Picard group of hypersurfaces in toric 3-folds

We show that the usual sufficient criterion for a generic hypersurface in a smooth projective manifold to have the same Picard number as the ambient variety can be generalized to hypersurfaces in complete simplicial toric varieties. This sufficient condition is always satisfied by generic K3 surfaces embedded in Fano toric 3-folds.Comment: 14 pages. v2: some typos corrected. v3: Slightly changed title. Final version to appear in Int. J. Math., incorporates many (mainly expository) changes suggested by the refere

Cyclic cocycles on twisted convolution algebras

We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted convolution algebra and twisted cohomology groups which is similar to a construction of Mathai and Stevenson. When the groupoid is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial techniques to construct a simplicial curvature 3-form representing the class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial curvature 3-form to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras. The results in this article were originally published in the author's Ph.D. thesis.Comment: 39 page

Inactivation of mammalian Ero 1α is catalysed by specific protein disulfide isomerases

Disulfide formation within the endoplasmic reticulum is a complex process requiring a disulfide exchange protein such as protein disulfide isomerase and a mechanism to form disulfides de novo. In mammalian cells, the major pathway for de novo disulfide formation involves the enzyme Ero1α which couples oxidation of thiols to the reduction of molecular oxygen to form hydrogen peroxide. Ero1α activity is tightly regulated by a mechanism that requires the formation of regulatory disulfides. These regulatory disulfides are reduced to activate and reform to inactive the enzyme. To investigate the mechanism of inactivation we analysed regulatory disulfide formation in the presence of various oxidants under controlled oxygen concentration. Neither molecular oxygen, nor hydrogen peroxide was able to oxidise Ero1α efficiently to form the correct regulatory disulfides. However, specific members of the PDI family such as PDI or ERp46 were able to catalyse this process. Further studies showed that both active sites of PDI contribute to the formation of regulatory disulfides in Ero1α and that the PDI substrate binding domain is crucial to allow electron transfer between the two enzymes. These results demonstrate a simple feedback mechanism of regulation of mammalian Ero1α involving its primary substrate

Concise theory of chiral lipid membranes

A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.}, Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC$_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0$^\circ$ and 35$^\circ$, which are close to the most frequent values 5$^\circ$ and 28$^\circ$ observed in the experiment [N. Mahajan \textit{et al.}, Langmuir \textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left- and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda \textit{et al.}, Nature (London) \textbf{399}, 566 (1999)].Comment: 14 pages, 7 figure

Classical Poisson structures and r-matrices from constrained flows

We construct the classical Poisson structure and $r$-matrix for some finite dimensional integrable Hamiltonian systems obtained by constraining the flows of soliton equations in a certain way. This approach allows one to produce new kinds of classical, dynamical Yang-Baxter structures. To illustrate the method we present the $r$-matrices associated with the constrained flows of the Kaup-Newell, KdV, AKNS, WKI and TG hierarchies, all generated by a 2-dimensional eigenvalue problem. Some of the obtained $r$-matrices depend only on the spectral parameters, but others depend also on the dynamical variables. For consistency they have to obey a classical Yang-Baxter-type equation, possibly with dynamical extra terms.Comment: 16 pages in LaTe

JSC-Rocknest: a Large-Scale Mojave Mars Simulant (MMS) Based Soil Simulant for In-Situ Resource Utilization Water-Extraction Studies

The Johnson Space Center Rocknest (JSC-RN) simulant was developed in response to a need by NASA's Advanced Exploration Systems (AES) In Situ Resource Utilization (ISRU) project for a simulant to be used in component and system testing for water extraction from Mars regolith. JSC-RN was de-signed to be chemically and mineralogically similar to material from the aeolian sand shadow named Rocknest in Gale Crater, particularly the 1-3 weight percentage water release as measured by the Sample Analysis at Mars (SAM) instrument. Rocknest material is a proxy for average martian soils, which are unconsolidated and could be easily scooped by rovers or landers in order to extract water. One way in which water can be extracted from aeolian material is through heating, where adsorbed and structural water is thermally removed from minerals. The water can then be condensed and used as drinking water or split and used as propellant for spacecraft or as a source of breathable O2. As such, it was essential that JSC-RN contained evolved gas profiles, especially low temperature water (less than 400 degrees Centigrade), that mimicked what is observed in martian soils. Because many of these ISRU tests require hundreds of kilograms of Mars soil simulant, it was essential that JSC-RN be cost-effective and based on com-ponents that could be purchased commercially (i.e., not synthesized in the lab). Here, we describe the JSC-RN martian soil simulant, which is ideal for large-scale production and use in ISRU water extraction studies

Geometric Random Inner Products: A New Family of Tests for Random Number Generators

We present a new computational scheme, GRIP (Geometric Random Inner Products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors generated in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants which can be used to evaluate the quality of random number generators. We explicitly apply the GRIP tests to several random number generators frequently used in Monte Carlo simulations, and demonstrate a new statistical property for good random number generators

Stability of Actinolite on Venus

Venus currently has a hostile surface environment with temperatures of ~460 C, pres-sures near 92 bars, and an atmosphere composed of super critical CO2 hosting a myriad of other potentially reactive gases (e.g., SO2, HCl, HF). However, it has been proposed that its surface may not have always been so harsh. Models suggest there may have been billions of years of clement conditions allowing an Earth-like environment with liquid water oceans. If such conditions existed, it is possible Venus formed a similar array of hydrous or aqueous minerals as seen on other planets with liquid surface water (e.g., Mars, Earth). Based on thermodynamic modeling, many of these phases would not be stable under the current atmospheric conditions on Venus, dehydrating due to the high temperatures and low concentration of H2O in the atmosphere. However, the rate of decomposition of these phases may allow them to remain present on the surface over geologic time. For example, experiments on the reaction rate of tremolite (Ca2Mg5Si8O22(OH)2) show a 50% decomposition time of 2.7 Gyr for micrometer sized grains in unreactive atmospheres (i.e., without SO2) at 740 K, and a 50% decomposition time of 70 Gyr for crystals several millimeters to centimeters in size. If hydrous minerals can remain on the surface of Venus over geologic time, it has implications for our detection of evidence of these past environments, and also for the overall water budget of the planet. If after surficial dehydration the planet was able to still store water in its crust, possible processes such as subduction or metamorphism could still have operated using stored water long after liquid surface water evaporated. Several previous studies have focused on experimental investigations of mineral stability on Venus. In particular, the works of studied the decomposition rate of tremolite under conditions relevant to Venus. As their focus was on decomposition of the mineral due to lack of water in the atmosphere, their experiments were undertaken using only CO2 or N2 gas at atmospheric pressure. Re-cent experiments have examined reactivity of other minerals with the Venusian atmosphere using more complex gas compositions at similar pressures to those seen on Venus. These studies show reaction of silicate minerals with atmospheric components on relatively short timescales (i.e., on the order of days). The reported reactions of silicate materials in both studies produced iron oxides, Ca sulfates, and Na sulfates. These ions are present in many amphiboles, and Ca was proposed by Johnson and Fegley to potentially have an important role in the decomposition mechanism for tremolite, with the Ca-O bond being the first to break during decomposition. The potential involvement of Ca in both processes raises the question of whether or not the reaction to form a secondary mineral phase will influence the rate of amphibole break-down (e.g., discussion in for tremolite). Additionally, reaction of Ca with atmospheric gases may result in a different secondary mineral assemblage than simple amphibole decomposition, which will need to be recognized when searching for evidence of past hydrated minerals on the Venusian surface. In order to understand the effect of this reaction on the overall preservation potential of amphibole on the surface of Venus, we are conducting experiments in both reactive and nonreactive atmospheres using the mineral actinolite (Ca2(Mg,Fe)5Si8O22(OH)2), an amphibole with similar crystal structure to tremolite that contains both Ca and Fe

Outcomes of Randomized Clinical Trials of Interventions to Enhance Social, Emotional, and Spiritual Components of Wisdom: A Systematic Review and Meta-analysis.

ImportanceWisdom is a neurobiological personality trait made up of specific components, including prosocial behaviors, emotional regulation, and spirituality. It is associated with greater well-being and happiness.ObjectiveTo evaluate the effectiveness of interventions to enhance individual components of wisdom.Data sourcesMEDLINE and PsycINFO databases were searched for articles published through December 31, 2018.Study eligibility criteriaRandomized clinical trials that sought to enhance a component of wisdom, used published measures to assess that component, were published in English, had a minimum sample size of 40 participants, and presented data that enabled computation of effect sizes were included in this meta-analysis.Data extraction and synthesisRandom-effect models were used to calculate pooled standardized mean differences (SMDs) for each wisdom component and random-effects meta-regression to assess heterogeneity of studies.Main outcomes and measuresImprovement in wisdom component using published measures.ResultsFifty-seven studies (N = 7096 participants) met review criteria: 29 for prosocial behaviors, 13 for emotional regulation, and 15 for spirituality. Study samples included people with psychiatric or physical illnesses and from the community. Of the studies, 27 (47%) reported significant improvement with medium to large effect sizes. Meta-analysis revealed significant pooled SMDs for prosocial behaviors (23 studies; pooled SMD, 0.43 [95% CI, 0.22-0.3]; P = .02), emotional regulation (12 studies; pooled SMD, 0.67 [95% CI, 0.21-1.12]; P = .004), and spirituality (12 studies; pooled SMD, 1.00 [95% CI, 0.41-1.60]; P = .001). Heterogeneity of studies was considerable for all wisdom components. Publication bias was present for prosocial behavior and emotional regulation studies; after adjusting for it, the pooled SMD for prosocial behavior remained significant (SMD, 0.4 [95% CI, 0.16-0.78]; P = .003). Meta-regression analysis found that effect sizes did not vary by wisdom component, although for trials on prosocial behaviors, large effect sizes were associated with older mean participant age (β, 0.08 [SE, 0.04]), and the reverse was true for spirituality trials (β, -0.13 [SE, 0.04]). For spirituality interventions, higher-quality trials had larger effect sizes (β, 4.17 [SE, 1.07]), although the reverse was true for prosocial behavior trials (β, -0.91 [SE 0.44]).Conclusions and relevanceInterventions to enhance spirituality, emotional regulation, and prosocial behaviors are effective in a proportion of people with mental or physical illnesses and from the community. The modern behavioral epidemics of loneliness, suicide, and opioid abuse point to a growing need for wisdom-enhancing interventions to promote individual and societal well-being

On the Toda Lattice Equation with Self-Consistent Sources

The Toda lattice hierarchy with self-consistent sources and their Lax representation are derived. We construct a forward Darboux transformation (FDT) with arbitrary functions of time and a generalized forward Darboux transformation (GFDT) for Toda lattice with self-consistent sources (TLSCS), which can serve as a non-auto-Backlund transformation between TLSCS with different degrees of sources. With the help of such DT, we can construct many type of solutions to TLSCS, such as rational solution, solitons, positons, negetons, and soliton-positons, soliton-negatons, positon-negatons etc., and study properties and interactions of these solutions.Comment: 20 page