103 research outputs found
Studies Towards the Synthesis of [10]-Annulenes
This thesis begins with a historical perspective on aromaticity and benzene, including the discovery and proposed structures for benzene as well as proposed criteria for measuring aromaticity. The history of the synthesis and characterization of [10]-annulene is also discussed.
Studies towards the synthesis of an aromatic all-cis-[10]-annulene derivative is covered in this dissertation. Two routes that were explored in efforts to obtain a chlorinated all-cis-[10]-annulene derivative, 40, are described. The primary route utilizes six chlorine atoms on the hydrocarbon skeleton (R=H) and uses a carbene [2+1] cycloaddition reaction as a key step to incorporate one of the two cyclopropane substituents (Scheme 1.0). The second cyclopropane unit is incorporated through a Diels-Alder reaction between diene 49 and tetrachlorocyclopropene 50, which also established the 10-carbon framework. The cleavage of the central olefin in the 10-carbon skeleton 51 is discussed, as well as difficulties encountered. In attempts to obtain the planar, aromatic [10]-annulene, efforts towards the elimination and oxidation reactions which lead to the aromatization of 55 are also presented.
This thesis also discusses an alternative route that incorporates an additional chlorine atom on the carbon framework (R=Cl). The alternative route mirrors the previous pathway; one cyclopropane substituent is incorporated through a carbene [2+1] cycloaddition reaction, whereas the second unit is established via a Diels-Alder reaction (Scheme 1.0). Efforts towards cleaving the olefin in 51 to obtain the carbon skeleton 40 are also discussed.
This work concludes with a general discussion and proposal for future directions, with an emphasis on alternative synthetic pathways. This study demonstrates the Diels-Alder reactions and ozonolysis of 51 is a viable strategy to form the functionalized skeleton required for [10]-annulene derivative 40
Lineshape distortion in a nonlinear auto-oscillator near generation threshold: Application to spin-torque nano-oscillators
The lineshape in an auto-oscillator with a large nonlinear frequency shift in
the presence of thermal noise is calculated. Near the generation threshold,
this lineshape becomes strongly non-Lorentzian, broadened, and asymmetric. A
Lorentzian lineshape is recovered far below and far above threshold, which
suggests that lineshape distortions provide a signature of the generation
threshold. The theory developed adequately describes the observed behavior of a
strongly nonlinear spin-torque nano-oscillator.Comment: 4 pages, 3 figure
Nash embedding and equilibrium in pure quantum states
With respect to probabilistic mixtures of the strategies in non-cooperative
games, quantum game theory provides guarantee of fixed-point stability, the
so-called Nash equilibrium. This permits players to choose mixed quantum
strategies that prepare mixed quantum states optimally under constraints. In
this letter, we show that fixed-point stability of Nash equilibrium can also be
guaranteed for pure quantum strategies via an application of the Nash embedding
theorem, permitting players to prepare pure quantum states optimally under
constraints.Comment: 7 pages, 1 figure. arXiv admin note: text overlap with
arXiv:1609.0836
Quantum feedback with weak measurements
The problem of feedback control of quantum systems by means of weak
measurements is investigated in detail. When weak measurements are made on a
set of identical quantum systems, the single-system density matrix can be
determined to a high degree of accuracy while affecting each system only
slightly. If this information is fed back into the systems by coherent
operations, the single-system density matrix can be made to undergo an
arbitrary nonlinear dynamics, including for example a dynamics governed by a
nonlinear Schr\"odinger equation. We investigate the implications of such
nonlinear quantum dynamics for various problems in quantum control and quantum
information theory, including quantum computation. The nonlinear dynamics
induced by weak quantum feedback could be used to create a novel form of
quantum chaos in which the time evolution of the single-system wave function
depends sensitively on initial conditions.Comment: 11 pages, TeX, replaced to incorporate suggestions of Asher Pere
Analyzing three-player quantum games in an EPR type setup
We use the formalism of Clifford Geometric Algebra (GA) to develop an
analysis of quantum versions of three-player non-cooperative games. The quantum
games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting.
In this setting, the players' strategy sets remain identical to the ones in the
mixed-strategy version of the classical game that is obtained as a proper
subset of the corresponding quantum game. Using GA we investigate the outcome
of a realization of the game by players sharing GHZ state, W state, and a
mixture of GHZ and W states. As a specific example, we study the game of
three-player Prisoners' Dilemma.Comment: 21 pages, 3 figure
Analysis of two-player quantum games in an EPR setting using geometric algebra
The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR)
type setting is investigated using the mathematical formalism of Clifford
geometric algebra (GA). In this setting, the players' strategy sets remain
identical to the ones in the classical mixed-strategy version of the game,
which is then obtained as proper subset of the corresponding quantum game. As
examples, using GA we analyze the games of Prisoners' Dilemma and Stag Hunt
when played in the EPR type setting.Comment: 20 pages, no figure, revise
HIPK2 and extrachromosomal histone H2B are separately recruited by Aurora-B for cytokinesis
Cytokinesis, the final phase of cell division, is necessary to form two distinct daughter cells with correct distribution of genomic and cytoplasmic materials. Its failure provokes genetically unstable states, such as tetraploidization and polyploidization, which can contribute to tumorigenesis. Aurora-B kinase controls multiple cytokinetic events, from chromosome condensation to abscission when the midbody is severed. We have previously shown that HIPK2, a kinase involved in DNA damage response and development, localizes at the midbody and contributes to abscission by phosphorylating extrachromosomal histone H2B at Ser14. Of relevance, HIPK2-defective cells do not phosphorylate H2B and do not successfully complete cytokinesis leading to accumulation of binucleated cells, chromosomal instability, and increased tumorigenicity. However, how HIPK2 and H2B are recruited to the midbody during cytokinesis is still unknown. Here, we show that regardless of their direct (H2B) and indirect (HIPK2) binding of chromosomal DNA, both H2B and HIPK2 localize at the midbody independently of nucleic acids. Instead, by using mitotic kinase-specific inhibitors in a spatio-temporal regulated manner, we found that Aurora-B kinase activity is required to recruit both HIPK2 and H2B to the midbody. Molecular characterization showed that Aurora-B directly binds and phosphorylates H2B at Ser32 while indirectly recruits HIPK2 through the central spindle components MgcRacGAP and PRC1. Thus, among different cytokinetic functions, Aurora-B separately recruits HIPK2 and H2B to the midbody and these activities contribute to faithful cytokinesis
N-player quantum games in an EPR setting
The -player quantum game is analyzed in the context of an
Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's
strategies are not unitary transformations as in alternate quantum
game-theoretic frameworks, but a classical choice between two directions along
which spin or polarization measurements are made. The players' strategies thus
remain identical to their strategies in the mixed-strategy version of the
classical game. In the EPR setting the quantum game reduces itself to the
corresponding classical game when the shared quantum state reaches zero
entanglement. We find the relations for the probability distribution for
-qubit GHZ and W-type states, subject to general measurement directions,
from which the expressions for the mixed Nash equilibrium and the payoffs are
determined. Players' payoffs are then defined with linear functions so that
common two-player games can be easily extended to the -player case and
permit analytic expressions for the Nash equilibrium. As a specific example, we
solve the Prisoners' Dilemma game for general . We find a new
property for the game that for an even number of players the payoffs at the
Nash equilibrium are equal, whereas for an odd number of players the
cooperating players receive higher payoffs.Comment: 26 pages, 2 figure
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