ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study a nonlocal reaction-diffusion-mutation equation modeling the spreading of a cane toads population structured by a phenotypical trait responsible for the spatial diffusion rate. When the trait space is bounded, the cane toads equation admits traveling wave solutions [7]. Here, we prove a Bramson type spreading result: the lag between the position of solutions with localized initial data and that of the traveling waves grows as (3/(2$\lambda$ *)) log t. This result relies on a present-time Harnack inequality which allows to compare solutions of the cane toads equation to those of a Fisher-KPP type equation that is local in the trait variable.
We analyze the effect of foregrounds on the observed alignment of CMBR quadrupole and octopole. The alignment between these multipoles is studied by using a symmetry based approach which assigns a principal eigenvector (PEV) or an axis with each multipole. We determine the significance of alignment between these multipoles by using the Internal Linear Combination (ILC) 5 and 7 year map s and also the maps obtained by using the Internal Power Spectrum Estimation (IPSE) procedure. The effect of foreground cleaning is studied in detail within the framework of the IPSE method both analytically and numerically. By using simulated CMBR data, we study how the PEVs of the pure simulated CMB map differ from those of the final cleaned map. We find that, in general, the shift in the PEVs is relatively small and in random directions. Due to the random nature of the shift we conclude that it can only lead to misalignment rather than alignment of multipoles. We also directly estimate the significance of alignment by using simulated cleaned maps. We find that the results in this case are identical to those obtained by simple analytic estimate or by using simulated pure CMB maps.
In this paper, we provide an alternative method to calculate the values of generalized multiple Hurwitz zeta function at non-positive integers by means of \emph{Raabe}'s formula and the \textit{Bernoulli} numbers.
We check the accuracy of the constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two- and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away from the Fermi level. Using numerically exact quantum Monte Carlo simulations of the full and downfolded model we demonstrate that depending on filling the effective interaction in the low-energy theory is either barely screened, or antiscreened, in contrast to the cRPA prediction. This observation is explained by a functional renormalization group analysis which shows that the cRPA contribution to the screening is to a large extent cancelled by other diagrams in the direct particle-hole channel. We comment on the implications of this finding for the ab-initio estimation of interaction parameters in low-energy descriptions of solids.
We introduce a certain ring of rigid-analytic distributions on $p$-adic weight space (modulo torsion) and show that it is canonically isomorphic to Colmez's ring $B_{\mathrm{Sen}}$.
The ground state of the quantum spin ice candidate magnet Yb2Ti2O7 is known to be sensitive to weak disorder at the 1 percent level which occurs in single crystals grown from the melt. Powders produced by solid state synthesis tend to be stoichiometric and display large and sharp heat capacity anomalies at relatively high temperatures, with Tc about 0.26 K. We have carried out neutron elastic and inelastic measurements on well characterized and equilibrated stoichiometric powder samples of Yb2Ti2O7 which show resolution-limited Bragg peaks to appear at low temperatures, but whose onset correlates with temperatures much higher than Tc. The corresponding magnetic structure is best described as an ice-like splayed ferromagnet. The spin dynamics in Yb2Ti2O7 are shown to be gapless on an energy scale smaller than 0.09 meV at all temperatures, and organized into a continuum of scattering with vestiges of highly overdamped ferromagnetic spin waves present. These excitations differ greatly from conventional spin waves predicted for Yb2Ti2O7 s mean field ordered state, but appear robust to weak disorder as they are largely consistent with those displayed by non stoichiometric crushed single crystals and single crystals, as well as by powder samples of Yb2Ti2O7 s sister quantum magnet Yb2Sn2O7.
There are many examples of optimization problems whose associated polyhedra can be described much nicer, and with way less inequalities, by projections of higher dimensional polyhedra than this would be possible in the original space. However, currently not many general tools to construct such extended formulations are available. In this paper, we develop a framework of polyhedral relations that generalizes inductive constructions of extended formulations via projections, and we particularly elaborate on the special case of reflection relations. The latter ones provide polynomial size extended formulations for several polytopes that can be constructed as convex hulls of the unions of (exponentially) many copies of an input polytope obtained via sequences of reflections at hyperplanes. We demonstrate the use of the framework by deriving small extended formulations for the G-permutahedra of all finite reflection groups G (generalizing both Goeman's extended formulation of the permutahedron of size O(n log n) and Ben-Tal and Nemirovski's extended formulation with O(k) inequalities for the regular 2^k-gon) and for Huffman-polytopes (the convex hulls of the weight-vectors of Huffman codes).
Context. Sheen and collaborators recently found that a surprisingly large portion (38%) of massive early-type galaxies in heavy clusters show strong merger-related disturbed features. This contradicts the general understanding that massive clusters are hostile environments for galaxy mergers. Considering the significance of mergers in galaxy evolution, it is important to understand this. Aims. We aim to present a theoretical foundation that explains galaxy mergers in massive clusters. Methods. We used the N-body simulation technique to perform a cosmological-volume simulation and derive dark-halo merger trees. Then, we used the semi-analytic modeling technique to populate each halo with galaxies. We ran hydrodynamic simulations of galaxy mergers to estimate the lifetime of merger features for the imaging condition used by Sheen and collaborators. We applied this merger feature lifetime to our semi-analytic models. Finally, we counted the massive early-type galaxies in heavy model clusters that would show strong merger features. Results. While there still are substantial uncertainties, our preliminary results are remarkably close to the observed fraction of galaxies with merger features. Key ingredients for the success are twofold: firstly, the subhalo motion in dark haloes has been accurately traced, and, second, the lifetime of merger features has been properly estimated. As a result, merger features are expected to last very long in cluster environments. Many massive early-type galaxies in heavy clusters therefore show merger features not because they experience mergers in the current clusters in situ, but because they still carry their merger features from their previous halo environments. Conclusions. Investigating the merger relics of cluster galaxies is potentially important, because it uniquely allows us to backtrack the halo merger history.
Let $(X, \Delta)$ be a log pair in characteristic $p>0$ and $P$ be a (not necessarily closed) point of $X$. We show that there exists a constant $\delta>0$ such that $\tau(X, \Delta)_P= \tau(X, \Delta + D)_P$ for each effective $\mathbb{Q}$-Cartier divisor $D$ with $\mathrm{mult}_P(D) <\delta$. As its application, we show that if $D$ is an $\mathbb{R}$-Cartier divisor on a strongly $F$-regular projective variety, then the non-nef locus of $D$ coincides with the restricted base locus of $D$. This is a generalization of a result of Musta\c{t}\v{a} to the singular case and can be viewed as a characteristic $p$ analogue of a result of Cacciola--Di Biagio.
In principle, by accepting the idea of a non-zero vacuum energy, the physical vacuum of present particle physics might represent a preferred reference frame. By treating this quantum vacuum as a relativistic medium, the non-zero energy-momentum flow expected in a moving frame should effectively behave as a small thermal gradient and could, in principle, induce a measurable anisotropy of the speed of light in a loosely bound system as a gas. We explore the phenomenological implications of this scenario by considering a new class of dedicated ether-drift experiments where arbitrary gaseous media fill the resonating optical cavities. Our predictions cover most experimental set up and should motivate precise experimental tests of these fundamental issues.
We have studied quantum wires using the Green's function technique and the density-functional theory, calculating the electronic structure and the conductance. All the numerics are implemented using the finite-element method with a high-order polynomial basis. For short wires, i.e. quantum point contacts, the zero-bias conductance shows, as a function of the gate voltage and at a finite temperature, a plateau at around 0.7G_0. (G_0 = 2e^2/h is the quantum conductance). The behavior, which is caused in our mean-field model by spontaneous spin polarization in the constriction, is reminiscent of the so-called 0.7-anomaly observed in experiments. In our model the temperature and the wire length affect the conductance-gate voltage curves in the same way as in the measured data.
Einstein's general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric and spatial vielbein as canonical coordinates. This results in a Hamiltonian in standard form that consists of Hamiltonian and momentum constraints as well as constraints that generate spatial frame transformations---all appearing as primary, first class constraints on phase space. The formalism encompasses the standard coordinate frame and vielbein approaches to general relativity, and the constraint algebra derived herein reproduces known results in either limit.
For a long time, the vision community tries to learn the spatio-temporal representation by combining convolutional neural network together with various temporal models, such as the families of Markov chain, optical flow, RNN and temporal convolution. However, these pipelines consume enormous computing resources due to the alternately learning process for spatial and temporal information. One natural question is whether we can embed the temporal information into the spatial one so the information in the two domains can be jointly learned once-only. In this work, we answer this question by presenting a simple yet powerful operator -- temporal interlacing network (TIN). Instead of learning the temporal features, TIN fuses the two kinds of information by interlacing spatial representations from the past to the future, and vice versa. A differentiable interlacing target can be learned to control the interlacing process. In this way, a heavy temporal model is replaced by a simple interlacing operator. We theoretically prove that with a learnable interlacing target, TIN performs equivalently to the regularized temporal convolution network (r-TCN), but gains 4% more accuracy with 6x less latency on 6 challenging benchmarks. These results push the state-of-the-art performances of video understanding by a considerable margin. Not surprising, the ensemble model of the proposed TIN won the $1^{st}$ place in the ICCV19 - Multi Moments in Time challenge. Code is made available to facilitate further research at https://github.com/deepcs233/TIN
Fully entangled fraction (FEF) is a significant figure of merit for density matrices. In bipartite $ d \otimes d $ quantum systems, the threshold value FEF $ > 1/d $, carries significant implications for quantum information processing tasks. Like separability, the value of FEF is also related to the choice of global basis of the underlying Hilbert space. A state having its FEF $ \le 1/d $, might give a value $ > 1/d $ in another global basis. A change in the global basis corresponds to a global unitary action on the quantum state. In the present work, we find that there are quantum states whose FEF remains less than $ 1/d $, under the action of any global unitary i.e., any choice of global basis. We invoke the hyperplane separation theorem to demarcate the set from states whose FEF can be increased beyond $ 1/d $ through global unitary action. Consequent to this, we probe the marginals of a pure three party system in qubits. We observe that under some restrictions on the parameters, even if two parties collaborate (through unitary action on their combined system) they will not be able to breach the FEF threshold. The study is further extended to include some classes of mixed three qubit and three qutrit systems. Furthermore, the implications of our work pertaining to $ k- $copy nonlocality and teleportation are also investigated.
We report the discovery of an RR Lyrae star that experienced a switching of its pulsation mode. OGLE-BLG-RRLYR-12245 was discovered as a double-mode RRd star from the observations conducted in years 2001-2006 during the third phase of the Optical Gravitational Lensing Experiment (OGLE-III). The OGLE-IV observations carried out since 2010 reveal that this object is now a fundamental-mode RRab star, with no sign of the first-overtone pulsation. The analysis of the OGLE photometry shows that the final stage of the mode switching occurred on a relatively short timescale of a few months in 2005. We study the behavior of the star during this process, showing changes of the pulsational amplitudes and periods. We also discuss possible causes for the mode switching in RR Lyr stars.
We prove new cases of Fontaine-Mazur conjecture on two-dimensional Galois representations over Q when the residual representation is reducible. Our approach is via a semi-simple local-global compatibility of the completed cohomology and a Taylor-Wiles patching argument for the completed homology in this case. As a key input, we generalize the work of Skinner-Wiles in the ordinary case. In addition, we also treat the residually irreducible case at the end of the paper. Combining with people's earlier work, we can prove the Fontaine-Mazur conjecture completely in the regular case when p is at least 5.
Assessments of the cold-gas reservoir in galaxies are a cornerstone for understanding star-formation processes and the role of feedback and baryonic cycling in galaxy evolution. Here we exploit a sample of 392 galaxies (dubbed MAGMA, Metallicity and Gas for Mass Assembly), presented in a recent paper, to quantify molecular and atomic gas properties across a broad range in stellar mass, Mstar, from $\sim 10^7 - 10^{11}$ Msun. First, we find the metallicity ($Z$) dependence of alpha_CO to be shallower than previous estimates, with alpha_CO$\propto (Z/Z_\odot)^{-1.55}$. Second, molecular gas mass MH2 is found to be strongly correlated with Mstar and star-formation rate (SFR), enabling predictions of MH2 good to within $\sim$0.2 dex. The behavior of atomic gas mass MHI in MAGMA scaling relations suggests that it may be a third, independent variable that encapsulates information about the circumgalactic environment and gas accretion. If Mgas is considered to depend on MHI, together with Mstar and SFR, we obtain a relation that predicts Mgas to within $\sim$0.05 dex. Finally, the analysis of depletion times and the scaling of MHI/Mstar and MH2/Mstar over three different mass bins suggests that the partition of gas and the regulation of star formation through gas content depends on the mass regime. Dwarf galaxies tend to be overwhelmed by (HI) accretion, while for galaxies in the intermediate Mstar "gas-equilibrium" bin, star formation proceeds apace with gas availability. In the most massive "gas-poor, bimodality" galaxies, HI does not apparently participate in star formation, although it generally dominates in mass over H2. Our results confirm that atomic gas plays a key role in baryonic cycling, and is a fundamental ingredient for current and future star formation, especially in dwarf galaxies. (abridged for arXiv)
We consider the task of estimating 3D human pose and shape from videos. While existing frame-based approaches have made significant progress, these methods are independently applied to each image, thereby often leading to inconsistent predictions. In this work, we present a video-based learning algorithm for 3D human pose and shape estimation. The key insights of our method are two-fold. First, to address the inconsistent temporal prediction issue, we exploit temporal information in videos and propose a self-attention module that jointly considers short-range and long-range dependencies across frames, resulting in temporally coherent estimations. Second, we model human motion with a forecasting module that allows the transition between adjacent frames to be smooth. We evaluate our method on the 3DPW, MPI-INF-3DHP, and Human3.6M datasets. Extensive experimental results show that our algorithm performs favorably against the state-of-the-art methods.
In this work, I investigate the properties of Lyman limit systems (LLSs) using state-of-the-art zoom-in cosmological galaxy formation simulations with on the fly radiative transfer, which includes both the cosmic UV background (UVB) and local stellar sources. I compare the simulation results to observations of the incidence frequency of LLSs and the HI column density distribution function over the redshift range $z=2-5$ and find good agreement. I explore the connection between LLSs and their host halos and find that LLSs reside in halos with a wide range of halo masses with a nearly constant covering fraction within a virial radius. Over the range $z=2-5$, I find that more than half of the LLSs reside in halos with $M < 10^{10}h^{-1}M_\odot$, indicating that absorption line studies of LLSs can probe these low-mass galaxies which H$_2$-based star formation models predict to have very little star formation. I study the physical state of individual LLSs and test a simple model (Schaye 2001) which encapsulates many of their properties. I confirm that LLSs have a characteristic absorption length given by the Jeans length and that they are in photoionization equilibrium at low column densities. Finally, I investigate the self-shielding of LLSs to the UVB and explore how the non-sphericity of LLSs affects the photoionization rate at a given $N_{\rm HI}$. I find that at $z\approx 3$, LLSs have an optical depth of unity at a column density of $\sim 10^{18} {\rm cm}^{-2}$ and that this is the column density which characterizes the onset of self-shielding.
We investigate the role of the eccentric disc resonance in systems with mass ratios q greater than 1/4, and demonstrate the effects that changes in the mass flux from the secondary star have upon the disc radius and structure. The addition of material with low specific angular momentum to its outer edge restricts a disc radially. Should the mass flux from the secondary be reduced, it is possible for the disc in a system with mass ratio as large as 1/3 to expand to the 3:1 eccentric inner Lindblad resonance and for superhumps to be excited.
This paper presents a review of human activity recognition and behaviour understanding in video sequence. The key objective of this paper is to provide a general review on the overall process of a surveillance system used in the current trend. Visual surveillance system is directed on automatic identification of events of interest, especially on tracking and classification of moving objects. The processing step of the video surveillance system includes the following stages: Surrounding model, object representation, object tracking, activity recognition and behaviour understanding. It describes techniques that use to define a general set of activities that are applicable to a wide range of scenes and environments in video sequence.
In this paper we prove a refined version of the canonical key formula for projective abelian schemes in the sense of Moret-Bailly, we also extend this discussion to the context of Arakelov geometry. Precisely, let $\pi: A\to S$ be a projective abelian scheme over a locally noetherian scheme $S$ with unit section $e: S\to A$ and let $L$ be a symmetric, rigidified, relatively ample line bundle on $A$. Denote by $\omega_A$ the determinant of the sheaf of differentials of $\pi$ and by $d$ the rank of the locally free sheaf $\pi_*L$. In this paper, we shall prove the following results: (i). there is an isomorphism {\rm det}(\pi_*L)^{\otimes 24}\cong (e^*\omega_A^\vee)^{\otimes 12d} which is canonical in the sense that it is compatible with arbitrary base-change; (ii). if the generic fibre of $S$ is separated and smooth, then there exist positive integer $m$, canonical metrics on $L$ and on $\omega_A$ such that there exists an isometry {\rm det}(\pi_*\bar{L})^{\otimes 2m}\cong (e^*\bar{\omega}_A^\vee)^{\otimes md} which is canonical in the sense of (i). Here the constant $m$ only depends on $g,d$ and is independent of $L$.
We present a framework for modeling superconducting circuits that integrates classical microwave analysis with circuit quantization. Our framework enables the calculation of the lossy eigenmodes of superconducting circuits, and we demonstrate the method by analyzing several circuits relevant to multiplexed, Purcell filtered transmon readout architectures. We show that the transmon relaxation times obtained by our method agree with the established approximation $T_1 \approx C/\text{Re}[Y(i\omega_q)]$ away from environmental resonances and do not vanish on resonance. We also show that the hybridization of the modes in the readout circuit is highly sensitive to the bandwidth of the Purcell filter.
We perform comprehensive theoretical analysis of high magnetic field behavior of the heavy-fermion (HF) compound YbRh2Si2. At low magnetic fields B, YbRh2Si2 has a quantum critical point related to the suppression of antiferromagnetic ordering at a critical magnetic field. Our calculations of the thermodynamic properties of YbRh2Si2 in wide magnetic field range allow us to straddle a possible metamagnetic transition region and probe the properties of both low-field HF liquid and high-field fully polarized one. Namely, high magnetic fields B\sim B^*\sim 10 T fully polarize corresponding quasiparticle band generating Landau Fermi liquid (LFL) state and suppressing HF (actually NFL) one, while at elevating temperatures both HF state and corresponding NFL properties are restored. Our calculations are in good agreement with experimental facts and show that the fermion condensation quantum phase transition is indeed responsible for the observed NFL behavior and quasiparticles survive both high temperatures and high magnetic fields.
Microwave detectors based on the spin-transfer torque diode effect are among the key emerging spintronic devices. By utilizing the spin of electrons in addition to charge, they have the potential to overcome the theoretical performance limits of their semiconductor (Schottky) counterparts, which cannot operate at low input power. Here, we demonstrate nanoscale microwave detectors exhibiting record-high detection sensitivity of 75400 mV mW$^{-1}$ at room temperature, without any external bias fields, for input microwave power down to 10 nW. This sensitivity is 20x and 6x larger than state-of-the-art Schottky diode detectors (3800 mV mW$^{-1}$) and existing spintronic diodes with >1000 Oe magnetic bias (12000 mV mW$^{-1}$), respectively. Micromagnetic simulations supported by microwave emission measurements reveal the essential role of the injection locking to achieve this sensitivity performance. The results enable dramatic improvements in the design of low input power microwave detectors, with wide-ranging applications in telecommunications, radars, and smart networks.