ShantanuT01/DACTYL-Pretraining huggingface dataset:
In neuroimaging studies, the human cortex is commonly modeled as a sphere to preserve the topological structure of the cortical surface. Cortical neuroimaging measures hence can be modeled in spherical representation. In this work, we explore analyzing the human cortex using spherical CNNs in an Alzheimer's disease (AD) classification task using cortical morphometric measures derived from structural MRI. Our results show superior performance in classifying AD versus cognitively normal and in predicting MCI progression within two years, using structural MRI information only. This work demonstrates for the first time the potential of the spherical CNNs framework in the discriminative analysis of the human cortex and could be extended to other modalities and other neurological diseases.
We predict that a temperature gradient can induce a magnon-mediated intrinsic torque and a transverse spin current in systems with non-trivial magnon Berry curvature. With the help of a microscopic linear response theory of nonequilibrium magnon-mediated torques and spin currents we identify the interband and intraband components that manifest in ferromagnets with Dzyaloshinskii-Moriya interactions and magnetic textures. To illustrate and assess the importance of such effects, we apply our theory to the magnon-mediated spin Nernst and torque responses in a kagome lattice ferromagnet.
Many animals and humans process the visual field with a varying spatial resolution (foveated vision) and use peripheral processing to make eye movements and point the fovea to acquire high-resolution information about objects of interest. This architecture results in computationally efficient rapid scene exploration. Recent progress in self-attention-based Vision Transformers, an alternative to the traditionally convolution-reliant computer vision systems. However, the Transformer models do not explicitly model the foveated properties of the visual system nor the interaction between eye movements and the classification task. We propose Foveated Transformer (FoveaTer) model, which uses pooling regions and eye movements to perform object classification tasks using a Vision Transformer architecture. Using square pooling regions or biologically-inspired radial-polar pooling regions, our proposed model pools the image features from the convolution backbone and uses the pooled features as an input to transformer layers. It decides on subsequent fixation location based on the attention assigned by the Transformer to various locations from past and present fixations. It dynamically allocates more fixation/computational resources to more challenging images before making the final image category decision. Using five ablation studies, we evaluate the contribution of different components of the Foveated model. We perform a psychophysics scene categorization task and use the experimental data to find a suitable radial-polar pooling region combination. We also show that the Foveated model better explains the human decisions in a scene categorization task than a Baseline model. We demonstrate our model's robustness against PGD adversarial attacks with both types of pooling regions, where we see the Foveated model outperform the Baseline model.
Si(100) surfaces were prepared by wet-chemical etching followed by 0.3-1.5keV Ar ion sputtering, either at elevated or room temperature. After a brief anneal under ultrahigh vacuum conditions, the resulting surfaces were examined by scanning tunneling microscopy. We find that wet-chemical etching alone cannot produce a clean and flat Si(100) surface. However, subsequent 300eV Ar ion sputtering at room temperature followed by a 973K anneal yields atomically clean and flat Si(100) surfaces suitable for nanoscale device fabrication.
The $ND\Lambda_c$ coupling constant is evaluated in a full QCD sum rule calculation. We study the Borel sum rule for the three point function of one pseudoscalar one nucleon and one $\Lambda_c$ current up to order seven in the operator product expansion. The Borel transform is performed with respect to the nucleon and $\Lambda_c$ momenta, which are taken to be equal, whereas the momentum $q^2$ of the pseudoscalar vertex is taken to be zero. This coupling constant is relevant in the meson cloud description of the nucleon which has been recently used to explain exotic events observed by the H1 and ZEUS Collaborations at HERA.
Convex geometry is a closure space $(G,\phi)$ with the anti-exchange property. A classical result of Edelman and Jamison (1985) claims that every finite convex geometry is a join of several linear sub-geometries, and the smallest number of such sub-geometries necessary for representation is called the convex dimension. In our work we find necessary and sufficient conditions on a closure operator $\phi$ of convex geometry $(G,\phi)$ so that its convex dimension equals 2, equivalently, they are represented by segments on a line. These conditions can be checked in polynomial time in two parameters: the size of the base set $|G|$ and the size of the implicational basis of $(G,\phi)$.
We say that $(a_1,...,a_k)$ is pairwise non-coprime if $\gcd(a_i,a_j) \ne 1$ for all $1 \le i <j \le k$. Let $a_1,a_2,a_3$ be positive integers less than $H$. We obtain an asymptotic formula for the number of $(a_1,a_2,a_3)$ that are pairwise non-coprime. The probability that a randomly chosen unbounded positive integer triple is pairwise non-coprime is approximately 17.4%. Let $\varphi(n)$ be the Euler totient function. We also give an upper bound on the error term in an asymptotic formula for $\sum_{n=1}^H (\varphi(n)/n)^m$ for $m \ge 2$ and as $H \rightarrow \infty$.
Motivated by the recent interest in the possible ordering of the CH$_3$NH$_3$ dipoles in the material CH$_3$NH$_3$PbI$_3$, we investigate the properties of domain boundaries in a simple cubic lattice of dipoles. We perform numerical simulations in which we set the boundary conditions such that the dipoles at opposite sides of the simulated sample are ordered in different directions, hence simulating a domain boundary. We calculate the lowest energy configuration under this constraint. We find that if we consider only dipole-dipole interactions the dipole orientations tend to gradually transform between the two orientations at the two opposite ends of the sample. When we take into consideration the finite spatial size of the CH$_3$NH$_3$ molecules and go beyond the point dipole approximation, we find that the domain boundary becomes sharper. For the parameters of CH$_3$NH$_3$PbI$_3$, our results indicate that the optimal energy structure has a boundary region of a width on the order of a single unit cell.
We consider the synchrotron emission from electrons out in the Galactic halo bubble region where the Fermi bubble structures reside. Utilising a simple analytical expression for the non-thermal electron distribution and a toy magnetic field model, we simulate polarised synchrotron emission maps at a frequency of 30~GHz. Comparing these maps with observational data, we obtain constraints on the parameters of our toy Galactic halo bubble magnetic field model. Utilising this parameter value range for the toy magnetic field model, we determine the corresponding range of arrival directions and suppression factors of ultra high energy cosmic rays (UHECRs) from potential local source locations. We find that high levels of flux suppression (down to 2\%) and large deflection angles ($\geq 80^{\circ}$) are possible for source locations whose line-of-sight pass through the Galactic halo bubble region. We conclude that the magnetic field out in the Galactic halo bubble region can strongly dominate the level of deflection UHECRs experience whilst propagating from local sources to Earth.
We present a new method to model a HST/COS spectrum, aimed to analyze intrinsic UV absorption from the outflow of Mrk 290, a Seyfert I galaxy. We use newly updated XSTAR to generate photoionization models for the intrinsic absorption from the AGN outflow, the line emission from the AGN broad and narrow line regions, and the local absorption from high velocity clouds and Galactic interstellar medium. The combination of these physical models accurately fit the COS spectrum. Three intrinsic absorbers outflowing with velocities ~500 km/s are identified, two of which are found directly from two velocity components of the N V and C IV doublets, while the third is required by the extra absorption in the Lyman alpha. Their outflow velocities, ionization states and column densities are consistent with the lowest and moderately ionization warm absorbers (WAs) in the X-ray domain found by Chandra observations, suggesting an one-to-one correspondence between the absorbing gas in the UV and X-ray bands. The small turbulent velocities of the WAs (v_turb~<100 km/s) support our previous argument from the X-ray study that the absorbers originate from the inner side of the torus due to thermal evaporation. Given the covering fractions of ~65% for the three WAs, we deduce that the lengths and the thicknesses of the WAs are comparable, which indicates that the geometry of WAs are more likely clouds rather than flat and thin layers. In addition, the modeling of the broad line emission suggests a higher covering fraction of clouds when they are very closer to the black hole.
A homogeneous set of UBV photometry (354 data points obtained between 1983 and 1998) for the Be/X-ray binary A0535+26 = V725Tau is analysed, aiming to look for possible periodic component(s). After subtraction of the long-term variation it was found that only a 103-day periodic component remains in the power spectra in both the V and B colour bands. The probability of chance occurrence of such a peak is less than 0.1%. There are no signs of optical variability at the X-ray period (111 d). We discuss possible reasons for a 103-day modulation and suggest that it corresponds to a beat frequency of the orbital period of the neutron star and the precession period (~1400 d) either of an accretion disc around the neutron star or a warped decretion disc around the Be star.
We prove birational superrigidity of generic Fano complete intersections $V$ of type $2^{k_1}\cdot 3^{k_2}$ in the projective space ${\mathbb P}^{2k_1+3k_2}$, under the condition that $k_2\geq 2$ and $k_1+2k_2=\mathop{\rm dim} V\geq 12$, and of a few families of Fano complete intersections of dimension 10 and 11. This is the third version: minor corrections were made, including a few typos.
Pick n points independently at random in R^2, according to a prescribed probability measure mu, and let D^n_1 <= D^n_2 <= ... be the areas of the binomial n choose 3 triangles thus formed, in non-decreasing order. If mu is absolutely continuous with respect to Lebesgue measure, then, under weak conditions, the set {n^3 D^n_i : i >= 1} converges as n --> infinity to a Poisson process with a constant intensity c(mu). This result, and related conclusions, are proved using standard arguments of Poisson approximation, and may be extended to functionals more general than the area of a triangle. It is proved in addition that, if mu is the uniform probability measure on the region S, then c(mu) <= 2/|S|, where |S| denotes the area of S. Equality holds in that c(mu) = 2/|S| if S is convex, and essentially only then. This work generalizes and extends considerably the conclusions of a recent paper of Jiang, Li, and Vitanyi.
The Pan-STARRS (PS1) Medium Deep Survey discovered over 5,000 likely supernovae (SNe) but obtained spectral classifications for just 10% of its SN candidates. We measured spectroscopic host galaxy redshifts for 3,147 of these likely SNe and estimate that $\sim$1,000 are Type Ia SNe (SNe Ia) with light-curve quality sufficient for a cosmological analysis. We use these data with simulations to determine the impact of core-collapse SN (CC SN) contamination on measurements of the dark energy equation of state parameter, $w$. Using the method of Bayesian Estimation Applied to Multiple Species (BEAMS), distances to SNe Ia and the contaminating CC SN distribution are simultaneously determined. We test light-curve based SN classification priors for BEAMS as well as a new classification method that relies upon host galaxy spectra and the association of SN type with host type. By testing several SN classification methods and CC SN parameterizations on large SN simulations, we estimate that CC SN contamination gives a systematic error on $w$ ($\sigma_w^{CC}$) of 0.014, 29% of the statistical uncertainty. Our best method gives $\sigma_w^{CC} = 0.004$, just 8% of the statistical uncertainty, but could be affected by incomplete knowledge of the CC SN distribution. This method determines the SALT2 color and shape coefficients, $\alpha$ and $\beta$, with $\sim$3% bias. However, we find that some variants require $\alpha$ and $\beta$ to be fixed to known values for BEAMS to yield accurate measurements of $w$. Finally, the inferred abundance of bright CC SNe in our sample is greater than expected based on measured CC SN rates and luminosity functions.
Recently, it has been shown that cross-correlating CMB lensing and 3D cosmic shear allows to considerably tighten cosmological parameter constraints. We investigate whether similar improvement can be achieved in a conventional tomographic setup. We present Fisher parameter forecasts for a Euclid-like galaxy survey in combination with different ongoing and forthcoming CMB experiments. In contrast to a fully three-dimensional analysis we find only marginal improvement. Assuming Planck-like CMB data we show that including the full covariance of the combined CMB and cosmic shear data improves the dark energy figure of merit by only three per cent. The marginalized error on the sum of neutrino masses is reduced at the same level. For a next generation CMB satellite mission such as Prism the predicted improvement of the dark energy figure of merit amounts to approximately 25 per cent. Furthermore, we show that the small improvement is contrasted by an increased bias in the dark energy parameters when the intrinsic alignment of galaxies is not correctly accounted for in the full covariance matrix.
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are marked by adding elements to them that impart a specific phase shift to the particle as it enters or leaves the edge. If the complete graph has N vertices and the subgraph has K vertices, the particle becomes localized on the subgraph in O(N/K) steps. This leads to a quantum search that is quadratically faster than a corresponding classical search. We show how to implement the quantum walk using a quantum circuit and a quantum oracle, which allows us to specify the resource needed for a quantitative comparison of the efficiency of classical and quantum searches -- the number of oracle calls.
We consider the genus of $20$ classes of unimodular Hermitian lattices of rank $12$ over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global Arthur parameters for the associated automorphic representations, which recover the computed Hecke eigenvalues. Congruences between Hecke eigenspaces, combined with the assumed parameters, recover known congruences for classical modular forms, and support new instances of conjectured Eisenstein congruences for $\mathbb{U}(2,2)$ automorphic forms.
The nanoscale distribution of magnetic anisotropies was measured in core@shell MnFe$_2$O$_4$@CoFe$_2$O$_4$ 7.0 nm particles using a combination of element selective magnetic spectroscopies with different probing depths. As this picture is not accessible by any other technique, emergent magnetic properties were revealed. The coercive field is not constant in a whole nanospinel. The very thin (0.5 nm) CoFe$_2$O$_4$ hard shell imposes a strong magnetic anisotropy to the otherwise very soft MnFe$_2$O$_4$ core: a large gradient in coercivity was measured inside the MnFe$_2$O$_4$ core with lower values close to the interface region, while the inner core presents a substantial coercive field (0.54 T) and a very high remnant magnetization (90% of the magnetization at saturation).
A general study of excitations up to two-phonon states is carried out using the intrinsic-state formalism of the Interacting Boson Model (IBM). Spectra and transitions for the different dynamical symmetries are analyzed and the correspondence with states in the laboratory frame is established. The influence of multi-phonon states is discussed. The approach is useful in problems where the complexity of the IBM spectrum renders the analysis in the laboratory frame difficult.
We define, basing upon semiorthogonal decompositions of $\Db(X)$, categorical representability of a projective variety $X$ and describe its relation with classical representabilities of the Chow ring. For complex threefolds satisfying both classical and categorical representability assumptions, we reconstruct the intermediate Jacobian from the semiorthogonal decomposition. We discuss finally how categorical representability can give useful information on the birational properties of $X$ by providing examples and stating open questions.
The aim of this note is to present the recent results in [16] where we provide the existence of solutions of some nonlinear resonant PDEs on the 2-dimensional torus exchanging energy among Fourier modes in a \emph{chaotic-like} way. We say that a transition of energy is \emph{chaotic-like} if either the choice of activated modes or the time spent in each transfer can be chosen randomly. We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations. The key point of the construction of the special solutions is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form of those equations.
Current and future imaging surveys will measure cosmic shear with a statistical precision that demands a deeper understanding of potential systematic biases in galaxy shape measurements than has been achieved to date. We investigate the effects of using the point spread function (PSF) measured with stars to determine the shape of a galaxy that has a different spectral energy distribution (SED) than the star. We demonstrate that a wavelength dependent PSF size, for example as may originate from atmospheric seeing or the diffraction limit of the primary aperture, can introduce significant shape measurement biases. This analysis shows that even small wavelength dependencies in the PSF may introduce biases, and hence that achieving the ultimate precision for weak lensing from current and future imaging surveys will require a detailed understanding of the wavelength dependence of the PSF from all sources, including the CCD sensors.
In this paper we describe the pseudoparticles, holons, and spinons whose occupancy configurations describe the energy eigenstates of the one-dimensional (1D) Hubbard model in terms of rotated electrons. Rotated electrons are related to electrons by a mere unitary transformation such that rotated electron double occupation is a good quantum number. Moreover, we introduce the concepts of local pseudoparticle and effective pseudoparticle lattice. Our findings provide useful information about the relation of the exotic pseudoparticles, holons, and spinons that diagonalize the non-perturbative many-electron problem to the original electrons. We provide an example showing how the derived local pseudoparticle representation can be used in the evaluation of finite-energy few-electron spectral function expressions.
The field-theoretic one-loop effective action in a static scalar background depending nontrivially on a single spatial coordinate is related, in the proper-time formalism, to the trace of the evolution kernel (or heat kernel) for an appropriate, one dimensional, quantum-mechanical Hamiltonian. We describe a recursive procedure applicable to these traces for shape-invariant Hamiltonians, resolving subtleties from the continuum mode contributions by utilizing the expression for the regularized Witten index. For some cases which include those of domain-wall-type scalar backgrounds, our recursive procedure yields the full expression for the scalar or fermion one-loop effective action in both (1+1) and (3+1)-dimensions.
There is an observational correlation between astrophysical shocks and non-thermal particle distributions extending to high energies. As a first step toward investigating the possible feedback of these particles on the shock at the microscopic level, we perform particle-in-cell (PIC) simulations of a simplified environment consisting of uniform, interpenetrating plasmas, both with and without an additional population of cosmic rays. We vary the relative density of the counterstreaming plasmas, the strength of a homogeneous parallel magnetic field, and the energy density in cosmic rays. We compare the early development of the unstable spectrum for selected configurations without cosmic rays to the growth rates predicted from linear theory, for assurance that the system is well represented by the PIC technique. Within the parameter space explored, we do not detect an unambiguous signature of any cosmic-ray-induced effects on the microscopic instabilities that govern the formation of a shock. We demonstrate that an overly coarse distribution of energetic particles can artificially alter the statistical noise that produces the perturbative seeds of instabilities, and that such effects can be mitigated by increasing the density of computational particles.
This note aims to give an explicit solution for backward stochastic Volterra integral equations with linear time delayed generators. The process $Y$ is expressed by an integral whose kernel is explicitly given. The processes $Z$ is expressed by Hida-Malliavin derivatives involving $Y$.
We have identified a first group of 33 new candidates for symbiotic stars (SySt) of the accreting-only variety among the 600,255 stars so far observed by the GALAH high-resolution spectroscopic survey of the Southern Hemisphere, more than doubling the number of those previously known. GALAH aims to high latitudes and this offers the possibility to sound the Galaxy for new SySt away from the usual Plane and Bulge hunting regions. In this paper we focus on SySt of the M spectral type, showing an Halpha emission with a peak in excess of 0.5 above the adjacent continuum level, and not affected by coherent radial pulsations. These constraints will be relaxed in future studies. The 33 new candidate SySt were subjected to a vast array of follow-up confirmatory observations (X-ray/UV observations with the Swift satellite, search for optical flickering, presence of a near-UV upturn in ground-based photometric and spectroscopic data, radial velocity changes suggestive of orbital motion, variability of the emission line profiles). According to Gaia eDR3 parallaxes, the new SySt are located at the tip of the Giant Branch, sharing the same distribution in M(Ks) of the well established SySt. The accretion luminosities of the new SySt are in the range 1-10 Lsun, corresponding to mass-accretion rates of 0.1-1x10(-9) Msun/yr for WDs of 1 Msun. The M giant of one of the new SySt presents a large Lithium over-abundance.