On Determining Minimal Spectrally Arbitrary Patterns

In this paper we present a new family of minimal spectrally arbitrary patterns which allow for arbitrary spectrum by using the Nilpotent-Jacobian method. The novel approach here is that we use the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.Comment: 8 page

Nucleation at the DNA supercoiling transition

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition state theory, we predict the rate of this plectoneme nucleation to be of order 10^4 Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscosity of the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.Comment: 18 pages, 15 figure

Generating Cosmological Gaussian Random Fields

We present a generic algorithm for generating Gaussian random initial conditions for cosmological simulations on periodic rectangular lattices. We show that imposing periodic boundary conditions on the real-space correlator and choosing initial conditions by convolving a white noise random field results in a significantly smaller error than the traditional procedure of using the power spectrum. This convolution picture produces exact correlation functions out to separations of L/2, where L is the box size, which is the maximum theoretically allowed. This method also produces tophat sphere fluctuations which are exact at radii $R \le L/4$. It is equivalent to windowing the power spectrum with the simulation volume before discretizing, thus bypassing sparse sampling problems. The mean density perturbation in the volume is no longer constrained to be zero, allowing one to assemble a large simulation using a series of smaller ones. This is especially important for simulations of Lyman-$\alpha$ systems where small boxes with steep power spectra are routinely used. We also present an extension of this procedure which generates exact initial conditions for hierarchical grids at negligible cost.Comment: 12 pages incl 3 figures, accepted in ApJ Letter

A Tool for Generating Controllable Variations of Musical Themes Using Variational Autoencoders with Latent Space Regularisation

A common musical composition practice is to develop musical pieces using variations of musical themes. In this study, we present an interactive tool which can generate variations of musical themes in real-time using a variational autoencoder model. Our tool is controllable using semantically meaningful musical attributes via latent space regularisation technique to increase the explainability of the model. The tool is integrated into an industry standard digital audio workstation - Ableton Live - using the Max4Live device framework and can run locally on an average personal CPU rather than requiring a costly GPU cluster. In this way we demonstrate how cutting-edge AI research can be integrated into the exiting workflows of professional and practising musicians for use in the real-world beyond the research lab

In vivo nuclear magnetic resonance imaging

A number of physiological changes have been demonstrated in bone, muscle and blood after exposure of humans and animals to microgravity. Determining mechanisms and the development of effective countermeasures for long duration space missions is an important NASA goal. The advent of tomographic nuclear magnetic resonance imaging (NMR or MRI) gives NASA a way to greatly extend early studies of this phenomena in ways not previously possible; NMR is also noninvasive and safe. NMR provides both superb anatomical images for volume assessments of individual organs and quantification of chemical/physical changes induced in the examined tissues. The feasibility of NMR as a tool for human physiological research as it is affected by microgravity is demonstrated. The animal studies employed the rear limb suspended rat as a model of mucle atrophy that results from microgravity. And bedrest of normal male subjects was used to simulate the effects of microgravity on bone and muscle

Comparison of reaction networks of Wnt signaling

Wnt signaling is a vital biological mechanism that regulates crucial development processes and maintenance of tissue homeostasis. Here, we extended the parameter-free analysis of four mathematical models of the beta-catenin-dependent Wnt signaling pathway performed by MacLean et al. (PNAS USA 2015) using chemical reaction network theory. We showed that the reaction networks of the four models considered (Lee, Schmitz, MacLean, and Feinberg) coincide in basic structural and kinetic properties except in their mono-stationarity/multi-stationarity, and their capacity for admitting a degenerate equilibrium. Moreover, we showed that the embedded networks of the Lee and Feinberg models are very similar, and the discordance of the Lee network limits its mono-stationarity to mass action kinetics, which challenge the absoluteness of model discrimination into mono-stationarity versus multi-stationarity alone. Focusing, henceforth, on the three multi-stationary networks, we showed that their finest independent decompositions are very different and can be used to study further similarities and differences among them. We also determined equilibria parametrizations of the networks and inferred the presence of species with absolute concentration robustness. Finally, direct comparison of the Schmitz and Feinberg networks with the MacLean network yielded new results in three aspects: structural/kinetic relationships between embedded networks relative to their set of common species, connections between the positive equilibria of the subnetwork of common reactions and the positive equilibria of the whole networks, and construction of maximal concordant subnetwork containing the common reactions of the networks under comparison. Thus, this work can provide general insights in comparing mathematical models of the same or closely-related systems

Optimal classical-communication-assisted local model of n-qubit Greenberger-Horne-Zeilinger correlations

We present a model, motivated by the criterion of reality put forward by Einstein, Podolsky, and Rosen and supplemented by classical communication, which correctly reproduces the quantum-mechanical predictions for measurements of all products of Pauli operators on an n-qubit GHZ state (or ``cat state''). The n-2 bits employed by our model are shown to be optimal for the allowed set of measurements, demonstrating that the required communication overhead scales linearly with n. We formulate a connection between the generation of the local values utilized by our model and the stabilizer formalism, which leads us to conjecture that a generalization of this method will shed light on the content of the Gottesman-Knill theorem.Comment: New version - expanded and revised to address referee comment

The Dirichlet-to-Robin Transform

A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest cases this observation enables the exact construction of the Green functions for the wave, heat, and Schrodinger problems with a Robin boundary condition. The resulting physical picture is that the field can exchange energy with the boundary, and a delayed reflection from the boundary results. In more general situations the method allows at least approximate and local construction of the appropriate reflected solutions, and hence a "classical path" analysis of the Green functions and the associated spectral information. By this method we solve the wave equation on an interval with one Robin and one Dirichlet endpoint, and thence derive several variants of a Gutzwiller-type expansion for the density of eigenvalues. The variants are consistent except for an interesting subtlety of distributional convergence that affects only the neighborhood of zero in the frequency variable.Comment: 31 pages, 5 figures; RevTe

The velocity field of baryonic gas in the universe

The dynamic evolution of the baryonic intergalactic medium (IGM) caused by the underlying dark matter gravity is governed by the Navier-Stokes equations in which many cooling and heating processes are involved. However, it has long been recognized that the growth mode dynamics of cosmic matter clustering can be sketched by a random force driven Burgers' equation if cooling and heating are ignored. Just how well the dynamics of the IGM can be described as a Burgers fluid has not been fully investigated probably because cooling and heating are essential for a detailed understanding of the IGM. Using IGM samples produced by a cosmological hydrodynamic simulation in which heating and cooling processes are properly accounted for, we show that the IGM velocity field in the nonlinear regime shows the features of a Burgers fluid, that is, when the Reynolds number is high, the velocity field consists of an ensemble of shocks. Consequently, (1) the IGM velocity $v$ is generally smaller than that of dark matter; (2) for the smoothed field, the IGM velocity shows tight correlation with dark matter given by $v \simeq s v_{dm}$, with $s<1$, such that the lower the redshift, the smaller $s$; (3) the velocity PDFs are asymmetric between acceleration and deceleration events; (4) the PDF of velocity difference $\Delta v=v(x+r)-v(x)$ satisfies the scaling relation for a Burgers fluid, i.e., $P(\Delta v)=(1 r^y)F(\Delta v/r^y)$. We find the scaling function and parameters for the IGM which are applicable to the entire scale range of the samples (0.26 - 8 h$^{-1}$ Mpc). These properties show that the similarity mapping between the IGM and dark matter is violated on scales much larger than the Jeans length of the IGM.Comment: 14 pages, 10 jpg-figures, accepted for publication in the Astrophysical Journal. References adde