ShantanuT01/DACTYL-Pretraining huggingface dataset:
If Alice and Bob start out with an entangled state $|\Psi_{AB}\rangle$, Bob may update his state to $|\varphi_B\rangle$ either by performing a suitable measurement himself, or by receiving the information that a measurement by Alice has steered that state. While Bob's update on his state is identical, his update on Alice's state differs: if Bob has performed the measurement, he has steered the state $|\chi_{\leftarrow}(\varphi)\rangle_A$ of Alice; if Alice has made the measurement, to steer $|\varphi\rangle_B$ on Bob she must have found a different state $|\chi_{\rightarrow}(\varphi)\rangle_A$. Based on this observation, a consequence of the well-known `Hardy's ladder', we show that information from direct measurement must trump inference from steering. The erroneous belief that both paths should lead to identical conclusions can be traced to the usual prejudice that measurements should reveal a pre-existing state of affairs. We also prove a technical result on Hardy's ladder: the minimum overlap between the steered and the steering state is $2\sqrt{p_{0}p_{n-1}}/(p_0+p_{n-1})$, where $p_0$ and $p_{n-1}$ are the smallest (non-zero) and the largest Schmidt coefficients of $|\Psi\rangle_{AB}$.
Predictive models allow subject-specific inference when analyzing disease related alterations in neuroimaging data. Given a subject's data, inference can be made at two levels: global, i.e. identifiying condition presence for the subject, and local, i.e. detecting condition effect on each individual measurement extracted from the subject's data. While global inference is widely used, local inference, which can be used to form subject-specific effect maps, is rarely used because existing models often yield noisy detections composed of dispersed isolated islands. In this article, we propose a reconstruction method, named RSM, to improve subject-specific detections of predictive modeling approaches and in particular, binary classifiers. RSM specifically aims to reduce noise due to sampling error associated with using a finite sample of examples to train classifiers. The proposed method is a wrapper-type algorithm that can be used with different binary classifiers in a diagnostic manner, i.e. without information on condition presence. Reconstruction is posed as a Maximum-A-Posteriori problem with a prior model whose parameters are estimated from training data in a classifier-specific fashion. Experimental evaluation is performed on synthetically generated data and data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Results on synthetic data demonstrate that using RSM yields higher detection accuracy compared to using models directly or with bootstrap averaging. Analyses on the ADNI dataset show that RSM can also improve correlation between subject-specific detections in cortical thickness data and non-imaging markers of Alzheimer's Disease (AD), such as the Mini Mental State Examination Score and Cerebrospinal Fluid amyloid-$\beta$ levels. Further reliability studies on the longitudinal ADNI dataset show improvement on detection reliability when RSM is used.
In this note we present a fast algorithm that finds for any $r$ the number $N_r$ of $\mathbb{F}_{q^r}$ rational points on a smooth absolutely irreducible curve $C$ defined over $\mathbb{F}_{q}$ assuming that we know $N_1,\cdots,N_g$, where $g$ is the genus of $C$. The proof of its validity is given in detail and its working are illustrated with several examples. In an Appendix we list the Python function in which we have implemented the algorithm together with other routines used in the examples.
Using effective theories for jets and heavy quarks it is possible to prove that the double differential top-antitop invariant mass distribution for the process $e^+e^-\to t\bar t$ in the resonance region for c.m. energies $Q$ much larger than the top mass can factorized into perturbatively computable hard coefficients and jet functions and a non-perturbative soft function. For invariant mass prescriptions based on hemispheres defined with respect to the thrust axis the soft function can be extracted from massless jet event shape distributions. This approach allows in principle for top mass determinations without uncertainties from hadronization using the reconstruction method and to quantify the top mass scheme dependence of the measured top quark mass value.
We have used the Submillimeter Array to image, at ~1" resolution, C2H(3-2) emission from the molecule-rich circumstellar disks orbiting the nearby, classical T Tauri star systems TW Hya and V4046 Sgr. The SMA imaging reveals that the C2H emission exhibits a ring-like morphology within each disk, the inner hole radius of the C2H ring within the V4046 Sgr disk (~70 AU) is somewhat larger than than of its counterpart within the TW Hya disk (~45 AU). We suggest that, in each case, the C2H emission likely traces irradiation of the tenuous surface layers of the outer disks by high-energy photons from the central stars.
We argue that the behavior of string theory at high temperature and high longitudinal boosts, combined with the emergence of p-branes as necessary ingredients in various string dualities, point to a possible reformulation of strings, as well as p-branes, as composites of bits. We review the string-bit models, and suggest generalizations to incorporate p-branes.
We analyze the two-orbital Hubbard model by means of the Composite Operator Method with the aim at studying the phenomenon of orbital selective Mott transition (OSMT). The model contains an interorbital interaction $U'$, in addition to the usual intraorbital one $U$. As warming-up approximation, we use a basis of two operators only, the Hubbard operators. The analysis of the density of states at the chemical potential as a function of the ratio between the bandwidths of the two orbitals shows the clear signature of an orbital selective Mott transition as expected.
Zero-shot learning, the task of learning to recognize new classes not seen during training, has received considerable attention in the case of 2D image classification. However, despite the increasing ubiquity of 3D sensors, the corresponding 3D point cloud classification problem has not been meaningfully explored and introduces new challenges. In this paper, we identify some of the challenges and apply 2D Zero-Shot Learning (ZSL) methods in the 3D domain to analyze the performance of existing models. Then, we propose a novel approach to address the issues specific to 3D ZSL. We first present an inductive ZSL process and then extend it to the transductive ZSL and Generalized ZSL (GZSL) settings for 3D point cloud classification. To this end, a novel loss function is developed that simultaneously aligns seen semantics with point cloud features and takes advantage of unlabeled test data to address some known issues (e.g., the problems of domain adaptation, hubness, and data bias). While designed for the particularities of 3D point cloud classification, the method is shown to also be applicable to the more common use-case of 2D image classification. An extensive set of experiments is carried out, establishing state-of-the-art for ZSL and GZSL on synthetic (ModelNet40, ModelNet10, McGill) and real (ScanObjectNN) 3D point cloud datasets.
The mean-field limit of systems of rank-based interacting diffusions is known to be described by a nonlinear diffusion process. We obtain a similar description at the level of stationary distributions. Our proof is based on explicit expressions for the Laplace transforms of these stationary distributions and yields convergence of the marginal distributions in Wasserstein distances of all orders. We highlight the consequences of this result on the study of rank-based models of equity markets, such as the Atlas model.
For an $\cF_T$-measurable payoff of a European type contingent claim, the recursive utility process/dynamic risk measure can be described by the adapted solution to a backward stochastic differential equation (BSDE). However, for an $\cF_T$-measurable stochastic process (called a position process, not necessarily $\dbF$-adapted), mimicking BSDE's approach will lead to a time-inconsistent recursive utility/dynamic risk measure. It is found that a more proper approach is to use the adapted solution to a backward stochastic Volterra integral equation (BSVIE). The corresponding notions are called equilibrium recursive utility and equilibrium dynamic risk measure, respectively. Motivated by this, the current paper is concerned with BSVIEs whose generators are allowed to have quadratic growth (in $Z(t,s)$). The existence and uniqueness for both the so-called adapted solutions and adapted M-solutions are established. A comparison theorem for adapted solutions to the so-called Type-I BSVIEs is established as well. As consequences of these results, some general continuous-time equilibrium dynamic risk measures and equilibrium recursive utility processes are constructed.
A semimicroscopical approach is formulated to describe the direct nucleon decay of various giant resonances in intermediate and heavy mass spherical nuclei. The approach consists in: (i) the exact continuum-RPA calculations for amplitudes of the reactions accompanied by excitation and the nucleon decay of the collective particle-hole states (doorway states); (ii) the Breit-Wigner parametrization of the RPA reaction-amplitudes in the vicinity of the giant giant-resonance energy and evaluation of the doorway-state parameter (the energy, entrance and partial nucleon, escape widths); (iii) the phenomenological consideration for the doorway-state coupling to many-particle configurations with the use of reasonable statistical assumptions and derivation on this base the expressions for the energy-averaged reaction amplitudes. The nuclear mean field and quasiparticle interaction are the input quantities for calculations. Examples of description for the direct nucleon decay of a number of giant resonances in the $^{208}Pb$ parent nucleus are given together with the comparison with corresponding experimental data.
The recent trend in multiple object tracking (MOT) is heading towards leveraging deep learning to boost the tracking performance. However, it is not trivial to solve the data-association problem in an end-to-end fashion. In this paper, we propose a novel proposal-based learnable framework, which models MOT as a proposal generation, proposal scoring and trajectory inference paradigm on an affinity graph. This framework is similar to the two-stage object detector Faster RCNN, and can solve the MOT problem in a data-driven way. For proposal generation, we propose an iterative graph clustering method to reduce the computational cost while maintaining the quality of the generated proposals. For proposal scoring, we deploy a trainable graph-convolutional-network (GCN) to learn the structural patterns of the generated proposals and rank them according to the estimated quality scores. For trajectory inference, a simple deoverlapping strategy is adopted to generate tracking output while complying with the constraints that no detection can be assigned to more than one track. We experimentally demonstrate that the proposed method achieves a clear performance improvement in both MOTA and IDF1 with respect to previous state-of-the-art on two public benchmarks. Our code is available at https://github.com/daip13/LPC_MOT.git.
The black hole binary Cygnus X-1 was observed in late-2012 with the Nuclear Spectroscopic Telescope Array (NuSTAR) and Suzaku, providing spectral coverage over the ~1-300 keV range. The source was in the soft state with a multi-temperature blackbody, power-law, and reflection components along with absorption from highly ionized material in the system. The high throughput of NuSTAR allows for a very high quality measurement of the complex iron line region as well as the rest of the reflection component. The iron line is clearly broadened and is well-described by a relativistic blurring model, providing an opportunity to constrain the black hole spin. Although the spin constraint depends somewhat on which continuum model is used, we obtain a*>0.83 for all models that provide a good description of the spectrum. However, none of our spectral fits give a disk inclination that is consistent with the most recently reported binary values for Cyg X-1. This may indicate that there is a >13 degree misalignment between the orbital plane and the inner accretion disk (i.e., a warped accretion disk) or that there is missing physics in the spectral models.
We construct a scaling function $f(\psi^{\prime})$ for inclusive electron scattering from nuclei within the Coherent Density Fluctuation Model (CDFM). The latter is a natural extension to finite nuclei of the Relativistic Fermi Gas (RFG) model within which the scaling variable $\psi^{\prime}$ was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental data for different transfer momenta showing superscaling for negative values of $\psi^{\prime}$, including those smaller than -1.
We study the transport of ultracold impurity atoms immersed in a Bose-Einstein condensate (BEC) and trapped in a tight optical lattice. Within the strong-coupling regime, we derive an extended Hubbard model describing the dynamics of the impurities in terms of polarons, i.e. impurities dressed by a coherent state of Bogoliubov phonons. Using a generalized master equation based on this microscopic model we show that inelastic and dissipative phonon scattering results in (i) a crossover from coherent to incoherent transport of impurities with increasing BEC temperature and (ii) the emergence of a net atomic current across a tilted optical lattice. The dependence of the atomic current on the lattice tilt changes from ohmic conductance to negative differential conductance within an experimentally accessible parameter regime. This transition is accurately described by an Esaki-Tsu-type relation with the effective relaxation time of the impurities as a temperature-dependent parameter.
Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree-3 connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes.
The improvement of sensitivity to gravitational waves (GWs) at lower frequencies is still challenging on account of displacement noise. One of the solutions is the neutron displacement-noise-free interferometer (DFI). We focus on a simplification of the detector configuration by taking advantage of the ability to adjust the neutron speed depending on the configuration. The new configuration consists of two beamsplitters and two mirrors, which constitute a single Mach-Zehnder interferometer (MZI). It is simpler than the configuration with two MZIs in previous research. All displacement noise of mirrors and beamsplitters can be canceled in the frequency domain. This cancellation can be explained intuitively using a phasor diagram.
In this paper, we present a canonical structure for controlling information flow in neural networks with an efficient feedback routing mechanism based on a strategy of Distributed Iterative Gating (DIGNet). The structure of this mechanism derives from a strong conceptual foundation and presents a light-weight mechanism for adaptive control of computation similar to recurrent convolutional neural networks by integrating feedback signals with a feed-forward architecture. In contrast to other RNN formulations, DIGNet generates feedback signals in a cascaded manner that implicitly carries information from all the layers above. This cascaded feedback propagation by means of the propagator gates is found to be more effective compared to other feedback mechanisms that use feedback from the output of either the corresponding stage or from the previous stage. Experiments reveal the high degree of capability that this recurrent approach with cascaded feedback presents over feed-forward baselines and other recurrent models for pixel-wise labeling problems on three challenging datasets, PASCAL VOC 2012, COCO-Stuff, and ADE20K.
An important question in solar physics is whether solar microflares, the smallest currently observable flare events in X-rays, possess the same energetic properties as large flares. Recent surveys have suggested that microflares may be less efficient particle accelerators than large flares, and hence contribute less nonthermal energy, which may have implications for coronal heating mechanisms. We therefore explore the energetic properties of microflares by combining Extreme Ultraviolet (EUV) and X-ray measurements.   We present forward-fitting differential emission measure (DEM) analysis of 10 microflares. The fitting is constrained by combining, for the first time, high temperature RHESSI observations and flux data from SDO/AIA. Two fitting models are tested for the DEM; a Gaussian distribution and a uniform DEM profile. A Gaussian fit proved unable to explain the observations for any of the studied microflares. However, 8 of 10 events studied were reasonably fit by a uniform DEM profile. Hence microflare plasma can be considered to be significantly multi-thermal, and may not be significantly peaked or contain resolvable fine structure, within the uncertainties of the observational instruments.   The thermal and non-thermal energy is estimated for each microflare, comparing the energy budget with an isothermal plasma assumption. From the multithermal fits the minimum non-thermal energy content was found to average approximately 30% of the estimated thermal energy. By comparison, under an isothermal model the non-thermal and thermal energy estimates were generally comparable. Hence, multi-thermal plasma is an important consideration for solar microflares that substantially alters their thermal and non-thermal energy content.
In this paper we review the hole argument for the space-time points and elementary particles and generalize the hole argument to include all geometric object fields and diffeomorphisms; and, by application of forgetful functors to abstract from differentiability and even continuity, the hole argument is applied to a much wider class of mathematical objects. We discuss the problem concerning the individuation of the objects in more general settings such that fibered manifolds, fibered sets and n-ary relations.
We formulate an energy-storage concept based on the free energy associated with metastable magnetic configurations. Despite the active, magnetic region of the battery being electrically insulating, it can sustain effective hydrodynamics of spin textures, whose conservation law is governed by topology. To illustrate the key physics and potential functionality, we focus here on the simplest quasi-one-dimensional case of planar winding of the magnetic order parameter. The energy is stored in the metastable winding number, which can be injected electrically by an appropriately tailored spin torque. Due to the nonvolatility and the endurance of magnetic systems, the injected energy can be stored essentially indefinitely, with charging/discharging cycles that do not degrade over time.
The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.
The Leuven workshop on the `Quantum Structure of Space-time and the Geometrical Nature of the Fundamental Interactions' had a special session dedicated to the memory of Sonia Stanciu. This is the summary of a talk delivered by the author on this occasion.
The presence of Multiple Stellar Populations (MSPs) in Galactic Globular Clusters (GCs) is a poorly understood phenomenon. By probing different spectral ranges that are affected by different absorption lines using the multi-band photometric survey S-PLUS, we study four GCs -- NGC 104, NGC 288, NGC 3201 and NGC 7089 -- that span a wide range in metallicities. With the combination of broad and narrow-band photometry in 12 different filters from 3485A (u) to 9114A (z), we identified MSPs along the rectified red-giant branch in colour-magnitude diagrams (CMDs) and separated them using a K-means clustering algorithm. Additionally, we take advantage of the large Field of View of the S-PLUS detector to investigate radial trends in our sample. We report on six colour combinations that can be used to successfully identify two stellar populations in all studied clusters and show that they can be characterized as Na-rich and Na-poor. For both NGC 288 and NGC 7089, their radial profiles show a clear concentration of 2P. This directly supports the formation theories that propose an enrichment of the intra-cluster medium and subsequent star formation in the more dense central regions. However, in the case of NGC 3201, the trend is reversed. The 1P is more centrally concentrated, in direct contradiction with previous literature studies. NGC 104 shows a well-mixed population. We also constructed radial profiles up to 1 half-light radius of the clusters with HST data to highlight that radial differences are lost in the inner regions of the GCs and that wide-field studies are essential when studying this.
Dynamical conductivity spectra s(w) have been measured for a diverse range of heavy-fermion (HF) Ce and Yb compounds. A characteristic excitation peak has been observed in the mid-infrared region of s(w) for all the compounds, and has been analyzed in terms of a simple model based on conduction (c)-f electron hybridized band. A universal scaling is found between the observed peak energies and the estimated c-f hybridization strengths of these HF compounds. This scaling demonstrates that the model of c-f hybridized band can generally and quantitatively describe the charge excitation spectra of a wide range of HF compounds.
After an introduction to the sequential version of FORM and the mechanisms behind it we report on the status of our ongoing project of its parallelization. An analysis of the parallel platforms used is given and the structure of a parallel prototype of FORM is explained.
This paper intends to focus on the universal property of this Hesse pencil and of its twists. The main goal is to do this as explicit and elementary as possible, and moreover to do it in such a way that it works in every characteristic different from three.