhaps because the experiment was performed only on a restricted set of predicted proteins related to multi-cellular functions. The H. sapiens data set [9] shows the highest number of true positives at 67. 9%. This data set was obtained from a study that focused on the identification of putative protein complexes in the TNF-α/NF-κB signal transduction pathway using Co-IP [9]. There are two possible reasons for the high number of true positives. Firstly, the choice of proteins from a specific signal transduction pathway precludes many random interactions between proteins of unrelated functionality. Secondly, the Co-IP approach to the identification of protein complexes, and thus interactions, is known to have a low false positive rate of around 20% [1, 9], in comparison to Y2H approaches.

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: This presents an exciting opportunity to use novel computational and mathematical design approaches to inform experimental data and use the results to refine the design approach. While direct Watson–Crick binding of the STAR to the target is a critical component of the STAR function, the function of this molecule will also likely be impacted by its potential to form secondary structures in the absence of the target RNA. Some level of secondary structure could be beneficial, perhaps by providing the STAR a level of stability from spontaneous degradation or nuclease-mediated degradation whereas other structures may negatively impact its stability for the same reasons. Additionally, a high amount of structural potential may create too much intramolecular binding and not allow for the intermolecular binding between the STAR and the target. However, for other reasons that might not be easily predicted, a certain level of STAR structure might be beneficial in the intermolecular binding. conclusion, our methods provide a mathematical tool to find patterns in sequence data and to quantify the effect of the corresponding phenotype on the underlying sequence structure. Using this vector-based orthogonal polynomial approach, we can not only look at global patterns of sequence structure but can also identify the nucleotide state at each given site and how this affects phenotype at first and higher order levels. Implementing this approach can be thought of as a two-step process. First, we analyze the existing covariance structure in the sequence data to see how different parts of the sequence might be correlated with one another (5). Second, we use the observed patterns of covariance to construct an orthogonal sequence space, into which we can project another variable to see which, if any, properties of the sequence predict the functional variable (Figures 7–9). In the case of the STAR sequence, the covariance analysis showed that a group of adjacent nucleotides near the 5′ end of the sequence were correlated with other nucleotides spread throughout the rest of the sequence. To see if this correlation corresponds to functional interactions between those nucleotides, we projected the experimental STAR fluorescence data into the orthogonal sequence space. This analysis identified a number of pairs of nucleotides that interact in their effect on fluorescence (Figure 9). However, these were not the pairs of nucleotides that were correlated with one another (Figure 5). The method thus allows us to tease apart structural properties of a sequence and functional interactions between different elements of that sequence.

Output: corroborate


Input: Claim: Quantum mechanics can be completely understood through classical physics. [SEP] Text: The LW fields obtained from those potentials are then E ( x t ) = e [ ( n − β → ) ( 1 − β 2 ) κ 3 R 2 + n c κ 3 R × ( ( n − β → ) × d β → d t ) ] retarded and B ( r t ) = n retarded × E ( r t ) E2 The LW fields have some interesting properties. The 1 R fields are radiation fields, and they make a Poynting vector (energy flow per unit area per unit time) that lies along n retarded : P = c 4 π E radiative × B radiative = c 4 π E radiative × ( n retarded × E radiative ) = c 4 π ( E radiative ) 2 n retarded E3 But the 1 R 2 fields are Coulomb-Ampère fields, and the Coulomb field does not lie along n retarded as one might naively expect; instead, it lies along ( n − β → ) retarded. Assume that β → does not change much over the total field propagation time, in which case ( n − β → ) retarded is virtually indistinguishable from n present. So then the Coulomb field and the radiation are arriving to the observer from different directions. One can feel moved to check this surprising result. Fortunately, one can look up the original sources, obtain translations if necessary, and verify the original algebra. There is no problem with the algebra. There are also numerous re-derivations that use more modern techniques involving the Dirac delta function and the Heaviside step function. These are ‘generalized’ functions of some parameter that, when driven to infinity, produces an infinite pulse or a unit step. One can study these re-derivations too. One finds various re-orderings of the mathematical operators ‘differentiate’, ‘integrate’, and ‘go to parameter limit’. These re-orderings are dodgy because the generalized functions lack the mathematical property of uniform convergence, so these operations don’t necessarily commute; it is possible to change the result by changing operation order. But even so, such findings do not change the fact that the original LW derivations, although pedestrian, were correct.

Output: contrast


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: This is also reflected in the prediction of a larger number (73%) of true positive interactions in the Co-IP data sets of yeast[5, 6] by our method. We also studied the overlap of the predicted true interactions with the high-confidence and low-confidence interactions as given by the respective authors. Though the number of interactions predicted in high-confidence data sets is higher, 17–28% of the interactions in low-confidence data sets are also predicted to be true, except in the H. sapiens data set. This shows that some low-confidence interactions can be biologically relevant. When compared to other data sets, the predicted true interactions in H. sapiens data set show a much higher overlap (68. 7%) with the low confidence interactions. This is because the high confidence data set given by Bouwmeester et al. primarily focuses on interactions, novel or otherwise, that are most likely to be a part of the signalling cascade triggered by TNF-α [9]. Hence, interactions of proteins that are also part of other systems, like the cell cycle, are not included in this high confidence data set. These include interactions of nucleasome assembly proteins and MCM proteins, among others. Other interactions which have been filtered out include those of frequently copurified proteins like the Proteins. In order to limit their interaction map to the TNF-α/NF-κB signal transduction pathway, the authors have chosen a very stringent statistical criterion to identify the interactions of proteins that are expressed well above their normal levels on being triggered by TNF-α [9]. As a result, the high confidence data set as given by Bouwmeester et al. forms only 10% of the total interactions identified in their study, while our method predicts a large number of low confidence interactions to be true. We were also able to confirm several of the low confidence interactions, that were predicted as true, in literature using iHOP [33]. In fact, most of the interactions of the Lsm proteins, shown in Figure 5B, are found in iHOP. Several interactions from the human dataset are also found in iHOP and the [34].

Output: pass


Input: Claim: Bioinformatics is crucial for analyzing genomic data. [SEP] Text: Given structural data, our approach can be utilized to yield insight into potential non-canonical base pairing interactions for different RNA families. And when combined with existing tools such as it can identify these interactions and thus allow for the construction of candidate sequences that can be used for downstream experimental analyses. The limitations of this method largely lie with the computational power and memory required to compute polynomials for sequences with a large number of sites for which higher than second order analyses are sought. The proof of concept shown here consists of 99 sequences that are 40 sites long. However, a large number of sequences with a smaller number of sites might be more optimal for this method. A further area of investigation is potentially implementing a hybrid approach that utilizes a deep neural network to identify sites along the sequence that are functionally more important and then using just these sites as inputs to the tensor-based orthogonal polynomial approach described here. The existing program and the resulting command line tool is written in the Python programming language, however, efforts to optimize and parallelize the program using other languages such as C++ or Rust is one of the current objectives. While we have given proof of concept of this approach using an example of regulatory RNAs, this method can be applied to other questions that aim to understand sequence–phenotype interactions such as transcription factor binding sites and how their sequence composition gives rise to different TF binding energies along with applications in synthetic biology that aim to understand the relationships between the underlying RNA sequence and corresponding secondary structure (25,28). are available at. authors would like to thank Dhruba, for their insightful comments and ideas. We would like to thank the authors of the paper, including James Chappell, for doing the initial work that we used to apply our methods to and for stimulating discussions and comments. We would like to acknowledge the program, the TTU Department of Biohub for their support throughout the time this work was being done. of Biological Sciences, University; (Center for the Integration of STEM Education & Research) Program. Conflict of interest statement. None declared. 1. Lee D. , Redfern O. , Orengo C. Predicting protein function from sequence and structure. Nat. Rev. Mol. Cell. Biol. 2007; 8:995–1005. 2. Kel A. , Goessling E. , Reuter I. , Cheremushkin E.

Output: corroborate