A Sign-Changing Solution for a Superlinear Dirichlet Problem, II

In previous work by Castro, Cossio, and Neuberger [2], it was shown that a superlinear Dirichlet problem has at least three nontrivial solutions when the derivative of the nonlinearity at zero is less than the first eigenvalue of -Δ with zero Dirichlet boundry condition. One of these solutions changes sign exactly-once and the other two are of one sign. In this paper we show that when this derivative is between the k-th and k+1-st eigenvalues there still exists a solution which changes sign at most k times. In particular, when k=1 the sign-changing exactly-once solution persists although one-sign solutions no longer exist

Altered connectivity of the right anterior insula drives the pain connectome changes in chronic knee osteoarthritis

Resting-state functional connectivity (FC) has proven a powerful approach to understand the neural underpinnings of chronic pain, reporting altered connectivity in three main networks: the default mode (DMN), central executive (CEN), and the salience network (SN). The interrelation and possible mechanisms of these changes are less well understood in chronic pain. Based on emerging evidence of its role to drive switches between network states, the right anterior insula (rAI, an SN hub) may play a dominant role in network connectivity changes underpinning chronic pain. To test this hypothesis, we used seed-based resting-state FC analysis including dynamic and effective connectivity metrics in 25 people with chronic osteoarthritis (OA) pain and 19 matched healthy volunteers. Compared to controls, participants with painful knee OA presented with increased anticorrelation between the right anterior insula (SN) and DMN regions. Also, the left dorsal prefrontal cortex (CEN hub) showed more negative FC with the right temporal gyrus. Granger causality analysis revealed increased negative influence of the right anterior insula on the posterior cingulate (DMN) in OA patients in line with the observed enhanced anticorrelation. Moreover, dynamic FC was lower in the DMN of patients and thus more similar to temporal dynamics of the SN. Together, these findings evidence a widespread network disruption in patients with persistent osteoarthritis pain, and point toward a driving role of the rAI

HCO+ detection of dust-depleted gas in the inner hole of the LkCa 15 pre-transitional disk

LkCa 15 is an extensively studied star in the Taurus region, known for its pre-transitional disk with a large inner cavity in the dust continuum and normal gas accretion rate. The most popular hypothesis to explain the LkCa 15 data invokes one or more planets to carve out the inner cavity, while gas continues to flow across the gap from the outer disk onto the central star. We present spatially unresolved HCO+ J = 4 → 3 observations of the LkCa 15 disk from the James Clerk Maxwell telescope (JCMT) and model the data with the ProDiMo code. We find that: (1) HCO+ line-wings are clearly detected, certifying the presence of gas in the cavity within ≲50 au of the star. (2) Reproducing the observed line-wing flux requires both a significant suppression of cavity dust (by a factor ≥ 104 compared to the interstellar medium (ISM)) and a substantial increase in the gas scale-height within the cavity (H0/R0 ∼ 0.6). An ISM dust-to-gas ratio (d:g = 10-2) yields too little line-wing flux, regardless of the scale-height or cavity gas geometry, while a smaller scale-height also under-predicts the flux even with a reduced d:g. (3) The cavity gas mass is consistent with the surface density profile of the outer disk extended inwards to the sublimation radius (corresponding to mass Md ∼ 0.03 M⊙), and masses lower by a factor ≥10 appear to be ruled out.Publisher PDFPeer reviewe

Affective touch and attachment style modulate pain: a laser-evoked potentials study

Affective touch and cutaneous pain are two sub-modalities of interoception with contrasting affective qualities (pleasantness/unpleasantness) and social meanings (care/harm), yet their direct relationship has not been investigated. In 50 women, taking into account individual attachment styles, we assessed the role of affective touch and particularly the contribution of the C tactile (CT) system in subjective and electrophysiological responses to noxious skin stimulation, namely N1 and N2-P2 laser-evoked potentials. When pleasant, slow (versus fast) velocity touch was administered to the (non-CT-containing) palm of the hand, higher attachment anxiety predicted increased subjective pain ratings, in the same direction as changes in N2 amplitude. By contrast, when pleasant touch was administered to CT-containing skin of the arm, higher attachment anxiety predicted attenuated N1 and N2 amplitudes. Higher attachment avoidance predicted opposite results. Thus, CT-based affective touch can modulate pain in early and late processing stages (N1 and N2 components), with the direction of effects depending on attachment style. Affective touch not involving the CT system seems to affect predominately the conscious perception of pain, possibly reflecting socio-cognitive factors further up the neurocognitive hierarchy. Affective touch may thus convey information about available social resources and gate pain responses depending on individual expectations of social support

Collective Decision Dynamics in the Presence of External Drivers

We develop a sequence of models describing information transmission and decision dynamics for a network of individual agents subject to multiple sources of influence. Our general framework is set in the context of an impending natural disaster, where individuals, represented by nodes on the network, must decide whether or not to evacuate. Sources of influence include a one-to-many externally driven global broadcast as well as pairwise interactions, across links in the network, in which agents transmit either continuous opinions or binary actions. We consider both uniform and variable threshold rules on the individual opinion as baseline models for decision-making. Our results indicate that 1) social networks lead to clustering and cohesive action among individuals, 2) binary information introduces high temporal variability and stagnation, and 3) information transmission over the network can either facilitate or hinder action adoption, depending on the influence of the global broadcast relative to the social network. Our framework highlights the essential role of local interactions between agents in predicting collective behavior of the population as a whole.Comment: 14 pages, 7 figure

Influence of molecular weight, temperature, and extensional rheology on melt blowing process stability for linear isotactic polypropylene

In this work, three linear isotactic polypropylenes with different weight-average molecular weights, M-w, and comparable polydispersities were used to produce nonwovens by melt blowing technology at two different temperatures, T. The air/polymer flow rate was changed to maintain the same average fiber diameter, resulting in a different broadness of fiber diameter distribution, which was quantified by the coefficient of variation, CV. The elasticity of the material was evaluated by the reptation-mode relaxation time, lambda(1), and the Rouse-mode reorientation time, lambda(2), determined from the deformation rate dependent shear viscosity data. Extensional rheology was evaluated using uniaxial extensional viscosity measured over a very wide range of strain rates (2 x 10(4) s(-1)-2 x 10(6) s(-1)) using entrance pressure drop and Gibson methods. An obtained plateau value of uniaxial extensional viscosity at the highest extensional strain rates, eta(E,infinity) (normalized by the three times zero-shear rate viscosity, eta(0)), and the minimum uniaxial extensional viscosity, eta(E,min), were related to M-w and T using simple equations. It has been found that the stability of fiber production captured by CV depends exclusively on the extensional properties of the polypropylene melts, namely, eta(E,U,)infinity/3 eta(0) and eta(E,U,min). These findings are important especially with regard to the stable production of polymeric nanofibers by melt blowing technology