ShantanuT01/DACTYL-Pretraining huggingface dataset:
Recall that a smooth complex projective curve has a very ample canonical bundle when it is non-hyperelliptic, and according to a theorem of M. Noether the resulting embedding is projectively normal. A theorem of Petri further asserts that the homogeneous ideal is generated by quadrics if the curve is neither trigonal nor a smooth plane quintic. In this note, we prove an analogue of Noether's theorem for the symmetric square of the curve - namely, the canonical bundle of the symmetric square determines a projectively normal embedding exactly when the curve itself is neither hyperelliptic, trigonal nor a smooth plane quintic. The theorem of Petri highlights the governing role played by quadric generation of the ideal of the curve.
We present a new method to renormalize stochastic differential equations subjected to multiplicative noise. The method is based on the widely used concept of effective potential in high energy physics, and has already been successfully applied to the renormalization of stochastic differential equations subjected to additive noise. We derive a general formula for the one-loop effective potential of a single ordinary stochastic differential equation (with arbitrary interaction terms) subjected to multiplicative Gaussian noise (provided the noise satisfies a certain normalization condition). To illustrate the usefulness (and limitations) of the method, we use the effective potential to renormalize a toy chemical model based on a simplified Gray-Scott reaction. In particular, we use it to compute the scale dependence of the toy model's parameters (in perturbation theory) when subjected to a Gaussian power-law noise with short time correlations.
It is at present well known that conditions at some massive binary systems allow acceleration of particles and production of the GeV-TeV gamma-rays. However, which particles are responsible for this emission and what radiation processes are engaged is at present not completely clear. We discuss what parameters can determine the acceleration process of particles and high energy radiation produced by them within massive binary systems.
Area per lipid (APL) is an important property of biological and artificial membranes. Newly constructed bilayers are characterized by their APL and newly elaborated force fields must reproduce APL. Computer simulations of APL are very expensive due to slow conformational dynamics. The simulated dynamics increases exponentially with respect to temperature. APL dependence on temperature is linear over an entire temperature range. I provide numerical evidence that thermal expansion coefficient of a lipid bilayer can be computed at elevated temperatures and extrapolated to the temperature of interest. Thus, sampling times to predict accurate APL are reduced by a factor of ~10.
[Abridged] We make use of a semi-analytic cosmological model that includes simple prescriptions for dust attenuation and emission to make predictions for the observable and physical properties of galaxies that may be detected by the recently launched Herschel Space Observatory in deep fields such as GOODS-Herschel. We compare our predictions for differential galaxy number counts in the PACS (100 & 160) and SPIRE (250, 350, and 500 micron) bands with available observations. We find very good agreement with the counts in the PACS bands, for the overall counts and for galaxies binned by redshift at z< 2. At z > 2 our model underpredicts the number of bright galaxies by a factor of ten. The agreement is much worse for all three SPIRE bands, and becomes progressively worse with increasing wavelength. We discuss a number of possible reasons for these discrepancies, and hypothesize that the effect of blending on the observational flux estimates is likely to be the dominant issue. We note that the PACS number counts are relatively robust to changes in the dust emission templates, while the predicted SPIRE number counts are more template dependent. We present quantitative predictions for the relationship between the observed PACS 160 and SPIRE 250 micron fluxes and physical quantities such as halo mass, stellar mass, cold gas mass, star formation rate, and total infrared (IR) luminosity, at different redshifts. We also present quantitative predictions for the correlation between PACS 160 micron flux and the probability that a galaxy has experienced a recent major or minor merger. Although our models predict a strong correlation between these quantities, such that more IR-luminous galaxies are more likely to be merger-driven, we find that more than half of all high redshift IR-luminous galaxies detected by Herschel are able to attain their high star formation rates without enhancement by a merger.
Results on the correlations of low density classical and quantum Coulomb systems at equilibrium in three dimensions are reviewed. The exponential decay of particle correlations in the classical Coulomb system -- Debye-H\"uckel screening -- is compared and contrasted with the quantum case where strong arguments are presented for the absence of exponential screening. Results and techniques for detailed calculations that determine the asymptotic decay of correlations for quantum systems are discussed. Theorems on the existence of molecules in the Saha regime are reviewed. Finally, new combinatoric formulas for the coefficients of Mayer expansions are presented and their role in proofs of results on Debye-H\"uckel screening is discussed.
Cross-modal correlation provides an inherent supervision for video unsupervised representation learning. Existing methods focus on distinguishing different video clips by visual and audio representations. We human visual perception could attend to regions where sounds are made, and our auditory perception could also ground their frequencies of sounding objects, which we call bidirectional local correspondence. Such supervision is intuitive but not well explored in the contrastive learning framework. This paper introduces a pretext task, Cross-Modal Attention Consistency (CMAC), for exploring the bidirectional local correspondence property. The CMAC approach aims to align the regional attention generated purely from the visual signal with the target attention generated under the guidance of acoustic signal, and do a similar alignment for frequency grounding on the acoustic attention. Accompanied by a remoulded cross-modal contrastive loss where we consider additional within-modal interactions, the CMAC approach works effectively for enforcing the bidirectional alignment. Extensive experiments on six downstream benchmarks demonstrate that CMAC can improve the state-of-the-art performance on both visual and audio modalities.
We present a cross-calibration of CO- and dust-based molecular gas masses at $z \leqslant 0.2$. Our results are based on a survey with the IRAM 30-m telescope collecting CO(1-0) measurements of 78 massive ($\log M_{\star} / M_{\odot} > 10$) galaxies with known gas-phase metallicities, and with IR photometric coverage from WISE (22 $\mu$m ) and Herschel SPIRE (250, 350, 500 $\mu$m). We find a tight relation ($\sim 0.17$ dex scatter) between the gas masses inferred from CO and dust continuum emission, with a minor systematic offset of 0.05 dex. The two methods can be brought into agreement by applying a metallicity-dependent adjustment factor ($\sim 0.13$ dex scatter). We illustrate that the observed offset is consistent with a scenario in which dust traces not only molecular gas, but also part of the ${\rm H \small I}$ reservoir, residing in the ${\rm H_2}$-dominated region of the galaxy. Observations of the CO(2-1) to CO(1-0) line ratio for two thirds of the sample indicate a narrow range in excitation properties, with a median ratio of luminosities $ \left\langle R_{21} \right\rangle \sim 0.64 $. Finally, we find dynamical mass constraints from spectral line profile fitting to agree well with the anticipated mass budget enclosed within an effective radius, once all mass components (stars, gas and dark matter) are accounted for.
A high-symmetry crystal surface may undergo a kinetic instability during the growth, such that its late stage evolution resembles a phase separation process. This parallel is rigorous in one dimension, if the conserved surface current is derivable from a free energy. We study the problem in presence of a physically relevant term breaking the up-down symmetry of the surface and which can not be derived from a free energy. Following the treatment introduced by Kawasaki and Ohta [Physica 116A, 573 (1982)] for the symmetric case, we are able to translate the problem of the surface evolution into a problem of nonlinear dynamics of kinks (domain walls). Because of the break of symmetry, two different classes ($A$ and $B$) of kinks appear and their analytical form is derived. The effect of the adding term is to shrink a kink $A$ and to widen the neighbouring kink $B$, in such a way that the product of their widths keeps constant. Concerning the dynamics, this implies that kinks $A$ move much faster than kinks $B$. Since the kink profiles approach exponentially the asymptotical values, the time dependence of the average distance $L(t)$ between kinks does not change: $L(t)\sim\ln t$ in absence of noise, and $L(t)\sim t^{1/3}$ in presence of (shot) noise. However, the cross-over time between the first and the second regime may increase even of some orders of magnitude. Finally, our results show that kinks $A$ may be so narrow that their width is comparable to the lattice constant: in this case, they indeed represent a discontinuity of the surface slope, that is an angular point, and a different approach to coarsening should be used.
UBVRI CCD photometry of a $2.^{\prime}1 \times 3.^{\prime}3$ field centered on the young open cluster Haffner~18 is presented and discussed. Spectroscopic classification of seven stars is also provided. 44 clusters members are identified, the earliest type being O6. The distance to the cluster is found to be 6.3 kpc, corresponding to a galactocentric distance of 12.7 kpc (for a Sun galactocentric distance of 8.5 kpc). Excellent fit to the observed main sequence is achieved by a solar composition isochrone of 2$\times 10^6$ years reddened by E$_{B-V}$=0.62 mag. Differential reddening of intra-cluster origin is present. Pre-main sequence members are likely to be present over the 6 mag range explored by our observations (reaching down to earliest A spectral types). The presence of differential reddening and pre-main sequence members agrees with the evidence for a bright parent nebulosity embedding the whole cluster. The radial velocity of the cluster is consistent with the Hron (1987) model of galactic rotation.
Relativistic electrons accelerated by both the first-order and the second-order Fermi accelerations in some synchrotron sources have a hybrid shape of thermal and nonthermal energy distribution. This particle acceleration result is supported by some recent numerical simulations. We calculate the synchrotron polarization by applying this electron energy distribution. The polarization degrees in the cases of active galactic nucleus (AGN) jets and gamma-ray bursts (GRBs) are given as examples. The possible application for the polarization study of Sgr A* is also mentioned. We finally suggest high-energy polarization measurements for these synchrotron sources to test our results.
Massive early-type galaxies have higher metallicities and higher ratios of $\alpha$ elements to iron than their less massive counterparts. Reproducing these correlations has long been a problem for hierarchical galaxy formation theory, both in semi-analytic models and cosmological hydrodynamic simulations. We show that a simulation in which gas cooling in massive dark haloes is quenched by radio-mode active galactic nuclei (AGNs) feedback naturally reproduces the observed trend between $\alpha$/Fe and the velocity dispersion of galaxies, $\sigma$. The quenching occurs earlier for more massive galaxies. Consequently, these galaxies complete their star formation before $\alpha$/Fe is diluted by the contribution from type Ia supernovae. For galaxies more massive than $\sim 10^{11}~M_\odot$ whose $\alpha$/Fe correlates positively with stellar mass, we find an inversely correlated mass-metallicity relation. This is a common problem in simulations in which star formation in massive galaxies is quenched either by quasar- or radio-mode AGN feedback. The early suppression of gas cooling in progenitors of massive galaxies prevents them from recapturing enriched gas ejected as winds. Simultaneously reproducing the [$\alpha$/Fe]-$\sigma$ relation and the mass-metallicity relation is, thus, difficult in the current framework of galaxy formation.
HR 4049 is a peculiar evolved binary which is surrounded by a circumbinary disk. Mid-infrared observations show that the disk is rich in molecular gas and radially extended. To study the properties of this disk, we re-analyzed a set of near-infrared observations at high spectral resolution obtained with Gemini-Phoenix. These data cover absorption lines originating from the first overtone of CO and from \hoh in the 2.3 $\mu$m region as well as more complex emission-absorption profiles from \hoh and the fundamental mode of CO near 4.6 $\mu$m. By using an excitation diagram and from modeling the spectrum, we find that most of the CO overtone and \hoh absorption originates from hot gas ($T_{\rm ex} \approx 1000$~K) with high column densities, consistent with the mid-infrared data. The strong emission in the wavelength range of the CO fundamental furthermore suggests that there is a significant quantity of gas in the inner cavity of the disk. In addition, there is a much colder component in the line of sight to the disk. A detailed analysis of the overtone line profiles reveals variations in the line widths which are consistent with a radially extended disk in Keplerian rotation with hotter gas closer to the central star. We estimate the mass of the primary to be $\sim 0.34$~M$_{\odot}$ and discuss the implications for its evolutionary status.
Generalizing our previous work, we show how $O(d,d)$ transformations can be used to "boost away" in new dimensions the physical singularities that occur generically in cosmological and/or black-hole string backgrounds. As an example, we show how a recent model by Nappi and Witten can be made singularity-free via $O(3,3)$ boosts involving a fifth dimension.
We analyse the aging dynamics of the one-dimensional Fredrickson-Andersen (FA) model in the nonequilibrium regime following a low temperature quench. Relaxation then effectively proceeds via diffusion limited pair coagulation (DLPC) of mobility excitations. By employing a familiar stochastic similarity transformation, we map exact results from the free fermion case of diffusion limited pair annihilation to DLPC. Crucially, we are able to adapt the mapping technique to averages involving multiple time quantities. This relies on knowledge of the explicit form of the evolution operators involved. Exact results are obtained for two-time correlation and response functions in the free fermion DLPC process. The corresponding long-time scaling forms apply to a wider class of DLPC processes, including the FA model. We are thus able to exactly characterise the violations of the fluctuation-dissipation theorem (FDT) in the aging regime of the FA model. We find nontrivial scaling forms for the fluctuation-dissipation ratio (FDR) X = X(tw/t), but with a negative asymptotic value X = -3*pi/(6*pi - 16) = -3.307. While this prevents a thermodynamic interpretation in terms of an effective temperature, it is a direct consequence of probing FDT with observables that couple to activated dynamics. The existence of negative FDRs should therefore be a widespread feature in non mean-field systems.
We discuss the structure of infrared singularities in on-shell QCD amplitudes at two-loop order. We present a general factorization formula that controls all the $\ep$-poles of the dimensionally regularized amplitudes. The dependence on the regularization scheme is considered and the coefficients of the $1/\ep^4, 1/\ep^3$ and $1/\ep^2$ poles are explicitly given in the most general case. The remaining single-pole contributions are also explicitly evaluated in the case of amplitudes with a $q{\bar q}$ pair.
Here we obtain all possible second-order theories for a rank-2 tensor which describe a massive spin-2 particle. We start with a general second-order Lagrangian with ten real parameters. The absence of lower spin modes and the existence of two local field redefinitions leads us to only one free parameter. The solutions split into three one-parameter classes according to the local symmetries of the massless limit. In the class which contains the usual massive Fierz-Pauli theory, the subset of spin-1 massless symmetries is maximal. In another class where the subset of spin-0 symmetries is maximal, the massless theory is invariant under Weyl transformations and the mass term does not need to fit in the form of the Fierz-Pauli mass term. In the remaining third class neither the spin-1 nor the spin-0 symmetry is maximal and we have a new family of spin-2 massive theories.
We discuss statics and dynamics of condensation in a zero-range process with compartments of limited sizes. For the symmetric dynamics the stationary state has a factorized form. For the asymmetric dynamics the steady state factorizes only for special hopping rules which allow for overjumps of fully occupied compartments. In the limit of large system size the grand canonical analysis is exact also in a condensed phase, and for a broader class of hopping rates as compared to the previously studied systems with infinite compartments. The dynamics of condensation exhibits a dynamical self-blocking which significantly prolongs relaxation times. These general features are illustrated with a concrete example: an inhomogeneous system with hopping rates that result in Bose-Einstein-like condensations.
The analogue of temporal coherence resonance for spatial degrees of freedom is reported. Specifically, we show that spatiotemporal noise is able to optimally extract an intrinsic spatial scale in nonlinear media close to (but before) a pattern-forming instability. This effect is observed in a model of pattern-forming chemical reaction and in the Swift-Hohenberg model of fluid convection. In the latter case, the phenomenon is described analytically via an approximate approach.
We present a family of six BVI template light curves for SNe Ia for days -5 and +80, based on high-quality data gathered at CTIO. These templates display a wide range of light curve morphologies, with initial decline rates of their B light curves between m15(B)=0.87 mag and 1.93 mag. We use these templates to study the general morphology of SNe Ia light curves. We find that several of the main features of the BVI templates correlate tightly with m15(B). In particular, the V light curves, which are probably a reasonably good approximation of the bolometric light curves, display an orderly progression in shapes between the most-luminous, slowest-declining events and the least-luminous, fastest-declining SNe. This supports the idea that the observed spectroscopic and photometric sequences of SNe Ia are due primarily to one parameter. Nevertheless, SNe with very similar initial decline rates do show significant differences in their light curve properties when examined in detail, suggesting the influence of one or more secondary parameters.
We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category which does not have a full exceptional collection consisting of line bundles. This provides a counterexample to a conjecture of Lekili and Ueda.
Bianchi modular forms are automorphic forms over an imaginary quadratic field, associated to a Bianchi group. Even though modern studies of Bianchi modular forms go back to the mid 1960's, most of the fundamental problems surrounding their theory are still wide open. Only for certain types of Bianchi modular forms, which we will call non-genuine, it is possible at present to develop dimension formulas: They are (twists of) those forms which arise from elliptic cuspidal modular forms via the Langlands Base-Change procedure, or arise from a quadratic extension of the imaginary quadratic field via automorphic induction (so-called CM-forms). The remaining Bianchi modular forms are what we call genuine, and they are of interest for an extension of the modularity theorem (formerly the Taniyama-Shimura conjecture, crucial in the proof of Femat's Last Theorem) to imaginary quadratic fields. In a preceding paper by Rahm and Sengun, an extreme paucity of genuine cuspidal Bianchi modular forms has been reported, but those and other computations were restricted to level One. In this paper, we are extending the formulas for the non-genuine Bianchi modular forms to deeper levels, and we are able to spot the first, rare instances of genuine forms at deeper level and heavier weight.
We discuss the two-channel Kondo problem with a pseudogap density of states, $\rho(\w)\propto|\w|^r$, of the bath fermions. Combining both analytical and numerical renormalization group techniques, we characterize the impurity phases and quantum phase transitions of the relevant Kondo and Anderson models. The line of stable points, corresponding to the overscreened non-Fermi liquid behavior of the metallic $r=0$ case, is replaced by a stable particle-hole symmetric intermediate-coupling fixed point for $0<r<\rmax\approx0.23$. For $r>\rmax$, this non-Fermi liquid phase disappears, and instead a critical fixed point with an emergent spin--channel symmetry appears, controlling the quantum phase transition between two phases with stable spin and channel moments, respectively. We propose low-energy field theories to describe the quantum phase transitions, all being formulated in fermionic variables. We employ epsilon expansion techniques to calculate critical properties near the critical dimensions $r=0$ and $r=1$, the latter being potentially relevant for two-channel Kondo impurities in neutral graphene. We find the analytical results to be in excellent agreement with those obtained from applying Wilson's numerical renormalization group technique.
We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We first prove that contrary to earlier claims, there is no strong nonlocality: a quantum state localized at the center of a well with infinitely high moving walls is not modified by the wall's motion. We then show the existence of a weak form of nonlocality: when a quantum state is extended over the well, the wall's motion induces a current density all over the box instantaneously. We indicate how this current density can in principle be measured by performing weak measurements of the particle's momentum.