ShantanuT01/DACTYL-Pretraining huggingface dataset:
Magnetic Resonance Fingerprinting (MRF) is a new approach to quantitative magnetic resonance imaging that allows simultaneous measurement of multiple tissue properties in a single, time-efficient acquisition. Standard MRF reconstructs parametric maps using dictionary matching and lacks scalability due to computational inefficiency. We propose to perform MRF map reconstruction using a recurrent neural network, which exploits the time-dependent information of the MRF signal evolution. We evaluate our method on multiparametric synthetic signals and compare it to existing MRF map reconstruction approaches, including those based on neural networks. Our method achieves state-of-the-art estimates of T1 and T2 values. In addition, the reconstruction time is significantly reduced compared to dictionary-matching based approaches.
One of the important issues regarding the final evolution of stars is the impact of binarity. A rich zoo of peculiar, evolved objects are born from the interaction between the loosely bound envelope of a giant, and the gravitational pull of a companion. However, binary interactions are not understood from first principles, and the theoretical models are subject to many assumptions. It is currently agreed upon that hot subdwarf stars can only be formed through binary interaction, either through common envelope ejection or stable Roche-lobe overflow (RLOF) near the tip of the red giant branch (RGB). These systems are therefore an ideal testing ground for binary interaction models. With our long term study of wide hot subdwarf (sdB) binaries we aim to improve our current understanding of stable RLOF on the RGB by comparing the results of binary population synthesis studies with the observed population. In this article we describe the current model and possible improvements, and which observables can be used to test different parts of the interaction model.
In order to reduce the Klein-Gordon equation (with minimal coupling), we introduce a generalization of the so-called "mode solutions" that are well-known in the special case of a Robertson-Walker universe. After separation of the variables, we end up with a partial differential equation in lower dimension. A reduced version of the Gordon current arises and is conserved. When the first factor-manifold is Lorentzian, distinct modes appear as mutually orthogonal in the sense of the sesquilinear form obtained from the customary Gordon current. Moreover, a sesquilinear form is defined on the space of solutions to the reduced equation. Extension of this picture to curvature coupling is possible when the second factor-manifold has a constant scalar curvature.
Semi-analytic models (SAMs) are currently one of the primary tools with which to model statistically significant ensembles of galaxies. The underlying physical prescriptions inherent to each SAM are, in many cases, different from one another. Several SAMs have been applied to the dark matter merger trees extracted from the Millennium Run, including those associated with the well-known Munich and Durham lineages. We compare the predicted luminosity distributions of galaxy groups using four publicly available SAMs (De Lucia et al. 2006; Bower et al. 2006; Bertone et al. 2007; Font et al. 2008), in order to explore a galactic environment in which the models have not been explored to the same degree as they have in the field or in rich clusters. We identify a characteristic "wiggle" in the group galaxy luminosity function generated using the De Lucia et al. (2006) SAM, that is not present in the Durham-based models, consistent to some degree with observations. However, a comparison between conditional luminosity functions of groups between the models and observations of Yang et al. (2007) suggest that neither model is a particularly good match. The luminosity function wiggle is interpreted as the result of the two-mode AGN feedback implementation used in the Munich models, which itself results in flattened magnitude gap distribution. An associated analysis of the magnitude gap distribution between first- and second-ranked group galaxies shows that while the Durham models yield distributions with approximately equal luminosity first- and second-ranked galaxies, in agreement with observations, the De Lucia et al. models favours the scenario in which the second-ranked galaxy is approximately one magnitude fainter than the primary,especially when the dynamic range of the mock data is limited to 3 magnitudes.
We investigate the Mott transitions in two-band Hubbard models with different bandwidths. Applying dynamical mean field theory, we discuss the stability of itinerant quasi-particle states in each band. We demonstrate that separate Mott transitions occur at different Coulomb interaction strengths in general, which merge to a single transition only under special conditions. This kind of behavior may be relevant for the physics of the single-layer ruthenates, Ca$_{2-x}$Sr$_x$RuO$_4$.
In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of the Navier-Stokes equation is given.
We give a generalization of the duality of a zero-dimensional complete intersection to the case of one-dimensional almost complete intersections, which results in a {\em Gorenstein module} $M=I/J$. In the real case the resulting pairing has a signature, which we show to be constant under flat deformations. In the special case of a non-isolated real hypersurface singularity $f$ with a one-dimensional critical locus, we relate the signature on the jacobian module $I/J_f$ to the Euler characteristic of the positive and negative Milnor fibre, generalising the result for isolated critical points. An application to real curves in $\P^2(\R)$ of even degree is given.
As a natural generalization of the Euler-Mascheroni constant $\gamma$, Y. Ihara introduced the Euler-Kronecker constant $\gamma_K$ attached to any number field $K$. In this paper, we prove that a certain bound on $\gamma_K$ in a tower of number fields $\mathcal{K}$ implies the generalized Brauer-Siegel conjecture for $\mathcal{K}$ as formulated by Tsfasman and Vl\v{a}du\c{t}. Moreover, we use known bounds on $\gamma_K$ for cyclotomic fields to obtain a finer estimate for the number of zeros of the Dedekind zeta-function $\zeta_K(s)$ in the critical strip.
This is a systematic exposition of recent results which completely describe the group of automorphisms and the group of autoequivalences of generic analytic K3 surfaces. These groups, hard to determine in the algebraic case, admit a good description for generic analytic K3 surfaces, and are in fact seen to be closely interrelated.
In this pedagogical paper, the comparative analysis of two common approaches describing the ferromagnetic phase transition in diluted magnetic semiconductors (DMS) is expounded in terms of Weiss field approximation. Assuming a finite spin polarization of the magnetic ions, the treatment of carrier-ion exchange interaction in first order evokes the homogeneous Weiss molecular field that polarizes the spins of free carriers. In turn, this spin polarization of the free carriers exerts the effective field that may stabilize DMS spin polarization below a critical temperature Tc. The treatment of such self-consistent spontaneous DMS magnetization can be done in terms of spin-spin interaction independent on inter-ion distance and infinitesimal in thermodynamic limit. On the other hand, the taking additionally into account the second order effects of carrier-ion exchange interaction treat a Weiss field in term of the RKKY indirect spin-spin interaction, which oscillates and not disappears at finite inter-ion distance in case of finite carriers concentration. These both approaches result in same Curie temperature Tc provided non-correlated homogeneous random distribution of the localized spin moments over sample volume. We discuss the origin of such coincidence and show when this is not a case in other more realistic models of the conducting DMSs.
We consider a class of global quantum quenches in the Heisenberg XXZ spin chain, where the initial states are given by products of local two-site states. The two main examples are the N\'eel state and the dimer state. We derive an exact analytic result for the "Loschmidt echo per site" at imaginary times and also consider the analytic continuation back to real times. As a by-product we obtain an exact result for the "overlap per site" between the N\'eel state and the ground state of the XXZ Hamiltonian in the massive regime.
Work is an observable quantity associated with a process, however there is no Hermitian operator associated with its measurement. We consider an ancilla-assisted protocol measuring the work done on a quantum system driven by a time-dependent Hamiltonian via two von-Neumann measurements of the system's energy carried out by a measuring apparatus modeled as a free particle of finite localization and interaction time with the system. We consider system Hamiltonians which both commute and do not commute at different times, finding corrections to fluctuation relations like the Jarzynski equality and the Crooks relation. This measurement model allows us to quantify the effect that measuring has on the estimated work distribution, and associated average work done on the system and average heat exchanged with the measuring apparatus.
We compute the one-loop partition function for quadratic tachyon background in open string theory.   Both closed and open string representations are developed. Using these representations we study the one-loop divergences in the partition function in the presence of the tachyon background. The divergences due to the open and closed string tachyons are treated by analytic continuation in the tachyon mass squared. We pay particular attention to the imaginary part of the analytically continued expressions. The last one gives the decay rate of the unstable vacuum. The dilaton tadpole is also given some partial consideration. The partition function is further used to study corrections to tachyon condensation processes describing brane descent relations. Assuming the boundary string field theory prescription for construction of the string field action via partition function holds at one loop level we study the one-loop corrections to the tachyon potential and to the tensions of lower-dimensional branes.
We present results from ab initio No-Core Full Configuration simulations of the exotic proton-rich nucleus $^{14}$F whose first experimental observation is expected soon. The calculations with JISP16 NN interaction are performed up to the $N_{\max}=8$ basis space. The binding energy is evaluated using an extrapolation technique. This technique is generalized to excitation energies, verified in calculations of $^6$Li and applied to $^{14}$B, the $^{14}$F mirror, for which some data are available.
We report on the coherent reflection spectroscopy of a high-quality factor micropillar, in the strong coupling regime with a single InGaAs annealed quantum dot. The absolute reflectivity measurement is used to study the characteristics of our device at low and high excitation power. The strong coupling is obtained with a g=16 \mueV coupling strength in a 7.3\mum diameter micropillar, with a cavity spectral width kappa=20.5 \mueV (Q=65 000). The factor of merit of the strong-coupling regime, 4g/kappa=3, is the current state-of-the-art for a quantum dot-micropillar system.
Despite advances in image classification methods, detecting the samples not belonging to the training classes is still a challenging problem. There has been a burst of interest in this subject recently, which is called Open-Set Recognition (OSR). In OSR, the goal is to achieve both the classification and detecting out-of-distribution (OOD) samples. Several ideas have been proposed to push the empirical result further through complicated techniques. We believe that such complication is indeed not necessary. To this end, we have shown that Maximum Softmax Probability (MSP), as the simplest baseline for OSR, applied on Vision Transformers (ViTs) as the base classifier that is trained with non-OOD augmentations can surprisingly outperform many recent methods. Non-OOD augmentations are the ones that do not alter the data distribution by much. Our results outperform state-of-the-art in CIFAR-10 datasets, and is also better than most of the current methods in SVHN and MNIST. We show that training augmentation has a significant effect on the performance of ViTs in the OSR tasks, and while they should produce significant diversity in the augmented samples, the generated sample OOD-ness must remain limited.
The metal-poor sub-population of globular cluster (GC) systems exhibits a correlation between the GC average colour and luminosity, especially in those systems associated with massive elliptical galaxies. More luminous (more massive) GCs are typically redder and hence more metal-rich. This 'blue tilt' is often interpreted as a mass-metallicity relation stemming from GC self-enrichment, whereby more massive GCs retain a greater fraction of the enriched gas ejected by their evolving stars, fostering the formation of more metal-rich secondary generations. We examine the E-MOSAICS simulations of the formation and evolution of galaxies and their GC populations, and find that their GCs exhibit a colour-luminosity relation similar to that observed in local galaxies, without the need to invoke mass-dependent self-enrichment. We find that the blue tilt is most appropriately interpreted as a dearth of massive, metal-poor GCs: the formation of massive GCs requires high interstellar gas surface densities, conditions that are most commonly fostered by the most massive, and hence most metal rich, galaxies, at the peak epoch of GC formation. The blue tilt is therefore a consequence of the intimate coupling between the small-scale physics of GC formation and the evolving properties of interstellar gas hosted by hierarchically-assembling galaxies.
We discuss critical gravitational collapse on the threshold of apparent horizon formation as a model both for the discussion of global aspects of critical collapse and for numerical studies in a compactified context. For our matter model we choose a self-gravitating massless scalar field in spherical symmetry, which has been studied extensively in the critical collapse literature. Our evolution system is based on Bondi coordinates, the mass function is used as an evolution variable to ensure regularity at null infinity. We compute radiation quantities like the Bondi mass and news function and find that they reflect the DSS behavior. Surprisingly, the period of radiation at null infinity is related to the formal result for the leading quasi-normal mode of a black hole with rapidly decreasing mass. Furthermore, our investigations shed some light on global versus local issues in critical collapse, and the validity and usefulness of the concept of null infinity when predicting detector signals.
In this note, we give a new proof of subcritical Trudinger-Moser inequality on $\mathbb{R}^n$. All the existing proofs on this inequality are based on the rearrangement argument with respect to functions in the Sobolev space $W^{1,n}(\mathbb{R}^n)$. Our method avoids this technique and thus can be used in the Riemannian manifold case and in the entire Heisenberg group.
The reconstruction on Ge(001) surface is locally and reversibly changed between c(4x2) and p(2x2) by controlling the bias voltage of a scanning tunneling microscope (STM) at 80K. It is c(4x2) with the sample bias voltage V_b =< -0.7V. This structure can be kept with V_b =< 0.6V. When V_b is higher than 0.8V during the scanning, the structure changes to p(2x2). This structure is then maintained with V_b >= - 0.6V. The observed local change of the reconstruction with hysteresis is ascribed to inelastic scattering during the electron tunneling in the electric field under the STM-tip.
Le n be any positive integer. A hyperbinary expansion of n is are presentation of n as sum of powers of 2, each power being used at most twice. In this paper we study some properties of a suitable edge-coloured and vertex-weighted oriented graph A(n) whose nodes are precisely the several hyperbinary representations of n. In particular, we identify those integers m in N such that the fundamental group of A(m) is abelian.
We propose a new approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations. Our formalism is based on a nonextensive generalization of the Wiener process. This allow us to obtain, in addition to significant physical insights, several analytical results with great simplicity. Indeed, we obtain analytical solutions for a nonextensive version of Brownian free-particle and Ornstein-Uhlenbeck process, and explain anomalous diffusive behaviours in terms of memory effects in a nonextensive generalization of Gaussian white noise. Finally, we apply the develop formalism to model thermal noise in electric circuits.
Galactic synchrotron emission exhibits large-angular-scale features known as radio spurs and loops. Determining the physical size of these structures is important for understanding the local interstellar structure and for modeling the Galactic magnetic field. However, the distance to these structures is either under debate or entirely unknown. We revisit a classical method of finding the location of radio spurs by comparing optical polarization angles with those of synchrotron emission as a function of distance. We consider three tracers of the magnetic field: stellar polarization, polarized synchrotron radio emission, and polarized thermal dust emission. We employ archival measurements of optical starlight polarization and Gaia distances, and construct a new map of polarized synchrotron emission from WMAP and Planck data. We confirm that synchrotron, dust emission, and stellar polarization angles all show a statistically significant alignment at high Galactic latitude. We obtain distance limits to three regions towards Loop I of 112$\pm$17 pc, 135$\pm$20 pc, and $<105$ pc. Our results strongly suggest that the polarized synchrotron emission towards the North Polar Spur at $b > 30^\circ$ is local. This is consistent with the conclusions of earlier work based on stellar polarization and extinction, but in stark contrast with the Galactic center origin recently revisited on the basis of X-ray data. We also obtain a distance measurement towards part of Loop IV (180$\pm$15 pc) and find evidence that its synchrotron emission arises from chance overlap of structures located at different distances. Future optical polarization surveys will allow the expansion of this analysis to other radio spurs.
Human matting refers to extracting human parts from natural images with high quality, including human detail information such as hair, glasses, hat, etc. This technology plays an essential role in image synthesis and visual effects in the film industry. When the green screen is not available, the existing human matting methods need the help of additional inputs (such as trimap, background image, etc.), or the model with high computational cost and complex network structure, which brings great difficulties to the application of human matting in practice. To alleviate such problems, most existing methods (such as MODNet) use multi-branches to pave the way for matting through segmentation, but these methods do not make full use of the image features and only utilize the prediction results of the network as guidance information. Therefore, we propose a module to generate foreground probability map and add it to MODNet to obtain Semantic Guided Matting Net (SGM-Net). Under the condition of only one image, we can realize the human matting task. We verify our method on the P3M-10k dataset. Compared with the benchmark, our method has significantly improved in various evaluation indicators.
We investigate Lyapunov exponents of Brownian motion in a nonnegative Poissonian potential $V$. The Lyapunov exponent depends on the potential $V$ and our interest lies in the decay rate of the Lyapunov exponent if the potential $V$ tends to zero. In our model the random potential $V$ is generated by locating at each point of a Poisson point process with intensity $\nu$ a bounded compactly supported nonnegative function $W$. We show that for sequences of potentials $V_n$ for which $\nu_n \|W_n\|_1 \sim D/n$ for some constant $D > 0$ ($n \to \infty$), the decay rates to zero of the quenched and annealed Lyapunov exponents coincide and equal $c n^{-1/2}$ where the constant $c$ is computed explicitly. Further we are able to estimate the quenched Lyapunov exponent norm from above by the corresponding norm for the averaged potential.
In a recent paper, Rose proves that certain generalized sum-of-divisor functions are quasi-modular forms for some congruence subgroup and conjectures that these forms are quasi-modular for $\Gamma_1(n)$. Here, we prove this conjecture.
We present a simple statistical analysis of recent numerical simulations exploring the correlation between the core mass function obtained from the fragmentation of a molecular cloud and the stellar mass function which forms from these collapsing cores. Our analysis shows that the distributions of bound cores and sink particles obtained in the simulations are consistent with the sinks being formed predominantly from their parent core mass reservoir, with a statistical dispersion of the order of one third of the core mass. Such a characteristic dispersion suggests that the stellar initial mass function is relatively tightly correlated to the parent core mass function, leading to two similar distributions, as observed. This in turn argues in favor of the IMF being essentially determined at the early stages of core formation and being only weakly affected by the various environmental factors beyond the initial core mass reservoir, at least in the mass range explored in the present study. Accordingly, the final IMF of a star forming region should be determined reasonably accurately, statistically speaking, from the initial core mass function, provided some uniform efficiency factor. The calculations also show that these statistical fluctuations, due e.g. to variations among the core properties, broaden the low-mass tail of the IMF compared with the parent CMF, providing an explanation for the fact that this latter appears to underestimate the number of "pre brown dwarf" cores compared with the observationally-derived brown dwarf IMF.
This article contains the introduction to the special volume of Stochastics dedicated to Priscilla Greenwood, her CV and her list of publications.
The ability to manipulate ferroelectrics at ultrafast speeds has long been an elusive target for materials research. Coherently exciting the ferroelectric mode with ultrashort optical pulses holds the promise to switch the ferroelectric polarization on femtosecond timescale, two orders of magnitude faster compared to what is possible today with pulsed electric fields. Here, we report on the demonstration of ultrafast optical reversal of the ferroelectric polarization in LiNbO3. Rather than driving the ferroelectric mode directly, we couple to it indirectly by resonant excitation of an auxiliary high-frequency phonon mode with femtosecond mid-infrared pulses. Due to strong anharmonic coupling between these modes, the atoms are directionally displaced along the ferroelectric mode and the polarization is transiently reversed, as revealed by time-resolved, phase-sensitive second-harmonic generation. This reversal can be induced in both directions, a key pre-requisite for practical applications.