### TABLE II EIGENVALUES AT HOPF BIFURCATION

### Table 3 Hopf bifurcation points of the clamped Hodgkin-Huxley equations.

"... In PAGE 21: ...1. During the continuation of equilibrium solutions, monitoring the test function (20), two Hopf bifurcation points of Type 1, A and B, were found, see Table3 , in which \Tp quot; denote the Type of the Hopf bifurcation points. For the computation of the test function (20), [12] and [7] suggested a nonlinear elimination.... ..."

### Table 2. Summary of HIV-1 clearance rate, infected cell loss rate, and virion production rate for three patients. Baseline values are measured from one week prior to administration of drug. After ritonavir was administered, a delay in its antiviral e ect was expected due to the time required for drug absorption, distribution, and penetration into the target cells. This pharmacokinetic delay could be estimated by the time elapsed before the rst drop in the titer of infectious HIV-1 in plasma (Table 2; Figure 5.2). However, even after the pharmacokinetic delay was accounted for, a lag of apos; 1day was observed before the plasma viral RNA fell (Figure 5.1). This additional delay is consistent

1999

"... In PAGE 16: ...16) has been used to analyze patient data [55]. The protease inhibitor ritonavir was administered orally (1200 mg/day) to ve HIV-infected patients, whose baseline CD4 cell counts and viral loads are shown in Table2 . HIV-1 RNA levels in plasma were measured after treatment at frequent intervals.... In PAGE 17: ... Using nonlinear regression analysis, we estimated c, the viral clearance rate con- stant, and , the rate of loss of virus-producing cells, for each of the patients by tting (5.16) to the plasma HIV-1 RNA measurements after an adjustment of t = 0 was made to account for the pharmacological delay ( Table2 ). The curves generated from (5.... In PAGE 18: ...0 and 2.7 days, with a mean of 1:6 0:6 days ( Table2 ). Note that the lifespans of productively infected cells, 1= , were not dramatically di erent among the study subjects, even though patients with low CD4 lymphocyte counts generally had decreased numbers of virus-speci c cytotoxic T cells that in principle can kill productively infected T cells [5].... In PAGE 18: ... A typical 70 kg man has a uid volume of about 15 liters. Table2 gives an estimate of each patient apos;s viral production based on a calculation of plasma and extracellular uid volumes using the patient apos;s body weight. The total daily viral production and clearance rates ranged from 0:4 109 to 32:1 109 virions per day, with a mean of 10:3 109 virions per day released into the extracellular uid (Table 2).... In PAGE 22: ... To be more precise, we rewrite the largest eigenvalue from (5.19) as 1 = ?c + 2 + c + 2 s 1 ? 4 c PI ( + c)2 : The parameter estimates in Table2 show that c , so that we can expand the square root to obtain 1 ?c + 2 + c + 2 (1 ? 2 c PI (c + )2 + : : : ); and obtain 1 ? c PI=(c+ ) ? PI. Thus, to rst-order the initial slope of viral decay after therapy initiation depends on the product of the death rate of productively... ..."

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### TABLE 2. Dependence of the first Hopf bifurcation on the horizontal resolution.

### Table 1: Reynolds number at which the Hopf bifurcation was observed for di erent truncations in wave number space in the case of = 0.

1995

"... In PAGE 3: ... For lt; 0:4 the steady state loses stability in a Hopf bifurcation. Table1 summarizes for the case of = 0 the values of the Reynolds number at which the Hopf bifurcation appears for di erent truncations. A dependence of the... ..."

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### Table 3: Summary of information on deaths and HIV-1 infection by study group. FF = formula feeding; BF = breastfeeding

"... In PAGE 18: ... Weibull logspline data p(t) exp(? L b(t) c(t)) ? exp(? R b(t) c(t)) p(t) R R L exp(Pj dj(t)Xj(s)) ds 0 lt; L lt; R lt; t [(1 ? )Y 1?Y ]D [(1 ? )Y 1?Y ]D p(t) exp(? L b(t) c(t)) p(t) R 1 L exp(Pj dj(t)Xj(s)) ds 0 lt; L lt; t lt; R [(1 ? )Y 1?Y ]D [(1 ? )Y 1?Y ]D 1 ? p(t) + p(t) 1 ? p(t) + p(t) 0 = L lt; R lt; t; (1 ? exp(? R b(t) c(t))) R R 0 exp(Pj dj(t)Xj(s)) ds D = 0 1 1 0 = L lt; t lt; R; D = 0 1 ? p(t) + (1 ? )p(t) 1 ? p(t) + (1 ? )p(t) 0 = L lt; R lt; t; (1 ? exp(? R b(t) c(t))) R R 0 exp(Pj dj(t)Xj(s)) ds D = 1; Y = 1 1 ? p(t) + (1 ? )p(t) 1 ? p(t) + (1 ? )p(t) 0 = L lt; t lt; R; D = 1; Y = 1 6 Application to a randomized clinical trial of breastfeeding vs. formula feeding in HIV-1 positive mothers Table3 summarizes the information on HIV-1 infection and death from the study described in section 2. Out of 401 live born infants (204 in the formula feeding groups and 197 in the breastfeeding group), 306 (154 FF and 152 BF) had complete endpoint information (i.... ..."

### Table 1. Performance of virologic tests in detecting HIV-1 infection in exposed infants.

1999

### Table 3. Summary of information on deaths and HIV-1 infection by study group. FF = formula feeding; BF = breastfeeding FF BF

"... In PAGE 13: ... APPLICATION TO A RANDOMIZED CLINICAL TRIAL OF BREASTFEEDING VS. FORMULA FEEDING IN HIV-1 POSITIVE MOTHERS Table3 summarizes the information on HIV-1 infection and death from the study described in section 2. Out of 401 live born infants (204 in the formula feeding (FF) group and 197 in the breastfeeding (BF) group), 306 (154 FF and 152 BF) had complete endpoint information (i.... ..."

### Table 2: Spatiotemporal symmetry of bifurcating solutions in nonHopf bifurcation from a discrete rotating wave with (O(2) Z2; O(2)) symmetry. All bifurcations are period-preserving. All bifurcations are pitchforks unless stated otherwise.

1999

"... In PAGE 19: ...hoices of for which k is arbitrarily large or for which k = 1.) As in Example 5.1, we have suppression of period doubling. The irreducible representations of O(2) (all of which are absolutely irreducible) are as follows: V0;+ V0;? Vj; j 1 R 1 1 cos j ? sin j sin j cos j 1 ?1 0 ?1 1 0 The corresponding branches of periodic solutions are summarized in Table2 . The details are similar to, but easier than, the arguments in Example 5.... In PAGE 19: ...imensional wake ows behind cylinders. See [2, 26] and references therein. In par- ticular, von K arm an vortices (a periodic two-dimensional state with spatiotemporal symmetry (O(2) Z2)) undergo period-preserving bifurcations to fully three dimen- sional states where the continuous SO(2) symmetry is broken. (Such bifurcations correspond to the representations Vj, j 1 in Table2 .) The bifurcating states have two di erent forms, mode A and mode B [26].... ..."

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### Table 5: Spatiotemporal symmetry of bifurcating solutions in nonHopf bifurcation from a discrete rotating wave with (D n; Zn) symmetry. All bifurcations are period- preserving. All bifurcations are pitchforks unless stated otherwise. Notation: j0 = gcd(j; n).

1999

"... In PAGE 44: ...uppression of period-doubling even though Remark 4.6 does not apply. We note that [17] shows that period doubling is suppressed for this example, but under a simplifying hypothesis on the action of a certain group. The branches of periodic solutions are summarized in Table5 . The veri cation of these results proceeds in the same way as the arguments in Example 5.... ..."

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