def rep_hill(x, n):
    """Dimensionless production rate for a gene repressed by x.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of repressor.
    n : float
        Hill coefficient.

    Returns
    -------
    output : NumPy array or float
        1 / (1 + x**n)
    """
    return 1.0 / (1.0 + x ** n)


def act_hill(x, n):
    """Dimensionless production rate for a gene activated by x.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    n : float
        Hill coefficient.

    Returns
    -------
    output : NumPy array or float
        x**n / (1 + x**n)
    """
    return 1.0 - rep_hill(x, n)


def aa_and(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    activators with AND logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first activator.
    y : float or NumPy array
        Concentration of second activator.
    nx : float
        Hill coefficient for first activator.
    ny : float
        Hill coefficient for second activator.

    Returns
    -------
    output : NumPy array or float
        x**nx * y**ny / (1 + x**nx) / (1 + y**ny)
    """
    return x ** nx * y ** ny / (1.0 + x ** nx) / (1.0 + y ** ny)


def aa_or(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    activators with OR logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first activator.
    y : float or NumPy array
        Concentration of second activator.
    nx : float
        Hill coefficient for first activator.
    ny : float
        Hill coefficient for second activator.

    Returns
    -------
    output : NumPy array or float
        (x**nx + y**ny + x**nx * y**ny) / (1 + x**nx) / (1 + y**ny)
    """
    denom = (1.0 + x ** nx) * (1.0 + y ** ny)
    return (denom - 1.0) / denom


def aa_or_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    activators with OR logic in the absence of leakage with single
    occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first activator.
    y : float or NumPy array
        Concentration of second activator.
    nx : float
        Hill coefficient for first activator.
    ny : float
        Hill coefficient for second activator.

    Returns
    -------
    output : NumPy array or float
        (x**nx + y**ny) / (1 + x**nx + y**ny)
    """
    num = x ** nx + y ** ny
    return num / (1.0 + num)


def rr_and(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    repressors with AND logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first repressor.
    y : float or NumPy array
        Concentration of second repressor.
    nx : float
        Hill coefficient for first repressor.
    ny : float
        Hill coefficient for second repressor.

    Returns
    -------
    output : NumPy array or float
        1 / (1 + x**nx) / (1 + y**ny)
    """
    return 1.0 / (1.0 + x ** nx) / (1.0 + y ** ny)


def rr_and_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    repressors with AND logic in the absence of leakage with
    single occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first repressor.
    y : float or NumPy array
        Concentration of second repressor.
    nx : float
        Hill coefficient for first repressor.
    ny : float
        Hill coefficient for second repressor.

    Returns
    -------
    output : NumPy array or float
        1 / (1 + x**nx + y**ny)
    """
    return 1.0 / (1.0 + x ** nx + y ** ny)


def rr_or(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    repressors with OR logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first repressor.
    y : float or NumPy array
        Concentration of second repressor.
    nx : float
        Hill coefficient for first repressor.
    ny : float
        Hill coefficient for second repressor.

    Returns
    -------
    output : NumPy array or float
        (1 + x**nx + y**ny) / (1 + x**nx) / (1 + y**ny)
    """
    return (1.0 + x ** nx + y ** ny) / (1.0 + x ** nx) / (1.0 + y ** ny)


def ar_and(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with AND logic in the absence of
    leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        x ** nx / (1 + x**nx) / (1 + y**ny)
    """
    return x ** nx / (1.0 + x ** nx) / (1.0 + y ** ny)


def ar_or(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with OR logic in the absence of
    leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        (1 + x**nx + x**nx * y**ny)) / (1 + x**nx) / (1 + y**ny)
    """
    return (1.0 + x ** nx * (1.0 + y ** ny)) / (1.0 + x ** nx) / (1.0 + y ** ny)


def ar_and_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with AND logic in the absence of
    leakage with single occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        x ** nx / (1 + x**nx + y**ny)
    """
    return x ** nx / (1.0 + x ** nx + y ** ny)


def ar_or_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with OR logic in the absence of
    leakage with single occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        (1 + x**nx) / (1 + x**nx + y**ny)
    """
    return (1.0 + x ** nx) / (1.0 + x ** nx + y ** ny)

def rep_hill(x, n):
    """Dimensionless production rate for a gene repressed by x.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of repressor.
    n : float
        Hill coefficient.

    Returns
    -------
    output : NumPy array or float
        1 / (1 + x**n)
    """
    return 1.0 / (1.0 + x ** n)


def act_hill(x, n):
    """Dimensionless production rate for a gene activated by x.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    n : float
        Hill coefficient.

    Returns
    -------
    output : NumPy array or float
        x**n / (1 + x**n)
    """
    return 1.0 - rep_hill(x, n)


def aa_and(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    activators with AND logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first activator.
    y : float or NumPy array
        Concentration of second activator.
    nx : float
        Hill coefficient for first activator.
    ny : float
        Hill coefficient for second activator.

    Returns
    -------
    output : NumPy array or float
        x**nx * y**ny / (1 + x**nx) / (1 + y**ny)
    """
    return x ** nx * y ** ny / (1.0 + x ** nx) / (1.0 + y ** ny)


def aa_or(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    activators with OR logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first activator.
    y : float or NumPy array
        Concentration of second activator.
    nx : float
        Hill coefficient for first activator.
    ny : float
        Hill coefficient for second activator.

    Returns
    -------
    output : NumPy array or float
        (x**nx + y**ny + x**nx * y**ny) / (1 + x**nx) / (1 + y**ny)
    """
    denom = (1.0 + x ** nx) * (1.0 + y ** ny)
    return (denom - 1.0) / denom


def aa_or_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    activators with OR logic in the absence of leakage with single
    occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first activator.
    y : float or NumPy array
        Concentration of second activator.
    nx : float
        Hill coefficient for first activator.
    ny : float
        Hill coefficient for second activator.

    Returns
    -------
    output : NumPy array or float
        (x**nx + y**ny) / (1 + x**nx + y**ny)
    """
    num = x ** nx + y ** ny
    return num / (1.0 + num)


def rr_and(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    repressors with AND logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first repressor.
    y : float or NumPy array
        Concentration of second repressor.
    nx : float
        Hill coefficient for first repressor.
    ny : float
        Hill coefficient for second repressor.

    Returns
    -------
    output : NumPy array or float
        1 / (1 + x**nx) / (1 + y**ny)
    """
    return 1.0 / (1.0 + x ** nx) / (1.0 + y ** ny)


def rr_and_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    repressors with AND logic in the absence of leakage with
    single occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first repressor.
    y : float or NumPy array
        Concentration of second repressor.
    nx : float
        Hill coefficient for first repressor.
    ny : float
        Hill coefficient for second repressor.

    Returns
    -------
    output : NumPy array or float
        1 / (1 + x**nx + y**ny)
    """
    return 1.0 / (1.0 + x ** nx + y ** ny)


def rr_or(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by two
    repressors with OR logic in the absence of leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of first repressor.
    y : float or NumPy array
        Concentration of second repressor.
    nx : float
        Hill coefficient for first repressor.
    ny : float
        Hill coefficient for second repressor.

    Returns
    -------
    output : NumPy array or float
        (1 + x**nx + y**ny) / (1 + x**nx) / (1 + y**ny)
    """
    return (1.0 + x ** nx + y ** ny) / (1.0 + x ** nx) / (1.0 + y ** ny)


def ar_and(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with AND logic in the absence of
    leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        x ** nx / (1 + x**nx) / (1 + y**ny)
    """
    return x ** nx / (1.0 + x ** nx) / (1.0 + y ** ny)


def ar_or(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with OR logic in the absence of
    leakage.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        (1 + x**nx + x**nx * y**ny)) / (1 + x**nx) / (1 + y**ny)
    """
    return (1.0 + x ** nx * (1.0 + y ** ny)) / (1.0 + x ** nx) / (1.0 + y ** ny)


def ar_and_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with AND logic in the absence of
    leakage with single occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        x ** nx / (1 + x**nx + y**ny)
    """
    return x ** nx / (1.0 + x ** nx + y ** ny)


def ar_or_single(x, y, nx, ny):
    """Dimensionless production rate for a gene regulated by one
    activator and one repressor with OR logic in the absence of
    leakage with single occupancy.

    Parameters
    ----------
    x : float or NumPy array
        Concentration of activator.
    y : float or NumPy array
        Concentration of repressor.
    nx : float
        Hill coefficient for activator.
    ny : float
        Hill coefficient for repressor.

    Returns
    -------
    output : NumPy array or float
        (1 + x**nx) / (1 + x**nx + y**ny)
    """
    return (1.0 + x ** nx) / (1.0 + x ** nx + y ** ny)

Dimensionless production rate for a gene repressed by x.      Parameters     ----------     x : float or NumPy array         Concentration of repressor.     n : float         Hill coefficient.      Returns     -------     output : NumPy array or float         1 / (1 + x**n) Dimensionless production rate for a gene activated by x.      Parameters     ----------     x : float or NumPy array         Concentration of activator.     n : float         Hill coefficient.      Returns     -------     output : NumPy array or float         x**n / (1 + x**n) Dimensionless production rate for a gene regulated by two     activators with AND logic in the absence of leakage.      Parameters     ----------     x : float or NumPy array         Concentration of first activator.     y : float or NumPy array         Concentration of second activator.     nx : float         Hill coefficient for first activator.     ny : float         Hill coefficient for second activator.      Returns     -------     output : NumPy array or float         x**nx * y**ny / (1 + x**nx) / (1 + y**ny) Dimensionless production rate for a gene regulated by two     activators with OR logic in the absence of leakage.      Parameters     ----------     x : float or NumPy array         Concentration of first activator.     y : float or NumPy array         Concentration of second activator.     nx : float         Hill coefficient for first activator.     ny : float         Hill coefficient for second activator.      Returns     -------     output : NumPy array or float         (x**nx + y**ny + x**nx * y**ny) / (1 + x**nx) / (1 + y**ny) Dimensionless production rate for a gene regulated by two     activators with OR logic in the absence of leakage with single     occupancy.      Parameters     ----------     x : float or NumPy array         Concentration of first activator.     y : float or NumPy array         Concentration of second activator.     nx : float         Hill coefficient for first activator.     ny : float         Hill coefficient for second activator.      Returns     -------     output : NumPy array or float         (x**nx + y**ny) / (1 + x**nx + y**ny) Dimensionless production rate for a gene regulated by two     repressors with AND logic in the absence of leakage.      Parameters     ----------     x : float or NumPy array         Concentration of first repressor.     y : float or NumPy array         Concentration of second repressor.     nx : float         Hill coefficient for first repressor.     ny : float         Hill coefficient for second repressor.      Returns     -------     output : NumPy array or float         1 / (1 + x**nx) / (1 + y**ny) Dimensionless production rate for a gene regulated by two     repressors with AND logic in the absence of leakage with     single occupancy.      Parameters     ----------     x : float or NumPy array         Concentration of first repressor.     y : float or NumPy array         Concentration of second repressor.     nx : float         Hill coefficient for first repressor.     ny : float         Hill coefficient for second repressor.      Returns     -------     output : NumPy array or float         1 / (1 + x**nx + y**ny) Dimensionless production rate for a gene regulated by two     repressors with OR logic in the absence of leakage.      Parameters     ----------     x : float or NumPy array         Concentration of first repressor.     y : float or NumPy array         Concentration of second repressor.     nx : float         Hill coefficient for first repressor.     ny : float         Hill coefficient for second repressor.      Returns     -------     output : NumPy array or float         (1 + x**nx + y**ny) / (1 + x**nx) / (1 + y**ny) Dimensionless production rate for a gene regulated by one     activator and one repressor with AND logic in the absence of     leakage.      Parameters     ----------     x : float or NumPy array         Concentration of activator.     y : float or NumPy array         Concentration of repressor.     nx : float         Hill coefficient for activator.     ny : float         Hill coefficient for repressor.      Returns     -------     output : NumPy array or float         x ** nx / (1 + x**nx) / (1 + y**ny) Dimensionless production rate for a gene regulated by one     activator and one repressor with OR logic in the absence of     leakage.      Parameters     ----------     x : float or NumPy array         Concentration of activator.     y : float or NumPy array         Concentration of repressor.     nx : float         Hill coefficient for activator.     ny : float         Hill coefficient for repressor.      Returns     -------     output : NumPy array or float         (1 + x**nx + x**nx * y**ny)) / (1 + x**nx) / (1 + y**ny) Dimensionless production rate for a gene regulated by one     activator and one repressor with AND logic in the absence of     leakage with single occupancy.      Parameters     ----------     x : float or NumPy array         Concentration of activator.     y : float or NumPy array         Concentration of repressor.     nx : float         Hill coefficient for activator.     ny : float         Hill coefficient for repressor.      Returns     -------     output : NumPy array or float         x ** nx / (1 + x**nx + y**ny) Dimensionless production rate for a gene regulated by one     activator and one repressor with OR logic in the absence of     leakage with single occupancy.      Parameters     ----------     x : float or NumPy array         Concentration of activator.     y : float or NumPy array         Concentration of repressor.     nx : float         Hill coefficient for activator.     ny : float         Hill coefficient for repressor.      Returns     -------     output : NumPy array or float         (1 + x**nx) / (1 + x**nx + y**ny)