ShantanuT01/DACTYL-Pretraining huggingface dataset:
Multiple instance learning (MIL) is a supervised learning methodology that aims to allow models to learn instance class labels from bag class labels, where a bag is defined to contain multiple instances. MIL is gaining traction for learning from weak labels but has not been widely applied to 3D medical imaging. MIL is well-suited to clinical CT acquisitions since (1) the highly anisotropic voxels hinder application of traditional 3D networks and (2) patch-based networks have limited ability to learn whole volume labels. In this work, we apply MIL with a deep convolutional neural network to identify whether clinical CT head image volumes possess one or more large hemorrhages (> 20cm$^3$), resulting in a learned 2D model without the need for 2D slice annotations. Individual image volumes are considered separate bags, and the slices in each volume are instances. Such a framework sets the stage for incorporating information obtained in clinical reports to help train a 2D segmentation approach. Within this context, we evaluate the data requirements to enable generalization of MIL by varying the amount of training data. Our results show that a training size of at least 400 patient image volumes was needed to achieve accurate per-slice hemorrhage detection. Over a five-fold cross-validation, the leading model, which made use of the maximum number of training volumes, had an average true positive rate of 98.10%, an average true negative rate of 99.36%, and an average precision of 0.9698. The models have been made available along with source code to enabled continued exploration and adaption of MIL in CT neuroimaging.
A popular universal gate set for quantum computing with qubits is Clifford+T, as this can be readily implemented on many fault-tolerant architectures. For qutrits, there is an equivalent T gate, that, like its qubit analogue, makes Clifford+T approximately universal, is injectable by a magic state, and supports magic state distillation. However, it was claimed that a better gate set for qutrits might be Clifford+R, where R=diag(1,1,-1) is the metaplectic gate, as certain protocols and gates could more easily be implemented using the R gate than the T gate. In this paper we show that when we have at least two qutrits, the qutrit Clifford+R unitaries form a strict subset of the Clifford+T unitaries, by finding a direct decomposition of $R \otimes \mathbb{I}$ as a Clifford+T circuit and proving that the T gate cannot be exactly synthesized in Clifford+R. This shows that in fact the T gate is at least as powerful as the R gate, up to a constant factor. Moreover, we additionally show that it is impossible to find a single-qutrit Clifford+T decomposition of the R gate, making our result tight.
I analyze a metrological strategy for improving the precision of frequency estimation via Ramsey interferometry with strings of atoms in the presence of correlated dephasing. This strategy does not employ entangled states, but rather a product state which evolves into a stationary state under the influence of correlated dephasing. It is shown that by using this state an improvement in precision compared to standard Ramsey interferometry can be gained. This improvement is not an improvement in scaling, i.e. the estimation precision has the same scaling with the number of atoms as the standard quantum limit, but an improvement proportional to the free evolution time in the Ramsey interferometer. Since a stationary state is used, this evolution time can be substantially larger than in standard Ramsey interferometry which is limited by the coherence time of the atoms.
We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the rationality of motivic zeta-function.
Since the quark-gluon plasma, which is unstable due to anisotropic momentum distribution, evolves fast in time, plasma's characteristics have to be studied as initial value problems. The chromodynamic fluctuations and the momentum broadening of a fast parton traversing the plasma are discussed here. The two quantities are shown to exponentially grow in time.
We introduce a method to estimate the HI mass within the optical radius of disk galaxies from integrated HI spectra, with an uncertainty of 0.09 dex. We use these estimates to study how inner HI fuels star formation in late-type disk galaxies. We find that star formation rate (SFR) at a given stellar mass ($M_*$) is well correlated with the inner HI surface density ($\Sigma_{\rm HI,in}$) and inner HI mass-to-stellar mass ratio. For the massive ($M_*>10^{10} M_{\odot}$) disk galaxies, higher SFR at a given stellar mass is also related with higher efficiency of converting inner HI to molecular gas, but no such correlation is found for the total HI mass. The highest $\Sigma_{\rm HI,in}$ and the fastest depletion of the total neutral gas within the optical disks are found in the most compact and star-forming disk galaxies at a given stellar mass. These results highlight the important role of inner HI as an intermediate step of fueling star formation in disk galaxies.
We present a study of the cosmological Ly$\alpha$ emission signal at $z > 4$. Our goal is to predict the power spectrum of the spatial fluctuations that could be observed by an intensity mapping survey. The model uses the latest data from the HST legacy fields and the abundance matching technique to associate UV emission and dust properties with the halos, computing the emission from the interstellar medium (ISM) of galaxies and the intergalactic medium (IGM), including the effects of reionization, self-consistently. The Ly$\alpha$ intensity from the diffuse IGM emission is 1.3 (2.0) times more intense than the ISM emission at $z = 4(7)$; both components are fair tracers of the star-forming galaxy distribution. However the power spectrum is dominated by ISM emission on small scales ($k > 0.01 h{\rm Mpc}^{-1}$) with shot noise being significant only above $k = 1 h{\rm Mpc}^{-1}$. At very lange scales ($k < 0.01h{\rm Mpc}^{-1}$) diffuse IGM emission becomes important. The comoving Ly$\alpha$ luminosity density from IGM and galaxies, $\dot \rho_{{\rm Ly}\alpha}^{\rm IGM} = 8.73(6.51) \times 10^{40} {\rm erg}{\rm s}^{-1}{\rm Mpc}^{-3}$ and $\dot \rho_{{\rm Ly}\alpha}^{\rm ISM} = 6.62(3.21) \times 10^{40} {\rm erg}{\rm s}^{-1}{\rm Mpc}^{-3}$ at $z = 4(7)$, is consistent with recent SDSS determinations. We predict a power $k^3 P^{{\rm Ly}\alpha}(k, z)/2\pi^2 = 9.76\times 10^{-4}(2.09\times 10^{-5}){\rm nW}^2{\rm m}^{-4}{\rm sr}^{-2}$ at $z = 4(7)$ for $k = 0.1 h {\rm Mpc}^{-1}$.
We show how some special production matrices may be used to define families of generalized Eulerian triangles. We furthermore show that these generalized Eulerian triangles are the coefficient arrays of polynomials which are the moments of families of orthogonal polynomials. Using the previously defined $\mathcal{T}$ transform, we associate these generalized Eulerian triangles to triangles defined by Catalan generating functions. Again, these new triangles are the coefficient arrays of polynomial moment sequences. The main tools used are the Sumudu transform, Jacobi continued fractions and Riordan arrays.
Let $(F_n)_{n\geq 0}$ and $(L_n)_{n\geq 0}$ be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of $ a $ and $ b $, we mean the both concatenations $\overline{ab}$ and $\overline{ba}$ together, where $ a $ and $ b $ are any two non negative integers. So, the mathematical formulation of this problem leads us searching the solutions of two Diophantine equations $ F_n=10^d F_m +L_k $ and $ F_n=10^d L_m+F_k $ in non-negative integers $ (n,m,k) ,$ where $ d $ denotes the number of digits of $ L_k $ and $ F_k $, respectively. We use lower bounds for linear forms in logarithms and reduction method in Diophantine approximation to get the results.
We prove that the near-horizon geometries of minimal gauged five-dimensional supergravity preserve at least half of the supersymmetry. If the near-horizon geometries preserve a larger fraction, then they are locally isometric to $AdS_5$. Our proof is based on Lichnerowicz type theorems for two horizon Dirac operators constructed from the supercovariant connection restricted to the horizon sections, and on an application of the index theorem. An application is that all half-supersymmetric five-dimensional horizons admit an $\mathfrak{sl}(2, {\mathbb{R}})$ symmetry subalgebra.
We analyze the generation of primordial magnetic fields during de Sitter inflation in a Lorentz-violating theory of Electrodynamics containing a Chern-Simons term which couples the photon to an external four-vector. We find that, for appropriate magnitude of the four-vector, the generated field is maximally helical and, through an inverse cascade caused by turbulence of primeval plasma, reaches at the time of protogalactic collapse an intensity and correlation length such as to directly explain galactic magnetism.
We propose two asymptotic expansions of two interrelated integral-type averages, in the context of the fractional $\infty$-Laplacian $\Delta_\infty^s$ for $s\in (\frac{1}{2},1)$. This operator has been introduced and first studied in [Bjorland, C., Caffarelli, L. and Figalli, A., \textsl{Nonlocal Tug-of-War and the inifnity fractional Laplacian}, Comm. Pure Appl. Math., \textbf{65}, pp. 337--380, (2012)]. Our expansions are parametrised by the radius of the removed singularity $\epsilon$, and allow for the identification of $\Delta_\infty^s\phi(x)$ as the $\epsilon^{2s}$-order coefficient of the deviation of the $\epsilon$-average from the value $\phi(x)$, in the limit $\epsilon\to 0+$. The averages are well posed for functions $\phi$ that are only Borel regular and bounded.
We revisit in more detail a model for element abundance fractionation in the solar chromosphere, that gives rise to the "FIP Effect" in the solar corona and wind. Elements with first ionization potential below about 10 eV, i.e. those that are predominantly ionized in the chromosphere, are enriched in the corona by a factor 3-4. We model the propagation of Alfven waves through the chromosphere using a non-WKB treatment, and evaluate the ponderomotive force associated with these waves. Under solar conditions, this is generally pointed upwards in the chromosphere, and enhances the abundance of chromospheric ions in the corona. Our new approach captures the essentials of the solar coronal abundance anomalies, including the depletion of He relative to H, and also the putative depletion of Ne, recently discussed in the literature. We also argue that the FIP effect provides the strongest evidence to date for energy fluxes of Alfven waves sufficient to heat the corona. However it appears that these waves must also be generated in the corona, in order to preserve the rather regular fractionation pattern without strong variations from loop to loop observed in the solar corona and slow speed solar wind.
Crack propagation is studied in a two dimensional decagonal model quasicrystal. The simulations reveal the dominating role of highly coordinated atomic environments as structure intrinsic obstacles for both dislocation motion and crack propagation. For certain overloads, these obstacles and the quasiperiodic nature of the crystal result in a specific crack propagation mechanism: The crack tip emits a dislocation followed by a phason wall, along which the material opens up.
We investigate how different cosmological parameters, such as those delivered by the WMAP and Planck missions, affect the nature and evolution of dark matter halo substructure. We use a series of flat $\Lambda$ cold dark matter ($\Lambda$CDM) cosmological $N$-body simulations of structure formation, each with a different power spectrum but the same initial white noise field. Our fiducial simulation is based on parameters from the WMAP 7th year cosmology. We then systematically vary the spectral index, $n_s$, matter density, $\Omega_M$, and normalization of the power spectrum, $\sigma_8$, for 7 unique simulations. Across these, we study variations in the subhalo mass function, mass fraction, maximum circular velocity function, spatial distribution, concentration, formation times, accretion times, and peak mass. We eliminate dependence of subhalo properties on host halo mass and average over many hosts to reduce variance. While the "same" subhalos from identical initial overdensity peaks in higher $\sigma_8, n_s$, and $\Omega_m$ simulations accrete earlier and end up less massive and closer to the halo center at $z=0$, the process of continuous subhalo accretion and destruction leads to a steady state distribution of these properties across all subhalos in a given host. This steady state mechanism eliminates cosmological dependence on all properties listed above except subhalo concentration and $V_{max}$, which remain greater for higher $\sigma_8, n_s$ and $\Omega_m$ simulations, and subhalo formation time, which remains earlier. We also find that the numerical technique for computing scale radius and the halo finder used can significantly affect the concentration-mass relationship computed for a simulation.
We consider the Hardy constant associated with a domain in the $n$-dimensional Euclidean space and we study its variation upon perturbation of the domain. We prove a Fr\'{e}chet differentiability result and establish a Hadamard-type formula for the corresponding derivatives. We also prove a stability result for the minimizers of the Hardy quotient. Finally, we prove stability estimates in terms of the Lebesgue measure of the symmetric difference of domains.
The capacity for solving eigenstates with a quantum computer is key for ultimately simulating physical systems. Here we propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method. A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution. We first consider a continuous-variable quantum mode (qumode) for realizing such a linear combination as an integral, with weights being encoded into a qumode resource state. We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems, including molecules and quantum many-body models. We also discuss a hybrid quantum-classical algorithm that directly sums up Hamiltonian evolution with different durations for comparison. It is revealed that continuous-variable resources are valuable for reducing the coherent evolution time of Hamiltonians in quantum algorithms.
We show that the quantum Hall wave functions for the ground states in the Jain series can be exactly expressed in terms of correlation functions of local vertex operators, V_n, corresponding to composite fermions in the n:th composite-fermion (CF) Landau level. This allows for the powerful mathematics of conformal field theory to be applied to the successful CF phenomenology. Quasiparticle and quasihole states are expressed as correlators of anyonic operators with fractional (local) charge, allowing a simple algebraic understanding of their topological properties that are not manifest in the CF wave functions.
X-rays illuminating the accretion disc in active galactic nuclei give rise to an iron K line and its associated reflection spectrum which are lagged behind the continuum variability by the light-travel time from the source to the disc. The measured lag timescales in the iron band can be as short as $\sim R_g/c$, where $R_g$ is the gravitational radius, which is often interpreted as evidence for a very small continuum source close to the event horizon of a rapidly spinning black hole. However, the short lags can also be produced by reflection from more distant material, because the primary photons with no time-delay dilute the time-lags caused by the reprocessed photons. We perform a Monte-Carlo simulation to calculate the dilution effect in the X-ray reverberation lags from a half-shell of neutral material placed at $100\,R_g$ from the central source. This gives lags of $\sim2\,R_g/c$, but the iron line is a distinctly narrow feature in the lag-energy plot, whereas the data often show a broader line. We show that both the short lag and the line broadening can be reproduced if the scattering material is outflowing at $\sim0.1c$. The velocity structure in the wind can also give shifts in the line profile in the lag-energy plot calculated at different frequencies. Hence we propose that the observed broad iron reverberation lags and shifts in profile as a function of frequency of variability can arise from a disc wind at fairly large distances from the X-ray source.
The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson-meson states with the four-quark states is considered. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitudes are obtained. The four-quark amplitudes of cryptoexotic mesons including the quarks of three flavours (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks are calculated.
Quantum mechanics forces us to reconsider certain aspects of classical causality. The 'central mystery' of quantum mechanics manifests in different ways, depending on the interpretation. This mystery can be formulated as the possibility of selecting part of the initial conditions of the Universe 'retroactively'. This talk aims to show that there is a global, timeless, 'bird's view' of the spacetime, which makes this mystery more reasonable. We will review some well-known quantum effects from the perspective of global consistency.
We show that formally for the standard ansatz relativistic point-coupling mean-field (RMF-PC) model a lagrangian density L is not equivalent in Hartree and Hartree-Fock approximations. The equivalency can be achieved only if we use a ``complete'' ansatz at the cost of introducing new parameters in the model. An approximate treatment of the exchange terms from standard RMF-PC indicates that these effects cannot be easily, if at all, absorbed by a Dirac-Hartree approximation.
Artificial neural networks are trained by a standard backpropagation learning algorithm with regularization to model and predict the systematics of -decay of heavy and superheavy nuclei. This approach to regression is implemented in two alternative modes: (i) construction of a statistical global model based solely on available experimental data for alpha-decay half-lives, and (ii) modeling of the {\it residuals} between the predictions of state-of-the-art phenomenological model (specifically, the effective liquid-drop model (ELDM)) and experiment. Analysis of the results provide insights on the strengths and limitations of this application of machine learning (ML) to exploration of the nuclear landscape in regions beyond the valley of stability.
A common method of adjusting the metal-insulator transition temperature of M$_{1}$ VO$_{2}$ is via disruption of the Peierls pairing by doping, or inputting stress or strain. However, since adding even small amounts of dopants will change the band structure, it is unclear how doped VO$_{2}$ retains its insulating character observed in experiments. While strong correlations may be responsible for maintaining a gap, theoretical evidence for this has been very difficult to obtain due to the complexity of the many-body problem involved. In this work we use GW calculations modified to include strong local $\textbf{k}$-space interactions to investigate the changes in band structure from tungsten doping. We find that the combination of carrier doping and the experimentally observed structural defects introduced by inclusion of tungsten are consistent with a change from band-like to Mott-insulating behavior.
The flattening of the 10mu silicate emission feature observed in the spectra of T Tauri and Herbig Ae/Be stars is usually interpreted as an indicator of grain growth. We show in this paper that a similar behaviour of the feature shape occurs when the porosity of composite grains varies. The fluffy aggregates, having inclusions of different sizes, were modeled by multi-layered spheres consisting of amorphous carbon, amorphous silicate and vacuum. It is also found that the inclusion of crystalline silicates in composite porous particles can lead to a shift of the known resonances and production of new ones.
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of random variables. However, every now and again we are forced to deal with non-distributional properties. In this paper we investigate how different random variables with the same distribution can be. Specifically, we construct random variables that are all uniformly distributed on the unit interval, but that nonetheless have strikingly different properties.
Traditional cryptography is facing great challenges with the development of quantum computing. Not only public-key cryptography, the applications of quantum algorithms to symmetric cryptanalysis has also drawn more and more attention. In this paper, we apply quantum algorithms to the miss-in-the-middle technique and propose a quantum algorithm for finding impossible differentials of general block ciphers. We prove that, as long as the attacked block cipher satisfies certain algebraic conditions, the outputs of the quantum algorithm will be impossible differentials of it except for a negligible probability. The proposed quantum algorithm has polynomial quantum complexity and does not require any quantum or classical query to the encryption oracle of the block cipher. Compared with traditional miss-in-the-middle technique, which is difficult to find impossible differentials as the number of rounds increases, the quantum version of miss-in-the-middle technique proposed in this paper is more conducive to find impossible differentials when the block cipher has a large number of rounds.
Structural symmetry breaking in magnetic materials is responsible for a variety of outstanding physical phenomena. Examples range from the existence of multiferroics, to current induced spin orbit torques (SOT) and the formation of topological magnetic structures. In this letter we bring into light a novel effect of the structural inversion asymmetry (SIA): a chiral damping mechanism. This phenomenon is evidenced by measuring the field driven domain wall (DW) motion in perpendicularly magnetized asymmetric Pt/Co/Pt trilayers. The difficulty in evidencing the chiral damping is that the ensuing DW dynamics exhibit identical spatial symmetry to those expected from the Dzyaloshinskii-Moriya interaction (DMI). Despite this fundamental resemblance, the two scenarios are differentiated by their time reversal properties: while DMI is a conservative effect that can be modeled by an effective field, the chiral damping is purely dissipative and has no influence on the equilibrium magnetic texture. When the DW motion is modulated by an in-plane magnetic field, it reveals the structure of the internal fields experienced by the DWs, allowing to distinguish the physical mechanism. The observation of the chiral damping, not only enriches the spectrum of physical phenomena engendered by the SIA, but since it can coexists with DMI it is essential for conceiving DW and skyrmion devices.