The virtue signaler has been bamboozled by second-hand virtue signaling! While Kaepernick has been a king complainer, draped in a veil of social justice of course, it seems that only the media is interested in dealing with him.
I guess outwardly expressing how anti-American you are, while the American people are the ones contributing to your success, isn’t as woke of a fad as Kaepernick was initially led to believe.
According to a source to Pro Football Talk, no one has contacted Colin Kaepernick’s agents about signing their client to an NFL contract.
“Per a source with knowledge of the situation, there was some “fake” interest expressed immediately after Floyd’s death, seemingly out of guilt,” Pro Football Talk’s Mike Florio writes.
While attracting attention does in fact help the views, which corresponds to monetary gain in some shape or form, there’s also the wrong kind of attention that no one wants to even put up with.
Nike can, by all means, be proud to have Kaepernick on their side. They can collectively post their tweets expressing their anti-Americanism on all the corresponding holidays to do so (such as the Fourth of July and Labor Day), while encouraging Americans to buy their merchandise.
… merchandise I can’t promise I’ll stay away from, BUT, if it has Kaepernick’s name on it, I’m gonna take a hard PASS. I don’t need my freaking workout gear to be politicized too. The year 2020 hasn’t given the public very many breaks from politics as it is.
It’s probably best that Kaepernick throws in the metaphorical towel for his football career and he can go out as a Nike confidant, as opposed to some washed up social justice warrior with a bad ACL. They pretty much amount to the same damn thing anyways.A Data-Driven Learning Method for Constitutive Modeling: Application to Vascular Hyperelastic Soft Tissues

We address the problem of machine learning of constitutive laws when large experimental deviations are present. This is particularly important in soft living tissue modeling, for instance, where large patient-dependent data is found. We focus on two aspects that complicate the problem, namely, the presence of an important dispersion in the experimental results and the need for a rigorous compliance to thermodynamic settings. To address these difficulties, we propose to use, respectively, Topological Data Analysis techniques and a regression over the so-called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC) formalism (M. Grmela and H. Ch. Oettinger, Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E 56, 6620, 1997). This allows us, on one hand, to unveil the true “shape” of the data and, on the other, to guarantee the fulfillment of basic principles such as the conservation of energy and the production of entropy as a consequence of viscous dissipation. Examples are provided over pseudo-experimental and experimental data that demonstrate the feasibility of the proposed approach.


Introduction
Computational (bio-)mechanics is not absent of the data "fever". Even if the so-called data-driven computational mechanics discipline presents distinctive features over what is commonly known as "big data", the possibility of employing raw experimental data to perform simulations has attracted the attention of many researchers recently [1][2][3][4][5][6][7][8][9]. In these approaches, basic equations-those with a higher epistemic value, such as equilibrium or compatibility-are kept, while those which are frequently phenomenological in nature-constitutive equations-are substituted by experimental data, and hence, the name of this family of methods. In a related approach, the so-called equation-free approach substitutes the constitutive law of a material not by experimental data, but by a pseudo-experimental result coming from microscale, first-principle computations [10].
This approach allows us to avoid complex, costly-and often unsuccessful-parameter fitting to obtain the precise form of a constitutive equation. On the other hand, widely accepted constitutive equations have been built under rigorous standards that give rise to the automatic satisfaction of first principles. This is not evident for data-driven approaches. and experimental tests, described in Sections 2.3 and 2.4, respectively. The numerical fitting results of both experiments are shown in Section 3. The paper ends in Section 4 with a discussion of the obtained results on the use of the proposed GENERIC-TDA methodology on the mechanical modeling of biological tissues.

A GENERIC Approach to the Learning Procedure
Recently, W. E and coworkers established a very useful parallelism between DNNs and dynamical systems [33]. Consider a system governed by some state variables z(z 0, t) : I → S, z ∈ C 1 (0, T], such that its time evolution is established in the form where f is, in general, a nonlinear function-otherwise, the method is of little interest. S represents the phase space of the system (a set of judiciously chosen variables that both describe the energy of the system and can be measured experimentally). I = (0, T] represents the considered time interval. For the selected time horizon T, the f low map is a nonlinear function of z. The dynamical system approach to supervised learning consists in determining f so that the resulting flow map is able to reproduce the experimental data. This parallelism offers the advantage of the vast knowledge developed so far in the field of dynamical systems, which could help us in developing both theoretical insights about DNNs and also to devise alternative routes for developing efficient learning strategies. DNNs can be thought of as discretized dynamical systems, such that every time step corresponds to a layer of the DNN. In this work, we consider viscous-hyperelastic materials. Therefore, the learned function f must satisfy certain well-known principles dictated by thermodynamics. In the hyperelastic case, the right choice for f could arise from Hamiltonian mechanics, i.e., where E represents the Hamiltonian or, in other words, the energy of the system. L(z) represents the so-called Poisson matrix, a skew-symmetric matrix that depends on z, in general, but that results to be constant in many cases. Should the system of interest not be conservative (or Hamiltonian), a new potential needs to be introduced in the formulation-entropy-giving rise to the GENERIC formalism [30] For Equation (2) to represent valid nonequilibrium thermodynamic processes, it must be supplemented with the so-called degeneracy conditions, i.e., If, as stated before, L is skew-symmetric; and choosing M to be symmetric, positive semidefinite, we obtainĖ (z) = ∇E(z) ·ż = ∇E(z) · L(z)∇E(z) + ∇E(z) · M(z)∇S(z) = 0 i.e., one ensures the conservation of energy in closed systems. In turn,Ṡ (z) = ∇s(z) ·ż = ∇S(z) · L(z)∇E(z) + ∇S(z) · M(z)∇S(z) ≥ 0 which is equivalent to the fulfillment of the second principle of thermodynamics. Thus, we notice how, by leveraging the dynamical systems equivalence, we efficiently enforce the conservation of energy and the production of entropy. For an in-depth discussion of the implications of the choice of phase space variables z, we refer the interested reader to our previous works in the field, [31,32]. In general, it is well-known that neither a particular choice of variables is needed, nor a particular scale for the description of the system at hand. The only need is that the variables in the phase space would be able to account for the energy of the system. That is why, in general, a Langevin equation is not suitable for this purpose, see [35] and references therein.
Following the dynamical systems equivalence, the next step consists in the determination, by regression from data, of the form of the elements of the GENERIC description of the dynamics, i.e., L, M, ∇E(z), and ∇S(z). To do so, assume a standard finite difference discretization of the time derivative, where we denote z n+1 = z t+∆t and where L and M are the discrete version of the Poisson and friction operators, respectively. DE and DS represent the discrete gradients. In general, matrix L is constant over the process, while matrix M frequently varies. While there exist machine learning techniques that are able to provide with the precise expressions of the terms involved in a particular PDE from data [2], we pursue a purely numerical route, in which we assume that the elements of the GENERIC formula have a particular manifold structure which is to be unveiled by our method. This is the concept of constitutive manifold that we first stated in our previous works [4,7,36].
The dynamical systems approach to the problem will thus consist of solving the following (possibly constrained) minimization problem within a time interval J ⊆ I: with z meas ⊆ Z, a subset of the total available experimental results. L, M, DE, DS will in general be dependent on z, and therefore the choice of size of z meas (in other words, the number of regressions performed along the time interval, or the number of layers in the DNNs equivalent) will affect the accuracy of the method. An analysis of the influence of this choice was made in [31]. We finally approximate z by employing piecewise polynomials, so that gradient operators can be