ShantanuT01/DACTYL-Pretraining huggingface dataset:
This Ph.D. thesis studies the relation between the Harder-Narasimhan filtration and a notion of GIT maximal unstability. When constructing a moduli space by using Geometric Invariant Theory (GIT), a notion of GIT stability appears, which is determined by 1-parameter subgroups. This thesis shows a correspondence between the 1-parameter subgroup giving maximal unstability from the GIT point of view and the Harder-Narasimhan filtration for different moduli problems: torsion free coherent sheaves, holomorphic pairs, Higgs sheaves, rank 2 tensors and quiver representations.   The article [GSZ] contains the correspondence for torsion free coherent sheaves, whereas [Za1] and [Za2] are devoted to finite dimensional quiver representations and rank 2 tensors.   In [HK], the authors explore this kind of correspondences while identifying the Hesselink stratification on conjugacy classes of 1-parameter subgroups with the one on Harder-Narasimhan types, showing that the Hesselink's adapted 1-parameter subgroup corresponds to the Harder-Narasimhan filtration (which is previously prescribed on each strata). Futher work of Hoskins (c.f. [Ho1, Ho2]) continues on the same direction for other moduli problems, comprising finite dimensional quiver representations as it is done in [Za1], and coherent sheaves using the functorial construction of Alvarez-Consul and King (c.f. [ACK]), as it appears in Section 3.2 of this thesis.
Let $G$ be a simple connected graph, and $D(G)$ be the distance matrix of $G$. Suppose that $D_{\max}(G)$ and $\lambda_1(G)$ are the maximum row sum and the spectral radius of $D(G)$, respectively. In this paper, we give a lower bound for $D_{\max}(G)-\lambda_1(G)$, and characterize the extremal graphs attaining the bound. As a corollary, we solve a conjecture posed by Liu, Shu and Xue.
We study hemispherical power asymmetry (Eriksen et. al. 2004, Hansen et. al. 2004, Hansen et. al. 2009) in the WMAP 9-year data. We analyse the combined V- and W-band sky maps, after application of the KQ85 mask, and find that the asymmetry is statistically significant at the 3.4sigma confidence level for ell=2-600, where the data is signal dominated, with a preferred asymmetry direction (l,b)=(227,-27). Individual asymmetry axes estimated from six independent multipole ranges are all consistent with this direction. Subsequently, we estimate cosmological parameters on different parts of the sky and show that the parameters A_s, n_s and Omega_b are the most sensitive to this power asymmetry. In particular, for the two opposite hemispheres aligned with the preferred asymmetry axis, we find n_s = 0.959 \pm 0.022 and n_s = 0.989 \pm 0.024, respectively.
Crossing symmetry appears in Dbrane-anti-Dbrane dynamics in the form of an analytic continuation from U(N) for N brane amplitudes to U(N-p,p) for the interactions of N-p branes with p anti-branes. I consider the consequences for supersymmetry and brane-anti-brane forces.
We show that the derived category of any singularity over a field of characteristic 0 can be embedded fully and faithfully into a smooth triangulated category which has a semiorthogonal decomposition with components equivalent to derived categories of smooth varieties. This provides a categorical resolution of the singularity.
We make contact between the infinite-dimensional non-local symmetry of the typeIIB superstring on AdS5xS5 worldsheet theory and a non-abelian infinite-dimensional symmetry algebra for the weakly coupled superconformal gauge theory. We explain why the planar limit of the one-loop dilatation operator is the Hamiltonian of a spin chain, and show that it commutes with the g*2 N = 0 limit of the non-abelian charges.
The particle flux through a two micron diameter orifice into vacuum from a source chamber filled with solid He exhibits a striking periodic behavior similar to that of a geyser. This phenomenon is attributed to a periodic collapse of the solid inside the source induced by the accumulation of excess vacancies injected at the orifice. The flux-time curves agree well with a kinetic model and provide direct information on the diffusivity of vacancies in solid He.
We present the discovery and the very first analysis of four stellar systems showing two periods of eclipses, that are the objects classified as doubly eclipsing systems. Some of them were proved to orbit each other thanks to their eclipse-timing-variations (ETVs) of both pairs, hence they really constitute rare quadruples with two eclipsing pairs. Some of them do not, as we are still waiting for more data to detect their mutual movement. Their light curves and period changes were analysed. All of them are detached and near-contact, but none of them contact; moreover, to our knowledge none of these stars can be considered as blend of two spatially unresolved close components on the sky. These systems are CzeV2647 (0.5723296 + 0.9637074 days), proved to orbit with 4.5-year periodicity; CzeV1645 (1.0944877 + 1.6594641 days), with a rather questionable detection of ETV; CzeV3436 (0.6836870 + 0.3833930 days); and, finally, OGLE SMC-ECL-1758 (0.9291925 + 3.7350826 days), proved to move on its 30-year orbit. Even more surprising is the fact that most of these systems show the ratio of their two orbital periods close to coupling near some resonant values of small integers, namely CzeV2647, with only 1% from 3:5 resonance, CzeV1645 1% from 2:3 resonance, and OGLE SMC-ECL-1758 with only 0.49% from 1:4 resonance. The nature of these near-resonant states still remains a mystery.
The focus of this thesis is the study and construction of covering arrays, relying on maximal period sequences and other tools from finite fields. A covering array of strength $t$, denoted $\mathrm{CA}(N; t, k,v)$, is an $N\times k$ array with entries from an alphabet $A$ of size $v$, with the property that in the $N\times t$ subarray defined by any $t$ columns, each of the $v^t$ vectors in $A^t$ appears at least once as a row. Covering arrays generalize orthogonal arrays, which are classic combinatorial objects that have been studied extensively. Constructing covering arrays with a small row-to-column ratio is important in the design of statistical experiments, however it is also a challenging mathematical problem.   Linear feedback shift register (LFSR) sequences are sequences of elements from a finite field that satisfy a linear recurrence relation. It is well-known that these are periodic; LFSR sequences that attain the maximum possible period are maximal (period) sequences, often abbreviated to m-sequences in the literature. Arrays constructed from cyclic shifts of maximal sequences possess strong combinatorial properties and have been previously used to construct orthogonal and covering arrays (Moura et al., 2016), although only one of the known constructions is for covering arrays that are not orthogonal arrays (Raaphorst et al., 2014). In this thesis we present several new such constructions.   The cornerstone of our results is a study of the combinatorial properties of arrays constructed from maximal sequences, where we make fundamental connections with concepts from diverse areas of discrete mathematics, such as orthogonal arrays, error-correcting codes, divisibility of polynomials and structures of finite geometry.   One aspect of our work involves [..]
We report a comprehensive structural and valence study of the intermediate valent materials YbNiGa$_{4}$ and YbNiIn$_{4}$ under pressures up to 60 GPa. YbNiGa$_{4}$ undergoes a smooth volume contraction and shows steady increase in Yb-valence with pressure, though the Yb-valence reaches saturation around 25 GPa. In YbNiIn$_{4}$, a change in pressure dependence of the volume and a peak in Yb-valence suggest a pressure induced electronic topological transition occurs around 10-14 GPa. In the pressure region where YbNiIn$_{4}$ and YbNiGa$_{4}$ possess similar Yb-Yb spacings the Yb-valence reveals a precipitous drop. This drop is not captured by density-functional-theory calculations and implies that both the lattice degrees of freedom and the chemical environment play an important role in establishing the valence of Yb.
This Resource Letter provides some guidance on issues that arise in teaching general relativity at both the undergraduate and graduate levels. Particular emphasis is placed on strategies for presenting the mathematical material needed for the formulation of general relativity.
We present a model for electron scattering off nuclei and photon absorption in the resonance energy region (W <= 2 GeV). The elementary gamma/gamma* N-vertex is described using in-medium kinematics and up-to-date form factors for QE-scattering, pion-production form-factors and resonance helicity amplitudes of the MAID analysis. We find good agreement with inclusive data on electron scattering off Oxygen. For photon absorption in Carbon we find a large impact of the momentum dependent mean-field acting on initial- and final-state baryons.
We examine the behavior of sound attenuation and bulk viscosity near the 2'nd order QCD phase transition at finite density. A dynamical model is presented describing the coupled evolution of sound mode and a slow mode of fluctuations.
The dark matter sector remains completely unknown. It is therefore crucial to keep an open mind regarding its nature and possible interactions. Focusing on the case of Weakly Interacting Massive Particles, in this work we make this general philosophy more concrete by applying modern machine learning techniques to dark matter direct detection. We do this by encoding and decoding the graphical representation of background events in the XENONnT experiment with a convolutional variational autoencoder. We describe a methodology that utilizes the `anomaly score' derived from the reconstruction loss of the convolutional variational autoencoder as well as a pre-trained standard convolutional neural network, in a semi-supervised fashion. Indeed, we observe that optimum results are obtained only when both unsupervised and supervised anomaly scores are considered together. A data set that has a higher proportion of anomaly score is deemed anomalous and deserves further investigation. Contrary to classical analyses, in principle all information about the events is used, preventing unnecessary information loss. Lastly, we demonstrate the reach of learning-focused anomaly detection in this context by comparing results with classical inference, observing that, if tuned properly, these techniques have the potential to outperform likelihood-based methods.
We calculate analytically low frequency quasi-normal modes of gravitational perturbations of AdS Schwarzschild black holes in $d$ dimensions. We arrive at analytic expressions which are in agreement with their counterparts from linearized hydrodynamics in $S^{d-2}\times \mathbb{R}$, in accordance with the AdS/CFT correspondence. Our results are also in good agreement with results of numerical calculations.
Using controlled numerical N-body experiments, we show how, in the collapse dynamics of an initially cold and uniform distribution of particles with a generic asymmetric shape, finite $N$ fluctuations and perturbations induced by the anisotropic gravitational field compete to determine the physical properties of the asymptotic quasi-stationary state. When finite $N$ fluctuations dominate the dynamics, the particle energy distribution changes greatly and the final density profile {decays outside its core} as $r^{-4}$ with an $N$-dependent amplitude. On the other hand, in the limit where the anisotropic perturbations dominate, the collapse is softer and the density profile shows a decay as $r^{-3}$, as is typical of halos in cosmological simulations. However, even in this limit, convergence with $N$ of the macroscopic properties of the virialized system, such as the particle energy distributions, the bound mass, and the density profile, is very slow and not clearly established, including for our largest simulations (with $N \sim 10^6$). Our results illustrate the challenges of accurately simulating the first collapsing structures in standard-type cosmological models
We study structure of excited states of 10Be with the method of variation after spin parity projection in the framework of antisymmetrized molecular dynamics. Present calculations describe many excited states and reproduce the experimental data of E2 and E1 transitions and the new data of the $\beta$ transition strength successfully. We make systematic discussions on the molecule-like structures of light unstable nuclei and the important role of the valence neutrons based on the results obtained with the framework which is free from such model assumptions as the existence of inert cores and clusters.
The complexity and the chaos degree can be used to examine the chaotic aspects of not only several nonlinear classical and quantum physical physics but also life sciences. We will construct a model describing the function of brain in the context of Quantum Information Dynamics.
We study the convergence of a Finite Volume scheme for the linear advection equation with a Lipschitz divergence-free speed in $\R^d$. We prove a $h^{1/2}$-error estimate in the $L^\infty(0,t;L^1)$-norm for $BV$ data. This result was expected from numerical experiments and is optimal.
Following the faint gamma-ray burst, GRB 170817A, coincident with a gravitational wave-detected binary neutron star merger at $d\sim40$ Mpc, we consider the constraints on a local population of faint short duration GRBs (defined here broadly as $T_{90}<4$ s). We review proposed low-redshift short-GRBs and consider statistical limits on a $d\lessapprox200$ Mpc population using Swift/Burst Alert Telescope (BAT), Fermi/Gamma-ray Burst Monitor (GBM), and Compton Gamma-Ray Observatory (CGRO) Burst and Transient Source Experiment (BATSE) GRBs. Swift/BAT short-GRBs give an upper limit for the all-sky rate of $<4$ y$^{-1}$ at $d<200$ Mpc, corresponding to $<5$% of SGRBs. Cross-correlation of selected CGRO/BATSE and Fermi/GBM GRBs with $d<100$ Mpc galaxy positions returns a weaker constraint of $\lessapprox12\ {\rm y^{-1}}$. A separate search for correlations due to SGR giant flares in nearby ($d<11$ Mpc) galaxies finds an upper limit of $<3\ {\rm y^{-1}}$. Our analysis suggests that GRB 170817A-like events are likely to be rare in existing SGRB catalogues. The best candidate for an analogue remains GRB 050906, where the Swift/BAT location was consistent with the galaxy IC0327 at $d\approx132$ Mpc. If binary neutron star merger rates are at the high end of current estimates, then our results imply that at most a few percent will be accompanied by detectable gamma-ray flashes in the forthcoming LIGO/Virgo science runs.
We compute the special values for the spinor L-function L(s,F12) in the critical strip s={12,...,19}, where F12 is the unique (up to a scalar) Siegel cusp form of degree 3 and weight 12, which was constructed by Miyawaki. These values are proportional to the product of Petersson inner products of Ramanujan's Delta by itself and the cusp form of weight 20 for SL(2,Z) by itself by a rational number and some power of Pi. We also verify this result numerically using Dokchitser's ComputeL PARI package. To our knowledge this is the first example of a spinor L-function of Siegel cusp forms of degree 3, when the special values can be computed explicitly.
We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.
The pp -> pp eta' reaction is investigated within a relativistic meson-exchange model of hadronic interactions. We explore the role of nucleonic and mesonic, as well as the N* resonance currents, in producing eta' mesons. In order to learn more about the production mechanisms, new measurements in the energy region far from the threshold are required.
Two-dimensional electrons confined to GaAs quantum wells are hallmark platforms for probing electron-electron interaction. Many key observations have been made in these systems as sample quality improved over the years. Here, we present a breakthrough in sample quality via source-material purification and innovation in GaAs molecular beam epitaxy vacuum chamber design. Our samples display an ultra-high mobility of $44\times10^6$ cm$^2$/Vs at an electron density of $2.0\times10^{11}$ /cm$^2$. These results imply only 1 residual impurity for every $10^{10}$ Ga/As atoms. The impact of such low impurity concentration is manifold. Robust stripe/bubble phases are observed, and several new fractional quantum Hall states emerge. Furthermore, the activation gap of the $\nu=5/2$ state, which is widely believed to be non-Abelian and of potential use for topological quantum computing, reaches $\Delta\simeq820$ mK. We expect that our results will stimulate further research on interaction-driven physics in a two-dimensional setting and significantly advance the field.
Formation and evolution of fragmentation instabilities in fractal islands, obtained by deposition of silver clusters on graphite, are studied. The fragmentation dynamics and subsequent relaxation to the equilibrium shapes are controlled by the deposition conditions and cluster composition. Sharing common features with other materials' breakup phenomena, the fragmentation instability is governed by the length-to-width ratio of the fractal arms.
We report on the discovery of two emission features observed in the X-ray spectrum of the afterglow of the gamma-ray burst (GRB) of 16 Dec. 1999 by the Chandra X-Ray Observatory. These features are identified with the Ly$_{\alpha}$ line and the narrow recombination continuum by hydrogenic ions of iron at a redshift $z=1.00\pm0.02$, providing an unambiguous measurement of the distance of a GRB. Line width and intensity imply that the progenitor of the GRB was a massive star system that ejected, before the GRB event, $\approx 0.01 \Ms$ of iron at a velocity $\approx 0.1 c$, probably by a supernova explosion.
We present a new method to study 4-dimensional linear spaces of skew-symmetric matrices of constant co-rank 2, based on rank 2 vector bundles on P^3 and derived category tools. The method allows one to prove the existence of new examples of size 10x10 and 14x14 via instanton bundles of charge 2 and 4 respectively, and provides an explanation for what used to be the only known example (Westwick 1996). We also give an algorithm to construct explicitly a matrix of size 14 of this type.
The systematics of one-quasiparticle configurations in neutron-rich Sr, Zr, and Mo odd isotopes is studied within the Hartree-Fock-Bogoliubov plus Equal Filling Approximation method preserving both axial and time reversal symmetries. Calculations based on the Gogny energy density functional with both the standard D1S parametrization and the new D1M incarnation of this functional are included in our analysis. The nuclear deformation and shape coexistence inherent to this mass region are shown to play a relevant role in the understanding of the spectroscopic features of the ground and low-lying one-quasineutron states.
The equivalence of mass and energy is indelibly linked with relativity, both by scientists and in the popular mind. I prove that E = mc^2 by demanding momentum conservation of an object that emits two equal electromagnetic wave packets in opposite directions in its own frame. In contrast to Einstein's derivation of this equation, which applies energy conservation to a similar thought experiment, the new derivation employs no effects that are greater than first order in v/c and therefore does not rely on results from Special Relativity. In addition to momentum conservation, it uses only aberration of starlight and the electromagnetic-wave momentum-energy relation p=E/c, both of which were established by 1884. In particular, no assumption is made about the constancy of the speed of light, and the derivation proceeds equally well if one assumes that light is governed by a Galilean transformation. In view of this, it is somewhat puzzling that the equivalence of mass and energy was not derived well before the advent of Special Relativity. The new derivation is simpler and more transparent than Einstein's and is therefore pedagogically useful.
By performing a slow adiabatic change between two traps of a quantum particle, it is possible to transform an eigenstate of the original trap into the corresponding eigenstate of the final trap. If no level crossings are involved, the process can be made faster than adiabatic by setting first the interpolated evolution of the wave function from its initial to its final form and inferring from this evolution the trap deformation. We find a simple and compact formula which gives the trap shape at any time for any interpolation scheme. It is applicable even in complicated scenarios where there is no adiabatic process for the desired state-transformation, e.g., if the state changes its topological properties. We illustrate its use for the expansion of a harmonic trap, for the transformation of a harmonic trap into a linear trap and into an arbitrary number of traps of a periodic structure. Finally, we study the creation of a node exemplified by the passage from the ground state to the first excited state of a harmonic oscillator.
We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S.Fisher \cite{letterTBF}. Furthermore, we review some of our previous works on Kinetically Constrained Models.   The Knights models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when $\rho\nearrow\rho_c$. These properties give rise for Knight models to an ergodicity breaking transition at $\rho_c$: at and above $\rho_{c}$ a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.