Primordial magnetogenesis

Magnetic fields appear everywhere in the universe. From stars and galaxies, all the way to galaxy clusters and remote protogalactic clouds, magnetic fields of considerable strength and size have been repeatedly observed. Despite their widespread presence, however, the origin of cosmic magnetic fields is still a mystery. The galactic dynamo is believed capable of amplifying weak magnetic seeds to strengths like those measured in ours and other galaxies. But the question is where do these seed fields come from? Are they a product of late, post-recombination, physics or are they truly cosmological in origin? The idea of primordial magnetism is attractive because it makes the large-scale magnetic fields, especially those found in early protogalactic systems, easier to explain. As a result, a host of different scenarios have appeared in the literature. Nevertheless, early magnetogenesis is not problem-free, with a number of issues remaining open and a matter of debate. We review the question of the origin of primordial magnetic fields and consider the limits set on their strength by the current observational data. The various mechanisms of pre-recombination magnetogenesis are presented and their advantages and shortcomings are debated. We consider both classical and quantum scenarios, that operate within as well as outside the standard model, and also discuss how future observations could be used to decide whether the large-scale magnetic fields we see in the universe today are truly primordial or not.     

Bounds for sorting by prefix reversal

For a permutation σ of the integers from 1 to n, let ?(σ) be the smallest number of prefix reversals that will transform σ to the identity permutation, and let ?(n) be the largest such ?(σ) for all σ in (the symmetric group) S_n. We show that $\text{?(n)?}\text{(5n+5)}\text{3}$, and that $\text{?(n)?}\text{17n}\text{16}$ for n a multiple of 16. If, furthermore, each integer is required to participate in an even number of reversed prefixes, the corresponding function g(n) is shown to obey $\text{3n}\text{2?1}\text{?g(n)?2n+3}$.     

Development of an optimised, standard-compliant procedure to calculate sound transmission loss: design of transmission rooms

A numerical procedure to estimate the transmission loss of sound insulating structures is proposed based upon the technology of acoustic measurements and standards. A virtual laboratory (VL), namely, a numerical representation of a real laboratory consisting of two reverberation rooms meeting certain sound field quality criteria is designed. VL is to be used for the numerical simulation of standardised measurements under predefined, controlled, acoustic conditions. In this paper, the design and optimisation of VL is investigated. The geometry of the transmission rooms is designed following first principles, in order for diffuse field conditions and sufficiently smooth primary mode distribution in the low frequency to be achieved. A finite element-based optimisation procedure, introduced by the author in previous work, is extended to arbitrarily shaped rooms. It is used to predict the appropriate local geometric modifications so as for improved mode distribution and smoother sound pressure fluctuations of the transmission rooms in the low-frequency range to be achieved and low-frequency measurement reproducibility and accuracy to be increased. Steady-state acoustic response analysis is performed in order to quantify the acoustic field quality of the virtual transmission rooms in the frequency range of measurements. A method to calculate the total absorption, A, of the receiving room is introduced by simulation of the reverberation time measurement procedure using Transient acoustic response analysis. The acoustic performance of VL is overall considered and is shown to meet in a sufficient degree, relative laboratory measurement standards in the frequency range of 100÷704 Hz.     

On efficient portfolio selection using convex risk measures

In this article we systematically revisit the classic portfolio selection theory in both of its branches, the determination of the efficient financial positions among such a choice set and the selection of the financial position which maximizes some utility function whose functional form involves some ‘measure of risk’. We study these problems by considering certain classes of convex risk measures and we show that for these classes the solution of the utility maximization problems in reflexive spaces take the form of a zero-sum game between the investor and the market.     

Multiplicative intrinsic component optimization (MICO) for MRI bias field estimation and tissue segmentation

This paper proposes a new energy minimization method called multiplicative intrinsic component optimization (MICO) for joint bias field estimation and segmentation of magnetic resonance (MR) images. The proposed method takes full advantage of the decomposition of MR images into two multiplicative components, namely, the true image that characterizes a physical property of the tissues and the bias field that accounts for the intensity inhomogeneity, and their respective spatial properties. Bias field estimation and tissue segmentation are simultaneously achieved by an energy minimization process aimed to optimize the estimates of the two multiplicative components of an MR image. The bias field is iteratively optimized by using efficient matrix computations, which are verified to be numerically stable by matrix analysis. More importantly, the energy in our formulation is convex in each of its variables, which leads to the robustness of the proposed energy minimization algorithm. The MICO formulation can be naturally extended to 3D/4D tissue segmentation with spatial/sptatiotemporal regularization. Quantitative evaluations and comparisons with some popular softwares have demonstrated superior performance of MICO in terms of robustness and accuracy.     

Spectra of Some Interesting Combinatorial Matrices Related to Oriented Spanning Trees on a Directed Graph

The Laplacian of a directed graph G is the matrix L(G) = O(G) –, A(G) where A(G) is the adjaceney matrix of G and O(G) the diagonal matrix of vertex outdegrees. The eigenvalues of G are the eigenvalues of A(G). Given a directed graph G we construct a derived directed graph D(G) whose vertices are the oriented spanning trees of G. Using a counting argument, we describe the eigenvalues of D(G) and their multiplicities in terms of the eigenvalues of the induced subgraphs and the Laplacian matrix of G. Finally we compute the eigenvalues of D(G) for some specific directed graphs G. A recent conjecture of Propp for D(H _n ) follows, where H _n stands for the complete directed graph on n vertices without loops.     

High-yield syntheses and reactivity studies of Fe10 "ferric wheels": structural, magnetic, and computational characterization of a star-shaped Fe8 complex

Convenient, high-yield routes have been developed to [Fe 10(OMe) 20(O 2CR) 10] ( 1) "ferric wheels" involving the alcoholysis of [Fe 3O(O 2CR) 6(H 2O) 3] (+) salts in MeOH in the presence of NEt 3. Reactivity studies have established [Fe 10(OMe) 20(O 2CMe) 10] ( 1a) to undergo clean carboxylate substitution with a variety of other RCO 2H groups to the corresponding [Fe 10(OMe) 20(O 2CR) 10] product. In contrast, the reaction with phenol causes a nuclearity change to give a smaller [Fe 8(OH) 4(OPh) 8(O 2CR) 12] ( 2) wheel. Similarly, reactions of [Fe 10(OMe) 20(O 2CR) 10] with the bidentate chelate ethylenediamine (en) cause a structural change to give either [Fe 8O 5(O 2CMe) 8(en) 8](ClO 4) 6 ( 3) or [Fe 2O(O 2CBu (t))(en) 4](NO 3) 3 ( 4), depending on conditions. Complex 3 possesses a "Christmas-star" Fe 8 topology comprising a central planar [Fe 4(mu 4-O)] (10+) square subunit edge-fused to four oxide-centered [Fe 3(mu 3-O)] (7+) triangular units. Variable-temperature, solid-state dc and ac magnetization studies on complexes 1a- 4 in the 5.0-300 K range established that all the complexes possess an S = 0 ground state. The magnetic susceptibility data for 4 were fit to the theoretical chi M versus T expression derived by the use of an isotropic Heisenberg spin Hamiltonian and the Van Vleck equation, and this revealed an antiferromagnetic exchange parameter with a value of J = -107.7(5) cm (-1). This value is consistent with that predicted by a previously published magnetostructural relationship. Theoretically computed values of the exchange constants in 3 were obtained with the ZILSH method, and the pattern of spin frustration within its core and the origin of its S = 0 ground state have been analyzed in detail.