Weak Hopf algebras corresponding to Cartan matrices

We replace the group of group-like elements of the quantized enveloping algebra $U_q({\frak{g}})$ of a finite dimensional semisimple Lie algebra ${\frak g}$ by some regular monoid and get the weak Hopf algebra ${\frak{w}}_q^{\sf d}({\frak g})$. It is a new subclass of weak Hopf algebras but not Hopf algebras. Then we devote to constructing a basis of ${\frak{w}}_q^{\sf d}({\frak g})$ and determine the group of weak Hopf algebra automorphisms of ${\frak{w}}_q^{\sf d}({\frak g})$ when $q$ is not a root of unity.Comment: 21 page

Biodegradable cationic poly(carbonates): effect of varying side chain hydrophobicity on key aspects of gene transfection

The degree of hydrophobicity in cationic polymers plays an important but often underappreciated role in the safety and efficacy of gene delivery processes. In order to further elucidate structure-activity relationships of biodegradable cationic poly(carbonate) gene carriers, we synthesized a series of narrowly dispersed homo-polymers via metal-free organocatalytic living ring-opening polymerization (ROP) of cyclic carbonate monomers bearing either alkyl (propyl, hexyl or nonyl) or 4-methyl benzyl halide side chains. The polymers were then quaternized using bis-tertiary amines to install both quaternary ammoniums and tertiary amines for DNA binding and endosomal escape, respectively. Among the polymers with similar molecular lengths and charge densities, it was found that an increase in side chain alkyl spacer length from 3 to 6 carbons significantly enhanced cellular uptake and luciferase gene expression in HepG2 and HeLa cell lines without causing overt hemolysis and cytotoxicity. A further increase of side chain alkyl length to 9 carbons, however, led to a drastic decline in gene expression due to increased cellular toxicity, which was correlated with an increased disruption and lysis of red blood cell membranes. Interestingly, the incorporation of an aromatic 4-methyl benzyl spacer increased DNA binding strength, reduced particle sizes of resultant DNA complexes, and enhanced cellular uptake, leading to improved luciferase gene expression, albeit with higher levels of hemolysis and cytotoxicity. Taken together, the findings of this study demonstrate that a delicate balance between cationic charge density and hydrophobicity could be achieved by utilizing a hexyl spacer in the side chains of cationic poly(carbonates), hence providing insights on the future development of non-viral cationic polymeric gene delivery systems. Statement of Significance: Owing to their ease of synthesis and well-controlled polymerization, biodegradable cationic poly(carbonates) have emerged as a highly promising class of biomaterials for gene delivery. The hydrophobicity of side chains in cationic polymers plays an important but often underappreciated role in influencing key aspects of gene transfection. In our efforts to improve gene transfection and understand structure-activity relationships, we synthesized a series of cationic polymers bearing a common poly(carbonate) backbone, and with side chains containing various hydrophobic spacers (propyl, hexyl, 4-methyl benzyl or nonyl) before the cationic moiety. A moderate degree of hydrophobicity was optimal as the cationic poly(carbonate) with hexyl side chains mediated high gene transfection efficiencies while causing low cytotoxicities. (111 words

Memory usage verification using Hip/Sleek.

Embedded systems often come with constrained memory footprints. It is therefore essential to ensure that software running on such platforms fulfils memory usage specifications at compile-time, to prevent memory-related software failure after deployment. Previous proposals on memory usage verification are not satisfactory as they usually can only handle restricted subsets of programs, especially when shared mutable data structures are involved. In this paper, we propose a simple but novel solution. We instrument programs with explicit memory operations so that memory usage verification can be done along with the verification of other properties, using an automated verification system Hip/Sleek developed recently by Chin et al.[10,19]. The instrumentation can be done automatically and is proven sound with respect to an underlying semantics. One immediate benefit is that we do not need to develop from scratch a specific system for memory usage verification. Another benefit is that we can verify more programs, especially those involving shared mutable data structures, which previous systems failed to handle, as evidenced by our experimental results

A Note on the Bounded Solution of the Bilateral Monopoly Model

As is well known in the bilateral monopoly model, the solution regarding the price of the intermediate product cannot be determined uniquely. In this note, the author proposes a new solution that has narrower solution bound than that suggested by J. M. Henderson and R. E. Quandt (1971). Furthermore, these solutions are shown to be special cases of a generalized goal programming model with conflicting objectives between two monopolists. It was shown that with more information on taxes or preference weights, the solution range can be greatly improved.Bilateral Monopoly; Monopolists; Monopoly

A Note on the Musgravian Transformation

It has been long recognized that an ad valorem tax rate on revenues (demand) has its counterpart in costs (supply). Such a one to one correspondence is referred to as the Musgravian transformation. The transformation is monotonic and nonlinear. However, the property of concavity of the tax revenue curve is not preserved under the transformation. Even if the tax revenue curve of the demand ad valorem tax is strictly concave everywhere, the tax revenue curve of the supply ad valorem tax is guaranteed to be concave only before its own revenue-maximizing tax rate.

Type I collagen from bullfrog (Rana catesbeiana) fallopian tube

Pepsin-soluble collagen (PSC) was extracted from the fallopian tube of bullfrog (Rana catesbeiana) with a yield of 16.4%, on a dry weight basis. Sodium dodecyl sulphate polyacylamide-gel electrophoresis (SDS-PAGE) showed that the PSC contained two alpha components (α1 and α2) and was classified as type I collagen. PSC was found to contain 19.5% of amino acids. PSC exhibited a maximum absorbance at 230 nm, but little absorbance near to 280 nm. The denaturation temperature for PSC was determined to be 29.6°C. These results suggest that bullfrog fallopian tube has potential as a supplement to the sources of vertebrate collagens.Key words: Bullfrog (Rana catesbeiana), pepsin-soluble collagen, type I collagen

Predicate Abstraction for Linked Data Structures

We present Alias Refinement Types (ART), a new approach to the verification of correctness properties of linked data structures. While there are many techniques for checking that a heap-manipulating program adheres to its specification, they often require that the programmer annotate the behavior of each procedure, for example, in the form of loop invariants and pre- and post-conditions. Predicate abstraction would be an attractive abstract domain for performing invariant inference, existing techniques are not able to reason about the heap with enough precision to verify functional properties of data structure manipulating programs. In this paper, we propose a technique that lifts predicate abstraction to the heap by factoring the analysis of data structures into two orthogonal components: (1) Alias Types, which reason about the physical shape of heap structures, and (2) Refinement Types, which use simple predicates from an SMT decidable theory to capture the logical or semantic properties of the structures. We prove ART sound by translating types into separation logic assertions, thus translating typing derivations in ART into separation logic proofs. We evaluate ART by implementing a tool that performs type inference for an imperative language, and empirically show, using a suite of data-structure benchmarks, that ART requires only 21% of the annotations needed by other state-of-the-art verification techniques

Phosphatidylinositol 4,5-bisphosphate (PIP2) controls magnesium gatekeeper TRPM6 activity

TRPM6 is crucial for human Mg2+ homeostasis as patients carrying TRPM6 mutations develop hypomagnesemia and secondary hypocalcemia (HSH). However, the activation mechanism of TRPM6 has remained unknown. Here we demonstrate that phosphatidylinositol-4,5-bisphophate (PIP2) controls TRPM6 activation and Mg2+ influx. Stimulation of PLC-coupled M1-receptors to deplete PIP2 potently inactivates TRPM6. Translocation of over-expressed 5-phosphatase to cell membrane to specifically hydrolyze PIP2 also completely inhibits TRPM6. Moreover, depolarization-induced-activation of the voltage-sensitive-phosphatase (Ci-VSP) simultaneously depletes PIP2 and inhibits TRPM6. PLC-activation induced PIP2-depletion not only inhibits TRPM6, but also abolishes TRPM6-mediated Mg2+ influx. Furthermore, neutralization of basic residues in the TRP domain leads to nonfunctional or dysfunctional mutants with reduced activity by PIP2, suggesting that they are likely to participate in interactions with PIP2. Our data indicate that PIP2 is required for TRPM6 channel function; hydrolysis of PIP2 by PLC-coupled hormones/agonists may constitute an important pathway for TRPM6 gating, and perhaps Mg2+ homeostasis