Plurisubharmonic polynomials and bumping

We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain \Omega\subset C^n in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with bdy(\Omega), at the site of the bumping, are explicitly realised. Generally, when \Omega\subset C^n, n\geq 3, the known methods lead to bumpings with high orders of contact -- which are not explicitly known either -- at the site of the bumping. Precise orders are known for h-extendible/semiregular domains. This paper is motivated by certain families of non-semiregular domains in C^3. These families are identified by the behaviour of the least-weight plurisubharmonic polynomial in the Catlin normal form. Accordingly, we study how to perturb certain homogeneous plurisubharmonic polynomials without destroying plurisubharmonicity.Comment: 24 pages; corrected typos, fixed errors in Lemma 3.3; accepted for publication in Math.

Bergman kernel and complex singularity exponent

We give a precise estimate of the Bergman kernel for the model domain defined by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where $F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$, in terms of the complex singularity exponent of $F$.Comment: to appear in Science in China, a special issue dedicated to Professor Zhong Tongde's 80th birthda

Pluripolarity of Graphs of Denjoy Quasianalytic Functions of Several Variables

In this paper we prove pluripolarity of graphs of Denjoy quasianalytic functions of several variables on the spanning se

Resonant tunneling through a C60 molecular junction in liquid environment

We present electronic transport measurements through thiolated C$_{60}$ molecules in liquid environment. The molecules were placed within a mechanically controllable break junction using a single anchoring group per molecule. When varying the electrode separation of the C$_{60}$-modified junctions, we observed a peak in the conductance traces. The shape of the curves is strongly influenced by the environment of the junction as shown by measurements in two distinct solvents. In the framework of a simple resonant tunneling model, we can extract the electronic tunneling rates governing the transport properties of the junctions.Comment: 13 pages, 4 figures. To appear in Nanotechnolog

Remarks on the rank properties of formal CR maps

We prove several new transversality results for formal CR maps between formal real hypersurfaces in complex space. Both cases of finite and infinite type hypersurfaces are tackled in this note

Post-Partum Pituitary Insufficiency and Livedo Reticularis Presenting a Diagnostic Challenge in a Resource Limited Setting in Tanzania: A Case Report, Clinical Discussion and Brief Review of Existing Literature.

Pituitary disorders following pregnancy are an important yet under reported clinical entity in the developing world. Conversely, post partum panhypopituitarism has a more devastating impact on women in such settings due to high fertility rates, poor obstetric care and scarcity of diagnostic and therapeutic resources available. A 37 year old African female presented ten years post partum with features of multiple endocrine deficiencies including hypothyroidism, hypoadrenalism, lactation failure and secondary amenorrhea. In addition she had clinical features of an underlying autoimmune condition. These included a history of post-partum thyroiditis, alopecia areata, livedo reticularis and deranged coagulation indices. A remarkable clinical response followed appropriate hormone replacement therapy including steroids. This constellation has never been reported before; we therefore present an interesting clinical discussion including a brief review of existing literature. Post partum pituitary insufficiency is an under-reported condition of immense clinical importance especially in the developing world. A high clinical index of suspicion is vital to ensure an early and correct diagnosis which will have a direct bearing on management and patient outcome

Cervical artery dissection: An atypical presentation with Ehlers-Danlos-like collagen pathology?

The authors took skin biopsies of the macroscopically normal skin of seven consecutive patients with spontaneous cervical artery dissection (SCAD). Histologically, alterations of the collagen and elastic fiber networks were found in six patients. In five, the histologic, immunohistochemical, and ultrastructural changes were similar to those usually found in Ehlers-Danlos syndrome (EDS). This suggests that SCAD is frequently associated with the dermal alterations seen in EDS

Cooperation, Norms, and Revolutions: A Unified Game-Theoretical Approach

Cooperation is of utmost importance to society as a whole, but is often challenged by individual self-interests. While game theory has studied this problem extensively, there is little work on interactions within and across groups with different preferences or beliefs. Yet, people from different social or cultural backgrounds often meet and interact. This can yield conflict, since behavior that is considered cooperative by one population might be perceived as non-cooperative from the viewpoint of another. To understand the dynamics and outcome of the competitive interactions within and between groups, we study game-dynamical replicator equations for multiple populations with incompatible interests and different power (be this due to different population sizes, material resources, social capital, or other factors). These equations allow us to address various important questions: For example, can cooperation in the prisoner's dilemma be promoted, when two interacting groups have different preferences? Under what conditions can costly punishment, or other mechanisms, foster the evolution of norms? When does cooperation fail, leading to antagonistic behavior, conflict, or even revolutions? And what incentives are needed to reach peaceful agreements between groups with conflicting interests? Our detailed quantitative analysis reveals a large variety of interesting results, which are relevant for society, law and economics, and have implications for the evolution of language and culture as well

Size-Matched Radical Multivalency

Persistent π-radicals such as MV^+• (MV refers to methyl viologen, i.e., N,Nꞌ-dimethyl-4,4ꞌ-bipyridinum) engage in weak radical-radical interactions. This phenomenon has been utilized recently in supramolecular chemistry with the discovery that MV+• and [cyclobis(paraquat-p-phenylene)]2(+•) (CBPQT2(+•)) form a strong 1:1 host-guest complex [CBPQT⊂MV]3(+•). In this full paper, we describe the extension of radical-pairing-based molecular recognition to a larger, square-shaped diradical host, [cyclobis(paraquat-4,4ꞌ-biphenylene)]2(+•) (MS2(+•)). This molecular square was assessed for its ability to bind an isomeric series of possible diradical cyclophane guests, which consist of two radical viologen units that are linked by two ortho-, meta-, or para-xylylene bridges to provide different spacings between the planar radicals. UV-Vis-NIR measurements reveal that only the m-xylylene-linked isomer (m-CBPQT2(+•)) binds strongly inside of MS2(+•), resulting in the formation of a tetra-radical complex [MS⊂m-CBPQT]4(+•). Titration experiments and variable temperature UV-Vis-NIR and EPR spectroscopic data indicate that, relative to the smaller tris-radical complex [CBPQT⊂MV]3(+•), the new host-guest complex forms with a more favorable enthalpy change that is offset by a greater entropic penalty. As a result, the association constant (Ka = (1.12+/- 0.08) x 10^5 M^(-1)) for [MS⊂m-CBPQT]4(+•) is similar to that previously determined for [CBPQT⊂MV]3(+•). The (super)structures of MS2(+•), m-CBPQT2(+•), and [MS⊂m-CBPQT]4(+•) were examined by single-crystal X-ray diffraction measurements and DFT calculations. The solid-state and computational structural analyses reveal that m-CBPQT2(+•) is ideally sized to bind inside of MS2(+•). The solid-state superstructures also indicate that localized radical-radical interactions in m-CBPQT2(+•) and [MS⊂m-CBPQT]4(+•) disrupt the extended radical-pairing interactions that are common in crystals of other viologen radical cations. Lastly, the formation of [MS⊂m-CBPQT]4(+•) was probed by cyclic voltammetry, demonstrating that the radical states of the cyclophanes are stabilized by the radical-pairing interactions

Using Semantic Technologies in Digital Libraries- A Roadmap to Quality Evaluation

Abstract. In digital libraries semantic techniques are often deployed to reduce the expensive manual overhead for indexing documents, maintaining metadata, or caching for future search. However, using such techniques may cause a decrease in a collection’s quality due to their statistical nature. Since data quality is a major concern in digital libraries, it is important to be able to measure the (loss of) quality of metadata automatically generated by semantic techniques. In this paper we present a user study based on a typical semantic technique use