Deformed diagonal harmonic polynomials for complex reflection groups

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded W-module, to the undeformed version.Comment: 11 pages, 1 figur

Analysis of a quantum memory for photons based on controlled reversible inhomogeneous broadening

We present a detailed analysis of a quantum memory for photons based on controlled and reversible inhomogeneous broadening (CRIB). The explicit solution of the equations of motion is obtained in the weak excitation regime, making it possible to gain insight into the dependence of the memory efficiency on the optical depth, and on the width and shape of the atomic spectral distributions. We also study a simplified memory protocol which does not require any optical control fields.Comment: 9 pages, 4 figures (Accepted for publication in Phys. Rev. A

Some relational structures with polynomial growth and their associated algebras II: Finite generation

The profile of a relational structure $R$ is the function $\varphi_R$ which counts for every integer $n$ the number, possibly infinite, $\varphi_R(n)$ of substructures of $R$ induced on the $n$-element subsets, isomorphic substructures being identified. If $\varphi_R$ takes only finite values, this is the Hilbert function of a graded algebra associated with $R$, the age algebra $A(R)$, introduced by P.~J.~Cameron. In a previous paper, we studied the relationship between the properties of a relational structure and those of their algebra, particularly when the relational structure $R$ admits a finite monomorphic decomposition. This setting still encompasses well-studied graded commutative algebras like invariant rings of finite permutation groups, or the rings of quasi-symmetric polynomials. In this paper, we investigate how far the well know algebraic properties of those rings extend to age algebras. The main result is a combinatorial characterization of when the age algebra is finitely generated. In the special case of tournaments, we show that the age algebra is finitely generated if and only if the profile is bounded. We explore the Cohen-Macaulay property in the special case of invariants of permutation groupoids. Finally, we exhibit sufficient conditions on the relational structure that make naturally the age algebra into a Hopf algebra.Comment: 27 pages; submitte

Improving binding affinity through cyclization

Cancer chemotherapy results in systematic damage as the drugs used are also toxic to benign tissue. Sensitizing a cancer cell to therapy by interfering with the DNA repair mechanisms would decrease overall toxicity, as the necessary dosage of chemotherapy drugs would be lowered. The Hartman lab developed a peptide (8.6) that binds with a KD of 1 μM to the C-terminal domain of breast cancer associated protein (BRCA1), blocking homologous recombination. The crystal structure of the peptide shows the tyrosine and threonine residues are close together, suggesting that by cyclizing these positions, the peptide may already be constrained into its bound conformation. A series of dibromomethylnaphthalene linkers of various length were synthesized and cyclized through alkylation of the cysteine residues on peptide 8.6. The binding of the cyclic peptides with the BRCA1 (BRCT)2 domain will be compared to peptide 8.6 through the use of fluorescence polarization.https://scholarscompass.vcu.edu/uresposters/1248/thumbnail.jp

The history of video quality model validation

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Uncertainty modelling in reliable preliminary space mission design

In the early phase of the design of a space mission, it is generally desirable to investigate as many feasible alternative solutions as possible. At this particular stage, an insufficient consideration for uncertainty would lead to a wrong decision on the feasibility of the mission. Traditionally a system margin approach is used in order to take into account the inherent uncertainties within the subsystem budgets. The reliability of the mission is then independently computed in parallel. An iteration process between the solution design and the reliability assessment should finally converge to an acceptable solution. By combining modern statistical methods to model uncertainties and global search techniques for multidisciplinary design, the present work proposes a way to introduce uncertainties in the mission design problem formulation. By minimising the effect of these uncertainties on both constraints and objective functions, while optimising the mission goals, the aim is to increase the reliability of the produced results

Temporal-mode continuous-variable cluster states using linear optics

I present an extensible experimental design for optical continuous-variable cluster states of arbitrary size using four offline (vacuum) squeezers and six beamsplitters. This method has all the advantages of a temporal-mode encoding [Phys. Rev. Lett. 104, 250503], including finite requirements for coherence and stability even as the computation length increases indefinitely, with none of the difficulty of inline squeezing. The extensibility stems from a construction based on Gaussian projected entangled pair states (GPEPS). The potential for use of this design within a fully fault tolerant model is discussed.Comment: 9 pages, 19 color figure

Capital Controls: An Evaluation

The literature on capital controls has (at least) four very serious apples-to-oranges problems: (i) There is not unified theoretical framework to analyze the macroeconomic consequences of controls; (ii) there is significant heterogeneity across countries and time in the control measures implemented; (iii) there are multiple definitions of what constitutes a "success" and (iv) the empirical studies lack a common methodology -- furthermore these are significantly "overweighted" by a couple of country cases (Chile and Malaysia). In this paper, we attempt to address some of these shortcomings by: being very explicit about what measures are construed as capital controls. Also, given that success is measured so differently across studies, we sought to "standardize" the results of over 30 empirical studies we summarize in this paper. The standardization was done by constructing two indices of capital controls: Capital Controls Effectiveness Index (CCE Index), and Weighted Capital Control Effectiveness Index (WCCE Index). The difference between them lies only in that the WCCE controls for the differentiated degree of methodological rigor applied to draw conclusions in each of the considered papers. Inasmuch as possible, we bring to bear the experiences of less well known episodes than those of Chile and Malaysia.

Spectral gap for random-to-random shuffling on linear extensions

In this paper, we propose a new Markov chain which generalizes random-to-random shuffling on permutations to random-to-random shuffling on linear extensions of a finite poset of size $n$. We conjecture that the second largest eigenvalue of the transition matrix is bounded above by $(1+1/n)(1-2/n)$ with equality when the poset is disconnected. This Markov chain provides a way to sample the linear extensions of the poset with a relaxation time bounded above by $n^2/(n+2)$ and a mixing time of $O(n^2 \log n)$. We conjecture that the mixing time is in fact $O(n \log n)$ as for the usual random-to-random shuffling.Comment: 16 pages, 10 figures; v2: typos fixed plus extra information in figures; v3: added explicit conjecture 2.2 + Section 3.6 on the diameter of the Markov Chain as evidence + misc minor improvements; v4: fixed bibliograph