ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove two results on arithmetic quantum chaos for dihedral Maass forms, both of which are manifestations of Berry's random wave conjecture: Planck scale mass equidistribution and an asymptotic formula for the fourth moment. For level $1$ forms, these results were previously known for Eisenstein series and conditionally on the generalised Lindelof hypothesis for Hecke-Maass eigenforms. A key aspect of the proofs is bounds for certain mixed moments of $L$-functions that imply hybrid subconvexity.
The shear viscosity for a heated granular binary mixture of smooth hard spheres at low-density is analyzed. The mixture is heated by the action of an external driving force (Gaussian thermostat) which exactly compensate for cooling effects associated with the dissipation of collisions. The study is made from the Boltzmann kinetic theory, which is solved by using two complementary approaches. First, a normal solution of the Boltzmann equation via the Chapman-Enskog method is obtained up to first order in the spatial gradients. The mass, heat, and momentum fluxes are determined and the corresponding transport coefficients identified. As in the free cooling case [V. Garz\'o and J. W. Dufty, Phys. Fluids {\bf 14}, 1476 (2002)], practical evaluation requires a Sonine polynomial approximation, and here it is mainly illustrated in the case of the shear viscosity. Second, to check the accuracy of the Chapman-Enskog results, the Boltzmann equation is numerically solved by means of the Direct Simulation Monte Carlo (DSMC) method. The simulation is performed for a system under uniform shear flow, using the Gaussian thermostat to control inelastic cooling. The comparison shows an excellent agreement between theory and simulation over a wide range of values of the restitution coefficients and the parameters of the mixture (masses, concentrations, and sizes).
We compute the parton distributions for the chiral quark model. We present a new technique for performing such computations based on Green functions. This approach avoids a discretization of the spectrum. It therefore does not need any smoothing procedures.   The results are similar to those of other groups, however the distributions peak at smaller $x$.
For a plane near-triangulation $G$ with the outer face bounded by a cycle $C$, let $n^\star_G$ denote the function that to each $4$-coloring $\psi$ of $C$ assigns the number of ways $\psi$ extends to a $4$-coloring of $G$. The block-count reducibility argument (which has been developed in connection with attempted proofs of the Four Color Theorem) is equivalent to the statement that the function $n^\star_G$ belongs to a certain cone in the space of all functions from $4$-colorings of $C$ to real numbers. We investigate the properties of this cone for $|C|=5$, formulate a conjecture strengthening the Four Color Theorem, and present evidence supporting this conjecture.
Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is activated at that node, and begins its own random walk. The model described belongs to a class of problems that are collectively referred to as the frog model. Building on a recent proof of recurrence (meaning infinitely many frogs hit the root with probability one) on the regular binary tree, this paper establishes recurrence for the 3,2-alternating case.
We present high spatial resolution MIR observations for several nearby radio loud active galactic nuclei (RLAGN), which were obtained using the Gemini North and South telescopes. Of the six observed objects, we detected five in the Si-2 (8.7 microns) and Si-6 (12.3 microns) filters, of which two objects show some evidence of low level extended emission surrounding the unresolved nucleus. In Pictor A, we also obtained an image in Qs (18.3 microns) that has a flux of only half that seen in the Spitzer image, suggesting structure on arcsecond scales. We also used the Si-6 (12.3 microns) flux measurement to investigate correlation between our MIR flux and xray luminosity and compare this to results for AGN in general. This work also forms a basis for future high resolution imaging and spectroscopy of these objects.
Consider the Cauchy problem for the 3-d linear wave equation $\square_{1+3}U=0$ with radial initial data $U(0,x)=\Phi(x)=\phi(|x|)$, $U_t(0,x)=\Psi(x)=\psi(|x|)$. A standard result gives that $U$ belongs to $C([0,T];H^s(\mathbb{R}^3))$ whenever $(\Phi,\Psi)\in H^s\times H^{s-1}(\mathbb{R}^3)$. In this note we are interested in the question of how $U$ can be realized as a limit of solutions to initial-boundary value problems on the exterior of vanishing balls $B_\varepsilon$ about the origin. We note that, as the solutions we compare are defined on different domains, the answer is not an immediate consequence of $H^s$ well-posedness for the wave equation.   We show how explicit solution formulae yield convergence and optimal regularity for the Cauchy solution via exterior solutions, when the latter are extended continuously as constants on $B_\varepsilon$ at each time. We establish that for $s=2$ the solution $U$ can be realized as an $H^2$-limit (uniformly in time) of exterior solutions on $\mathbb{R}^3\setminus B_\varepsilon$ satisfying vanishing Neumann conditions along $|x|=\varepsilon$, as $\varepsilon\downarrow 0$. Similarly for $s=1$: $U$ is then an $H^1$-limit of exterior solutions satisfying vanishing Dirichlet conditions along $|x|=\varepsilon$.
The Hall effect of LuRh2Si2--the non-magnetic homologue of the heavy-fermion material YbRh2Si2--is studied with two different setups: In the conventional single-field geometry, the field dependence is analyzed in terms of the differential Hall coefficient. Beyond that, the recently developed crossed-field experiment allows to examine the linear-response Hall coefficient as a function of magnetic field. The results reveal the expected analogy between both experiments which corroborates the equivalent findings in YbRh2Si2. This emphasizes the applicability to investigate field-induced quantum critical points with both methods.
We consider semi-orthogonal decompositions of derived categories for 3-dimensional projective varieties in the case when the varieties have ordinary double points.
We study quadrilaterals inscribed and circumscribed about conics. Our research is guided by experiments in software Cinderella. We extend the known results in projective geometry of conics and show how modern mathematical software brings new ideas in pure and applied mathematics. Poncelet theorem for quadrilaterals is proved by elementary means together with Poncelet's grid property.
Two classically identical expressions for the mutual information generally differ when the two systems involved are quantum. We investigate this difference -- quantum discord -- and show that it can be used as a criterion for the classicality of the correlations. We also show that quantum discord can be used for describing the selection of the preferred, effectively classical, pointer states.
We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter region where the uniform solution is stable against a localized perturbation. We also found an oscillatory solution in the linearly unstable region and its period is not commensurate with the periodicity of the car index space. The oscillatory solution has some features in common with the synchronized flow observed in real traffic.
Macroscopic dark matter -- "macros"-- refers to a broad class of alternative candidates to particle dark matter with still unprobed regions of parameter space. These candidates would transfer energy primarily through elastic scattering with approximately their geometric cross-section. For sufficiently large cross-sections, the linear energy deposition could produce observable signals if a macro were to pass through compact objects such as white dwarfs or neutron stars in the form of thermonuclear runaway, leading to a type IA supernova or superburst respectively. We update the constraints from white dwarfs. These are weaker than previously inferred in important respects because of more careful treatment of the passage of a macro through the white dwarf and greater conservatism regarding the size of the region that must be heated to initiate runaway. On the other hand, we place more stringent constraints on macros at low cross-section, using new data from the Montreal White Dwarf Database. New constraints are inferred from the low mass X-ray binary 4U 1820-30, in which more than a decade passed between successive superbursts. Updated microlensing constraints are also reported.
Suzaku has, for the first time, enabled the hard X-ray variability of the Seyfert 1 galaxy MCG-6-30-15 to be measured. The variability in the 14-45 keV band, which is dominated by a strong reflection hump, is quenched relative to that at a few keV. This directly demonstrates that the whole reflection spectrum is much less variable than the power-law continuum. The broadband spectral variability can be decomposed into two components - a highly variable power-law and constant reflection - as previously inferred from other observations in the 2-10 keV band. The strong reflection and high iron abundance give rise to a strong broad iron line, which requires the inner disc radius to be at about 2 gravitational radii. Our results are consistent with the predictions of the light bending model which invokes the very strong gravitational effects expected very close to a rapidly spinning black hole.
We analyze the observations from Solar TErrestrial RElations Observatory (STEREO)-A\&B/COR-1 of an eruptive prominence in the intermediate corona on 7 June 2011 at 08:45 UT, which consists of magnetic Rayleigh-Taylor (MRT) unstable plasma segments. Its upper northward segment shows spatio-temporal evolution of MRT instability in form of finger structures upto the outer corona and low inter-planetary space. Using method of Dolei et al.(2014), It is estimated that the density in each bright finger is greater than corresponding dark region lying below of it in the surrounding intermediate corona. The instability is evolved due to wave perturbations that are parallel to the magnetic field at the density interface. We conjecture that the prominence plasma is supported by tension component of the magnetic field against gravity. Using linear stability theory, magnetic field is estimated as 21-40 mG to suppress growth of MRT in the observed finger structures. In the southward plasma segment, a horn-like structure is observed at 11:55 UT in the intermediate corona that also indicates MRT instability. Falling blobs are also observed in both the plasma segments. In the outer corona upto 6-13 solar radii, the mushroom-like plasma structures have been identified in the upper northward MRT unstable plasma segment using STEREO-A/COR-2. These structures most likely grew due to the breaking and twisting of fingers at large spatial scales in weaker magnetic fields. In the lower inter-planetary space upto 20 solar radii, these structures are fragmented into various small-scale localized plasma spikes most likely due to turbulent mixing.
Recent interest in flavour or horizontal symmetry building (mass textures) has been spurred mainly by the large top mass and, hence, the strong hierarchy in quark masses. Recently, various symmetry breaking schemes have been proposed based on the discrete, non-Abelian group S3L x S3R, which is broken according to S3L x S3R > S3_diag > S2_diag. The group S3 treats three objects symmetrically, while the hierarchical nature of the Yukawa matrices is a consequence of the representation structure, 1 + 2, of S3, which treats the generations differently. Different ansaetze for the breaking of the sub-nuclear democracy give different Hermitian mass matrices, M, of the same modified Fritzsch type which differ in the numerical value of the ratio M_23/M_22. A fit to the experimentally determined absolute values of the elements of the CKM matrix gives bounds on the possible values of the CP violating phase and gives a clear indication on the preferred symmetry breaking scheme. A parametrization of the CKM mixing matrix in terms of four quark mass ratios and one CP violating phase in very good agreement with the absolute value of the experimentally determined values of the CKM matrix elements is obtained.
We analyze a confined flare that developed a hot cusp-like structure high in the corona (H ~ 66 Mm). A growing cusp-shaped flare arcade is a typical feature in the standard model of eruptive flares, caused by magnetic reconnection at progressively larger coronal heights. In contrast, we observe a static hot cusp during a confined flare. Despite an initial vertical temperature distribution similar to that in eruptive flares, we observe a distinctly different evolution during the late (decay) phase, in the form of prolonged hot emission. The distinct cusp shape, rooted at locations of non-thermal precursor activity, was likely caused by a magnetic field arcade that kinked near the top. Our observations indicate that the prolonged heating was a result of slow local reconnection and an increased thermal pressure near the kinked apexes due to continuous plasma upflows.
The physical mechanism for triggering the changing-look phenomenon in active galactic nuclei (AGNs) is still unclear. We explore this issue based on the multi-wavelength spectral and flux variations for a changing-look AGN Mrk~1018 with long-term observations in the X-ray, optical/ultraviolet(UV), and radio bands. Both the optical and the X-ray emission experience rapid decay in changing-look phase during 2010--2015, where a re-flare appears in the optical/UV and X-ray bands. We find a time lag of $\sim 20 $ days of optical/UV behind X-ray variations in type 1.9 phase. The 5 GHz radio flux decreases by $\sim 20$\% in type 1.9 phase during 2016--2017. We find both X-ray photon index ($\Gamma$) and the optical-to-X-ray spectral index (\alphaox\,) are anti-correlated with the Eddington scaled 2--10~keV X-ray luminosity ($L_\mathrm{X}/L_\mathrm{Edd}$) in the type 1.9 phase. However, the type 1 phase deviates from these two anti-correlations, which suggests that the change of broad emission lines might be regulated by the evolution of accretion disk (e.g., disappearing of the inner cold disk in the type 1.9 phase).
IRAS 19312+1950 is a peculiar object that has eluded firm characterization since its discovery, with combined maser properties similar to an evolved star and a young stellar object (YSO). To help determine its true nature, we obtained infrared spectra of IRAS 19312+1950 in the range 5-550 $\mu$m using the Herschel and Spitzer space observatories. The Herschel PACS maps exhibit a compact, slightly asymmetric continuum source at 170 $\mu$m, indicative of a large, dusty circumstellar envelope. The far-IR CO emission line spectrum reveals two gas temperature components: $\approx0.22M_{\odot}$ of material at $280\pm18$ K, and $\approx1.6M_{\odot}$ of material at $157\pm3$ K. The OI 63 $\mu$m line is detected on-source but no significant emission from atomic ions was found. The HIFI observations display shocked, high-velocity gas with outflow speeds up to 90 km s$^{-1}$ along the line of sight. From Spitzer spectroscopy, we identify ice absorption bands due to H$_2$O at 5.8 $\mu$m and CO$_2$ at 15 $\mu$m. The spectral energy distribution is consistent with a massive, luminous ($\sim2\times10^4L_{\odot}$) central source surrounded by a dense, warm circumstellar disk and envelope of total mass $\sim500$-$700M_{\odot}$, with large bipolar outflow cavities. The combination of distinctive far-IR spectral features suggest that IRAS 19312+1950 should be classified as an accreting high-mass YSO rather than an evolved star. In light of this reclassification, IRAS 19312+1950 becomes only the 5th high-mass protostar known to exhibit SiO maser activity, and demonstrates that 18 cm OH maser line ratios may not be reliable observational discriminators between evolved stars and YSOs.
Observations of young star clusters reveal that the high-mass end of the cluster initial mass function (CIMF) deviates from a pure power-law and instead truncates exponentially. We investigate the effects of this truncation on the formation of globular cluster (GC) systems by updating our analytic model for cluster formation and evolution, which is based on dark matter halo merger trees coupled to empirical galactic scaling relations, and has been shown in previous work to match a wide array of observational data. The cutoff masses of $M_c=10^{6.5} M_{\odot}$ or $10^{7}M_{\odot}$ match many scaling relations: between the GC system mass and host halo mass, between the average metallicity of the GC system and host halo mass, and the distribution of cluster masses. This range of $M_c$ agrees with indirect measurements from extragalactic GC systems. Models with $M_c<10^{6.5}M_{\odot}$ cannot reproduce the observed GC metallicity and mass distributions in massive galaxies. The slope of the mass-metallicity relation for metal-poor clusters (blue tilt) for all $M_c$ models is consistent with observations within their errors, when measured using the same method. We introduce an alternative, more robust fitting method, which reveals a trend of increasing tilt slope for lower $M_c$. In our model the blue tilt arises because the metal-poor clusters form in relatively low-mass galaxies which lack sufficient cold gas to sample the CIMF at highest masses. Massive blue clusters form in progressively more massive galaxies and inherit their higher metallicity. The metal-rich clusters do not exhibit such a tilt because they form in significantly more massive galaxies, which have enough cold gas to fully sample the CIMF.
Recent advances in facial expression synthesis have shown promising results using diverse expression representations including facial action units. Facial action units for an elaborate facial expression synthesis need to be intuitively represented for human comprehension, not a numeric categorization of facial action units. To address this issue, we utilize human-friendly approach: use of natural language where language helps human grasp conceptual contexts. In this paper, therefore, we propose a new facial expression synthesis model from language-based facial expression description. Our method can synthesize the facial image with detailed expressions. In addition, effectively embedding language features on facial features, our method can control individual word to handle each part of facial movement. Extensive qualitative and quantitative evaluations were conducted to verify the effectiveness of the natural language.
We use a random pinning procedure to investigate stable glassy states associated with large deviations of the activity in a model glass-former. We pin particles both from active (equilibrium) configurations and from stable (inactive) glassy states. By comparing the distribution of the overlap between states that share pinned particles, we infer that the inactive states are characterised by a structural length scale that is comparable with the system size. This is a manifestation of amorphous order in these glassy states, which helps to explain their stability.
Using infrared, radio continuum and spectral observations, we performed a detailed investigation of the HII region RCW175. We determined that RCW175, which actually consists of two separate HII regions, G29.1-0.7 and G29.0-0.6, is located at a distance of 3.2+/-0.2 kpc. Based on the observations we infer that the more compact G29.0-0.6 is less evolved than G29.1-0.7 and was possibly produced as a result of the expansion of G29.1-0.7 into the surrounding interstellar medium. We compute a star formation rate for RCW175 of (12.6+/-1.9)x10^{-5} M_{\sun}/yr, and identified 6 possible young stellar object candidates within its vicinity. Additionally, we estimate that RCW175 contains a total dust mass of 215+/-53 M_{\sun}.   RCW175 has previously been identified as a source of anomalous microwave emission (AME), an excess of emission at cm wavelengths often attributed to electric dipole radiation from the smallest dust grains. We find that the AME previously detected in RCW175 is not correlated with the smallest dust grains (polycyclic aromatic hydrocarbons or small carbonaceous dust grains), but rather with the exciting radiation field within the region. This is a similar result to that found in the Perseus molecular cloud, another region which harbors AME, suggesting that the radiation field may play a pivotal role in the production of this new Galactic emission mechanism. Finally, we suggest that these observations may hint at the importance of understanding the role played by the major gas ions in spinning dust models.
In this paper we establish the boundedness of the extremal solution u^* in dimension N=4 of the semilinear elliptic equation $-\Delta u=\lambda f(u)$, in a general smooth bounded domain Omega of R^N, with Dirichlet data $u|_{\partial \Omega}=0$, where f is a C^1 positive, nondecreasing and convex function in [0,\infty) such that $f(s)/s\rightarrow\infty$ as $s\rightarrow\infty$.   In addition, we prove that, for N>=5, the extremal solution $u^*\in W^{2,\frac{N}{N-2}}$. This gives $u^\ast\in L^\frac{N}{N-4}$, if N>=5 and $u^*\in H_0^1$, if N=6.
It is known that relative entropy of entanglement for entangled state $\rho$ is defined via its closest separable (or positive partial transpose) state $\sigma$. Recently, it has been shown how to find $\rho$ provided that $\sigma$ is given in two-qubit system. In this paper we study on the inverse process, i.e. how to find $\sigma$ provided that $\rho$ is given. It is shown that if $\rho$ is one of Bell-diagonal, generalized Vedral-Plenio and generalized Horodecki states, one can always find $\sigma$ from a geometrical point of view. This is possible due to the following two facts: (i) The Bloch vectors of $\rho$ and $\sigma$ are identical with each other (ii) The qubit-interaction vector of $\sigma$ can be computed from a crossing point between minimal geometrical object, in which all separable states reside in the presence of Bloch vectors, and a straight line, which connects the point corresponding to the qubit-interaction vector of $\rho$ and the nearest vertex of the maximal tetrahedron, where all two-qubit states reside. It is shown, however, that these nice properties are not maintained for the arbitrary two-qubit states.
It was found in the two-dimensional quantum gravity both in the de Donder gauge and in the lightcone gauge that one of field equations breaks down at the level of the representation, though the breakdown is very little. It is shown that this anomalous behavior occurs also in a very simple model analogous to the lightcone-gauge two-dimensional quantum gravity. This model, however, can be transformed into a free field theory by a nonsingular transformation. Of course, the latter has no anomaly. The cause of the discrepancy is analyzed.