multi scale community detection algorithm
q space diffeomorphic reconstruction method
visual inspection of numerical simulations
multi layer community detection algorithm

TR=11, 400 ms, TE=128 ms, voxel size 2.4 mm^3

Pupil responses to hidden photoreceptor-specific modulations in movies

Bird community shifts associated with saltwater exposure in coastal forests at the leading edge of rising sea level

95% posterior distribution credible intervals

The effect of paternal cues in prenatal care settings on men's involvement intentions

Fast phage detection and quantification: An optical density-based approach

performance of currently available method

A cluster randomised, double-blind pilot and feasibility trial of an active behavioural physiotherapy intervention for acute whiplash-associated disorder (WAD)II

inflation factor=4.312 using cluster size=10

The structure and existence of solutions of the problem of consumption with satiation in continuous time

s 0<0</disp formula><disp formula id="pone.0216383.e006">removedGRAPHIC c<0</disp formula><disp formula id="pone.0216383.e007">removedGRAPHIC ∫ [0]
constraint (2),<disp formula id="pone.0216383.e008">removedGRAPHIC c=1
pone.0216383.e013">removedGRAPHIC alpha=alpha s=-s - d 2
increasing if<disp formula id="pone.0216383.e016">removedGRAPHIC n + gamma - (1 - alpha)>0
Eq (2) is<disp formula id="pone.0216383.e017">removedGRAPHIC s t=e - gamma - t - (s 0 + f - ∫ [0, T ] e gamma - t 1 - c (t 1) - d t 1),</disp formula>hence s t>0
pone.0216383.e046">removedGRAPHIC [d Θ d x ] x=0
we obtain<disp formula id="pone.0216383.e047">removedGRAPHIC [d Θ d x ] x=0=lambda W - e - r - T - lambda c T - delta s T + ∫ [0]
pone.0216383.e049">removedGRAPHIC [d Θ d x ] x=0=-lambda c T - delta s T + ∫ [0]
t</disp formula>since delta s (0)=0, hence<disp formula id="pone.0216383.e051">removedGRAPHIC [d Θ d x ] x=0=-∫ [0]
x=0, we have<disp formula id="pone.0216383.e058">removedGRAPHIC 0
t</disp formula><disp formula id="pone.0216383.e060">removedGRAPHIC integration by parts=1
Let<disp formula id="pone.0216383.e072">removedGRAPHIC lambda W=sup t ∈ [0, T ] M t - e r - t>0
interval [0, T ], hence inf t ∈[0, T ] s t>0
T -<0, hence s T - s (T^-)>0 because removedGRAPHIC d 2
<disp formula id="pone.0216383.e100">removedGRAPHIC lim s ->0
pone.0216383.e108">removedGRAPHIC c t=1 f - (d σ d t + gamma - σ)=1
pone.0216383.e115">removedGRAPHIC lambda c (0)=0</disp formula>For t ∈ (0, T), from (20
t 1, t 2) c t - lambda c - d t - ∫ (t 1, t 2) r - n alpha S (σ (t, lambda W) + gamma ] - σ (t, lambda W) - lambda c - d t=-∫ (t 1, t 2) r + gamma - alpha S - n alpha S - σ (t, lambda W) - lambda c - d t,</disp formula>since c t - lambda c t=0
T s iff<disp formula id="pone.0216383.e157">removedGRAPHIC lambda W>1
s 2<0, we obtain<disp formula id="pone.0216383.e167
s 0 - e - gamma - T f</disp formula>Proposition 30 removedGRAPHIC lambda c l>0
t</disp formula>Remark 32 If s 0=0, then it is reasonable accept W^u=W^l=0
pone.0216383.e191">removedGRAPHIC s t={ s 0, t=0 σ (t, lambda W), t ∈ (0
d s (s 0 - e - gamma - T s) - (r - n + gamma - alpha s)>0,</disp formula>thanks-(40
T=e - n - T - s T -1 - lambda W - e n - r - T ].</disp formula>Their solutions are<disp formula id="pone.0216383.e239">removedGRAPHIC σ (t, lambda W)=1 lambda W - n gamma + r - e - n - r - t, s T=1
is<disp formula id="pone.0216383.e257">removedGRAPHIC s t={ s 0, t=0 s T - n gamma + r - e n - r - T - t, t ∈ (0, T) s T, t=T }, lambda c=0
constraint (62) f - W + s 0=s T - e^n - r - T, hence<disp formula id="pone.0216383.e258">removedGRAPHIC s t={ s 0, t=0 (f - W + s 0) - n gamma + r - e - n - r - t, t ∈ (0, T) (f - W + s 0) - e - n - r - T, t=T</disp formula>The corresponding consumption is<disp formula id="pone.0216383.e259">removedGRAPHIC c t=delta 0 t - (f - W + s 0) - n gamma + r - s 0 f + (r + gamma - n) - (f - W + s 0) - e - n - r - t - n gamma + r + delta T t - (f - W + s 0
Z -1 alpha - e - n - r alpha - T, t=T }, lambda c u=0
write<disp formula id="pone.0216383.e279">removedGRAPHIC s t={ s 0, t=0 s T - Z 1 alpha - e + n - r alpha - T - t, t ∈ (0, T) s T, t=T }, lambda c=0
B=1 - (1 - e - (r + delta - r alpha) - T) - E 3
r alpha)=Z 1 alpha - E 2, hence<disp formula id="pone.0216383.e283">removedGRAPHIC s t={ s 0, t=0 (f - W + s 0) - B -1 - Z 1 alpha - e - n - r alpha - t, t ∈ (0, T) (f - W + s 0) - B -1 - e - n - r alpha - T, t=T</disp formula>The corresponding consumption is<disp formula id="pone.0216383.e284">removedGRAPHIC c t=delta 0 t -1 f - (f - W + s 0) - B -1 - Z 1 alpha - s 0) + r + alpha - gamma - n alpha - (f - W + s 0) - B -1 - Z 1 alpha - e - n - r alpha - t + delta T t -1 f - (f - W + s 0) - B -1 - e - n - r alpha - T - (1 - Z 1