ShantanuT01/DACTYL-Pretraining huggingface dataset:
The shape phase structure and its transition of the nucleus in the transitional region between the U(5) and SU(3) symmetries is restudied within the framework of coherent-state theory with angular momentum projection in IBM-1. The certain angular momentum (or rotation-driven) effect on the nuclear shape is discussed. A coexistence of prolate and oblate shapes is found for the ground states of the transitional nuclei. A phase diagram in terms of the deformation parameter and angular momentum is given.
Colloidal nanocrystals (NCs), especially lead sulfide NCs, are promising candidates for solution-processed next-generation photodetectors with high-speed operation frequencies. However, the intrinsic response time of PbS-NC photodetectors, which is the material-specific physical limit, is still elusive, as the reported response times are typically limited by the device geometry. Here, we use the two-pulse coincidence photoresponse technique to identify the intrinsic response time of 1,2-ethanedithiol-functionalized PbS-NC photodetectors after fs-pulsed 1560 nm excitation. We obtain an intrinsic response time of ~1 ns, indicating an intrinsic bandwidth of ~0.55 GHz as the material-specific limit. Examination of the dependence on laser power, gating, bias, temperature, channel length and environmental conditions suggest that Auger recombination, assisted by NC-surface defects, is the dominant mechanism. Accordingly, the intrinsic response time might further be tuned by specifically controlling the ligand coverage and trap states. Thus, PbS-NC photodetectors are feasible for gigahertz optical communication in the third telecommunication window.
We deal with the general problem of scattering by open-arcs in two-dimensional space. We show that this problem can be solved by means of certain second-kind integral equations of the form $\tilde{N} \tilde{S}[\varphi] = f$, where $\tilde{N}$ and $\tilde{S}$ are first-kind integral operators whose composition gives rise to a generalized Calder\'on formula of the form $\tilde{N} \tilde{S} = \tilde{J}_0^\tau + \tilde{K}$ in a {\em weighted, periodized} Sobolev space. The $\tilde{N} \tilde{S}$ formulation provides, for the first time, a second-kind integral equation for the open-arc scattering problem with Neumann boundary conditions. Numerical experiments show that, for both the Dirichlet and Neumann boundary conditions, our second-kind integral equations have spectra that are bounded away from zero and infinity as $k\to \infty$; to the authors' knowledge these are the first integral equations for these problems that possess this desirable property. Our proofs rely on three main elements: 1) Algebraic manipulations enabled by the presence of integral weights; 2) Use of the classical result of continuity of the Ces\`aro operator; and 3) Explicit characterization of the point spectrum of $\tilde{J}^\tau_0$, which, interestingly, can be decomposed into the union of a countable set and an open set, both tightly clustered around -1/4. As shown in a separate contribution, the new approach can be used to construct simple spectrally-accurate numerical solvers and, when used in conjunction with Krylov-subspace solvers such as GMRES, gives rise to dramatic reductions of Krylov-subspace iteration numbers vs. those required by other approaches.
Generalized complex geometry is a new mathematical framework that is useful for describing the target space of N=(2,2) nonlinear sigma-models. The most direct relation is obtained at the N=(1,1) level when the sigma model is formulated with an additional auxiliary spinorial field. We revive a formulation in terms of N=(2,2) semi-(anti)chiral multiplets where such auxiliary fields are naturally present. The underlying generalized complex structures are shown to commute (unlike the corresponding ordinary complex structures) and describe a Generalized Kahler geometry. The metric, B-field and generalized complex structures are all determined in terms of a potential K.
The RCo2Mn (R= Ho and Er) alloys, crystallizing in the cubic MgCu2-type structure, are isostructural to RCo2 compounds. The excess Mn occupies both the R and the Co atomic positions. Magnetic, electrical and heat capacity measurements have been done in these comounds. The Curie temperature is found to be 248 K and 222 K for HoCo2Mn and ErCo2Mn respectively, which are considerably higher than that of the corresponding RCo2 compounds. Saturation magnetization values calculated in these samples are less compared to that of the corresponding RCo2 compounds. Heat capacity data have been fitted with the nonmagnetic contribution with Debye temperature =250 K and electronic coefficient=26 mJ mol^-1K^-2.
Let $E/\mathbb{Q}$ be an elliptic curve of level $N$ and rank equal to $1$. Let $p$ be a prime of ordinary reduction. We experimentally study conjecture $4$ of B. Mazur and J. Tate in his article "Refined Conjectures of the Birch and Swinnerton-Dyer Type". We report the computational evidence.
We consider future cosmological tests based on observations of Fast Radio Bursts (FRBs). We use Illustris Simulation to realistically estimate the scatter in the dispersion measure (DM) of FRBs caused by the inhomogeneous distribution of ionized gas in the Intergalactic Medium (IGM). We find ~13% scatter in DM to a source at z=1 and ~7% at z=3 (one sigma). The distribution of DM is close to Gaussian. We simulate samples of FRBs and examine their applicability to simple cosmological tests. Our calculations show that using a sample of 100 FRBs and fixing cosmological model one can find the redshift and sample averaged fraction of ionized gas with ~1% uncertainty. Finding the ionized fraction with ~1% accuracy at few different epochs would require ~10 000 FRBs with known redshifts. Because DM is proportional to the product of ionized fraction, baryon density and the Hubble constant it is impossible to constrain these parameters separately with FRBs. Constraints on cosmological densities are possible in a flat LCDM model but give uninterestingly low accuracy. Using FRBs with other type of data improves the constraints, but the role of FRBs is not crucial. Thus constraints on the distribution of ionized gas are probably the most promising application of FRBs which allow for "tomography" if sources redshifts are known, as opposed to measuring electron scattering optical depth or S-Z y parameters with CMB observations.
Many quantum key distribution systems employ a laser followed by an optical attenuator to prepare weak coherent states in the source. Their mean photon number must be pre-calibrated to guarantee the security of key distribution. Here we experimentally show that this calibration can be broken with a high-power laser attack. We have tested four fiber-optic attenuator types used in quantum key distribution systems, and found that two of them exhibit a permanent decrease in attenuation after laser damage. This results in higher mean photon numbers in the prepared states and may allow an eavesdropper to compromise the key.
Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF techniques are constructed on the optimization problems using L1-norm and L2-norm losses, which mainly deal with Laplacian and Gaussian noises, respectively. To make LRMF capable of adapting more complex noise, this paper proposes a new LRMF model by assuming noise as Mixture of Exponential Power (MoEP) distributions and proposes a penalized MoEP (PMoEP) model by combining the penalized likelihood method with MoEP distributions. Such setting facilitates the learned LRMF model capable of automatically fitting the real noise through MoEP distributions. Each component in this mixture is adapted from a series of preliminary super- or sub-Gaussian candidates. Moreover, by facilitating the local continuity of noise components, we embed Markov random field into the PMoEP model and further propose the advanced PMoEP-MRF model. An Expectation Maximization (EM) algorithm and a variational EM (VEM) algorithm are also designed to infer the parameters involved in the proposed PMoEP and the PMoEP-MRF model, respectively. The superseniority of our methods is demonstrated by extensive experiments on synthetic data, face modeling, hyperspectral image restoration and background subtraction.
We generalize Bell's hidden variable model describing the singlet state of a two-qubits system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for the hidden variables which are identified with the unit vectors of a 3-dimensional real space. By slightly modifying our model, we provide also a minimal hidden variable description of the two-qubits system, relying on a single hidden variable. We discuss the main features and the implications of the model.
We investigate the behavior of the solutions of a class of certain strictly hyperbolic equations defined on $(0,T]\times \mathbb{R}^n$ in relation to a class of metrics on the phase space. In particular, we study the global regularity and decay issues of the solution to an equation with coefficients polynomially bound in $x$ with their $x$-derivatives and $t$-derivative of order ${O}(t^{-\delta}),\delta \in [0,1),$ and ${O}(t^{-1})$ respectively. This type of singular behavior allows coefficients to be either oscillatory or logarithmically bounded at $t=0$. We use the Planck function associated with the metric to subdivide the extended phase space and define an appropriate generalized parameter dependent symbol class. We report that the solution not only experiences a finite loss of derivatives but also a decay in relation to the initial datum defined in a Sobolev space tailored to the metric. Our analysis suggests that an infinite loss is quite expected when the order of singularity of the first time derivative of the leading coefficients exceeds $O(t^{-1})$. We confirm this by providing counterexamples. Further, using the $L^1$ integrability of the logarithmic singularity in $t$ and the global properties of the operator with respect to $x$, we derive the anisotropic cone conditions in our setting.
We present a comprehensive space-based study of ten X-ray luminous galaxy clusters (L_X>=8e44erg/s[0.1-2.4keV]) at z=0.2. Hubble Space Telescope observations reveal numerous gravitationally-lensed arcs for which we present four new spectroscopic redshifts, bringing the total to thirteen confirmed arcs in this cluster sample. We combine the multiple-image systems with the weakly-sheared background galaxies to model the total mass distribution in the cluster cores (R<=500kpc). These models are complemented by high-resolution X-ray data from Chandra and used to develop quantitative criteria to classify the clusters as relaxed or unrelaxed. Formally, (30+/-20)% of the clusters form a homogeneous sub-sample of relaxed clusters; the remaining (70+/-20)% are unrelaxed and are a much more diverse population. Most of the clusters therefore appear to be experiencing a cluster-cluster merger, or relaxing after such an event. We also study the normalization and scatter of scaling relations between cluster mass, luminosity and temperature. The scatter in these relations is dominated by the unrelaxed clusters and is typically sigma~0.4. Most notably, we detect 2-3 times more scatter in the mass-temperature relation than theoretical simulations and models predict. The observed scatter is also asymmetric - the unrelaxed systems are systematically 40% hotter than the relaxed clusters at 2.5 sigma significance. This structural segregation should be a major concern for experiments designed to constrain cosmological parameters using galaxy clusters. Overall our results are consistent with a scenario of cluster-cluster merger induced boosts to cluster X-ray luminosities and temperatures. [Abridged]
Given a singular curve on a smooth surface, we determine which exceptional divisors on the minimal resolution of that curve contribute toward its jumping numbers.
The article is devoted to the relativistic study of elastic $pD$ backward scattering based on the one-nucleon exchange diagram. Calculations were performed using relativistic deuteron wave functions obtained by solving the Bethe-Salpeter equation in the Minkowski space with relativistic separable potentials. The unpolarized differential cross section as well as some polarization observables of the reaction for initial proton momentum up to 7.3 GeV were calculated. The obtained results are compared with the calculations of other authors.
In this work we explore the power of future large-scale surveys to constrain possible deviations from the standard single-field slow-roll inflationary scenario. Specifically, we parametrize possible fluctuations around the almost scale-invariant primordial scalar power spectrum in a model independent way. We then use their imprints on the simulated matter distribution, as observed by the galaxy clustering and weak lensing probes of Euclid and Square Kilometer Array, to construct the best constrainable patterns of fluctuations. For comparison, we make similar forecasts for a futuristic CMB-S4-like survey. The modes are found to have similar, yet shifted, patterns, with increasing number of wiggles as the mode number increases. The forecasted constraints are tightest for CMB anisotropies and galaxy clustering, depending on the details of the specifications of the survey. As case studies, we explore how two greatly different physically motivated patterns of primordial power spectrum are reconstructed by the proposed modes. We propose a figure of merit based on the amount of information delivered by the modes to truncate the mode hierarchy which is automatically generated by the analysis.
We study quantum point contacts in two-dimensional topological insulators by means of quantum transport simulations for InAs/GaSb heterostructures and HgTe/(Hg,Cd)Te quantum wells. In InAs/GaSb, the density of edge states shows an oscillatory decay as a function of the distance to the edge. This is in contrast to the behavior of the edge states in HgTe quantum wells, which decay into the bulk in a simple exponential manner. The difference between the two materials is brought about by spatial separation of electrons and holes in InAs/GaSb, which affects the magnitudes of the parameters describing the particle-hole asymmetry and the strength of intersubband coupling within the Bernevig-Hughes-Zhang model. We show that the character of the wave function decay impacts directly the dependence of the point contact conductance on the constriction width and the Fermi energy, which can be verified experimentally and serve to determine accurately the values of relevant parameters. In the case of InAs/GaSb heterostructures the conductance magnitude oscillates as a function of the constriction width following the oscillations of the edge state penetration, whereas in HgTe/(Hg,Cd)Te quantum wells a single switching from transmitting to reflecting contact is predicted.
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum computer can be built in a 1D chain with a fixed, translationally invariant Hamitonian consisting of nearest--neighbor interactions only. The result of the computation is obtained after a prescribed time with high probability.
The reduced chi-squared statistic is a commonly used goodness-of-fit measure, but it cannot easily detect features near the noise level, even when a large amount of data is available. In this paper, we introduce a new goodness-of-fit measure that we name the reduced psi-squared statistic. It probes the two-point correlations in the residuals of a fit, whereas chi-squared accounts for only the absolute values of each residual point, not considering the relationship between these points. The new statistic maintains sensitivity to individual outliers, but is superior to chi-squared in detecting wide, low level features in the presence of a large number of noisy data points. After presenting this new statistic, we show an instance of its use in the context of analyzing radio spectroscopic data for 21-cm cosmology experiments. We perform fits to simulated data with four components: foreground emission, the global 21-cm signal, an idealized instrument systematic, and noise. This example is particularly timely given the ongoing efforts to confirm the first observational result for this signal, where this work found its original motivation. In addition, we release a Python script dubbed $\texttt{psipy}$ which allows for quick, efficient calculation of the reduced psi-squared statistic on arbitrary data arrays, to be applied in any field of study.
An optical photometric and spectroscopic analysis of the slowly-evolving Type IIn SN2007rt is presented, covering a duration of 481 days after discovery. Its earliest spectrum, taken approximately 100 days after the explosion epoch, indicates the presence of a dense circumstellar medium, with which the supernova ejecta is interacting. This is supported by the slowly-evolving light curve. A notable feature in the spectrum of SN 2007rt is the presence of a broad He I 5875 line, not usually detected in Type IIn supernovae. This may imply that the progenitor star has a high He/H ratio, having shed a significant portion of its hydrogen shell via mass-loss. An intermediate resolution spectrum reveals a narrow Halpha P-Cygni profile, the absorption component of which has a width of 128 km/s. This slow velocity suggests that the progenitor of SN 2007rt recently underwent mass-loss with wind speeds comparable to the lower limits of those detected in luminous blue variables. Asymmetries in the line profiles of H and He at early phases bears some resemblance to double-peaked features observed in a number of Ib/c spectra. These asymmetries may be indicative of an asymmetric or bipolar outflow or alternatively dust formation in the fast expanding ejecta. In addition, the late time spectrum, at over 240 days post-explosion, shows clear evidence for the presence of newly formed dust.
Status of nonfactorizable effects in exclusive hadronic weak decays of $D$ and $B$ mesons is reviewed.
The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. Both the particle-hole symmetric and the more generic particle-hole asymmetric cases are studied. The treatment is based on two complementary non-crossing approximations, the first of which is constructed around the weak-coupling limit and the second around the polaron limit. In general, the two methods disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The frameworks used here can form the starting point for numerically exact methods based on bold-line continuous-time quantum Monte Carlo algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.
Let $i_t(G)$ be the number of independent sets of size $t$ in a graph $G$. Engbers and Galvin asked how large $i_t(G)$ could be in graphs with minimum degree at least $\delta$. They further conjectured that when $n\geq 2\delta$ and $t\geq 3$, $i_t(G)$ is maximized by the complete bipartite graph $K_{\delta, n-\delta}$. This conjecture has drawn the attention of many researchers recently. In this short note, we prove this conjecture.
A generalised Paley map is a Cayley map for the additive group of a finite field F, with a subgroup S=-S of the multiplicative group as generating set, cyclically ordered by powers of a generator of S. We characterise these as the orientably regular maps with orientation-preserving automorphism group acting primitively and faithfully on the vertices; allowing a non-faithful primitive action yields certain cyclic coverings of these maps. We determine the fields of definition and the orbits of the absolute Galois group on these maps, and we show that if (q-1)/(p-1) divides |S|, where |F|=q=p^e with p prime, then these maps are the only orientably regular embeddings of their underlying graphs; in particular this applies to the Paley graphs, where |S|=(q-1)/2 is even.
In this paper, the structure of the critical group of the graph $K_m\times C_n$ is determined, where $m, n\ge 3$.
We construct a manifestly $N=(4,0)$ world-sheet supersymmetric twistor-like formulation of the $D=6$ Green-Schwarz superstring, using the principle of double (target-space and world-sheet) Grassmann analyticity. The superstring action contains two Lagrange multiplier terms and a Wess-Zumino term. They are written down in the analytic subspace of the world-sheet harmonic $N=(4,0)$ superspace, the target manifold being too an analytic subspace of the harmonic $D=6\;\; N=1$ superspace. The kappa symmetry of the $D=6$ superstring is identified with a Kac-Moody extension of the world-sheet $N=(4,0)$ superconformal symmetry. It can be enlarged to include the whole world-sheet reparametrization group if one introduces the appropriate gauge Beltrami superfield into the action. To illustrate the basic features of the new $D=6$ superstring construction, we first give some details about the simpler (already known) twistor-like formulations of $D=3, N=(1,0)$ and $D=4, N=(2,0)$ superstrings.
The Monte Carlo Ferromagnetic Ising model was used to study the electrical properties of manganese oxides due to the charge ordering phase occurring at doping, x = 0.5. The half-doped manganites have an insulator antiferromagnetic ground state. We calculated the internal energy, specific heat, resistivity and the magneto-resistance, MR, with parallel and anti-parallel applied magnetic fields. Our simulation reveals that the resistivity decreases exponentially and the electric current increases with increasing temperature according the free charge increase, to transport from an insulator to conductor phase. The magnetoresistance has negative small values with parallel magnetic field but has positive high values with unti-parallel magnetic field. The obtained semiconductor-metal transition behavior candidates the half-doped manganites to be very good semiconductors diode junctions.
Deep learning models have been shown to learn spurious correlations from data that sometimes lead to systematic failures for certain subpopulations. Prior work has typically diagnosed this by crowdsourcing annotations for various protected attributes and measuring performance, which is both expensive to acquire and difficult to scale. In this work, we propose UDIS, an unsupervised algorithm for surfacing and analyzing such failure modes. UDIS identifies subpopulations via hierarchical clustering of dataset embeddings and surfaces systematic failure modes by visualizing low performing clusters along with their gradient-weighted class-activation maps. We show the effectiveness of UDIS in identifying failure modes in models trained for image classification on the CelebA and MSCOCO datasets.