General rigidity principles for stable and minimal elastic curves

For a wide class of curvature energy functionals defined for planar curves under the fixed-length constraint, we obtain optimal necessary conditions for global and local minimizers. Our results extend Maddocks' and Sachkov's rigidity principles for Euler's elastica by a totally different approach, and in particular lead to complete classification of stable closed $p$-elasticae for all $p\in(1,\infty)$ and of stable pinned $p$-elasticae for $p\in(1,2]$. Our proof is based on a simple but robust `cut-and-paste' trick without computing the energy nor its second variation, which works well for planar periodic curves but also extend to some non-periodic or non-planar cases.Comment: 26 pages, 14 figure

Pinned planar p-elasticae

Building on our previous work, we classify all planar $p$-elasticae under the pinned boundary condition, and then obtain uniqueness and geometric properties of global minimizers. As an application we establish a Li--Yau type inequality for the $p$-bending energy, and in particular discover a unique exponent $p \simeq 1.5728$ for full optimality. We also prove existence of minimal $p$-elastic networks, extending a recent result of Dall'Acqua--Novaga--Pluda.Comment: 41 pages, 11 figures, final versio

Absence of a chromatic linear motion mechanism in human vision

AbstractWe have investigated motion mechanisms in central and perifoveal vision using two-frame random Gabor kinematograms with isoluminant red-green or luminance stimuli. In keeping with previous results, we find that performance dominated by a linear motion mechanism is obtained using high densities of micropatterns and small temporal intervals between frames, while nonlinear performance is found with low densities and longer temporal intervals [Boulton, J. C., & Baker, C. L. (1994) Proceedings of SPIE, computational vision based on neurobiology, 2054, 124–133]. We compare direction discrimination and detection thresholds in the presence of variable luminance and chromatic noise. Our results show that the linear motion response obtained from chromatic stimuli is selectively masked by luminance noise; the effect is selective for motion since luminance noise masks direction discrimination thresholds but not stimulus detection. Furthermore, we find that chromatic noise has the reverse effect to luminance noise: detection thresholds for the linear chromatic stimulus are masked by chromatic noise but direction discrimination is relatively unaffected. We thus reveal a linear ‘chromatic’ mechanism that is susceptible to luminance noise but relatively unaffected by color noise. The nonlinear chromatic mechanism behaves differently since both detection and direction discrimination are unaffected by luminance noise but masked by chromatic noise. The double dissociation between the effects of chromatic and luminance noise on linear and nonlinear motion mechanisms is not based on stimulus speed or differences in the temporal presentations of the stimuli. We conclude that: (1) ‘chromatic’ linear motion is solely based on a luminance signal, probably arising from cone-based temporal phase shifts; (2) the nonlinear chromatic motion mechanism is purely chromatic; and (3) we find the same results for both perifoveal and foveal presentations

Water-in-CO2 Microemulsions Stabilized by an Efficient Catanionic Surfactant

To facilitate potential applications of water-in-supercritical CO2 microemulsions (W/CO2 μEs) efficient and environmentally responsible surfactants are required with low levels of fluorination. As well as being able to stabilize water–CO2 interfaces, these surfactants must also be economical, prevent bioaccumulation and strong adhesion, deactivation of enzymes, and be tolerant to high salt environments. Recently, an ion paired catanionic surfactant with environmentally acceptable fluorinated C6 tails was found to be very effective at stabilizing W/CO2 μEs with high water-to-surfactant molar ratios (W0) up to ∼50 (Sagisaka, M.; et al. Langmuir 2019, 35, 3445−3454). As the cationic and anionic constituent surfactants alone did not stabilize W/CO2 μEs, this was the first demonstration of surfactant synergistic effects in W/CO2 microemulsions. The aim of this new study is to understand the origin of these intriguing effects by detailed investigations of nanostructure in W/CO2 microemulsions using high-pressure small-angle neutron scattering (HP-SANS). These HP-SANS experiments have been used to determine the headgroup interfacial area and volume, aggregation number, and effective packing parameter (EPP). These SANS data suggest the effectiveness of this surfactant originates from increased EPP and decreased hydrophilic/CO2-philic balance, related to a reduced effective headgroup ionicity. This surfactant bears separate C6F13 tails and oppositely charged headgroups, and was found to have a EPP value similar to that of a double C4F9-tail anionic surfactant (4FG(EO)2), which was previously reported to be one of most efficient stabilizers for W/CO2 μEs (maximum W0 = 60–80). Catanionic surfactants based on this new design will be key for generating superefficient W/CO2 μEs with high stability and water solubilization

Lack of the Vitamin D Receptor is Associated with Reduced Epidermal Differentiation and Hair Follicle Growth

The active vitamin D metabolite, 1,25-dihydroxyvitamin D, acting through the vitamin D receptor, regulates the expression of genes in a variety of vitamin D-responsive tissues, including the epidermis. To investigate the role of the vitamin D receptor in mediating epidermal differentiation, we examined the histomorphology and expression of differentiation markers in the epidermis of vitamin D receptor knockout mice generated by gene targeting. The homozygous knockout mouse displayed a phenotype that closely resembles vitamin D-dependent rickets type II in humans, including the development of rickets and alopecia. Hair loss developed by 3mo after birth and gradually led to nearly total hair loss by 8mo. Histologic analysis of the skin of homozygous knockout mice revealed dilation of the hair follicles with the formation of dermal cysts starting at the age of 3wk. These cysts increased in size and number with age. Epidermal differentiation markers, including involucrin, profilaggrin, and loricrin, detected by immunostaining and in situ hybridization, showed decreased expression levels in homozygous knockout mice from birth until 3wk, preceding the morphologic changes observed in the hair follicles. Keratin 10 levels, however, were not reduced. At the ultrastructural level, homozygous knockout mice showed increased numbers of small dense granules in the granular layer with few or no surrounding keratin bundles and a loss of keratohyalin granules. Thus, both the interfollicular epidermis and the hair follicle appear to require the vitamin D receptor for normal differentiation. The temporal abnormalities between the two processes reflect the apparent lack of requirement for the vitamin D receptor during the anagen phase of the first (developmental) hair cycle, but with earlier effects on the terminal differentiation of the interfollicular epidermis

The sympathetic tone mediates leptin's inhibition of insulin secretion by modulating osteocalcin bioactivity

The osteoblast-secreted molecule osteocalcin favors insulin secretion, but how this function is regulated in vivo by extracellular signals is for now unknown. In this study, we show that leptin, which instead inhibits insulin secretion, partly uses the sympathetic nervous system to fulfill this function. Remarkably, for our purpose, an osteoblast-specific ablation of sympathetic signaling results in a leptin-dependent hyperinsulinemia. In osteoblasts, sympathetic tone stimulates expression of Esp, a gene inhibiting the activity of osteocalcin, which is an insulin secretagogue. Accordingly, Esp inactivation doubles hyperinsulinemia and delays glucose intolerance in ob/ob mice, whereas Osteocalcin inactivation halves their hyperinsulinemia. By showing that leptin inhibits insulin secretion by decreasing osteocalcin bioactivity, this study illustrates the importance of the relationship existing between fat and skeleton for the regulation of glucose homeostasis

An Osteoblast-dependent Mechanism Contributes to the Leptin Regulation of Insulin Secretion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72661/1/j.1749-6632.2009.05061.x.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72661/2/NYAS_5061_sm_SuppMat.pd

Development of a High-intensity Focused Ultrasound Exposure Device for Reducing Skin Burn Risk

High-intensity focused ultrasound（HIFU）can non-invasively irradiate inside the body. However, when used to treat fetuses, it can cause thermal burns of the mother’s abdominal wall at the skin interface. This study was carried out to determine whether a modified HIFU transducer enabling split-aperture irradiation can prevent thermal burns. Two HIFU transducers were compared: a conventional transducer using full-aperture irradiation and a modified transducer using split-aperture irradiation. The modified transducer was divided into six sectors for split-aperture irradiation and had a larger surface area and a smaller F number（focal length/aperture diameter）than the conventional transducer. HIFU was delivered to eight sites on the left and right leg of a three-month-old baby pig under general anesthesia, and the sites were assessed for thermal burning by two or more dermatologists. The same person performed all irradiations. Full-aperture irradiation with the conventional transducer caused deep dermal burns at all target sites, while split-aperture irradiation with the modified transducer caused only epidermal burns or superficial dermal burns. Split-aperture irradiation using a modified HIFU transducer with six sectors and a smaller F number reduces the severity of skin burns, and thus will improve the safety of HIFU therapy

C9orf72-derived arginine-rich poly-dipeptides impede phase modifiers

Nuclear import receptors (NIRs) not only transport RNA-binding proteins (RBPs) but also modify phase transitions of RBPs by recognizing nuclear localization signals (NLSs). Toxic arginine-rich poly-dipeptides from C9orf72 interact with NIRs and cause nucleocytoplasmic transport deficit. However, the molecular basis for the toxicity of arginine-rich poly-dipeptides toward NIRs function as phase modifiers of RBPs remains unidentified. Here we show that arginine-rich poly-dipeptides impede the ability of NIRs to modify phase transitions of RBPs. Isothermal titration calorimetry and size-exclusion chromatography revealed that proline:arginine (PR) poly-dipeptides tightly bind karyopherin-β2 (Kapβ2) at 1:1 ratio. The nuclear magnetic resonances of Kapβ2 perturbed by PR poly-dipeptides partially overlapped with those perturbed by the designed NLS peptide, suggesting that PR poly-dipeptides target the NLS binding site of Kapβ2. The findings offer mechanistic insights into how phase transitions of RBPs are disabled in C9orf72-related neurodegeneration