Bilinear electric field gradient focusing

Electric field gradient focusing (EFGF) uses an electric field gradient and a hydrodynamic counter flow to simultaneously separate and focus charged analytes in a channel. Previously, most EFGF devices were designed to form a linear field gradient in the channel. However, the peak capacity obtained using a linear gradient is not much better than what can be obtained using conventional CE. Dynamic improvement of peak capacity in EFGF can be achieved by using a nonlinear gradient. Numerical simulation results indicate that the peak capacity in a 4-cm long channel can be increased from 20 to 150 when changing from a linear to convex bilinear gradient. To demonstrate the increased capacity experimentally, an EFGF device with convex bilinear gradient was fabricated from poly(ethylene glycol) (PEG)-functionalized acrylic copolymers. The desired gradient profile was confirmed by measuring the focusing positions of a standard protein for different counter flow rates at constant voltage. Dynamically controlled elution of analytes was demonstrated using a monolith-filled bilinear EFGF channel. By increasing the flow rate, stacked proteins that were ordered but not resolved after focusing in the steep gradient segment were moved into the shallow gradient segment, where the analyte peak resolution increased significantly. In this way, the nonlinear field gradient was used to realize a dynamic increase in the peak capacity of the EFGF method.     

Stereodivergent Synthesis of 17‐α and 17‐β‐Aryl Steroids: Application and Biological Evaluation of D‐Ring Cortistatin Analogues

One stereocenter makes all the difference : The synthesis and biological evaluation of 17‐epi‐cortistatin A is reported from a common intermediate used to procure natural cortistatin A. The synthesis features a unique stereocontrolled Raney‐Ni reduction process that can be employed to reliably produce both α‐ and β‐configured D‐ring aryl steroids. Biological evaluations of these “cortalogs” are reported for the first time.

     

Equivalence relation groupoids associated with certain linearly ordered dimension groups

We consider linearly ordered, Archimedean dimension groups (G,G⁺,u) for which the group G/u is torsion-free. It will be shown that if, in addition, G/u is generated by a single element (i.e., ), then (G,G⁺,u) is isomorphic to for some irrational number τ(0,1). This amounts to an extension of related results where dimension groups for which G/u is torsion were considered. We will prove, in the case of the Fibonacci dimension group, that these results can be used to directly construct an equivalence relation groupoid whose C^*-algebra is the Fibonacci C^*-algebra.     

Hopf hypersurfaces of small Hopf principal curvature in $${\mathbb{C}{\rm H}^2}$$

Using the methods of moving frames and exterior differential systems, we show that there exist Hopf hypersurfaces in complex hyperbolic space with any specified value of the Hopf principal curvature α less than or equal to the corresponding value for the horosphere. We give a construction for all such hypersurfaces in terms of Weierstrass-type data, and also obtain a classification of pseudo-Einstein hypersurfaces in .      

On the evolution equation for magnetic geodesics

Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations (PDEs) whose solutions describe the orbits of closed p-branes under the effect of a “generalized physical force”. For the corresponding evolution equation, which is a system of parabolic nonlinear PDEs associated to the elliptic PDE, we can establish existence of short time solutions.     

The diameter game

A large class of Positional Games are defined on the complete graph on n vertices. The players, Maker and Breaker, take the edges of the graph in turns, and Maker wins iff his subgraph has a given — usually monotone — property. Here we introduce the d‐diameter game, which means that Maker wins iff the diameter of his subgraph is at most d. We investigate the biased version of the game; i.e., when the players may take more than one, and not necessarily the same number of edges, in a turn. Our main result is that we proved that the 2‐diameter game has the following surprising property: Breaker wins the game in which each player chooses one edge per turn, but Maker wins as long as he is permitted to choose 2 edges in each turn whereas Breaker can choose as many as (1/9)n^1/8/(lnn)^3/8. In addition, we investigate d‐diameter games for d ≥ 3. The diameter games are strongly related to the degree games. Thus, we also provide a generalization of the fair degree game for the biased case. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

A proposition on memes and meta-memes in computing for higher-order learning

In computational intelligence, the term ‘memetic algorithm’ has come to be associated with the algorithmic pairing of a global search method with a local search method. In a sociological context, a ‘meme’ has been loosely defined as a unit of cultural information, the social analog of genes for individuals. Both of these definitions are inadequate, as ‘memetic algorithm’ is too specific, and ultimately a misnomer, as much as a ‘meme’ is defined too generally to be of scientific use. In this paper, we extend the notion of memes from a computational viewpoint and explore the purpose, definitions, design guidelines and architecture for effective memetic computing. Utilizing two conceptual case studies, we illustrate the power of high-order meme-based learning. With applications ranging from cognitive science to machine learning, memetic computing has the potential to provide much-needed stimulation to the field of computational intelligence by providing a framework for higher order learning.     

Facilitating access to the most easily ionized molecule: an improved synthesis of the key intermediate, W2(hpp)4Cl2, and related compounds

A far superior synthesis is reported for W(2)(hpp)(4)Cl(2), a key intermediate in the synthesis of the most easily ionized closed-shell molecule W(2)(hpp)(4) (hpp = the anion of the bicyclic guanidine compound 1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-a]pyrimidine). At 200 degrees C, the one-pot reaction of the air-stable and commercially available compounds W(CO)(6) and Hhpp in o-dichlorobenzene produces W(2)(hpp)(4)Cl(2) in multigram quantities with isolated yields of over 90%. At lower temperatures, the reaction can lead to other compounds such as W(Hhpp)(2)(CO)(4) or W(2)(mu-CO)(2)(mu-hpp)(2)(eta(2)-hpp)(2), which are isolable in good purity depending upon the specific conditions employed. These compounds provide insight into the reaction pathway to W(2)(hpp)(4)Cl(2) and W(2)(hpp)(4). Two additional derivatives, W(2)(hpp)(4)X(2) where X is PF(6)(-) or the anion tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (TFPB), have also been synthesized and structurally characterized. A comparison of the electrode potentials of W(2)(mu-CO)(2)(mu-hpp)(2)(eta(2)-hpp)(2) and the di-p-anisylformamidinate analogue shows that oxidation of the hpp compound is significantly displaced (1.12 V) and shows that the bicyclic guanidinate ligand is considerably better than the formamidinate anion at stabilizing high oxidation states. A differential pulse voltammogram of W(2)(hpp)(4)(TFPB)(2) in THF shows two reduction processes with an E(1/2) of -0.97 V for the first and -1.81 V (vs Ag/AgCl) for the second. DFT calculations on the W(2)(hpp)(4)(2+) units in W(2)(hpp)(4)X(2) compounds show that the metal-metal bonding orbitals are destabilized by the axial ligands, which accounts for significant variations in the W-W distances. The low-energy gas-phase ionizations of W(2)(hpp)(4) are also reported and discussed.     

Conformational sampling via a self-regulating effective energy surface

The difficulty of efficiently sampling the phase space of complex systems with rough energy surfaces is well known. Typical solutions to the problem involve accelerating the crossing of barriers, but such methods often have the secondary problem that the low-energy states of interest are inadequately sampled, unless the parameters of the search algorithm are modified as the system evolves. A method is presented to improve the sampling with particular emphasis on the low-energy conformations, which make the most important contributions to the thermodynamics of the system. The algorithm proposed here samples the details of the minima, while easily surmounting barriers. This is achieved by introducing a self-regulating sampling variable which depends on the current state of the system. Two replicas of the system are introduced and the sampling variable is treated as a particle coupled to the physical system. The method is illustrated with a simple model system and is applied to the realistic example of barrier crossing in a protein-ligand complex.