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The Disease Mode will change the color and opacity representation of the nodes and edges of both the Cluster View and the Gene View based on a selected disease from the gene-disease association dataset. |
The Cluster View cluster nodes and edges that do not contain any genes associated to the selected disease will have a lower opacity in addition to their color and size. This reveals a disease sub-cluster graph network, which gives a sparse overview on the disease and cluster relations. Each cluster node will be colored... |
The Gene View gene nodes are color-coded according to the [MATH] -values associated to the study behind the selected disease obtained from the gene-disease association dataset. |
Application In figure and an example of the tool is given for the gene cluster dataset KEGG, gene-gene association dataset HIPPIE and gene-disease association dataset GWAS. Figure shows the UI of GeneVis with on the left side panel the clusters and the right side panel the genes associated to the Cytokine receptor clus... |
Implementation GeneVis is a web-based visualization tool written in HTML, CSS, JavaScript, jQuery and the framework D3.js . Roughly ~80% of the application uses the framework D3.js, which is a versatile data-driven HTML DOM element manipulation framework. D3.js made it possible to provide user’s with full interactive c... |
# Source: arxiv 1805.03108 # Title: FASK with Interventional Knowledge Recovers Edges from the Sachs Model # Sections: all # Downloaded: 2026-03-02T08:43:44.888910+00:00 |
FASK with Interventional Knowledge Recovers Edges from the Sachs Model Abstract We report a procedure that, in one step from continuous data with minimal preparation, recovers the graph found by Sachs et al. |
, with only a few edges different. The algorithm, Fast Adjacency Skewness (FASK), relies on a mixture of linear reasoning and reasoning from the skewness of variables; the Sachs data is a good candidate for this procedure since the skewness of the variables is quite pronounced. We review the ground truth model from Sac... |
Introduction Sachs et al. describe a procedure that recovers most of the edges in the ground truth for a single cell biological model of protein interactions. The Sachs data consists of nine files with varying interventions (one interventional context per file). There are between 700 and 900 data points in each file, f... |
. The goal of our analysis is to recover the ground truth that Sachs et al. provide (described below) and to find a model similar to the one found using their procedure. |
We report a procedure that finds essentially the same model (with a few edges in difference) using the continuous version of the data and information pertaining to the interventions performed on the data. Unlike the procedure reported by Sachs et al, the method reported here find the model without discretizing, excludi... |
, is run on the Sachs data augmented with intervention variables and background knowledge which forbids edges from measured variables to intervention variables and edges from intervention variables to other intervention variables. We first explain the ground truth, then give the Sachs and FASK models showing how they r... |
Although many people have analyzed this data with various methods, very few results have ended up in the public domain The best of these in terms of recovering the adjacencies in the ground truth described by Sachs et al. is |
, but the directions of influence were not estimated. For most, the adjacencies were either very sparse or quite different from the ground truth. Where orientations are reported close to the ground truth, adjacencies have traditionally been sparse. The best result we have found in the literature, bar none, with respect... |
. We aim to produce a result similar to theirs but with a faster and less heuristic approach. Ground Truth It is somewhat unclear as to what the ground truth is in Sachs et al |
. Most of the edges are not problematic but some require thought. Figure shows the Sachs et al. figure detailing the biologists’ view. |
Figure shows their figure comparing their model to the ground truth. Most of the edges in the ground truth graphs are included in the biologists’ view, above, if not as direct edges, then as indirect influences going through other (latent) variables. Figure shows Sachs et al.’s Figure 3A |
, giving their search result and also showing their primary ground truth. Edges in blue are edges where their model agrees with ground truth. These are edges that are reported widely throughout the literature. Dashed edges are edges in their ground truth that their model misses. Magenta edges in their model are edges t... |
In Sach et al.’s supplement Figure SOM3 , shown in Figure , Sachs et al. add additional “low confidence” edges. It seems proper to take the same attitude toward these as with the edges marked in green in Figure ; perhaps the adjacencies can be asserted but not the orientations. This suggests supplementing the ground tr... |
Pkc – Akt Raf – Akt Mek – Akt Akt – Plc Mek – Plc Mek – Jnk Pka – Plc Jnk – P38 These considerations lead to the graph shown in Figure , which we call the “supplemented ground truth”. |
The supplemented ground truth (Figure ) adds edges suggested by Sachs et al. in their Figures 3A and SOM3 . The PIP2 [MATH] PIP3 edge is marked with a bidirected edge in the biologists’ view. A survey of the literature suggests that this bidirected edge is intended to represent a 2-cycle. We use the direction suggested... |
Sachs et al.’s Procedure To produce the model shown in Figure , Sachs et al. use the following procedure, detailed in the supplement of their article. They combine the nine datasets in the following manner. First, they exclude points greater than three standard deviations form the mean and then discretize the data usin... |
by repeating a heuristic method 500 times. For each iteration, they start with a random directed acyclic graph (DAG) over the variables and then randomly add, remove, or reverse edges without violating acyclicity. At each step, if the score improves, they move to the new graph. Sometimes, to avoid a local minimum, they... |
; their code examples are provided in the bnlearn package to help the reader approximately reproduce the original results. It is pointed out in |
that interventional knowledge is treated by Sachs et al. as prior information, that is, as adjustments to the Bayesian scores used to score model. This clarifies how Sachs et al. can infer directions in places where Bayesian networks generally can only infer adjacencies. |
In this report, we will use the following statistics: AP - Adjacency Precision AR - Adjacency Recall AHP - Arrowhead Precision; not penalizing bidirected edges |
AHR - Arrowhead Recall With respect to the ground truth, the Sachs model on our measures performs as follows: AP AR AHP AHR 1.00 |
0.85 0.94 0.79 The 85% for AR is consistent with Sachs et al.’s conclusions. With respect to the supplemented ground truth, the Sachs model on our measures performs as follows: |
AP AR AHP AHR 1.00 0.61 0.94 0.75 FASK Results The idea of the FASK algorithm is as follows. First, FAS-stable is run on the data (this is the adjacency search of the PC-Stable algorithm, |
), producing an undirected graph. We use the linear, Gaussian BIC score as a conditional independence test and a specified penalty discount [MATH] . This score assumes the data are Gaussian, but is tolerant of non-Gaussianities. This yields an undirected graph [MATH] . The reason FAS-stable works for sparse cyclic mode... |
[EQUATION] otherwise orient [MATH] [MATH] will be a fully oriented graph. For some models, where the true coefficients of a 2-cycle between [MATH] and [MATH] are more or less equal in magnitude but opposite in sign, a correlation test may eliminate the edge between [MATH] and [MATH] when in fact a 2-cycle exists. In th... |
For our analysis, we use all 7466 records of the data, prepared as follows. Since interventional data is available, we add this to the data. We create a column in the data for each specific compound introduced (as noted in the names of the “main result” files in |
) and put a 1 in rows where that compound is introduced 0 otherwise. We merge the columns for the chemicals cd3 and cd28 since they always co-occur. We then jiggle the intervention data by adding draws from a normal distribution [MATH] , to avoid singularities. We take the view (as Sachs et al. |
do) that the protein data may be concatenated, if intervention data is taken into account. The reason for this is that all protein level measurements are carried out using the same procedure and thus are comparable. We log the data (after adding 10, so applying the transformation [MATH] ) and generate a concatenated da... |
are very skewed, making them a good candidate for this procedure. The log transformation applied to the data makes them somewhat more Gaussian for the adjacency search, while leaving them sufficiently skewed for the orientation search. Figure shows pairwise scatter plots over the measured variables for the resulting co... |
Using the prepared data as above, we created knowledge that the intervention variables are exogenous, a standard technique . This knowledge was supplied to the FASK algorithm along with the data augmented by intervention variables. The penalty discount for FAS was set to 1 (standard BIC). The depth of the FAS search wa... |
As for choices of FASK’s hyper-parameter settings, the extra edge threshold of 0.3 was a value learned from work with fMRI; this value needs to be noticeably different from zero. If it is lowered, the graph becomes more dense. The delta parameter is in the range -1 to 0; we use the default -0.2 here, though the output ... |
With respect to the ground truth, the FASK model performs as follows: AP AR AHP AHR 0.84 0.80 1.00 0.79 With respect to the supplemented ground truth, the FASK model performs as follows: |
AP AR AHP AHR .95 0.64 1.00 0.79 Aside from rendering some adjacencies as 2-cycles, this is how the FASK model modifies the Sachs model (target graph from FASK model, True graph from Sachs model): |
Edges added: 1. Pka [MATH] PIP2 2. Pka [MATH] Plc 3. Jnk [MATH] Mek Edges removed: 1. Mek [MATH] Erk Edges reoriented: 1. Pkc [MATH] Pka [MATH] Pka [MATH] Pkc |
2. Plc [MATH] PIP3 [MATH] PIP3 [MATH] Plc Three adjacencies are added, two of which correspond to adjacencies in the supplemented ground truth. The Pkc [MATH] Pka edge from the Sachs model is reversed, though the direction of this edge is reported but not expected. Two adjacencies are oriented as 2-cycles. A backward e... |
. Pka [MATH] Akt has the canonical direction Pka [MATH] Akt; here, it is rendered as a 2-cycle. There is at least one paper exploring cyclic models with this data |
finds Akt [MATH] Pka. Lastly, the Mek [MATH] Erk edge is removed. The latter is significant, since, as Sachs et al. point out, the inclusion of that edge in their model is evidence that their model has merit. Specifically, they include a path Raf [MATH] Mek [MATH] Erk; this is a well-known path in the literature. This ... |
Comments on the FASK Model The Mek [MATH] Erk edge aside, the remarkable thing about Figure is how much it recovers and the degree of accuracy with which this information is recovered. No expected orientation is reversed in the model; even Sachs et al.’s |
analysis reverses one expected orientation. Also, although it is not expected that this will be the case for every analysis, in this case the hyper-parameter values used FASK algorithm were used to recover this information essentially the same as the defaults learned from experience with fMRI data. It is also noteworth... |
As noted, there are two types of adjacencies in FASK. First, there are adjacencies due to the Fast Adjacency Search (FAS), that is, the PC adjacency search. We use the “-Stable” version of this algorithm |
. These assume the variables are distributed as approximately Gaussian. Second, there are adjacencies due to differences in correlation conditional on one or the other variable being greater than zero; the default cutoff for this difference is 0.3. As explained in Appendix A of |
, these respond to skewnesses of variables in the data. We give the two subgraphs separately. Figure shows the subgraph of FAS adjacencies, oriented using the FASK orientation rules. Figure shows the subgraph of conditional correlation differences adjacencies, again oriented by FASK rules. In this case, two subgraphs a... |
The adjacency rule used in Figure , adding an adjacency between [MATH] and [MATH] if [EQUATION] was a heuristic developed for search over fMRI data to handle the case where a control 2-cycle between [MATH] and [MATH] (a cycle in which coefficients in opposite directions have opposite sign) could not be discerned from c... |
FASK adds three edges to the Sachs model. Two of the edges are adjacencies in the extended ground truth but not in the Sachs model. The third, Pka [MATH] PIP2 directed out of Pka; perhaps this is not surprising, given that it transitively closes a short path from Pka through Plc to PIP2, but it is a false positive adja... |
Both the FASK procedure and Sachs et al.’s procedure get an adjacency between Pka and Pkc, oriented albeit in different directions. We do not feel that we have sufficient information to warrant a judgment in either direction; in fact, there is literature now claiming that cross-talk exists between Pka and Pkc, suggesti... |
, though again, judging from the literature, we do not feel we have sufficient information to know that this is not confounded by additional variables other than the common ancestors already in the graph, so we leave this edge unoriented in the ground truth, as we do for the additional unoriented edges shown in Figure ... |
AP AR AHP AHR 0.95 0.73 0.89 0.89 If we leave interventional knowledge out of the FASK search, we obtain the graph shown in Figure 10 , which modifies the Sachs model as follows (target graph from FASK without interventions, true graph from Sachs model): |
Edges added: 1. Plc [MATH] Pka 2. Pka [MATH] Plc 3. Plc [MATH] Pka 4. Pka [MATH] Plc 5. P38 [MATH] Akt 6. Jnk [MATH] PIP3 7. Jnk [MATH] P38 |
8. Plc [MATH] Akt 9. Pka [MATH] PIP2 10. Plc [MATH] P38 11. Jnk [MATH] Mek 12. Plc [MATH] Jnk 13. Mek [MATH] Akt Edges removed: 1. |
Mek [MATH] Erk Edges reoriented: 1. Pkc [MATH] Pka [MATH] Pka [MATH] Pkc 2. Plc [MATH] PIP3 [MATH] PIP3 [MATH] Plc Essentially, this manipulation adds several edges to the graph that otherwise would not have been there. |
If, on the other hand, we leave the interventional knowledge in place and raise the 2-cycle alpha to 0.05 in the FASK search, we obtain the graph in Figure 11 , with some additional 2-cycles. There is some rationale for each the additional backward edges. The Raf [MATH] Mek 2-cycle has already been discussed, as has th... |
, the “biologists’ view” as a bidirected edge. A survey of the literature indicates that this is meant to be a 2-cycle. Pkc [MATH] P38 is a 2-cycle that is often found in cyclic search with this data; the cyclic paper above finds it as well. Akt [MATH] Erk is a little harder to explain. This is one of Sachs et al.’s “g... |
With these 2-cycles marked in the graph, there are several possible cycles in the FASK model, but the set of edges in the model is nearly a superset of the set of edges in the Sachs model (with the exception of the Pka [MATH] PIP2 edge, and the reversals indicated above, for which supplemented ground truth on direction... |
The Mek [MATH] Erk Edge Sachs et al. take it as a selling point of their method (and rightly so) that it recovers the well-known Raf [MATH] Mek [MATH] Erk pathway. FASK recovers a Raf [MATH] Mek edge (along with a backward Mek [MATH] Raf edge that seems to be justified, as explained above). But it does not recover the ... |
The reason is shown in Figure 12 . Here we show a scatter plot of Erk versus Mek, color coded by intervention. The fourth interventional context is shown in blue, the sixth interventional context in green, the nineth interventional context in red, and the rest of the interventional contexts, lumped together, in teal. W... |
This appears to be a problem specific to the way FASK identifies edges, since FASK bases its judgments on correlation and (strong) skewness. One response is to use a more sensitive parameterization for FASK, and indeed if the 0.3 cutoff for the heuristic skewness adjacency rule is lowered, the edge does appear, though ... |
Another response is to consider revising FASK to take additional moments, such as kurtosis, into account. It is not clear that this would be effective; anecdotally, methods such as Two-Step |
that take all moments into account also do not recover the Mek [MATH] Erk edge. This, however, requires further study. A third response is to limit the judgment to just data from the fourth and sixth interventional contexts, where the greatest discrepancy lies. It is possible that including all of the intervention data... |
Conclusion We have found an algorithm that with interventional background knowledge is able to quickly recover a graph very close to the one found in Sachs et al. |
using a logged preparation of their continuous data and without excluding “outliers” . In addition, whereas Sachs et al.’s algorithm averaged over 500 models using a heuristic search to arrive at the final model, FASK arrives at the result in one iteration, without model averaging or heuristics, even without bootstrapp... |
, which gives only adjacencies for the model from a nonlinear, non-Gaussian search, without orientations, so directions of causal influence are not estimated. For other published models, adjacencies and orientations are taken together noticeably worse. |
An unsolved problem for FASK is the detection of latent confounders; these may show up as 2-cycles in the model for relaxed 2-cycle alphas, and it is difficult to know without further research whether these 2-cycles are genuine or represent confounding. One promising lead once again comes from the the Two Step algorith... |
. This method could sensibly be used to distinguish 2-cycles from confounders for FASK as well; we have not tried this tactic yet. The idea would be to estimate the FASK model using the Two-Step apparatus and check correlation of residuals, a pragmatic solution. |
Appendix For reference, we include below models from the papers listed in the Introduction, in the same layout as earlier figures. These are the comprarisons of these models, together with the Sachs and FASK models, to the Sachs et al. ground truth. |
Source AP AR AHP AHR Sachs 1.00 0.85 0.94 0.79 FASK [MATH] 0.84 0.80 1.00 0.79 FASK 0.05 0.84 0.80 1.00 0.79 Friedman 0.30 0.30 Aragam cont. |
0.50 0.35 0.43 0.16 Aragam discr. 0.77 0.50 0.56 0.26 Henao 0.90 0.45 0.67 0.32 Miller 0.85 0.85 Desgranges 0.90 0.45 Magliacane |
1.00 0.30 0.67 0.21 Goudet 0.95 0.90 0.72 0.68 Kalainathan 0.75 0.45 0.89 0.42 These are the same models, compared to the supplemented ground truth. |
Source AP AR AHP AHR Sachs 1.00 0.61 0.94 0.79 FASK [MATH] 0.95 0.64 1.00 0.79 FASK 0.05 0.95 0.64 1.00 0.79 Friedman 0.53 0.32 Aragam cont. |
0.83 0.36 0.43 0.16 Aragam discr. 0.92 0.43 0.56 0.26 Henao 1.00 0.36 0.67 0.32 Miller 1.00 0.71 Desgranges 1.00 0.36 Magliacane |
1.00 0.21 0.67 0.21 Goudet 0.95 0.64 0.72 0.68 Kalainathan 0.92 0.39 0.89 0.42 Figure 13 shows the Friedman et al. model found using GLASSO in |
, from continuous data. Figure 14 shows the Aragam et al. model in from continuous data. Figure 15 shows the model in from the same discrete data as in |
. Figure 16 shows the Henao and Winther maximum likelihood model from . Figure 17 shows the Miller et al. model from continuous data from |
. Figure 18 shows the model from Desgranges’ dissertation, . There are several models in that dissertation; the one shown here uses the KPC test with permutations. Figure 19 shows the model from Magliacane et al. |
. Figure 19 shows the Goudet et al. , applied to Sachs et al. continuous data (only the first dataset). This method orients the edges of a provided skeleton. Here Sachs et al.’s ground truth skeleton is provided to be oriented so perhaps it is unfair to compare this graph to the other presented in this report since it ... |
# Source: arxiv 1805.03949 # Title: MPI+X: task-based parallelization and dynamic load balance of finite element assembly # Sections: all # Downloaded: 2026-03-03T02:20:08.862788+00:00 |
MPI+X: task-based parallelization and dynamic load balance of finite element assembly Abstract The main computing tasks of a finite element code(FE) for solving partial differential equations (PDE’s) are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hyb... |
Introduction The two most intensive computing tasks of computational mechanics codes for unstructured meshes are the algebraic system assembly and the iterative solver to solve it. In this paper we will focus on improving the performance and execution of the first task, the algebraic system assembly. |
The algebraic system assembly consists of a loop over elements, in the Finite Element (FE) context, and faces or cells in the Finite Volume (FV) context. Although this work will focus on the first family of methods, all the strategies described here can be applied to the second one. |
For each element, the system assembly consists of two main steps: Compute the element matrix and right-hand side. Assembly the element system into the local algebraic system of each MPI partition. |
The element loop is local to each MPI partition and does not involve any communication. It is thus well-suited for shared memory parallelism. In an MPI+X hybrid parallelism context, X has consisted traditionally of loop parallelism using OpenMP. However, assembling the element system into the local one involves an upda... |
Several strategies have been proposed in the literature to circumvent this weakness, like the coloring or substructuring techniques to avoid the race condition appearing in the assembly of the element system into the local system. The main drawback of the first technique is the drop of the number of instructions per cy... |
We propose an alternative, based on the task parallelism of the element loop using an extension to the OpenMP programming model and implemented in the OmpSs model |
. The taskification of the assembly that we propose solves both aforementioned problems. The technique will be described in Section 3.2.2 |
In addition, in the context of MPI parallelization load imbalance is an issue that can degrade the performance and does not have a straightforward solution. The main issue when load balancing an MPI application comes from the fact that the data is not shared among the different MPI processes. Consequently, application ... |
Unfortunately a well balanced partition is not always easy to obtain as we will see in Section . And, even, if a well balanced partition is achieved it does not imply a well balanced execution. In some cases the load can change during the execution, i.e. particles moving or a dam breaking. In this case, a runtime solut... |
. This kind of solutions implies a redistribution of data and cannot be applied each timestep because of the overhead they introduce. Moreover, they cannot react to punctual load changes or load imbalance introduced by system noise. We will apply a dynamic load balance that does not require to modify the application ne... |
Finally, in Section , the efficiency of the proposed taskifying strategy will be compared to classical loop parallelism with OpenMP using an element coloring strategy. In this section we will also present the performance evaluation of the load balancing library. And we will demonstrate that both mechanisms can be usefu... |
Fluid and structure dynamics In this work we consider two different sets of partial differential equations (PDE’s), modeling incompressible flows and large deformations of structures. We will put more emphasis on the first set of equations, as the numerical modeling and system solution are more complex. Apart from the ... |
2.1 Fluid solver The high performance computational mechanics code used in this work is Alya , developed at BSC-CNS, and part of the Unified European Application Benchmark Suite (UEABS) |
. This suite provides a set of scalable, currently relevant and publically available codes and datasets, of a size which can realistically be run on large systems, and maintained into the future. In this section, will briefly describe the CFD module of Alya and its parallelization. |
2.1.1 Physical and Numerical models The equations governing the dynamics of an incompressible fluid are the so-called incompressible Navier-Stokes equations. They express the Newton’s second law for a fluid continuous medium, whose unknowns are the velocity [MATH] |
and the pressure [MATH] of the fluid. Two physical properties are involved, namely [MATH] be the viscosity, and [MATH] the density. At the continuous level, the problem is stated as follows: find the velocity [MATH] and pressure [MATH] in a domain [MATH] such that they satisfy in a given time interval |
[EQUATION] together with initial and boundary conditions. The velocity strain rate is defined as [MATH] The variational multiscale (VMS) method is applied to discretize this set of equations, as extensively described in |
. In addition, the velocity subgrid scale is tracked in convection and time. This means that apart from solving for the previous unknowns |
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