ShantanuT01/DACTYL-Pretraining huggingface dataset:
We classify del Pezzo surfaces with Du Val singularities that have infinite automorphism groups, and describe the connected components of their automorphisms groups.
The role played by velocity fields in the fragmentation of a cold medium and in the formation of protostars is studied.   The velocity field is modeled with a compressible turbulent flow. A supersonic turbulent velocity field can fragment the medium into clumps of mass smaller than a local Jeans' mass, and therefore stabilize the medium against the formation of protostars. Based on this idea, the protostar formation efficiency and the protostar mass distribution are determined as functions of the following ambient parameters: average density $n_{0}$, average temperature $T_{0}$, r.m.s. turbulent velocity $\sigma_{v,0}$ (or its Mach number ${\cal{M}}_{t}$), postshock cooling time (e.g. chemistry).   The main results are: i) the protostar mass distribution and its dependence on the ambient parameters are quantified; ii) the characteristic protostar mass is $M_{J,cl}\propto n_{0}^{-1/2}T_{0}^{2} \sigma_{v,0}^{-1}$; iii) the protostar formation efficiency $e$ is higher for larger mean density, larger mean temperature, lower velocity dispersion on a given scale and longer postshock cooling time (e.g. lower metallicity): $e\propto n_{0}^{{3/2}(\beta-1)}T_{0}^{\beta -1} \sigma_{v,0}^{-5(\beta-1)}L_{0}^{3(\beta-1)}$, where $\beta>1$ is the exponent of the clump mass distribution; iv) the efficiency is quite sensitive to the ambient parameters and therefore to the dynamical evolution of the star forming system.
Massive galaxies today typically are not forming stars despite being surrounded by hot gaseous halos with short central cooling times. This likely owes to some form of "quenching feedback" such as merger-driven quasar activity or radio jets emerging from central black holes. Here we implement heuristic prescriptions for these phenomena on-the-fly within cosmological hydrodynamic simulations. We constrain them by comparing to observed luminosity functions and color-magnitude diagrams from SDSS. We find that quenching from mergers alone does not produce a realistic red sequence, because 1 - 2 Gyr after a merger the remnant accretes new fuel and star formation reignites. In contrast, quenching by continuously adding thermal energy to hot gaseous halos quantitatively matches the red galaxy luminosity function and produces a reasonable red sequence. Small discrepancies remain - a shallow red sequence slope suggests that our models underestimate metal production or retention in massive red galaxies, while a deficit of massive blue galaxies may reflect the fact that observed heating is intermittent rather than continuous. Overall, injection of energy into hot halo gas appears to be a necessary and sufficient condition to broadly produce red and dead massive galaxies as observed.
We employ high resolution filtergrams and polarimetric measurements from Hinode to follow the evolution of a sunspot for eight days starting on June 28, 2007. The imaging data were corrected for intensity gradients, projection effects, and instrumental stray light prior to the analysis. The observations show the formation of a light bridge at one corner of the sunspot by a slow intrusion of neighbouring penumbral filaments. This divided the umbra into two individual umbral cores. During the light bridge formation, there was a steep increase in its intensity from 0.28 to 0.7 I_QS in nearly 4 hr, followed by a gradual increase to quiet Sun (QS) values in 13 hr. This increase in intensity was accompanied by a large reduction in the field strength from 1800 G to 300 G. The smaller umbral core gradually broke away from the parent sunspot nearly 2 days after the formation of the light bridge rendering the parent spot without a penumbra at the location of fragmentation. The penumbra in the fragment disappeared first within 34 hr, followed by the fragment whose area decayed exponentially with a time constant of 22 hr. The depleted penumbra in the parent sunspot regenerated when the inclination of the magnetic field at the penumbra-QS boundary became within 40 deg. from being completely horizontal and this occurred near the end of the fragment's lifetime. After the disappearance of the fragment, another light bridge formed in the parent which had similar properties as the fragmenting one, but did not divide the sunspot. The significant weakening in field strength in the light bridge along with the presence of granulation is suggestive of strong convection in the sunspot which might have triggered the expulsion and fragmentation of the smaller spot. Although the presence of QS photospheric conditions in sunspot umbrae could be a necessary condition for fragmentation, it is not a sufficient one.
The paper contains a survey of a class of Fourier integral operators defined by symbols with tempered weight. These operators are bounded (respectively compact) in $L^2$ if the weight of the amplitude is bounded (respectively tends to $0$).
Broad-line type Ic Supernovae (BL-Ic SNe) are characterized by high ejecta velocity ($\gtrsim 10^4$ km s$^{-1}$) and are sometimes associated with the relativistic jets typical of long duration ($\gtrsim 2$ s) Gamma-Ray Bursts (L-GRBs). The reason why a small fraction of BL-Ic SNe harbor relativistic jets is not known. Here we present deep X-ray and radio observations of the BL-Ic SN2014ad extending from $13$ to $930$ days post explosion. SN2014ad was not detected at either frequency and has no observational evidence of a GRB counterpart. The proximity of SN2014ad ($d\sim 26$ Mpc) enables very deep constraints on the progenitor mass-loss rate $\dot{M}$ and on the total energy of the fast ejecta $E$. We consider two synchrotron emission scenarios for a wind-like circumstellar medium (CSM): (i) uncollimated non-relativistic ejecta, and (ii) off-axis relativistic jet. Within the first scenario our observations are consistent with GRB-less BL-Ic SNe characterized by a modest energy budget of their fast ejecta ($E \lesssim 10^{45}$ erg), like SNe 2002ap and 2010ay. For jetted explosions, we cannot rule out a GRB with $E \lesssim 10^{51}$ erg (beam-corrected) with a narrow opening angle ($\theta_j \sim 5^{\circ}$) observed moderately off-axis ($\theta_{\rm obs} \gtrsim 30^{\circ}$) and expanding in a very low CSM density ($\dot{M}$ $\lesssim 10^{-6}$ M$_{\odot}$ yr$^{-1}$). Our study shows that off-axis low-energy jets expanding in a low-density medium cannot be ruled out even in the most nearby BL-Ic SNe with extensive deep observations, and might be a common feature of BL-Ic SNe.
A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.
We find that significant incompleteness in stellar number counts results in a significant overestimate of the microlensing optical depth $\tau$ and event rate per star per year $\Gamma$ toward the Galactic bulge from the first two years of the MOA-II survey. We find that the completeness in Red Clump Giant (RCG) counts $f_{\rm RC}$ decreases proportional to the galactic latitude $b$, as $f_{\rm RC}=(0.63\pm0.11)-(0.052\pm0.028)\times b$, ranging between 1 and 0.7 at $b=-6^\circ\sim-1.5^\circ$. The previous measurements using all sources by Difference Image Analysis (DIA) by MACHO and MOA-I suffer the same bias. On the other hand, the measurements using a RCG sample by OGLE-II, MACHO and EROS were free from this bias because they selected only the events associated with the resolved stars. Thus, the incompleteness both in the number of events and stellar number count cancel out. We estimate $\tau$ and $\Gamma$ by correcting this incompleteness. In the central fields with $|l|<5^\circ$, we find $\Gamma=[18.74\pm0.91]\times10^{-6}\exp[(0.53\pm0.05)(3-|b|)]$ star$^{-1}$ yr$^{-1}$ and $\tau_{200}=[1.84\pm0.14]\times10^{-6}\exp[(0.44\pm0.07)(3-|b|)]$ for the 427 events with $t_{\rm E}\leq200\,$days using all sources brighter than $I_s\leq20$ mag. Our revised all-source $\tau$ measurements are about 2-$\sigma$ smaller than the other all-source measurements and are consistent with the RCG measurements within 1-$\sigma$. We conclude that the long-standing problem on discrepancy between the high $\tau$ with all-source samples by DIA and low $\tau$ with RCG samples can probably be explained by the incompleteness of the stellar number count. A model fit to these measurements predicts $\Gamma=4.60\pm0.25\times10^{-5}$ star$^{-1}$ yr$^{-1}$ at $|b|\sim-1^\circ.4$ and $-2^\circ.25<l<3^\circ.75$ for sources with $I<20$, where the future space mission WFIRST will observe.
In prior work, Cho and Kim studied competition graphs arising from doubly partial orders. In this article, we consider a related problem where competition graphs are instead induced by permutations. We first show that this approach produces the same class of competition graphs as the doubly partial order. In addition, we observe that the $123$ and $132$ patterns in a permutation induce the edges in the associated competition graph. We classify the competition graphs arising from $132$-avoiding permutations and show that those graphs must avoid an induced path graph of length 3. Finally, we consider the weighted competition graph of permutations and give some initial enumerative and structural results in that setting.
The energy levels of the left and the right handed neutrinos is split in the background of gravitational waves generated during inflation which in presence of lepton number violating interactions gives rise to a net lepton asymmetry at equilibrium. Lepton number violation is achieved by the same dimension five operator which gives rise to neutrino masses after electro-weak symmetry breaking. A net baryon asymmetry of the same magnitude can be generated from this lepton asymmetry by electroweak sphaleron processes.
Recently, the quantum information processing power of closed timelike curves have been discussed. Because the most widely accepted model for quantum closed timelike curve interactions contains ambiguities, different authors have been able to reach radically different conclusions as to the power of such interactions. By tracing the information flow through such systems we are able to derive equivalent circuits with unique solutions, thus allowing an objective decision between the alternatives to be made. We conclude that closed timelike curves, if they exist and are well described by these simple models, would be a powerful resource for quantum information processing.
Molecular dynamics is a versatile and powerful method to study diffusion in solid-state ionic conductors, requiring minimal prior knowledge of equilibrium or transition states of the system's free energy surface. However, the analysis of trajectories for relevant but rare events, such as a jump of the diffusing mobile ion, is still rather cumbersome, requiring prior knowledge of the diffusive process in order to get meaningful results. In this work, we present a novel approach to detect the relevant events in a diffusive system without assuming prior information regarding the underlying process. We start from a projection of the atomic coordinates into a landmark basis to identify the dominant features in a mobile ion's environment. Subsequent clustering in landmark space enables a discretization of any trajectory into a sequence of distinct states. As a final step, the use of the smooth overlap of atomic positions descriptor allows distinguishing between different environments in a straightforward way. We apply this algorithm to ten Li-ionic systems and conduct in-depth analyses of cubic Li$_{7}$La$_{3}$Zr$_{2}$O$_{12}$, tetragonal Li$_{10}$GeP$_{2}$S$_{12}$, and the $\beta$-eucryptite LiAlSiO$_{4}$. We compare our results to existing methods, underscoring strong points, weaknesses, and insights into the diffusive behavior of the ionic conduction in the materials investigated.
Among the few known rigorous results for time-dependent equilibrium correlations, important for understanding transport properties, are the Mazur bound and the Suzuki equality. The Mazur inequality gives a lower bound, on the long-time average of the time-dependent auto-correlation function of observables, in terms of equilibrium correlation functions involving conserved quantities. On the other hand, Suzuki proposes an exact equality for quantum systems. In this paper, we discuss the relation between the two results and in particular, look for the analogue of the Suzuki result for classical systems. This requires us to examine as to what constitutes a complete set of conserved quantities required to saturate the Mazur bound. We present analytic arguments as well as illustrative numerical results from a number of different systems. Our examples include systems with few degrees of freedom as well as many-particle integrable models, both free and interacting.
Using an effective potential method we examine binary black holes where the individual holes carry spin. We trace out sequences of quasi-circular orbits and locate the innermost stable circular orbit as a function of spin. At large separations, the sequences of quasi-circular orbits match well with post-Newtonian expansions, although a clear signature of the simplifying assumption of conformal flatness is seen. The position of the ISCO is found to be strongly dependent on the magnitude of the spin on each black hole. At close separations of the holes, the effective potential method breaks down. In all cases where an ISCO could be determined, we found that an apparent horizon encompassing both holes forms for separations well inside the ISCO. Nevertheless, we argue that the formation of a common horizon is still associated with the breakdown of the effective potential method.
At the intersection of two unidirectional traffic flows a stripe formation instability is known to occur. In this paper we consider coupled time evolution equations for the densities of the two flows in their intersection area. We show analytically how the instability arises from the randomness of the traffic entering the area. The Green function of the linearized equations is shown to form a Gaussian wave packet whose oscillations correspond to the stripes. Explicit formulas are obtained for various characteristic quantities in terms of the traffic density and comparison is made with the much simpler calculation on a torus and with numerical solution of the evolution equations.
Several perspectives that can be opened by studying the electroexcitation of the delta via parity-violating electron scattering from nuclei are examined, working within the context of the relativistic Fermi gas model. A strong enhancement of the left-right asymmetry in the delta sector compared with that in the quasi-elastic regime is found and the potential to find clear signatures for the axial-vector contributions of the nucleon-to-delta transition to the asymmetry identified at specific low momentum transfer kinematics. Possibilities of probing the deformation of the delta are also explored, and using both the proton and nuclei as targets, the abilitiy to study the asymmetry on neutrons is studied.
We derive the symmetrized current-noise spectrum of a quantum dot, which is weakly tunnel-coupled to an electron reservoir and driven by a slow time-dependent gate voltage. This setup can be operated as an on-demand emitter of single electrons into a mesoscopic conductor. By extending a real-time diagrammatic technique which is perturbative in the tunnel coupling, we obtain the time-resolved finite-frequency noise as well as its decomposition into noise harmonics in the presence of both strong Coulomb interaction and slow time-dependent driving. We investigate the noise over a large range of frequencies and point out where the interplay of Coulomb interaction and driving leads to unique signatures in finite-frequency noise spectra, in particular in the first harmonic. Besides that, we employ the first noise harmonic as a spectroscopic tool to access individual fluctuation processes. We discuss how the inverse noise frequency sets a time scale for fluctuations, which competes with time scales of the quantum-dot relaxation dynamics as well as the driving.
Inspired by Polyakov's original formulation of quantum Liouville theory through functional integral, we analyze perturbation expansion around a classical solution. We show the validity of conformal Ward identities for puncture operators and prove that their conformal dimension is given by the classical expression. We also prove that total quantum correction to the central charge of Liouville theory is given by one-loop contribution, which is equal to 1. Applied to the bosonic string, this result ensures the vanishing of total conformal anomaly along the lines different from those presented by KPZ and Distler-Kawai.
This paper presents a detailed operational manual for TLUSTY. It provides a guide for understanding the essential features and the basic modes of operation of the program. To help the user, it is divided into two parts. The first part describes the most important input parameters and available numerical options. The second part covers additional details and a comprehensive description of all physical and numerical options, and a description of all input parameters, many of which needed only in special cases.
We show how the SL(5) duality in M-theory is explained from a canonical analysis of M2-brane mechanics. Diffeomorphism constraints for a M2-brane coupled to supergravity background in d=4 are reformulated in a SL(5) covariant form, in which spatial diffeomorphism constraints are recast into a SL(5) vector and the generalized metric in the Hamiltonian constraint is quartic in the SL(5) generalized vielbein. The Hamiltonian for a M2 brane has the SL(5) duality symmetry in a background dependent gauge.
We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in time-varying potential landscapes and thereby disclose the failure of the fractional Fokker-Planck equation (FFPE) in its commonly used form when generalized in an {\it ad hoc} manner to time-dependent forces. A modified FFPE (MFFPE) is rigorously derived, being valid for a family of dichotomously alternating force-fields. This MFFPE is numerically validated for a rectangular time-dependent force with zero average bias. For this case subdiffusion is shown to become enhanced as compared to the force free case. We question, however, the existence of any physically valid FFPE for arbitrary varying time-dependent fields that differ from this dichotomous varying family.
The open intervals in the Bruhat order on twisted involutions in a Coxeter group are shown to be PL spheres. This implies results conjectured by F. Incitti and sharpens the known fact that these posets are Gorenstein* over Z_2.   We also introduce a Boolean cell complex which is an analogue for twisted involutions of the Coxeter complex. Several classical Coxeter complex properties are shared by our complex. When the group is finite, it is a shellable sphere, shelling orders being given by the linear extensions of the weak order on twisted involutions. Furthermore, the h-polynomial of the complex coincides with the polynomial counting twisted involutions by descents. In particular, this gives a type independent proof that the latter is symmetric.
The estimation of viewpoints and keypoints effectively enhance object detection methods by extracting valuable traits of the object instances. While the output of both processes differ, i.e., angles vs. list of characteristic points, they indeed share the same focus on how the object is placed in the scene, inducing that there is a certain level of correlation between them. Therefore, we propose a convolutional neural network that jointly computes the viewpoint and keypoints for different object categories. By training both tasks together, each task improves the accuracy of the other. Since the labelling of object keypoints is very time consuming for human annotators, we also introduce a new synthetic dataset with automatically generated viewpoint and keypoints annotations. Our proposed network can also be trained on datasets that contain viewpoint and keypoints annotations or only one of them. The experiments show that the proposed approach successfully exploits this implicit correlation between the tasks and outperforms previous techniques that are trained independently.
Within a quantum molecular dynamics model we calculate the largest Lyapunov exponent (LLE), density fluctuation and mass distribution of fragments for a series of nuclear systems at different initial temperatures. It is found that the $LLE$ peaks at the temperature ("critical temperature") where the density fluctuation reaches a maximal value and the mass distribution of fragments is best fitted by the Fisher's power law from which the critical exponents for mass and charge distribution are obtained. The time-dependent behavior of the LLE and density fluctuation is studied. We find that the time scale of the density fluctuation is much longer than the inverse LLE, which indicates that the chaotic motion can be well developed during the process of fragment formation. The finite-size effect on "critical temperature" for nuclear systems ranging from Calcium to superheavy nuclei is also studied.
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space entities. The geometry of atoms and subatomic objects differs from that of classical objects. The systems that are non-local when measured in the classical space-time continuum may be localized in the quantum continuum. We compare this new description of space-time with the Bohmian picture of quantum mechanics.
We characterize all the solutions of the heat equation that have their (spatial) equipotential surfaces which do not vary with the time. Such solutions are either isoparametric or split in space-time. The result gives a final answer to a problem raised by M. S. Klamkin, extended by G. Alessandrini, and that was named the Matzoh Ball Soup Problem by L. Zalcman. Similar results can also be drawn for a class of quasi-linear parabolic partial differential equations with coefficients which are homogeneous functions of the gradient variable. This class contains the (isotropic or anisotropic) evolution p-Laplace and normalized p-Laplace equations.
We present our recent results for the pion elastic form factor [1] obtained within a local-duality three-point sum rule (a Borel sum rule in the limit of an infinite Borel parameter). Our analysis includes the O(1) and O(\alpha_s) contributions and is therefore applicable in a broad range of spacelike momentum transfers. Our results demonstrate in essentially model-independent way that the O(1) term, which provides the subleading 1/Q^4 power correction at asymptotically large momentum transfers, contributes more than half of the pion form factor in the region Q^2 \le 20 GeV^2. To probe the accuracy of local-duality sum rules for form factors, we apply precisely the same procedures to extract the form factor in a quantum-mechanical potential model. Comparison of the exact form factor known in this model with the result of the sum-rule calculation gives a probe of the systematic error of the method. In our example this error is found to be at the level of 10-20%. We expect similar systematic errors for form factors obtained from local-duality sum rules in QCD.
It is shown that quantitative information on spatial correlations in a system of polarizable particles can be extracted directly from its experimentally measurable optical spectra. For a collection of metallic nanoparticles (NPs), it is demonstrated that the degree of short-range correlation in NP's positions can be evaluated by an appropriate numerical analysis of the extinction spectrum in the surface plasmon resonance region, given the polarizability of an individual NP. The spectrum analysis consists in the evaluation of a single number, which is the derivative of the ensemble response function in the vanishing polarizability limit, to be compared to pre-calculated values for a model NP system with given density and correlation parameters.