Single Neutrino
For this study the Monte Carlo truth is varied, the first set of plots illustrate the possible resolution achievable using truth children, in particular truth b-quark and lepton, which are shown below as under Figure.1 collections. As for the Figure.2 collections, the truth b-quark is replaced with a truth-jet matched to the b-quark parton. In cases where the b-quark has no associated truth-jet, the event is skipped. Figure.3 collections use the detector reconstructed jets but still use the truth children lepton. Again for instances where no jet is matched to the associated b-quark, the event is skipped. Finally, Figure.4 collections illustrate the worst possible resolution, since the truth children lepton is replaced with detector based matched lepton. Similar to the (truth)-jet cases, if neither a b-quark has been matched to a jet or the truth children lepton has no associated matching, the event is skipped.
The latter part of the study focuses on bruteforcing the S-matrix values, which minimize the 
value of the difference between the truth and reconstructed neutrino kinematic values.
Selection Criteria
Events are required to have exactly one top-quark decaying leptonically.
The 
and 
of the detector is used as input for the algorithm, with the top and W masses being derived from the truth children or matched (truth)-jets and detector leptons.
The neutrino algorithm zero value is being set to 1e-10, since anything below this value creates large differences between C++ and Python floating point definitions.
Furthermore, the momentum imbalance uncertainty matrix S, has been assigned the values: 
.
These values were chosen arbitrarily, and not optimized for the bulk of the study.
For the S-Matrix optimization, only detector based jets and leptons are used.
Particle Definitions
Leptons and neutrinos are defined as:
electrons
muons
taus
Truth Children
Figure 1.a (PYC)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 1.b (PYC)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 1.c (PYC)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 1.d (REFERENCE)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 1.e (REFERENCE)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 1.f (REFERENCE)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 1.g
A projection plot in the 
direction illustrating differences between the reference and pyc implementions.
Figure 1.h
A projection plot in the 
direction illustrating differences between the reference and pyc implementions.
Figure 1.i
A projection plot in the 
direction illustrating differences between the reference and pyc implementions.
Figure 1.j
A plot illustrating the energy difference between the truth and reconstructed neutrino for the reference and pyc implementation.
Figure 1.k
Reconstructed invariant top-mass using the reference and pyc implementations, compared to the true top-mass parton mass.
Truth Jets
Figure 2.a (PYC)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 2.b (PYC)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 2.c (PYC)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 2.d (REFERENCE)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 2.e (REFERENCE)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 2.f (REFERENCE)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 2.g
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 2.h
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 2.i
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 2.j
A plot illustrating the energy difference between the truth and reconstructed neutrino for the reference and pyc implementation.
Figure 2.k
Reconstructed invariant top-mass using the reference and pyc implementations, compared to the true top-mass parton mass.
Jets
Figure 3.a (PYC)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 3.b (PYC)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 3.c (PYC)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 3.d (REFERENCE)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 3.e (REFERENCE)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 3.f (REFERENCE)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 3.g
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 3.h
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 3.i
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 3.j
A plot illustrating the energy difference between the truth and reconstructed neutrino for the reference and pyc implementation.
Figure 3.k
Reconstructed invariant top-mass using the reference and pyc implementations, compared to the true top-mass parton mass.
Jets with Detector Leptons
Figure 4.a (PYC)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 4.b (PYC)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 4.c (PYC)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using pyc). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 4.d (REFERENCE)
A heat-map of the momenta differential in the x and y direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 4.e (REFERENCE)
A heat-map of the momenta differential in the x and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 4.f (REFERENCE)
A heat-map of the momenta differential in the y and z direction between the truth and reconstructed neutrino (using reference). This is to validate whether the difference between the truth and the reconstructed neutrino is consistent. Ideally the heat-map should have a single bin at (0,0), indicating perfect reconstruction.
Figure 4.g
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 4.h
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 4.i
A projection plot in the direction illustrating differences between the reference and pyc implementions.
Figure 4.j
A plot illustrating the energy difference between the truth and reconstructed neutrino for the reference and pyc implementation.
Figure 4.k
Reconstructed invariant top-mass using the reference and pyc implementations, compared to the true top-mass parton mass.
S-Matrix (Momentum Imbalance Uncertainty Matrix)
A heat-map of the S-matrix values for the diagonal and non-diagonal elements.
Each bin counts the frequency of finding the lowest at the given matrix values.
Large clustering around particular 
pairs indicates a potential optimization point.
However, if no clustering is observed, the S-matrix values can be chosen arbitrarily, with no preferential values.
Note: This is for the pyc implementation.
A heat-map of the S-matrix values for the diagonal and non-diagonal elements.
Each bin counts the frequency of finding the lowest at the given matrix values.
Large clustering around particular pairs indicates a potential optimization point.
However, if no clustering is observed, the S-matrix values can be chosen arbitrarily, with no preferential values.
Note: This is for the reference implementation.
A histogram plot depicting the 
of the truth neutrino (truth children) and the reconstructed neutrino.
In order to compare the performance of the two implementations, clustering around 0 indicates perfect reconstruction.
A histogram plot depicting the 
of the truth neutrino (truth children) and the reconstructed neutrino.
In order to compare the performance of the two implementations, clustering around 0 indicates perfect reconstruction.
A histogram plot depicting the 
of the truth neutrino (truth children) and the reconstructed neutrino.
In order to compare the performance of the two implementations, clustering around 0 indicates perfect reconstruction.
A histogram plot depicting the of summing the difference between the individual momentum components of the truth and reconstructed neutrino.
Values close to 0, indicate better reconstruction performance.