prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the main focus of the research paper?

Read the following text and answer briefly.

Context 1: Paper Info

Title: Nuclear Liquid-Gas Transition in the Strong Coupling Regime of Lattice QCD
Publish Date: 28 Mar 2023
Author List: J Kim (from Institute for Advanced Simulation (IAS-4), Forschungszentrum Jülich), P Pattanaik (from Fakultät für Physik, Bielefeld University), W Unger (from Fakultät für Physik, Bielefeld University)

Figure

FIG  1 Typical 2-dimension configuration at β = 1 0, at non-zero quark mass, temperature, chemical potential The black dots are monomers, the blue lines are dimers, the red arrows are baryon loop segments (or triplets g b + f b = ±3 if adjacent to a non-trivial plaquette), and the green squares are plaquette occupations ±1 The actual configurations are 3+1-dimensional 
FIG 2 Chiral susceptibility on a 2 4 volume for various quark masses, as a function of the bare anisotropy γ (with aT = γ 2 /2), analytic results from enumeration compared to numerical data from simulations via the worm algorithm 
FIG 3 Various observables in the µB-T plane on a 2 4 volume at amq = 0 1 The back-bending of the first order transition at temperatures below aT = 0 5 in all observables is an artifact of the small volume, and vanishes in the thermodynamic limit The temperature aT = 1/2 corresponds to the isotropic lattice here 
FIG  4  The chiral condensate (left) and the baryon density (right) for quark mass m = 1 5 as a function of the chemical potential and for various temperatures 
FIG  7  ∆f at amq = 0 2 as a function of chemical potential and β the on a 6 3 × 4 lattice
FIG  8  Baryon mass from ∆E as a function of the quark mass amq, and contributions from different dual variables: monomers, dimers and baryon segments 
FIG  9  Baryon density for volume 4 3 × 8 in the full µB − mq plane, illustrating the strong quark mass dependence of the onset to nuclear matter 
FIG  10 Baryonic observables on various volumes in the first order region amq = 1 5 Vertical bands indicate the mean and error of the nuclear transition 
FIG  12  Left: Extrapolation of the pseudo-critical values of µB for the various volumes into the thermodynamic limit Right: Critical baryon chemical potential for different quark masses The first order transition region is shown in blue, the crossover region is shown in red and the range for critical end point is marked in black 
FIG  17  Nuclear interaction scaled with baryon mass As the quark mass increases, it tends to zero 
FIG  18  Critical baryon chemical potential and baryon mass from different approaches 
Parameters for the Monte Carlo runs to determine the nuclear transition at strong coupling, with statistics after thermalization 

abstract

The nuclear liquid-gas transition from a gas of hadrons to a nuclear phase cannot be determined numerically from conventional lattice QCD due to the severe sign problem at large values of the baryon chemical potential  In the strong coupling regime of lattice QCD with staggered quarks, the dual formulation is suitable to address the nuclear liquid gas transition 
We determine this first order transition at low temperatures and as a function of the quark mass and the inverse gauge coupling β  We also determine the baryon mass and discuss the nuclear interactions as a function of the quark mass, and compare to mean field results  It is known from experiments that at low temperatures, there is a phase transition between dilute hadron gas and dense nuclear matter as the baryon chemical potential increases 
This transition is of first order and terminates at about T c = 16 MeV in a critical end point  The value of the chemical potential µ 1st B at zero temperature is given roughly by the baryon mass m B , where the difference of µ 1st B −m B is due to nuclear interactions  For a review on nuclear interactions see  
As the nuclear force between baryons to form nuclear matter is due to the residual strong interactions between quarks and gluons, it should be accurately described by QCD  We choose to study the nuclear transition and nuclear interaction via lattice QCD , with its Lagrangian being a function of the quark mass and the inverse gauge coupling 
In order to understand the nature of the transition, it is helpful to study its dependence on these parameters  However, at finite baryon density, lattice QCD has the infamous sign problem which does not allow us to perform direct Monte Carlo simulations on the lattice  Various methods have been proposed to overcome the numerical sign problem, but they are either limited to µ B /T 3 or can not yet address full QCD in 3+1 dimensions in the whole µ B − T plane , in particular the nuclear transition is out of reach 
An alternative method is to study lattice QCD via the strong coupling expansion  There are two established effective theories for lattice QCD based on this: (1) the 3-dim  effective theory for Wilson fermions in terms of Polyakov loops, arising from a joint strong coupling and hopping parameter expansion , the dual representation for staggered fermions in 3+1 dimensions, with dual degrees of freedom describing mesons and baryons 
Both effective theories have their limitations: is limited to rather heavy quarks (but is valid for large values of β) whereas ( ) is limited to the strong coupling regime β 1 (but is valid for any quark mass)  We study lattice QCD in the dual formulation, both at infinite bare gauge coupling, β = 0, and at leading order of the strong coupling expansion in the regime β < 1, which is far from the continuum limit 
But since strong coupling lattice QCD shares important features with QCD, such as confinement, and chiral symmetry breaking and its restoration at the chiral transition temperature, and a nuclear liquid gas transition, we may get insights into the mechanisms, in particular as the dual variables give more information in terms of its world lines, as compared to the usual fermion determinant that depends on the gauge variables 
To establish a region of overlap of both effective theories, we have chosen to perform the Monte Carlo simulations in the dual formulation extending to rather large quark masses  This paper is organized as follows: in the first part we explain the dual formulation in the strong coupling regime, in the second part we provide analytic results based on exact enumeration and mean field theory, in the third part we explain the setup of our Monte Carlo simulations and present result on the m q -and β-dependence of the nuclear transition 
Since the strong coupling regime does not have a well defined lattice spacing, we also determine the baryon mass am B to set the parameters of the grand-canonical partition function, aT and aµ B , in units of am B   We conclude by discussing the resulting nuclear interactions, and compare our findings with other results 

Staggered action of strong coupling QCD and its dual representation

In the strong coupling regime, the gauge integration is performed first, followed by the Grassmann integration to obtain a dual formulation  This was pioneered for the strong coupling limit in and has been extended by one of us to include gauge corrections   The sign problem is mild in the strong coupling limit and still under control for β < 1, where we can apply sign reweighting 
The dual degrees of freedom are color-singlet mesons and baryons, which are point-like in the strong coupling limit, and become extended about a lattice spacing by incorporating leading order gauge corrections  The partition function of lattice QCD is given by where DU is the Haar measure, U ∈ SU(3) are the gauge fields on the lattice links (x, μ) and { χx , χ x } are the unrooted staggered fermions at the lattice sites x 
The gauge action S G [U] is given by the Wilson plaquette action and the staggered fermion action S F [ χ, χ, U] is: where the gauge action depends on the inverse gauge coupling β = 2Nc g 2 and the fermion action depends on the quark chemical potential aµ q which favors quarks in the positive temporal direction, and the bare quark mass am q  
First we consider the strong coupling limit where the inverse gauge coupling β=0 and hence the gauge action S G [U] drops out from the partition function in this limit  The gauge integration is over terms depending only on the individual links (x, μ) so the partition function factorizes into a product of one-link integrals and we can write it as:
with z(x, μ) the one-link gauge integral that can be eval-uated from invariant integration, as discussed in , where we write the one-link integral in terms of new hadronic variables: Only terms of the form (M (x)M (y)) k x, μ (with k x,μ called dimers which count the number of meson hoppings) and B(y)B(x) and B(x)B(y) (called baryon links) are present in the solution of the one-link integral 
The sites x and y = x + μ are adjacent lattice sites  It remains to perform the Grassmann integral of the fermion fields χ, χ  This requires to expand the exponential containing the quark mass in Eq  (4) (left), which results in the terms (2am q M (x)) nx (with n x called monomers)  To obtain non-vanishing results, at every site, the 2N c Grassman variables χ x,i and χx,i have to appear exactly once, resulting in the Grassmann constraint (GC):
where n x is the number of monomers, k x,μ is the number of dimers and the baryons form self-avoiding loops x,μ , which due to the constraint cannot coexist with monomers or dimers  With this, we obtain an exact rewriting of the partition function Eq  ( ) for N c = 3, in terms of integer-valued dual degrees of freedom {n, k, }:
where the sum over valid configurations has to respect the constraint (GC)  The first term in the partition function is the contribution from dimers and the second term is the contribution from monomers  The weight factor w( ) for each baryon loop depends on the baryon chemical potential µ B = 3µ q and induces a sign factor σ( ) which depends on the geometry of :
Here, ω is the winding number of the loop   The total sign factor σ( ) ∈ {±1} is explicitly calculated for every configuration  We apply sign reweighting as the dual formulation has a mild sign problem: baryons are non-relativistic and usually have loop geometries that have a positive signs  The dual partition function of the strong coupling limit is simulated with the worm algorithm (see Section III A) and the sign problem is essentially solved in this limit 

Extension to finite β

The leading order gauge corrections O(β) to the strong coupling limit are obtained by expanding the Wilson gauge action Eq  ( ) before integrating out the gauge links  A formal expression is obtained by changing the order of integration (first gauge links, then Grassmann-valued fermions) within the QCD partition function:
With this the O (β) partition function is The challenge in computing Z (1) is to address the SU(N c ) integrals that receive contributions from the elementary plaquette U P   Link integration no longer factorizes, however the tr[U P ] can be decomposed before integration: Integrals of the type J ij with two open color indices -as compared to link integration at strong coupling -have been derived from generating functions
for either J = 0 or for G = U(N c )   The SU(3) result was discussed in , in terms of the dual variables, neglecting rotation and reflection symmetries, there are 19 distinct diagrams to be considered  The resulting partition function, valid to O(β), is with q P ∈ {0, ±1}, and the site weights w x → ŵx , bond weights w b → ŵb and baryon loop weights w → ŵ receive modifications compared to the strong coupling limit Eq  ( ) for sites and bonds adjacent to an excited plaquette q P = 1 
The weights are given in , and are rederived for any gauge group in   The configurations {n, k, , q p } must satisfy at each site x the constraint inherited from Grassmann integration: which is the modified version of Eq  ( ) with q x = 1 if located at the corner of an excited plaquette q p = 0, otherwise q x = 0 
A more general expression that we obtained via group theory and is valid to higher orders of the strong coupling expansion is discussed in terms of tensor networks   A typical 2-dimensional configuration that arises at β = 1 in the Monte Carlo simulations is given in Fig    Note that if a baryon loop enters a non-trivial plaquette, one quark is separated from the two other quarks, resulting in the baryon being extended object, rather being point-like in the strong coupling limit 
The O(β) partition function has been used in the chiral limit to study the full µ B − T plane via reweighting from the strong coupling ensemble  Whereas the second order chiral transition for small values of the aµ B decreased up to the tri-critical point, the first order nuclear transition was invariant: aµ 1st B 1 78(1) at zero temperature has no β-dependence 
For the ratio T (µ B = 0)/µ 1st B (T 0) we found the values 0 787 for β = 0 and 0 529 β = 1, which should be compared to T c / 0 165 for full QCD   However, since reweighting cannot be fully trusted across a first order boundary, direct simulations at nonzero β are necessary  The Monte Carlo technique to update plaquette variables is discussed in Section III A 
In this section, we provide analytic results from exact enumeration for small volumes, and mean field results based on the 1/d expansion, valid in the thermodynamic limit  The main purpose is to compare our Monte Carlo results to these analytic predictions 

Exact enumeration

To establish that our Monte Carlo simulations indeed sample the partition functions Eq  ( ) and Eq  ( ), we have obtained analytic results on a 2 4 volume at strong coupling, and at finite beta in two dimensions on a 4 × 4 volume, comparing O (β) and O β 2 truncations  Our strategy to obtain an exact enumeration of the partition function Z is to enumerate plaquette configurations first, then fixing the fermion fluxes which together with the gauge fluxes that are induced by the plaquettes form a singlet, a triplet or anti-triplet, i e  on a given bond b, g b + f b ∈ {−3, 0, 3}, and last we perform the monomerdimer enumeration on the available sites not saturated by fermions yet by a depth-first algorithm  
At strong coupling, with no plaquettes, g b = 0 and f b are baryonic fluxes  All observables that can be written in terms of derivatives of log(z), such as the baryon density, the chiral condensate, the energy density, and also the average sign, are shown in Fig 

Expectations from mean field theory

Another analytical method to study strong coupling lattice QCD is the mean field approach, where the partition function is expanded in 1 d (d is the spatial dimension) and then a Hubbard-Stratonovich transformation performed   After this procedure, the free energy is a function of temperature T , the chiral condensate σ and chemical potential µ B :
here E[m] is one-dimensional quark excitation energy which is a function of the quark mass m = am q   For N c = 3 and d = 3 we determined the minimum of the free energy with respect to the chiral condensate  This gives us the equilibrium chiral condensate as a function of (T, m, µ B )  The chiral condensate and the baryon density as a function of the baryon chemical potential in lattice units aµ B and for various temperatures at quark mass m = 1 5 is shown in Fig    We have determined the critical temperature to be aT c = 0 23 , which is characterized by an infinite slope of the chiral condensate 
For lower temperatures, there is a clear discontinuity of the chiral con-densate, separating the low density phase from the high density phase  For temperatures above and in the vicinity of aT c the chiral condensate and baryon density has no discontinuity but rapidly changes, corresponding to a crossover transition 
With this method, the phase diagram is plotted for different quark masses in Fig    The second order phase transition in the chiral limit is plotted in solid blue line, the dotted lines show the first order phase transition for different quark masses and the solid red line indicates the critical end point for the different quark masses 
Mean field theory also gives an expression for the pion mass am π and the baryon mass am B : The mean field baryon mass for N c = 3, d = 3 is also plotted in red in Fig    Whereas the baryon mass is around N c in the chiral limit (am B 3 12 for N c = 3), it approximately doubles at m = 3 5 (am B 6 28) which corresponds to the pion mass am π = 4 45, i e  m π /m B = 0 708 
Hence, at around bare mass m = 3 5, the valence quark mass of the baryon corresponds roughly to 1/3 of the chiral limit value of the baryon mass  The first Monte Carlo simulations that could extend in the µ B − T plane was the MDP algorithm , but it required the introduction of the worm algorithm to make substantial progress 
First studies of the worm algorithm applied to the strong coupling limit QCD (with gauge group U(3)) are , and for gauge group SU   Monte Carlo simulations to extend the worm to incorporate leading order corrections were first proposed in   We will shortly review the setup of or Monte Carlo strategy for the nuclear transition, with an emphasis on the challenges to address large quark masses 

Strong Coupling

Without any further resummation, there is a mild sign problem in the dual formulation of lattice QCD in the strong coupling limit  When the average sign σ is not too small (close to zero), it implies that most of the configurations have a positive weight thus allowing us to perform sign reweighting strategies 
In Fig  , ∆f is plotted as a function of the baryon chemical potential and the quark masses  It is seen that ∆f is close to zero for most cases except near the critical chemical potential and for small quark masses, but never exceeds 5 × 10 −4   Hence sign reweighting can be performed in the full parameter space 
The result that the sign problem becomes even milder when increasing the mass is related to the fact that larger critical chemical potentials result in a larger fraction of static baryons (spatial baryon hoppings become rare)  FIG    ∆F at strong coupling as a function of chemical potential and quark mass on a 6 3 × 8 
The sign problem becomes milder as the quark mass increases 

Finite β

All runs at finite β have been obtained for N τ = 4, which corresponds to a moderately low temperature aT = 0 25 compared to the value of the chiral transition aT 1 54  Those simulations were too expensive to attempt N τ = 8 runs, in particular as a higher statistics was required  The spatial volumes are 4 3 , 6 3 and 8 3  
For β values are from 0 0 to 1 0 with step size 0 1, and for am q values from 0 00 to 1 00 with step size 0 01  The values of aµ were chosen close to the nuclear transition, the scanning range is shifted to large values as am q increases  At small quark masses the scanning range is from aµ = 0 4 to 1 0 and for the large quark masses, it is from 0 6 to 1 2 with step size 0 01 
The statistics used for are 15 × 10 4 measurements and between measurement, 40 × N 3 s worm updates 

Residual sign problem

Although it is possible to resum the sign problem at strong coupling with a resummation of baryon and pion world lines, this is not possible when including gauge corrections  In order to compare both sign problems, we kept the original dual formulation to monitor the severity of the sign problem  This is done via the relation
between the average sign σ and the difference of the free energy density ∆f between the full ensemble f and of the sign-quenched ensemble f ||  

Nuclear interactions

We have found that aµ 1st B is very different from the baryon mass  This must be due to strong attractive interactions of nucleons  In contrast to continuum physics, in the strong coupling limit there is no pion exchange due to the Grassmann constraint  Instead, nucleons are point like and hard core repulsive 
However, the pion bath, which is modified by the presence of static baryons, results in an attractive interaction  In , this has been analyzed in the chiral limit using the snake algorithm, and it has been found that the attractive force is of entropic origin  Here, we do not quantify the nuclear interaction via the nuclear potential, but via the difference between critical baryon chemical potential and baryon mass, in units baryon mass, as shown in Fig  , given the am B as measured in Section III C 
This compares better to the 3dim  effective theory  The nuclear interaction is maximal and more than 40% in the chiral limit, which is related to pions being massless: the modification of the pion bath is maximal  We clearly find that the nuclear interaction decreases drastically and almost linearly until it almost approaches zero at about am q = 2 0, corresponding to a pion mass am π = 3 36, see Section II B  The large error bars for larger quark masses, that are due to the subtraction of almost same magnitudes, makes it difficult to extract a non-zero nuclear interaction at the largest quark masses 
In this work, we have determined the baryon mass and the nuclear transition via Monte Carlo: the worm algorithm based on the dual formulation, at finite β equipped with additional updates  All those numerical results and various analytic expressions are summarized in Fig    We find that as the quark mass becomes large, spatial mesons hoppings (i e 
spatial dimers) become rare, which makes this 3+1-dimensional system closer to 1dim  QCD   Also, both the baryon mass and the baryon chemical potential obtained in our dual representation, i e  for staggered fermions, approaches the baryon mass of the 3-dim  effective theory which is based on Wilson fermions 
Another comparison that summarizes the validity of the mean field approach discussed in Section II B is shown in Fig    It is evident that mean field theory has strong deviations for small quark masses, but this discrepancy becomes smaller for larger quark masses  The extension of the study of the nuclear transition to finite inverse gauge coupling β is summarized in Fig  , which shows the β-dependence of aµ c B for various quark masses 
For all quark masses ranging from am q = 0 to am q = 1 0, there is only a very weak β-dependence, confirming the expectation from mean field theory   This works was restricted to isotropic lattices ξ = a/a t = 1, i e  we performed simulations at fixed temperature  Non-isotropic lattices are necessary to vary the temperature at fixed values of β 
This requires to include two bare anisotropies, γ for the fermionic action and γ G for the gauge action  Finite β has only been studied by us in the chiral limit   Clearly, it is interesting to study the location of the nuclear critical point also including higher order gauge corrections and at finite quark mass 
Simulations including O(β 2 ) are under preparation 
Context 2: Brooksley Elizabeth Born (born August 27, 1940) is an American attorney and former public official who, from August 26, 1996, to June 1, 1999, was chair of the Commodity Futures Trading Commission (CFTC), the federal agency which oversees the U S  futures and commodity options markets  During her tenure on the CFTC, Born lobbied Congress and the President to give the CFTC oversight of off-exchange markets for derivatives, in addition to its role with respect to exchange-traded derivatives, but her warnings were ignored or dismissed, and her calls for reform resisted by other regulators <ref name="nytimes">Goodman, Peter S  The Reckoning - Taking Hard New Look at a Greenspan Legacy, The New York Times, October 9, 2008 </ref> Born resigned as chairperson on June 1, 1999, shortly after Congress passed legislation prohibiting her agency from regulating derivatives 

In 2009, Born received the John F  Kennedy Profiles in Courage Award, along with Sheila Bair of the Federal Deposit Insurance Corporation, in recognition of the "political courage she demonstrated in sounding early warnings about conditions that contributed" to the 2007-08 financial crisis 

Early life and education
Born graduated from Abraham Lincoln High School (San Francisco, California) at the age of 16  She then attended Stanford University, where she majored in English and was graduated with the class of 1961   She initially wanted to become a doctor, but a guidance counsellor at Stanford advised her against medicine, so she majored in English literature instead 

She then attended Stanford Law School, one of only seven women in her class   She was the first female student ever to be named president of the Stanford Law Review  She received the "Outstanding Senior" award and graduated as valedictorian of the class of 1964 

Legal career
Immediately after law school Born was selected as a law clerk to judge Henry Edgerton of the U S  Court of Appeals for the District of Columbia Circuit  It was during this time that she met her first husband, Jacob C  Landau, who was a journalist covering the Federal courts at the time  Following her clerkship, she became an associate at the Washington, D C -based international law firm of Arnold & Porter  Born was attracted to Arnold & Porter because it was one of the few major law firms to have a woman partner at that time, Carolyn Agger, who was the head of the tax practice  Born took a two-year leave of absence from Arnold & Porter to accompany her first husband to Boston, where he had received a fellowship  During that time she worked as a research assistant to law professor Alan Dershowitz 

Born's early career at Arnold & Porter focused on international trade law, in which she represented a number of Swiss industries and the government of Switzerland  She developed a practice representing clients in numerous complex litigation and arbitration cases involving financial market transactions  Among her high-profile cases was the matter of the Hunt Brothers attempt to corner the market in silver in the 1970s  She made partner at Arnold & Porter, after moving to a three-day schedule to help raise her second child, and eventually rose to be the head of the firm's derivatives practice 

Born was among the first female attorneys to systematically address inequities regarding how the laws treated women  Born and another female lawyer, Marna Tucker, taught what is considered to have been the first "Women and the Law" course at Catholic University’s Columbus School of Law  The class exclusively concerned prejudicial treatment of women under the laws of the United States, past and present   Born and Tucker were surprised to discover that there was no textbook on the issue at the time   Born is also one of the co-founders of the National Women's Law Center  Born also helped rewrite the American Bar Association rules to make it possible for more women and minorities to sit on federal bench 

During her long legal career, and into her retirement, Born did much pro bono and other types of volunteer work  She was active in the American Bar Association, the largest professional organization of lawyers in the United States   Initially Born was named a member of the governing council of the ABA's Individual Rights Section, eventually becoming chairperson   Born and Tucker founded the ABA Women's Caucus, the first organization of female lawyers in the ABA   She held several other senior positions in the ABA, including being named the first woman member of the ABA's Standing Committee on the Federal Judiciary   As a member of the Judiciary Committee, Born provided testimony and opinion on persons nominated for federal judgeships  In 1980 she was named chair of the committee   As chair of the committee, Born was invited to address the U S  Congress regarding the nomination of Judge Sandra Day O'Connor to the U S  Supreme Court 

In 1993, Born's name was floated as a possible candidate for Attorney General of the United States, but Janet Reno was nominated 

In July 2009, Nancy Pelosi appointed Brooksley Born as a commissioner to the Financial Crisis Inquiry Commission (FCIC) 

Born and the OTC derivatives market
Born was appointed to the CFTC on April 15, 1994, by President Bill Clinton  Due to litigation against Bankers Trust Company by Procter and Gamble and other corporate clients, Born and her team at the CFTC sought comments on the regulation of over-the-counter derivatives, a first step in the process of writing CFTC regulations to supplement the existing regulations of the Federal Reserve System,  the Options Clearing Corporation, and the National Association of Insurance Commissioners  Born was particularly concerned about swaps, financial instruments that are traded over the counter between banks, insurance companies or other funds or companies, and thus have no transparency except to the two counterparties and the counterparties' regulators, if any   CFTC regulation was strenuously opposed by Federal Reserve chairman Alan Greenspan, and by Treasury Secretaries Robert Rubin and Lawrence Summers  On May 7, 1998, former SEC Chairman Arthur Levitt joined Rubin and Greenspan in objecting to the issuance of the CFTC's concept release  Their response dismissed Born's analysis and focused on the hypothetical possibility that CFTC regulation of swaps and other OTC derivative instruments could create a "legal uncertainty" regarding such financial instruments,  hypothetically reducing the value of the instruments  They argued that the imposition of regulatory costs would "stifle financial innovation" and encourage financial capital to transfer its  transactions offshore  The disagreement between Born and the Executive Office's top economic policy advisors has been described not only as a classic Washington turf war, but also a war of ideologies,  insofar as it is possible to argue that Born's actions were consistent with Keynesian and neoclassical economics while Greenspan, Rubin, Levitt, and Summers consistently espoused neoliberal, and neoconservative policies 

In 1998, a trillion-dollar hedge fund called Long Term Capital Management (LTCM) was near collapse   Using mathematical models to calculate debt risk, LTCM used derivatives to leverage $5 billion into more than $1 trillion, doing business with fifteen of Wall Street's largest financial institutions   The derivative transactions were not regulated, nor were investors able to evaluate LTCM's exposures   Born stated, "I thought that LTCM was exactly what I had been worried about"   In the last weekend of September 1998, the President's working group was told that the entire American economy hung in the balance   After intervention by the Federal Reserve, the crisis was averted   In congressional hearings into the crisis, Greenspan acknowledged that language had been introduced into an agriculture bill that would prevent CFTC from regulating the derivatives which were at the center of the crisis that threatened the US economy   U S  Representative Maurice Hinchey (D-NY) asked "How many more failures do you think we'd have to have before some regulation in this area might be appropriate?"  In response, Greenspan brushed aside the substance of Born's warnings with the simple assertion that "the degree of supervision of regulation of the over-the-counter derivatives market is quite adequate to maintain a degree of stability in the system"  Born's warning was that there wasn't any regulation of them   Born's chief of staff, Michael Greenberger summed up Greenspan's position this way: "Greenspan didn't believe that fraud was something that needed to be enforced, and he assumed she probably did  And of course, she did "  Under heavy pressure from the financial lobby, legislation prohibiting regulation of derivatives by Born's agency was passed by the Congress   Born resigned on June 1, 1999 

The derivatives market continued to grow yearly throughout both terms of George W  Bush's administration  On September 15, 2008, the bankruptcy of Lehman Brothers forced a broad recognition of a financial crisis in both the US and world capital markets   As Lehman Brothers' failure temporarily reduced financial capital's confidence, a number of newspaper articles and television programs suggested that the failure's possible causes included the conflict between the CFTC and the other regulators Faiola, Anthony, Nakashima, Ellen and Drew, Jill  The Crash: Risk and Regulation - What Went Wrong, The Washington Post, October 15, 2008 

Born declined to publicly comment on the unfolding 2008 crisis until March 2009, when she said: "The market grew so enormously, with so little oversight and regulation, that it made the financial crisis much deeper and more pervasive than it otherwise would have been " She also lamented the influence of Wall Street lobbyists on the process and the refusal of regulators to discuss even modest reforms 

An October 2009 Frontline documentary titled "The Warning"  described Born's thwarted efforts to regulate and bring transparency to the derivatives market, and the continuing opposition thereto  The program concluded with an excerpted interview with Born sounding another warning: "I think we will have continuing danger from these markets and that we will have repeats of the financial crisis -- may differ in details but there will be significant financial downturns and disasters attributed to this regulatory gap, over and over, until we learn from experience "

In 2009 Born, along with Sheila Bair of the FDIC, was awarded the John F  Kennedy Profiles in Courage Award in recognition of the "political courage she demonstrated in sounding early warnings about conditions that contributed" to the 2007-08 financial crisis   According to Caroline Kennedy, "Brooksley Born recognized that the financial security of all Americans was being put at risk by the greed, negligence and opposition of  powerful and well connected interests     The catastrophic financial events of recent months have  proved them [Born and Sheila Bair] right "  One member of the President's working group had a change of heart about Brooksley Born   SEC Chairman Arthur Levitt stated "I've come to know her as one of the most capable, dedicated, intelligent and committed public servants that I have ever come to know", adding that "I could have done much better  I could have made a difference" in response to her warnings 

In 2010, a documentary film Inside Job further alleged that derivatives regulation was ineffective from the Clinton administration on  Along with fellow whistleblower, former IMF Chief Economist Raghuram Rajan, who was also scorned by the economic establishment, Brooksley Born was cited as one of the authorities arguing that financial derivatives increase economic risk 

 Personal life 
Born is married to Alexander E  Bennett (also retired from Arnold & Porter)   She has five adult children - two from a previous marriage to Jacob Landau and three stepchildren  Notably, Born was named a partner at Arnold & Porter while working part-time so she could raise her two young children   When both of her children were school-age, Born returned to practice full-time 

References

External links
Attorney profile at Arnold & Porter
Brooksley Born (2009 Winner) of the Profiles in Courage Award, with acceptance speech transcript and NECN video

Profile at MarketsWiki
Speeches and statements
"Testimony Of Brooksley Born Chairperson of the CFTC Concerning The Over-The-Counter Derivatives Market", before the House Committee On Banking And Financial Services, July 24, 1998 
"The Lessons of Long Term Capital Management L P ", Remarks of Brooksley Born, Chairperson of the CFTC, Chicago-Kent-IIT Commodities Law Institute, Chicago, Illinois, October 15, 1998 
 Interview: Brooksley Born for "PBS Frontline: The Warning", PBS, (streaming VIDEO 1 hour), October 20, 2009 
Articles
Manuel Roig-Franzia  "Credit Crisis Cassandra:Brooksley Born's Unheeded Warning Is a Rueful Echo 10 Years On", The Washington Post, May 26, 2009
 Taibbi, Matt  "The Great American Bubble Machine", Rolling Stone'', July 9–23, 2009

1940 births
American women lawyers
Arnold & Porter people
Clinton administration personnel
Columbus School of Law faculty
Commodity Futures Trading Commission personnel
Heads of United States federal agencies
Lawyers from San Francisco
Living people
Stanford Law School alumni
21st-century American women
Stanford University alumni



ground_truth: Nuclear liquid-gas transition in lattice QCD.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When did Born resign as chairperson of the CFTC?

Read the following text and answer briefly.

Context 3: Paper Info

Title: Environmental variability and network structure determine the optimal plasticity mechanisms in embodied agents
Publish Date: Unkown
Author List: Sina Khajehabdollahi (from Department of Computer Science, University of Tübingen)

Figure

Figure2: An outline of the network controlling the foraging agent The sensor layer receives inputs at each time step (the ingredients of the nearest food), which are processed by the plastic layer in the same way as the static sensory network, Fig 1 The output of that network is given as input to the motor network, along with the distance d and angle α to the nearest food, the current velocity v, and energy E of the agent These signals are processed through two hidden layers to the final output of motor commands as the linear and angular acceleration of the agent
Figure4: The evolved parameters θ = (θ 1 ,      , θ 8 ) of the plasticity rule for the reward prediction (a ) and the decision (b ) tasks, for a variety of parameters (p tr = 0 01, d e ∈ 0, 0 1,      , 1, and σ ∈ 0, 0 1,      , 1 in all 100 combinations) Despite the relatively small difference between the tasks, the evolved learning rules differ considerably For visual guidance, the lines connect θs from the same run 
Figure5: a The trajectory of an agent (blue line) in the 2D environment A well-trained agent will approach and consume food with positive values (green dots) and avoid negative food (red dots) b The learning rate of the plastic sensory network eta p grows with the distance between environments d e c  and decreases with the frequency of environmental change d The fitness of an agent (measured as the total food consumed over its lifetime) increases over generations of the EA for both the scalar and binary readouts in the sensory network e The Pearson correlation coefficient of an evolved agent's weights with the ingredient value vector of the current environment (E 1 -blue, E 2 -red) In this example, the agent's weights are anti-correlated with its environment, which is not an issue for performance since the motor network can interpret the inverted signs of food 

abstract

The evolutionary balance between innate and learned behaviors is highly intricate, and different organisms have found different solutions to this problem  We hypothesize that the emergence and exact form of learning behaviors is naturally connected with the statistics of environmental fluctuations and tasks an organism needs to solve 
Here, we study how different aspects of simulated environments shape an evolved synaptic plasticity rule in static and moving artificial agents  We demonstrate that environmental fluctuation and uncertainty control the reliance of artificial organisms on plasticity  Interestingly, the form of the emerging plasticity rule is additionally determined by the details of the task the artificial organisms are aiming to solve 
Moreover, we show that coevolution between static connectivity and interacting plasticity mechanisms in distinct sub-networks changes the function and form of the emerging plasticity rules in embodied agents performing a foraging task  One of the defining features of living organisms is their ability to adapt to their environment and incorporate new information to modify their behavior 
It is unclear how the ability to learn first evolved , but its utility appears evident  Natural environments are too complex for all the necessary information to be hardcoded genetically and more importantly, they keep changing during an organism's lifetime in ways that cannot be anticipated ;   The link between learning and environmental uncertainty and fluctuation has been extensively demonstrated in both natural ; , and artificial environments  
Nevertheless, the ability to learn does not come without costs  For the capacity to learn to be beneficial in evolutionary terms, a costly nurturing period is often required, a phenomenon observed in both biological , and artificial organisms   Additionally, it has been shown that in some complex environments, hardcoded behaviors may be superior to learned ones given limits in the agent's lifetime and envi-ronmental uncertainty ; ;  
The theoretical investigation of the optimal balance between learned and innate behaviors in natural and artificial systems goes back several decades  However, it has recently found also a wide range of applications in applied AI systems ;   Most AI systems are trained for specific tasks, and have no need for modification after their training has been completed 
Still, technological advances and the necessity to solve broad families of tasks make discussions about life-like AI systems relevant to a wide range of potential application areas  Thus the idea of open-ended AI agents that can continually interact with and adapt to changing environments has become particularly appealing 
Many different approaches for introducing lifelong learning in artificial agents have been proposed  Some of them draw direct inspiration from actual biological systems ;   Among them, the most biologically plausible solution is to equip artificial neural networks with some local neural plasticity , similar to the large variety of synaptic plasticity mechanisms ; ; that performs the bulk of the learning in the brains of living organisms  
The artificial plasticity mechanisms can be optimized to modify the connectivity of the artificial neural networks toward solving a particular task  The optimization can use a variety of approaches, most commonly evolutionary computation  The idea of meta-learning or optimizing synaptic plasticity rules to perform specific functions has been recently established as an engineering tool that can compete with stateof-the-art machine learning algorithms on various complex tasks ; ; Pedersen and Risi (2021);  
Additionally, it can be used to reverse engineer actual plasticity mechanisms found in biological neural networks and uncover their functions ;   Here, we study the effect that different factors (environ-arXiv:2303 06734v1 [q-bio NC] 12 Mar 2023 mental fluctuation and reliability, task complexity) have on the form of evolved functional reward-modulated plasticity rules 
We investigate the evolution of plasticity rules in static, single-layer simple networks  Then we increase the complexity by switching to moving agents performing a complex foraging task  In both cases, we study the impact of different environmental parameters on the form of the evolved plasticity mechanisms and the interaction of learned and static network connectivity 
Interestingly, we find that different environmental conditions and different combinations of static and plastic connectivity have a very large impact on the resulting plasticity rules  We imagine an agent who must forage to survive in an environment presenting various types of complex food particles  Each food particle is composed of various amounts and combinations of N ingredients that can have positive (food) or negative (poison) values 
The value of a food particle is a weighted sum of its ingredients  To predict the reward value of a given resource, the agent must learn the values of these ingredients by interacting with the environment  The priors could be generated by genetic memory, but the exact values are subject to change  To introduce environmental variability, we stochastically change the values of the ingredients 
More precisely, we define two ingredient-value distributions E 1 and E 2 and switch between them, with probability p tr for every time step  We control how (dis)similar the environments are by parametrically setting E 2 = (1 − 2d e )E 1 , with d e ∈ [0, 1] serving as a distance proxy for the environments; when d e = 0, the environment remains unchanged, and when d e = 1 the value of each ingredient fully reverses when the environmental transition happens 
For simplicity, we take values of the ingredients in E 1 equally spaced between -1 and 1 (for the visualization, see Fig  )  The static agent receives passively presented food as a vector of ingredients and can assess its compound value using the linear summation of its sensors with the (learned or evolved) weights, see Fig   
The network consists of N sensory neurons that are projecting to a single post-synaptic neuron  At each time step, an input X t = (x 1 ,       , x N ) is presented, were the value x i , i ∈ {1,       , N } represents the quantity of the ingredient i  We draw x i independently form a uniform distribution on the [0, 1] interval (x i ∼ U (0, 1)) 
The value of each ingredient w c i is determined by the environment (E 1 or E 2 )  The postsynaptic neuron outputs a prediction of the food X t value as y t = g(W X T t )  Throughout the paper, g will be either the identity function, in which case the prediction neuron is linear, or a step-function; however, it could be any other nonlinearity, such as a sigmoid or ReLU 
After outputting the prediction, the neuron receives feedback in the form of the real value of the input R t   The real value is computed as R t = W c X T t + ξ, where W c = (w c 1 ,       , w c N ) is the actual value of the ingredients, and ξ is a term summarizing the noise of reward and sensing system ξ ∼ N (0, σ) 
Figure : An outline of the static agent's network  The sensor layer receives inputs representing the quantity of each ingredient of a given food at each time step  The agent computes the prediction of the food's value y t and is then given the true value R t ; it finally uses this information in the plasticity rule to update the weight matrix 
For the evolutionary adjustment of the agent's parameters, the loss of the static agent is the sum of the mean squared errors (MSE) between its prediction y t and the reward R t over the lifetime of the agent  The agent's initial weights are set to the average of the two ingredient value distributions, which is the optimal initial value for the case of symmetric switching of environments that we consider here 
As a next step, we incorporate the sensory network of static agents into embodied agents that can move around in an environment scattered with food  To this end, we merge the static agent's network with a second, non-plastic motor network that is responsible for controlling the motion of the agent in the environment 
Specifically, the original plastic network now provides the agent with information about the value of the nearest food  The embodied agent has additional sensors for the distance from the nearest food, the angle between the current velocity and the nearest food direction, its own velocity, and its own energy level (sum of consumed food values) 
These inputs are processed by two hidden layers (of 30 and 15 neurons) with tanh activation  The network's outputs are angular and linear acceleration, Fig    The embodied agents spawn in a 2D space with periodic boundary conditions along with a number of food particles that are selected such that the mean of the food value distribution is ∼ 0  An agent can eat food by approaching it sufficiently closely, and each time a food particle is eaten, it is The sensor layer receives inputs at each time step (the ingredients of the nearest food), which are processed by the plastic layer in the same way as the static sensory network, Fig   
The output of that network is given as input to the motor network, along with the distance d and angle α to the nearest food, the current velocity v, and energy E of the agent  These signals are processed through two hidden layers to the final output of motor commands as the linear and angular acceleration of the agent re-spawned with the same value somewhere randomly on the grid (following the setup of ) 
After 5000 time steps, the cumulative reward of the agent (the sum of the values of all the food it consumed) is taken as its fitness  During the evolutionary optimization, the parameters for both the motor network (connections) and plastic network (learning rule parameters) are co-evolved, and so agents must simultaneously learn to move and discriminate good/bad food 
Reward-modulated plasticity is one of the most promising explanations for biological credit assignment   In our network, the plasticity rule that updates the weights of the linear sensor network is a rewardmodulated rule which is parameterized as a linear combination of the input, the output, and the reward at each time step:
Additionally, after each plasticity step, the weights are normalized by mean subtraction, an important step for the stabilization of Hebbian-like plasticity rules   We use a genetic algorithm to optimize the learning rate η p and amplitudes of different terms θ = (θ 1 ,       , θ 8 )  The successful plasticity rule after many food presentations must converge to a weight vector that predicts the correct food values (or allows the agent to correctly decide whether to eat a food or avoid it) 
To have comparable results, we divide θ = (θ 1 ,       , θ 8 ) by We then multiply the learning rate η p with θ max to maintain the rule's evolved form unchanged, η norm p = η p • θ max   In the following, we always use normalized η p and θ, omitting norm   To evolve the plasticity rule and the moving agents' motor networks, we use a simple genetic algorithm with elitism  
The agents' parameters are initialized at random (drawn from a Gaussian distribution), then the sensory network is trained by the plasticity rule and finally, the agents are evaluated  After each generation, the bestperforming agents (top 10 % of the population size) are selected and copied into the next generation 
The remaining 90 % of the generation is repopulated with mutated copies of the best-performing agents  We mutate agents by adding independent Gaussian noise (σ = 0 1) to its parameters  To start with, we consider a static agent whose goal is to identify the value of presented food correctly  The static reward-prediction network quickly evolves the parameters of the learning rule, successfully solving the prediction task 
We first look at the evolved learning rate η p , which determines how fast (if at all) the network's weight vector is updated during the lifetime of the agents  We identify three factors that control the learning rate parameter the EA converges to: the distance between the environments, the noisiness of the reward, and the rate of environmental transition 
The first natural factor is the distance d e between the two environments, with a larger distance requiring a higher learning rate, Fig    This is an expected result since the convergence time to the "correct" weights is highly dependent on the initial conditions  If an agent is born at a point very close to optimality, which naturally happens if the environments are similar, the distance it needs to traverse on the fitness landscape is small 
Therefore it can afford to have a small learning rate, which leads to a more stable convergence and is not affected by noise  A second parameter that impacts the learning rate is the variance of the rewards  The reward an agent receives for the plasticity step contains a noise term ξ that is drawn from a zero mean Gaussian distribution with standard deviation σ 
This parameter controls the unreliability of the agent's sensory system, i e , higher σ means that the information the agent gets about the value of the foods it consumes cannot be fully trusted to reflect the actual value of the foods  As σ increases, the learning rate η p decreases, which means that the more unreliable an environment becomes, the less an agent relies on plasticity to update its weights, Fig   
Indeed for some combinations of relatively small distance d e and high reward variance σ, the EA converges to a learning rate of η p ≈ 0  This means that the agent opts to have no adaptation during its lifetime and remain at the mean of the two environments  It is an optimal solution when the expected loss due to ignoring the environmental transitions is, on average, lower than the loss the plastic network will incur by learning via the (often misleading because of the high σ) environmental cues 
A final factor that affects the learning rate the EA will converge to is the frequency of environmental change during an agent's lifetime  Since the environmental change is modeled as a simple, two-state Markov process (Fig  ), the control parameter is the transition probability p tr   When keeping everything else the same, the learning rate rapidly rises as we increase the transition probability from 0, and after reaching a peak, it begins to decline slowly, eventually reaching zero (Fig  ) 
This means that when environmental transition is very rare, agents opt for a very low learning rate, allowing a slow and stable convergence to an environment-appropriate weight vector that leads to very low losses while the agent remains in that environment  As the rate of environmental transition increases, faster learning is required to speed up convergence in order to exploit the (comparatively shorter) stays in each environment 
Finally, as the environmental transition becomes too fast, the agents opt for slower or even no learning, which keeps them ) and the decision (b ) tasks, for a variety of parameters (p tr = 0 01, d e ∈ 0, 0 1,       , 1, and σ ∈ 0, 0 1,       , 1 in all 100 combinations)  Despite the relatively small difference between the tasks, the evolved learning rules differ considerably 
For visual guidance, the lines connect θs from the same run  near the middle of the two environments, ensuring that the average loss of the two environments is minimal (Fig  )  The form of the evolved learning rule depends on the task: Decision vs  Prediction The plasticity parameters θ = (θ 1 ,       , θ 8 ) for the rewardprediction task converge on approximately the same point, regardless of the environmental parameters (Fig  ) 
In particular, θ 3 → 1, θ 5 → −1, θ i → 0 for all other i, and thus the learning rule converges to: Since by definition y t = g(W t X T t ) = W t X T t (g(x) = x in this experiment) and R t = W c X T t + ξ we get: Thus the distribution of ∆W t converges to a distribution with mean 0 and variance depending on η p and σ and W converges to W c  
So this learning rule will match the agent's weight vector with the vector of ingredient values in the environment  We examine the robustness of the learning rule the EA discovers by considering a slight modification of our task  Instead of predicting the expected food value, the agent now needs to decide whether to eat the presented food or not 
This is done by introducing a step-function nonlinearity (g(x) = 1 if x ≥ 1 and 0 otherwise)  Then the output y(t) is computed as: Instead of the MSE loss between prediction and actual value, the fitness of the agent is now defined as the sum of the food values it chose to consume (by giving y t = 1)  Besides these two changes, the setup of the experiments remains exactly the same 
The qualitative relation between η p and parameters of environment d e , σ and p tr is preserved in the changed experiment  However, the resulting learning rule is significantly different (Fig  )  The evolution converges to the following learning rule: In both cases, the rule has the form ∆W t = η p X t [α y R t + β y ] 
Thus, the ∆W t is positive or negative depending on whether the reward R t is above or below a threshold (γ = −β y /α y ) that depends on the output decision of the network (y t = 0 or 1)  Both learning rules (for the reward-prediction and decision tasks) have a clear Hebbian form (coordination of preand post-synaptic activity) and use the incoming reward signal as a threshold 
These similarities indicate some common organizing principles of reward-modulated learning rules, but their significant differences highlight the sensitivity of the optimization process to task details  We now turn to the moving embodied agents in the 2D environment  To optimize these agents, both the motor network's connections and the sensory network's plasticity parameters evolve simultaneously 
Since the motor network is initially random and the agent has to move to find food, the number of interactions an agent experiences in its lifetime can be small, slowing down the learning  However, having the larger motor network also has benefits for evolution because it allows the output of the plastic network to be read out and transformed in different ways, resulting in a broad set of solutions 
The fitness of an agent (measured as the total food consumed over its lifetime) increases over generations of the EA for both the scalar and binary readouts in the sensory network  e  The Pearson correlation coefficient of an evolved agent's weights with the ingredient value vector of the current environment (E 1 -blue, E 2 -red) 
In this example, the agent's weights are anti-correlated with its environment, which is not an issue for performance since the motor network can interpret the inverted signs of food  The agents can solve the task effectively by evolving a functional motor network and a plasticity rule that converges to interpretable weights (Fig  ) 
After ∼ 100 evolutionary steps (Fig  ), the agents can learn the ingredient value distribution using the plastic network and reliably move towards foods with positive values while avoiding the ones with negative values  We compare the dependence of the moving and the static agents on the parameters of the environment: d e and the state transition probability p tr  
At first, in order to simplify the experiment, we set the transition probability to 0, but fixed the initial weights to be the average of E 1 and E 2 , while the real state is E 2   In this experiment, the distance between states d e indicates twice the distance between the agent's initial weights and the optimal weights (the environment's ingredient values) since the agent is initialized at the mean of the two environment distributions 
Same as for the static agent, the learning rate increases with the distance d e (Fig  )  Then, we examine the effect of the environmental transition probability p tr on the evolved learning rate η p   In order for an agent to get sufficient exposure to each environment, we scale down the probability p tr from the equivalent experiment for the static agents 
We find that as the probability of transition increases, the evolved learning rate η p decreases (Fig  )  This fits with the larger trend for the static agent, although there is a clear difference when it comes to the increase for very small transition probabil-ities that were clearly identifiable in the static but not the moving agents 
This could be due to much sparser data and possibly the insufficiently long lifetime of the moving agent (the necessity of scaling makes direct comparisons difficult)  Nevertheless, overall we see that the associations observed in the static agents between environmental distance d e and transition probability p tr and the evolved learning rate η p are largely maintained in the moving agents 
Still, more data would be needed to make any conclusive assertions about the exact effect of these environmental parameters on the emerging plasticity mechanisms  A crucial difference between the static and the moving agents is the function the plasticity has to perform  While in the static agents, the plasticity has to effectively identify the exact value distribution of the environment in order to produce accurate predictions, in the embodied agents, the plasticity has to merely produce a representation of the environment that the motor network can evolve to interpret adequately enough to make decisions about which food to consume 
To illustrate the difference, we plot the Pearson correlation coefficient between an agent's weights and the ingredient values of the environment it is moving in (Fig  )  We use the correlation instead of the MSE loss (which we used for the static agents in Fig  ) because the amplitude of the vector varies a lot for different agents and meaningful The evolved parameters of moving agents' plasticity rule for the g(s) = x, identity (a ) and the step function (Eq 
4) (b ) sensory networks (the environmental parameters here are d e ∈ [0, 1], σ = 0 and p tr = 0 001)  The step function (binary output) network evolved a more structured plasticity rule (e g , θ 3 > 0 for all realizations) than the linear network  Moreover, the learned weights for the identity network (c ) have higher variance and correlate significantly less with the environment's ingredient distribution compared to the learned weights for the thresholded network (d )
conclusions cannot be drawn from the MSE loss  For many agents, the learned weights are consistently anti-correlated with the actual ingredient values (an example of such an agent is shown in Fig  )  This means that the output of the sensory network will have the opposite sign from the actual food value 
While in the static network, this would lead to very bad predictions and high loss, in the foraging task, these agents perform exactly as well as the ones where the weights and ingredients values are positively correlated, since the motor network can simply learn to move towards food for which it gets a negative instead of a positive sensory input 
This additional step of the output of the plastic network going through the motor network before producing any behavior has a strong effect on the plasticity rules that the embodied agents evolve  Specifically, if we look at the emerging rules the top performing agents have evolved (Fig  ), it becomes clear that, unlike the very well-structured rules of the static agents (Fig  ), there is now virtually no discernible pattern or structure 
The difference becomes even clearer if we look at the learned weights (at the end of a simulation) of the best-performing agents (Fig  )  While there is some correlation with the environment's ingredient value distribution, the variance is very large, and they do not seem to converge on the "correct" values in any way 
This is to some extent expected since, unlike the static agents where the network's output has to be exactly correct, driving the evolution of rules that converge to the precise environmental distribution, in the embodied networks, the bulk of the processing is done by the motor network which can evolve to interpret the scalar value of the sensory network's output in a variety of ways 
Thus, as long as the sensory network's plasticity rule co-evolves with the motor network, any plasticity rule that learns to produce consistent information about the value of encountered food can potentially be selected  To further test this assumption, we introduce a bottleneck of information propagation between the sensory and motor networks by using a step-function nonlinearity on the output of the sensory network (Eq 
4)  Similarly to the decision task of the static network, the output of the sensory network now becomes binary  This effectively reduces the flow of information from the sensory to the motor network, forcing the sensory network to consistently decide whether food should be consumed (with the caveat that the motor network can still interpret the binary sign in either of two ways, either consuming food marked with 1 or the ones marked with 0 by the sensory network) 
The agents perform equally well in this variation of the task as before (Fig  ), but now, the evolved plasticity rules seem to be more structured (Fig  )  Moreover, the variance of the learned weights in the bestperforming agents is significantly reduced (Fig  ), which indicates that the bottleneck in the sensory network is in-creasing selection pressure for rules that learn the environment's food distribution accurately 
We find that different sources of variability have a strong impact on the extent to which evolving agents will develop neuronal plasticity mechanisms for adapting to their environment  A diverse environment, a reliable sensory system, and a rate of environmental change that is neither too large nor too small are necessary conditions for an agent to be able to effectively adapt via synaptic plasticity 
Additionally, we find that minor variations of the task an agent has to solve or the parametrization of the network can give rise to significantly different plasticity rules  Our results partially extend to embodied artificial agents performing a foraging task  We show that environmental variability also pushes the development of plasticity in such agents 
Still, in contrast to the static agents, we find that the interaction of a static motor network with a plastic sensory network gives rise to a much greater variety of wellfunctioning learning rules  We propose a potential cause of this degeneracy; as the relatively complex motor network is allowed to read out and process the outputs from the plastic network, any consistent information coming out of these outputs can be potentially interpreted in a behaviorally useful way 
Reducing the information the motor network can extract from the sensory system significantly limits learning rule variability  Our findings on the effect of environmental variability concur with the findings of previous studies that have identified the constraints that environmental variability places on the evolutionary viability of learning behaviors 
We extend these findings in a mechanistic model which uses a biologically plausible learning mechanism (synaptic plasticity)  We show how a simple evolutionary algorithm can optimize the different parameters of a simple reward-modulated plasticity rule for solving simple prediction and decision tasks 
Reward-modulated plasticity has been extensively studied as a plausible mechanism for credit assignment in the brain ; ; and has found several applications in artificial intelligence and robotics tasks ;   Here, we demonstrate how such rules can be very well-tuned to take into account different environmental parameters and produce optimal behavior in simple systems 
Additionally, we demonstrate how the co-evolution of plasticity and static functional connectivity in different subnetworks fundamentally changes the evolutionary pressures on the resulting plasticity rules, allowing for greater diversity in the form of the learning rule and the resulting learned connectivity 
Several studies have demonstrated how, in biological networks, synaptic plasticity heavily interacts with and is driven by network topology   Moreover, it has been recently demonstrated that biological plasticity mechanisms are highly redundant in the sense that any observed neural connectivity or recorded activity can be achieved with a variety of distinct, unrelated learning rules  
This observed redundancy of learning rules in biological settings complements our results and suggests that the function of plasticity rules cannot be studied independently of the connectivity and topology of the networks they are acting on  The optimization of functional plasticity in neural networks is a promising research direction both as a means to understand biological learning processes and as a tool for building more autonomous artificial systems 
Our results suggest that reward-modulated plasticity is highly adaptable to different environments and can be incorporated into larger systems that solve complex tasks  This work studies a simplified toy model of neural network learning in stochastic environments  Future work could be built on this basic framework to examine more complex reward distributions and sources of environmental variability 
Moreover, a greater degree of biological realism could be added by studying more plausible network architectures (multiple plastic layers, recurrent and feedback connections) and more sophisticated plasticity rule parametrizations  Additionally, our foraging simulations were constrained by limited computational resources and were far from exhaustive 
Further experiments can investigate environments with different constraints, food distributions, multiple seasons, more complex motor control systems and interactions of those systems with different sensory networks as well as the inclusion of plasticity on the motor parts of the artificial organisms 



ground_truth: June 1, 1999.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What factors control the reliance of artificial organisms on plasticity?

Read the following text and answer briefly.

Context 4: 
\end{equation}
Assuming $\phi_m\in R_i$, then
\begin{equation}
\label{qqpp} \hat{\phi}^0_m =\frac{(i-1)\pi+i\pi}{4} 
\end{equation}
Table \ref{tab4} shows the structure of the modified PLMS-PPIC
method  It is to be notified that
\begin{itemize}
\item Equation (\ref{qte5}) shows the conventional bit detection
method when the receiver only knows the quarter of channel phase in
$(0,2\pi)$  \item With $L=1$ (i e  only one NLMS algorithm), the
modified PLMS-PPIC can be thought as a modified version of the
LMS-PPIC method 
\end{itemize}

In the following section some examples are given to illustrate the
effectiveness of the proposed method 

\section{Simulations}\label{S5}

In this section we have considered some simulation examples 
Examples \ref{ex2}-\ref{ex4} compare the conventional, the modified
LMS-PPIC and the modified PLMS-PPIC methods in three cases: balanced
channels, unbalanced channels and time varying channels  In all
examples, the receivers have only the quarter of each channel phase 
Example \ref{ex2} is given to compare the modified LMS-PPIC and the
PLMS-PPIC in the case of balanced channels 

\begin{example}{\it Balanced channels}:
\label{ex2}
\begin{table}
\caption{Channel phase estimate of the first user (example
\ref{ex2})} \label{tabex5} \centerline{{
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{6}{*}{\rotatebox{90}{$\phi_m=\frac{3\pi}{8},M=15~~$}} & N(Iteration) & Stage Number& NLMS & PNLMS  \\
&&&&\\
\cline{2-5} & \multirow{2}{*}{64}& s = 2 &  $\hat{\phi}^s_m=\frac{3 24\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 18\pi}{8}$ \\
\cline{3-5} & & s = 3 & $\hat{\phi}^s_m=\frac{3 24\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 18\pi}{8}$ \\
\cline{2-5} & \multirow{2}{*}{256}& s = 2 &  $\hat{\phi}^s_m=\frac{2 85\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 88\pi}{8}$ \\
\cline{3-5} & & s = 3 & $\hat{\phi}^s_m=\frac{2 85\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 88\pi}{8}$ \\
\cline{2-5} \hline
\end{tabular} }}
\end{table}
Consider the system model (\ref{e7}) in which $M$ users
synchronously send their bits to the receiver through their
channels  It is assumed that each user's information consists of
codes of length $N$  It is also assumd that the signal to noise
ratio (SNR) is 0dB  In this example there is no power-unbalanced or
channel loss is assumed  The step-size of the NLMS algorithm in
modified LMS-PPIC method is $\mu=0 1(1-\sqrt{\frac{M-1}{M}})$ and
the set of step-sizes of the parallel NLMS algorithms in modified
PLMS-PPIC method are
$\Theta=\{0 01,0 05,0 1,0 2,\cdots,1\}(1-\sqrt{\frac{M-1}{M}})$,
i e  $\mu_1=0 01(1-\sqrt{\frac{M-1}{M}}),\cdots,
\mu_4=0 2(1-\sqrt{\frac{M-1}{M}}),\cdots,
\mu_{12}=(1-\sqrt{\frac{M-1}{M}})$  Figure~\ref{Figexp1NonCoh}
illustrates the bit error rate (BER) for the case of two stages and
for $N=64$ and $N=256$  Simulations also show that there is no
remarkable difference between results in two stage and three stage
scenarios  Table~\ref{tabex5} compares the average channel phase
estimate of the first user in each stage and over $10$ runs of
modified LMS-PPIC and PLMS-PPIC, when the the number of users is
$M=15$ 
\end{example}

Although LMS-PPIC and PLMS-PPIC, as well as their modified versions,
are structured based on the assumption of no near-far problem
(examples \ref{ex3} and \ref{ex4}), these methods and especially the
second one have remarkable performance in the cases of unbalanced
and/or time varying channels 

\begin{example}{\it Unbalanced channels}:
\label{ex3}
\begin{table}
\caption{Channel phase estimate of the first user (example
\ref{ex3})} \label{tabex6} \centerline{{
\begin{tabular}{|c|c|c|c|c|}
\hline
\multirow{6}{*}{\rotatebox{90}{$\phi_m=\frac{3\pi}{8},M=15~~$}} & N(Iteration) & Stage Number& NLMS & PNLMS  \\
&&&&\\
\cline{2-5} & \multirow{2}{*}{64}& s=2 &  $\hat{\phi}^s_m=\frac{2 45\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 36\pi}{8}$ \\
\cline{3-5} & & s=3 & $\hat{\phi}^s_m=\frac{2 71\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 80\pi}{8}$ \\
\cline{2-5} & \multirow{2}{*}{256}& s=2 &  $\hat{\phi}^s_m=\frac{3 09\pi}{8}$ & $\hat{\phi}^s_m=\frac{2 86\pi}{8}$ \\
\cline{3-5} & & s=3 & $\hat{\phi}^s_m=\frac{2 93\pi}{8}$ & $\hat{\phi}^s_m=\frac{3 01\pi}{8}$ \\
\cline{2-5} \hline
\end{tabular} }}
\end{table}
Consider example \ref{ex2} with power unbalanced and/or channel loss
in transmission system, i e  the true model at stage $s$ is
\begin{equation}
\label{ve7} r(n)=\sum\limits_{m=1}^{M}\beta_m
w^s_m\alpha^{(s-1)}_m c_m(n)+v(n),
\end{equation}
where $0<\beta_m\leq 1$ for all $1\leq m \leq M$  Both the LMS-PPIC
and the PLMS-PPIC methods assume the model (\ref{e7}), and their
estimations are based on observations $\{r(n),X^s(n)\}$, instead of
$\{r(n),\mathbf{G}X^s(n)\}$, where the channel gain matrix is
$\mathbf{G}=\mbox{diag}(\beta_1,\beta_2,\cdots,\beta_m)$  In this
case we repeat example \ref{ex2}  We randomly get each element of
$G$ from $[0,0 3]$  Figure~\ref{Figexp2NonCoh} illustrates the BER
versus the number of users  Table~\ref{tabex6} compares the channel
phase estimate of the first user in each stage and over $10$ runs of
modified LMS-PPIC and modified PLMS-PPIC for $M=15$ 
\end{example}

\begin{example}
\label{ex4} {\it Time varying channels}: Consider example \ref{ex2}
with time varying Rayleigh fading channels  In this case we assume
the maximum Doppler shift of $40$HZ, the three-tap
frequency-selective channel with delay vector of $\{2\times
10^{-6},2 5\times 10^{-6},3\times 10^{-6}\}$sec and gain vector of
$\{-5,-3,-10\}$dB  Figure~\ref{Figexp3NonCoh} shows the average BER
over all users versus $M$ and using two stages 
\end{example}


\section{Conclusion}\label{S6}

In this paper, parallel interference cancelation using adaptive
multistage structure and employing a set of NLMS algorithms with
different step-sizes is proposed, when just the quarter of the
channel phase of each user is known  In fact, the algorithm has been
proposed for coherent transmission with full information on channel
phases in \cite{cohpaper}  This paper is a modification on the
previously proposed algorithm  Simulation results show that the new
method has a remarkable performance for different scenarios
including Rayleigh fading channels even if the channel is
unbalanced 





ground_truth: Environmental fluctuation and uncertainty control the reliance of artificial organisms on plasticity.