ShantanuT01/DACTYL-Pretraining huggingface dataset:
Satellite imagery analytics have numerous human development and disaster response applications, particularly when time series methods are involved. For example, quantifying population statistics is fundamental to 67 of the 231 United Nations Sustainable Development Goals Indicators, but the World Bank estimates that over 100 countries currently lack effective Civil Registration systems. To help address this deficit and develop novel computer vision methods for time series data, we present the Multi-Temporal Urban Development SpaceNet (MUDS, also known as SpaceNet 7) dataset. This open source dataset consists of medium resolution (4.0m) satellite imagery mosaics, which includes 24 images (one per month) covering >100 unique geographies, and comprises >40,000 km2 of imagery and exhaustive polygon labels of building footprints therein, totaling over 11M individual annotations. Each building is assigned a unique identifier (i.e. address), which permits tracking of individual objects over time. Label fidelity exceeds image resolution; this "omniscient labeling" is a unique feature of the dataset, and enables surprisingly precise algorithmic models to be crafted. We demonstrate methods to track building footprint construction (or demolition) over time, thereby directly assessing urbanization. Performance is measured with the newly developed SpaceNet Change and Object Tracking (SCOT) metric, which quantifies both object tracking as well as change detection. We demonstrate that despite the moderate resolution of the data, we are able to track individual building identifiers over time. This task has broad implications for disaster preparedness, the environment, infrastructure development, and epidemic prevention.
For affine processes on finite-dimensional cones, we give criteria for geometric ergodicity - that is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of the limiting distribution, where we exploit the crucial affine property, and finite moments, where we invoke the polynomial property of affine semigroups. Furthermore, we elaborate sufficient conditions for aperiodicity and irreducibility. Our results are applicable to Wishart processes with jumps on the positive semidefinite matrices, continuous-time branching processes with immigration in high dimensions, and classical term-structure models for credit and interest rate risk.
We fix an elliptic curve $E/\mathbb{F}_q(t)$ and consider the family $\{E\otimes\chi_D\}$ of $E$ twisted by quadratic Dirichlet characters. The one-level density of their $L$-functions is shown to follow orthogonal symmetry for test functions with Fourier transform supported inside $(-1,1)$. As an application, we obtain an upper bound of 3/2 on the average analytic rank. By splitting the family according to the sign of the functional equation, we obtain that at least $12.5\%$ of the family have rank zero, and at least $37.5\%$ have rank one. The Katz and Sarnak philosophy predicts that those percentages should both be $50\%$ and that the average analytic rank should be $1/2$. We finish by computing the one-level density of $E$ twisted by Dirichlet characters of order $\ell\neq 2$ coprime to $q$. We obtain a restriction of $(-1/2,1/2)$ on the support with a unitary symmetry.
This paper addresses the problem of finding $Q_{m,t}\left(n\right)$, the number of possible ways to partition any member $n$ of the cyclic group $\mathbb{Z}/m\mathbb{Z}$ into $t$ distinct parts. When $m$ is odd, it was previously known that the number of partitions of the identity element $0\bmod m$ with distinct parts is equal to the number of possible bi-color necklaces with $m$ beads. This paper will expand upon this result by showing the equivalence between $Q_{m,t}\left(n\right)$ and the number of bi-color necklaces meeting certain periodicity requirements, even when $m$ is even.
Let $K$ be a local field with algebraically closed residue field and $X_K$ a torsor under an elliptic curve $J_K$ over $K$. Let $X$ be a proper minimal regular model of $X_K$ over the ring of integers of $K$ and $J$ the identity component of the N\'eron model of $J_K$. We study the canonical morphism $q\colon \mathrm{Pic}^{0}_{X/S}\to J$ which extends the biduality isomorphism on generic fibres. We show that $q$ is pro-algebraic in nature with a construction that recalls Serre's work on local class field theory. Furthermore we interpret our results in relation to Shafarevich's duality theory for torsors under abelian varieties.
We give a new construction of the uniform infinite half-planar quadrangulation with a general boundary (or UIHPQ), analogous to the construction of the UIPQ presented by Chassaing and Durhuus, which allows us to perform a detailed study of its geometry. We show that the process of distances to the root vertex read along the boundary contour of the UIHPQ evolves as a particularly simple Markov chain and converges to a pair of independent Bessel processes of dimension $5$ in the scaling limit. We study the "pencil" of infinite geodesics issued from the root vertex as M\'enard, Miermont and the second author did for the UIPQ, and prove that it induces a decomposition of the UIHPQ into three independent submaps. We are also able to prove that balls of large radius around the root are on average $7/9$ times as large as those in the UIPQ, both in the UIHPQ and in the UIHPQ with a simple boundary; this fact we use in a companion paper to study self-avoiding walks on large quadrangulations.
We investigate the suppression of the visibility of Aharonov-Bohm oscillations in a two-electron Mach-Zehnder interferometer that leaves the single-electron current unchanged. In the case when the sources emit either spin-polarized or entangled electrons, partial distinguishability of electrons (coming from two different sources) suppresses the visibility. Two-particle entanglement may produce behavior similar to "dephasing" of two-particle interferometry.
A Kempe swap in a proper coloring interchanges the colors on some maximal connected 2-colored subgraph. Two $k$-colorings are $k$-equivalent if we can transform one into the other using Kempe swaps. The triangulated toroidal grid, $T[m\times n]$, is formed from (a toroidal embedding of) the Cartesian product of $C_m$ and $C_n$ by adding parallel diagonals inside all 4-faces. Mohar and Salas showed that not all 4-colorings of $T[m\times n]$ are 4-equivalent. In contrast, Bonamy, Bousquet, Feghali, and Johnson showed that all 6-colorings of $T[m\times n]$ are 6-equivalent. They asked whether the same is true for 5-colorings. We answer their question affirmatively when $m,n\ge 6$. Further, we show that if $G$ is 6-regular with a toroidal embedding where every non-contractible cycle has length at least 7, then all 5-colorings of $G$ are 5-equivalent. Our results relate to the antiferromagnetic Pott's model in statistical mechanics.
The results for the three-loop renormalization group equations for all fundamental parameters of the SM Lagrangian are presented. Special attention is paid to the Flavor sector of the SM, which parameterized by general complex non-diagonal Yukawa couplings. Some details of calculation techniques are given. In addition, ambiguities in the beta-functions for the matrix couplings are discussed.
Two-neutron densities obtained from microscopic wave functions of $^6$He and $^8$He are investigated to reveal di-neutron correlations. In particular, the comparison of the two-neutron density with the product of one-neutron densities is useful for a quantitative discussion of di-neutron correlations. The calculations show that the S=0 spatial two-neutron correlation increases at the surface of $^6$He$(0^+_1)$ and $^8$He$(0^+_2)$. The enhancement is remarkable in the $^6$He$(0^+_1)$ ground state but not as prominent in the $^8$He$(0^+_1)$ ground state. Configuration mixing of many Slater determinants is essential to describe the di-neutron correlations. Two-neutron densities in $^{12}$C wave functions with $\alpha$-cluster structures are also studied.
We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; the resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo (SMMC) methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of {\it pf}-shell nuclei, the thermal and rotational behavior of rare-earth and $\gamma$-soft nuclei, and the calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed.
Interest in the application of thermoelectric devices for renewable energy has risen over the past decade. In this paper, we calculate the transport properties of various configurations of the transition metal dichalcogenide (TMD) MSe$_2$ (M = Hf, Zr, Ti) in search of promising thermoelectric materials at low/high temperatures. We explore the properties of the pure monolayer at discrete levels of biaxial tensile strain (epsilon = 0%, 2%, 4%, 8%), as well as those of the van der Waals heterobilayers MSe$_2$/MSe$_2$ using first-principles calculations combined with semi-classical Boltzmann transport theory. It is found that all studied monolayers exhibit high thermoelectric performance at high temperatures, while the application of strain enhances Seebeck and thermopower non-linearly at low temperatures. The results also reveal the bilayer ZrSe$_2$/TiSe$_2$ to have remarkable thermopower at low temperatures. These findings offer insight into creating applications with enhanced performance at both low and high temperatures in future thermoelectric devices.
The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces admitting a non-trivial Ernst field constitutes a ``partially discretized'' subspace of the usual moduli space. The method allows us to construct new exact solutions of Einstein's equations in vacuo with non-trivial topology, such that different ``universes'', each of which may have several black holes on its symmetry axis, are connected through necks bounded by cosmic strings. We show how the extra topological degrees of freedom may lead to an extension of the Geroch group and discuss possible applications to string theory.
Consider a set of images of a scene consisting of moving objects captured using a hand-held camera. In this work, we propose an algorithm which takes this set of multi-view images as input, detects the dynamic objects present in the scene, and replaces them with the static regions which are being occluded by them. The proposed algorithm scans the reference image in the row-major order at the pixel level and classifies each pixel as static or dynamic. During the scan, when a pixel is classified as dynamic, the proposed algorithm replaces that pixel value with the corresponding pixel value of the static region which is being occluded by that dynamic region. We show that we achieve artifact-free removal of dynamic objects in multi-view images of several real-world scenes. To the best of our knowledge, we propose the first method which simultaneously detects and removes the dynamic objects present in multi-view images.
We study transport properties of weakly interacting one-dimensional electron systems including on an equal footing thermal equilibration due to three-particle collisions and the effects of large-scale inhomogeneities. We show that equilibration in an inhomogeneous quantum wire is characterized by the competition of interaction processes which reduce the electrons total momentum and such which change the number of right- and left-moving electrons. We find that the combined effect of interactions and inhomogeneities can dramatically increase the resistance of the wire. In addition, we find that the interactions strongly affect the thermoelectric properties of inhomogeneous wires and calculate their thermal conductance, thermopower, and Peltier coefficient.
We demonstrate that rectification ratios (RR) of >250 (>1000) at biases of 0.5 V (1.2 V) are achievable at the two-molecule limit for donor-acceptor bilayers of pentacene on fullerene on Cu using scanning tunneling spectroscopy and microscopy. Using first-principles calculations, we show that the system behaves as a molecular Schottky diode with a tunneling transport mechanism from semiconducting pentacene to Cu-hybridized metallic fullerene. Low-bias RRs vary by two orders-of-magnitude at the edge of these molecular heterojunctions due to increased Stark shifts and confinement effects.
We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications to the Milnor fibration and the motivic zeta function by J. Sebag and the author.
We present stellar age distributions of the Milky Way (MW) bulge region using ages for $\sim$6,000 high-luminosity ($\log(g) < 2.0$), metal-rich ($\rm [Fe/H] \ge -0.5$) bulge stars observed by the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Ages are derived using {\it The Cannon} label-transfer method, trained on a sample of nearby luminous giants with precise parallaxes for which we obtain ages using a Bayesian isochrone-matching technique. We find that the metal-rich bulge is predominantly composed of old stars ($>$8 Gyr). We find evidence that the planar region of the bulge ($|Z_{\rm GC}| \le 0.25$ kpc) enriched in metallicity, $Z$, at a faster rate ($dZ/dt \sim$ 0.0034 ${\rm Gyr^{-1}}$) than regions farther from the plane ($dZ/dt \sim$ 0.0013 ${\rm Gyr^{-1}}$ at $|Z_{\rm GC}| > 1.00$ kpc). We identify a non-negligible fraction of younger stars (age $\sim$ 2--5 Gyr) at metallicities of $\rm +0.2 < [Fe/H] < +0.4$. These stars are preferentially found in the plane ($|Z_{\rm GC}| \le 0.25$ kpc) and between $R_{\rm cy} \approx 2-3$ kpc, with kinematics that are more consistent with rotation than are the kinematics of older stars at the same metallicities. We do not measure a significant age difference between stars found in and outside of the bar. These findings show that the bulge experienced an initial starburst that was more intense close to the plane than far from the plane. Then, star formation continued at super-solar metallicities in a thin disk at 2 kpc $\lesssim R_{\rm cy} \lesssim$ 3 kpc until $\sim$2 Gyr ago.
In this paper we prove an infinitesimal version of the classical Terracini Lemma for 3--secant planes to a variety. Precisely we prove that if   $X\subseteq \PP^r$ is an irreducible, non--degenerate, projective complex variety of dimension $n$ with $r\geq 3n+2$, such that the variety of osculating planes to curves in $X$ has the expected dimension $3n$ and for every $0$--dimensional, curvilinear scheme $\gamma$ of length 3 contained in $X$ the family of hyperplanes sections of $X$ which are singular along $\gamma$ has dimension larger that $r-3(n+1)$, then $X$ is $2$--secant defective.
We look for graph polynomials which satisfy recurrence relations on three kinds of edge elimination: edge deletion, edge contraction and deletion of edges together with their end points. Like in the case of deletion and contraction only (W. Tutte, 1954), it turns out that there is a most general polynomial satisfying such recurrence relations, which we call $\xi(G,x,y,z)$. We show that the new polynomial simultaneously generalizes the Tutte polynomial, the matching polynomial, and the recent generalization of the chromatic polynomial proposed by K.Dohmen, A.P\"{o}nitz and P.Tittman (2003), including also the independent set polynomial of I. Gutman and F. Harary, (1983) and the vertex-cover polynomial of F,M. Dong, M.D. Hendy, K.T. Teo and C.H.C. Little (2002). We establish two definitions of the new polynomial: first, the most general confluent recursive definition, and then an explicit one, using a set expansion formula, and prove their identity. We further expand this result to edge-labeled graphs as was done for the Tutte polynomial by T. Zaslavsky (1992) and B. Bollob\'as and O. Riordan (1999). The edge labeled polynomial $\xi_{lab}(G,x,y,z, \bar{t})$ also generalizes the chain polynomial of R.C. Read and E.G. Whitehead Jr. (1999). Finally, we discuss the complexity of computing $\xi(G,x,y,z)$.
The Rossi X-ray Timing Explorer data of GRS 1915+105 from several observing periods are modeled with a thermal Comptonization model. Best-fit models indicate that there is a strong correlation between the inner disk temperature and the disk luminosity. The hard Comptonized luminosity does not depend significantly on the total luminosity. The spectral hardness of the Comptonized radiation, the fraction of seed soft photons scattered by the Comptonizing cloud, its Thomson optical depth, and the fraction of the total power dissipated in the optically thin hot plasma, all strongly anticorrelate with the luminosity. We find that the inner disk radius is almost constant and that the hot Comptonizing corona shrinks at high luminosities. We note that the fits using xspec diskbb + power law model underestimate the amplitude of the blackbody component (and therefore the corresponding size of the emitting region) and overestimate the absorption column density and the total, corrected for absorption, luminosity.
We present the first example of an exponentially decaying interaction which gives rise to non-periodic long-range order at positive temperatures.
Results of low temperature magnetoresistance ($\Delta\rho/\rho$) and isothermal magnetization (M) measurements on polycrystalline ferromagnetic (T_C close to 300 K) natural multilayers, LaMn_{2+x}Ge_{2-y}Si_y, are reported. It is found that the samples with large residual resistivity ratio, $\rho(300K)/\rho(4.2K)$, exhibit large positive magnetoresistance at high magnetic fields. The Kohler's rule is not obeyed in these alloys. In addition, at 4.5 K, there is a tendency towards linear variation of $\Delta\rho/\rho$ with magnetic field with increasing $\rho(300K)/\rho(4.2K$); however, the field dependence of $\Delta\rho/\rho$ does not track that of M, thereby suggesting that the magnetoresistance originates from non-magnetic layers. It is interesting that these experimental findings on bulk polycrystals are qualitatively similar to what is seen in artificially grown multilayer systems recently.
We study a series array of nonlinear electrical circuit elements that possess negative differential resistance and find that \emph{heterogeneity} in the element properties leads to the presence of multiple branches in current-voltage curves and a non-uniform distribution of voltages across the elements. An inhomogeneity parameter $r_{max}$ is introduced to characterize the extent to which the individual element voltages deviate from one another, and it is found to be strongly dependent on the rate of change of applied voltage. Analytical expressions are derived for the dependence of $r_{max}$ on voltage ramping rate in the limit of fast ramping and are confirmed by direct numerical simulation.
Let $n>1$ be an odd integer. We prove that there are infinitely many imaginary quadratic fields of the form $\mathbb{Q}(\sqrt{x^2-2y^n})$ whose ideal class group has an element of order $n$. This family gives a counter example to a conjecture by H. Wada \cite{WA70} on the structure of ideal class groups.
We analyse two phase transitions in exciton bilayer systems: a topological phase transition to a phase which hosts Majorana fermions and a phase transition to a Wigner crystal. Using generic simple models for the different phases we discuss the conductance properties of the latter when contacted to metallic leads and demonstrate the possibility to observe the different phase transitions by simple conductance measurements.
In low-temperature metallic magnets, ferromagnetic (FM) and antiferromagnetic (AFM) orders can exist in a single system in different parts of the phase diagram as a function of some control parameter. These phases can be adjacent, or exist concurrently, resulting in a phase transition between a FM phase and an AFM one, or between a phase of concurrent FM and AFM order and either of the pure phases. We show that universal quantum fluctuations qualitatively alter the known phase diagrams for classical magnets: They shrink the region of concurrent FM and AFM order, change various transitions from second to first order, and, in the presence of a magnetic field, lead to either a quantum triple point where the FM, AFM and paramagnetic phases coexist, or to a quantum critical end point.
In the frame of the collapsar model for long gamma ray bursts (GRBs), we investigate the formation of a torus around a spinning BH and we check what rotational properties a progenitor star must have in order to sustain torus accretion over relatively long activity periods. We also study the time evolution of the BH spin parameter. We take into account the coupling between BH mass, its spin parameter and the critical specific angular momentum of accreting gas, needed for the torus to form. The large BH spin reduces the critical angular momentum which in turn can increase the GRB duration with respect to the Schwarzschild BH case. We quantify this effect and estimate the GRB durations in three cases: when a hyper accreting torus operates or a BH spins very fast or both. We show under what conditions a given progenitor star produces a burst that can last as short as several seconds and as long as several hundred of seconds. Our models indicate that it is possible for a single collapse to produce three kinds of jets: (1) a very short, lasting between a fraction of a second and a few seconds, 'precursor' jet, powered only by a hyper accreting torus before the BH spins up, (2) an 'early' jet, lasting several tens of seconds and powered by both hyper accretion and BH rotation, and (3) a 'late' jet, powered only by the spinning BH.
Carbon nanotubes are of central importance for applications in nano-electronics thanks to their exceptional transport properties. They can be used as sensors, for example in biological applications, provided that they are functionalized to detect specific molecules. Due to their one-dimensional geometry the carbon nanotubes are very sensitive to the phenomenon of Anderson localization and it is therefore essential to know how the functionalization modifies their conduction properties and if they remain good conductors. Here we present a study of the quantum localization induced by functionalization in metallic single walled carbon nanotubes (SWCNT) with circumferences up to $ 15\; nm $. We consider resonant and non-resonant adsorbates that represent two types of covalently functionalized groups with moderate and strong scattering properties. The present study provides a detailed analysis of the localization behaviour and shows that the localization length can decrease down to $ 20-50\; nm $ at concentrations of about 1 percent of adsorbates. On this basis we discuss the possible electronic transport mechanisms which can be either metallic like or insulating like with variable range hopping.