Applications of DFT to the theory of twentieth-century harmony

Music theorists have only recently, following groundbreaking work by Quinn, recognized the potential for the DFT on pcsets, initially proposed by Lewin, to serve as the foundation of a theory of harmony for the twentieth century. This paper investigates pcset “arithmetic” – subset structure, transpositional combination, and interval content – through the lens of the DFT. It discusses relationships between interval classes and DFT magnitudes, considers special properties of dyads, pcset products, and generated collections, and suggest methods of using the DFT in analysis, including interpreting DFT magnitudes, using phase spaces to understand subset structure, and interpreting the DFT of Lewin’s interval function. Webern’s op. 5/4 and Bartok’s String Quartet 4, iv, are discussed.Accepted manuscrip

Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page

Decontextualizing contextual inversion

Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively decontextualizing contextual inversions.Accepted manuscrip

Repetitive higher cluster categories of type A_n

We show that the repetitive higher cluster category of type A_n, defined as the orbit category D^b(mod kA_n)/(tau^{-1}[m])^p, is equivalent to a category defined on a subset of diagonals in a regular p(nm+1)-gon. This generalizes the construction of Caldero-Chapoton-Schiffler, which we recover when p=m=1, and the work of Baur-Marsh, treating the case p=1, m>1. Our approach also leads to a geometric model of the bounded derived category D^b(mod kA_n)

Theoretical model for ultracold molecule formation via adaptive feedback control

We investigate pump-dump photoassociation of ultracold molecules with amplitude- and phase-modulated femtosecond laser pulses. For this purpose a perturbative model for the light-matter interaction is developed and combined with a genetic algorithm for adaptive feedback control of the laser pulse shapes. The model is applied to the formation of 85Rb2 molecules in a magneto-optical trap. We find for optimized pulse shapes an improvement for the formation of ground state molecules by more than a factor of 10 compared to unshaped pulses at the same pump-dump delay time, and by 40% compared to unshaped pulses at the respective optimal pump-dump delay time. Since our model yields directly the spectral amplitudes and phases of the optimized pulses, the results are directly applicable in pulse shaping experiments

Spectroscopy of the a^3\Sigma_u^+ state and the coupling to the X^1\Sigma_g^+ state of K_2

We report on high resolution Fourier-transform spectroscopy of fluorescence to the a^3\Sigma_u^+ state excited by two-photon or two-step excitation from the X^1\Sigma_g^+ state to the 2^3\Pi_g state in the molecule K_2. These spectroscopic data are combined with recent results of Feshbach resonances and two-color photoassociation spectra for deriving the potential curves of X^1\Sigma_g^+ and a^3\Sigma_u^+ up to the asymptote. The precise relative position of the triplet levels with respect of the singlet levels was achieved by including the excitation energies from the X^1\Sigma_g^+ state to the 2^3\Pi_g state and down to the a^3\Sigma_u^+ state in the simultaneous fit of both potentials. The derived precise potential curves allow for reliable modeling of cold collisions of pairs of potassium atoms in their ^2S ground state

Influence of Extraction Solvent on the Biological Properties of Maritime Pine Bark (Pinus pinaster)

Maritime pine bark (Pinus pinaster Aiton subsp. atlantica) is rich in polyphenols with known bioactive properties which are beneficial for human health. However, biological activities of bark extracts depend on the type of polyphenols extracted and the characteristics of these extractives depend on several factors such as the type of solvents used. The in uence of the extraction solvent on the composition and consequently on the properties of the extracts has been poorly described. Thus, in this study the in uence of the extraction solvent (water, ethanol and ethanol-water (50/50 v/v%)) on the antibacterial and anticancer properties of P. pinaster bark samples were evaluated. LC-DAD-MS profiling of the different extracts was also carried out to study their polyphenol composition. Results show that extraction solvent must be carefully chosen with respect to foreseeing use of bark extracts, since ethanolic and hydroethanolic extracts displayed the greatest antibacterial activity whereas water extracts showed increased anticancer properties. © 2022. International Journal of Food Studies.All Rights Reserve

Shall We (Math and) Dance?

Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and dance, and between music and categories. Then, we extend this formalism and diagrammatic thinking style to dance.Comment: preprin

Hepatocyte-like cells differentiated from human induced pluripotent stem cells: Relevance to cellular therapies

AbstractMaturation of induced pluripotent stem cells (hiPSCs) to hepatocyte-like cells (HLCs) has been proposed to address the shortage of human hepatocytes for therapeutic applications. The purpose of this study was to evaluate hiPSCs, HLCs and hepatocytes, all of human origin, in terms of performance metrics of relevance to cell therapies. hiPSCs were differentiated to HLCs in vitro using an established four-stage approach. We observed that hiPSCs had low oxygen consumption and possessed small, immature mitochondria located around the nucleus. With maturation to HLCs, mitochondria showed characteristic changes in morphology, ultrastructure, and gene expression. These changes in mitochondria included elongated morphology, swollen cristae, dense matrices, cytoplasmic migration, increased expression of mitochondrial DNA transcription and replication-related genes, and increased oxygen consumption. Following differentiation, HLCs expressed characteristic hepatocyte proteins including albumin and hepatocyte nuclear factor 4-alpha, and intrinsic functions including cytochrome P450 metabolism. But HLCs also expressed high levels of alpha fetoprotein, suggesting a persistent immature phenotype or inability to turn off early stage genes. Furthermore, the levels of albumin production, urea production, cytochrome P450 activity, and mitochondrial function of HLCs were significantly lower than primary human hepatocytes.Conclusion- hiPSCs offer an unlimited source of human HLCs. However, reduced functionality of HLCs compared to primary human hepatocytes limits their usefulness in clinical practice. Novel techniques are needed to complete differentiation of hiPSCs to mature hepatocytes