ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we discuss a class of mean field linear-quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our state is modeled by stochastic Volterra-type equation which leads to some new study on stochastic "integral" system. This feature makes our setup significantly different from the previous mean field games where the states always follow some stochastic "differential" equations. Actually, our stochastic integral system is rather general and can be viewed as natural generalization of stochastic differential equations. In addition, it also includes some types of stochastic delayed systems as its special cases. Second, some new techniques are explored to tackle our mean-field LQG games due to the special structure of integral system. For example, unlike the Riccati equation in linear controlled differential system, some Fredholm-type equations are introduced to characterize the consistency condition of our integral system via the resolvent kernels. Third, based on the state aggregation technique, the Nash certainty equivalence (NCE) equation is derived and the set of associated decentralized controls are verified to satisfy the $\epsilon$-Nash equilibrium property. To this end, some new estimates of stochastic Volterra equations are developed which also have their own interests.
By adopting the empirical constraints related to the estimates of Helium enhancement ($\Delta Y$), present mass ratio between first and second stellar generations ($M_{1G}/M_{2G}$) and the actual mass of Galactic globular clusters ($M_{GC}$), we envisage a possible scenario for the formation of these stellar systems. Our approach allows for the possible loss of stars through evaporation or tidal interactions and different star formation efficiencies. In our approach the star formation efficiency of the first generation ($\epsilon_{1G}$) is the central factor that links the stellar generations as it not only defines both the mass in stars of the first generation and the remaining mass available for further star formation, but it also fixes the amount of matter required to contaminate the second stellar generation. In this way, $\epsilon_{1G}$ is fully defined by the He enhancement between successive generations in a GC. We also show that globular clusters fit well within a $\Delta Y$ {\it vs} $M_{1G}/M_{2G}$ diagram which indicates three different evolutionary paths. The central one is for clusters that have not loss stars, through tidal interactions, from either of their stellar generations, and thus their present $M_{GC}$ value is identical to the amount of low mass stars ($M_* \le$ 1 M$_\odot$) that resulted from both stellar generations. Other possible evolutions imply either the loss of first generation stars or the combination of a low star formation efficiency in the second stellar generation and/or a loss of stars from the second generation. From these considerations we derive a lower limit to the mass ($M_{tot}$) of the individual primordial clouds that gave origin to globular clusters.
In a previous work, we presented a new method to account for the Gribov ambiguities in non-Abelian gauge theories. The method consists on the introduction of an extra constraint which directly eliminates the infinitesimal Gribov copies without the usual geometric approach. Such strategy allows to treat gauges with non-hermitian Faddeev-Popov operator. In this work, we apply this method to a gauge which interpolates among the Landau and maximal Abelian gauges. The result is a local and power counting renormalizable action, free of infinitesimal Gribov copies. Moreover, the interpolating tree-level gluon propagator is derived.
Motivated by applications in computing and telecommunication systems, we investigate the problem of estimating p-quantile of steady-state sojourn times in a single-server multi-class queueing system with non-preemptive priorities for p close to 1. The main challenge in this problem lies in efficient sampling from the tail event. To address this issue, we develop a regenerative simulation algorithm with importance sampling. In addition, we establish a central limit theorem for the estimator to construct the confidence interval. Numerical experiments show that our algorithm outperforms benchmark simulation methods. Our result contributes to the literature on rare event simulation for queueing systems.
The 16Cyg binary system hosts the solar-like Kepler targets with the most stringent observational constraints. Moreover, this system is particularly interesting since both stars are very similar in mass but the A component is orbited by a red dwarf, whereas the B component is orbited by a Jovian planet and thus could have formed a more complex planetary system. In our previous study, we showed that seismic inversions of integrated quantities could be used to constrain microscopic diffusion in the A component. In this study, we analyse the B component in the light of a more regularised inversion. We wish to analyse independently the B component of the 16Cyg binary system using the inversion of an indicator dedicated to analyse core conditions, denoted tu. Using this independent determination, we wish to analyse any differences between both stars due to the potential influence of planetary formation on stellar structure and/or their respective evolution. First, we recall the observational constraints for 16CygB and the method we used to generate reference stellar models. The inversion results were then used to analyse the differences between the A and B components. The tu indicator for 16CygB shows a disagreement with models including microscopic diffusion and sharing the chemical composition previously derived for 16CygA. Small changes in chemical composition are insufficient to solve the problem but that extra mixing can account for the differences seen between both stars. We use a parametric approach to analyse the impact of extra mixing in the form of turbulent diffusion on the behaviour of the tu values. We conclude on the necessity of further investigations using models with a physically motivated implementation of extra mixing including additional constraints to further improve the accuracy with which the fundamental parameters of this system are determined.
Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$ with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that $f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In this paper, we consider the problem of counting minimal permutations in $\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such structures are in one-to-one correspondence with a class of skew Young tableaux, which we call $2$-regular skew tableaux. Using the determinantal formula for the number of skew Young tableaux of a given shape, we find an explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence, we give a combinatorial interpretation of a formula for a refinement of the number $f_{n+1}(2n+1)$.
We study the stationary properties of the Ising model that, while evolving towards its equilibrium state at temperature $T$ according to the Glauber dynamics, is stochastically reset to its fixed initial configuration with magnetisation $m_0$ at a constant rate $r$. Resetting breaks detailed balance and drives the system to a non-equilibrium stationary state where the magnetisation acquires a nontrivial distribution, leading to a rich phase diagram in the $(T,r)$ plane. We establish these results exactly in one-dimension and present scaling arguments supported by numerical simulations in two-dimensions. We show that resetting gives rise to a novel "pseudo-ferro" phase in the $(T,r)$ plane for $r > r^*(T)$ and $T>T_c$ where $r^*(T)$ is a crossover line separating the pseudo-ferro phase from a paramagnetic phase. This pseudo-ferro phase is characterised by a non-zero typical magnetisation and a vanishing gap near $m=0$ of the magnetisation distribution.
We investigate $O(N)$-symmetric vector field theories in the double scaling limit. Our model describes branched polymeric systems in $D$ dimensions, whose multicritical series interpolates between the Cayley tree and the ordinary random walk. We give explicit forms of residual divergences in the free energy, analogous to those observed in the strings in one dimension.
We present a systematic investigation of the effect of H, B, C, and N interstitials on the electronic, lattice and magnetic properties of La(Fe,Si)$_{13}$ using density functional theory. The parent LaSiFe$_{12}$ alloy has a shallow, double-well free energy function that is the basis of itinerant metamagnetism. On increasing the dopant concentration, the resulting lattice expansion causes an initial increase in magnetisation for all interstitials that is only maintained at higher levels of doping in the case of hydrogen. Strong s-p band hybridisation occurs at high B,C and N concentrations. We thus find that the electronic effects of hydrogen doping are much less pronounced than those of other interstitials, and result in the double-well structure of the free energy function being least sensitive to the amount of hydrogen. This microscopic picture accounts for the vanishing first order nature of the transition by B,C, and N dopants as observed experimentally. We use our calculated electronic density of states for LaSiFe$_{12}$ and the hydrogenated alloy to infer changes in magneto-elastic coupling and in phonon entropy on heating through $T_C$ by calculating the fermionic entropy due to the itinerant electrons. Lastly, we predict the electron thermopower in a spin-mixing, high temperature limit and compare our findings to recent literature data.
We study electron propagation through a random array of rare, opaque and large (compared the de Broglie wavelength of electrons) scatterers. It is shown that for any convex scatterer the ratio of the transport to quantum lifetimes \eta=\tau_{tr}/\tau_{tot}$ does not depend on the shape of the scatterer but only on whether scattering is specular or diffuse and on the spatial dimensionality (D). In particular, for specular scattering, \eta is a universal constant determined only by the dimensionality of the system: \eta = 2 for D = 3 and \eta = 3/2 for D = 2. The crossover between classical and quantum regimes of scattering is discussed.
We consider the random walk in an independent and identically distributed (i.i.d.) random environment on a Cayley graph of a finite free product of copies of $\mathbb{Z}$ and $\mathbb{Z}_2$. Such a Cayley graph is readily seen to be a regular tree. Under a uniform elipticity assumption on the i.i.d. environment we show that the walk has positive speed and establish the annealed central limit theorem for the graph distance of the walker from the starting point.
We present results from a set of numerical simulations aimed at exploring the mechanism of coronal mass ejection (CME) suppression in active stars by an overlying large-scale magnetic field. We use a state-of-the-art 3D magnetohydrodynamic (MHD) code which considers a self-consistent coupling between an Alfv\'en wave-driven stellar wind solution, and a first-principles CME model based on the eruption of a flux-rope anchored to a mixed polarity region. By replicating the driving conditions used in simulations of strong solar CMEs, we show that a large-scale dipolar magnetic field of $75$ G is able to fully confine eruptions within the stellar corona. Our simulations also consider CMEs exceeding the magnetic energy used in solar studies, which are able to escape the large-scale magnetic field confinement. The analysis includes a qualitative and quantitative description of the simulated CMEs and their dynamics, which reveals a drastic reduction of the radial speed caused by the overlying magnetic field. With the aid of recent observational studies, we place our numerical results in the context of solar and stellar flaring events. In this way, we find that this particular large-scale magnetic field configuration establishes a suppression threshold around $\sim$$3 \times 10^{32}$~erg in the CME kinetic energy. Extending the solar flare-CME relations to other stars, such CME kinetic energies could be typically achieved during erupting flaring events with total energies larger than $6 \times 10^{32}$ erg (GOES class $\sim$X70).
Recently, great attention has been paid to the possibility of implementing hybrid electronic devices exploiting the self-assembling properties of single molecules. Impressive progress has been done in this field by using organic molecules and macromolecules. However, the use of biomolecules is of great interest because of their larger size (few nanometers) and of their intrinsic functional properties. Here, we show that electron-transfer proteins, such as the blue copper protein azurin (Az), can be used to fabricate biomolecular electronic devices exploiting their intrinsic redox properties, self assembly capability and surface charge distribution. The device implementation follows a bottom-up approach in which the self assembled protein layer interconnects nanoscale electrodes fabricated by electron beam lithography, and leads to efficient rectifying behavior at room temperature.
The second part of the First Byurakan Survey is aimed at detecting all bright (B<16.5) UV-excess starlike objects in a large area of the sky. By comparison with other major surveys such as the ROSAT All Sky Survey, the ROSAT WGACAT catalogue of point sources, the IRAS survey, the 6cm Green Bank, the 1.4GHz NRAO VLA and the 92cm Westerbork Northern sky surveys and with the catalogue of mean UBV data on stars, we estimate the number of AGNs present in the FBS survey and its completeness.   We have made spectroscopic observations of nine of the most promising FBS candidates. We have found six new QSOs bringing the total number of known QSOs in this survey to 42.   By comparison with the Bright Quasar Survey, we found that the completeness of this last survey is of the order of 70% rather than 30-50% as suggested by several authors.
The archetypical very-high-energy gamma-ray blazar Mrk 421 was monitored for more than 3 years with the Gas Slit Camera onboard Monitor of All Sky X-ray Image (MAXI), and its longterm X-ray variability was investigated. The MAXI lightcurve in the 3 -- 10 keV range was transformed to the periodogram in the frequency range $f = 1 \times 10^{-8}$ -- $2 \times 10^{-6}$ Hz. The artifacts on the periodogram, resulting from data gaps in the observed lightcurve, were extensively simulated for variations with a power-law like Power Spectrum Density (PSD). By comparing the observed and simulated periodograms, the PSD index was evaluated as $\alpha = 1.60 \pm 0.25$. This index is smaller than that obtained in the higher frequency range ($f > 1 \times 10^{-5}$ Hz), namely, $\alpha = 2.14 \pm 0.06$ in the 1998 ASCA observation of the object. The MAXI data impose a lower limit on the PSD break at $f_{\rm b} = 5 \times 10^{-6}$ Hz, consistent with the break of $f_{\rm b} = 9.5 \times 10^{-6}$ Hz, suggested from the ASCA data. The low frequency PSD index of Mrk 421 derived with MAXI falls well within the range of the typical value among nearby Seyfert galaxies ($\alpha = 1$ -- $2$). The physical implications from these results are briefly discussed.
We compute the x-ray emission spectrum (XES) of liquid methanol, with the dynamical effects that result from the creation of the core hole included in a semiclassical way. Our method closely reproduces a fully quantum mechanical description of the dynamical effects for relevant one-dimensional models of the hydrogen-bonded methanol molecules. For the liquid we find excellent agreement with the experimental spectrum, including the large isotope effect in the first split peak. The dynamical effects depend sensitively on the initial structure in terms of the local hydrogen-bonding (H-bonding) character; non-donor molecules contribute mainly to the high-energy peak while molecules with a strong donated H-bond contribute to the peak at lower energy. The spectrum thus reflects the initial structure mediated by the dynamical effects that are, however, seen to be crucial in order to reproduce the intensity distribution of the recently measured spectrum.
We consider the prepotential of Dijkgraaf and Vafa (DV) as one more (and in fact, singular) example of the Seiberg-Witten (SW) prepotentials and discuss its properties from this perspective. Most attention is devoted to the issue of complete system of moduli, which should include not only the sizes of the cuts (in matrix model interpretation), but also their positions, i.e. the number of moduli should be almost doubled, as compared to the DV consideration. We introduce the notion of regularized DV system (not necessarilly related to matrix model) and discuss the WDVV equations. These definitely hold before regularization is lifted, but an adequate limiting procedure, preserving all ingredients of the SW theory, remains to be found.
A point particle approximation to the classical dynamics of well separated vortices of the abelian Higgs model is developed. A static vortex is asymptotically identical to a solution of the linearized field theory (a Klein-Gordon/Proca theory) in the presence of a singular point source at the vortex centre. It is shown that this source is a composite scalar monopole and magnetic dipole, and the respective charges are determined numerically for various values of the coupling constant. The interaction potential of two well separated vortices is computed by calculating the interaction Lagrangian of two such point sources in the linear theory. The potential is used to model type II vortex scattering.
We use 350 mu angular diameter estimates from Planck to test the idea that some galaxies contain exceptionally cold (10-13 K) dust, since colder dust implies a lower surface brightness radiation field illuminating the dust, and hence a greater physical extent for a given luminosity. The galaxies identified from their spectral energy distributions as containing cold dust do indeed show the expected larger 350 mu diameters. For a few cold dust galaxies where Herschel data are available we are able to use submillimetre maps or surface brightness profiles to locate the cold dust, which as expected generally lies outside the optical galaxy.
We consider exact time-dependent analytic solutions to the Schr\"odinger equation for tunneling in one dimension with cut off wave initial conditions at $t=0$. We obtain that as soon as $t \neq 0$ the transmitted probability density at any arbitrary distance rises instantaneously with time in a linear manner. Using a simple model we find that the above nonlocal effect of the time-dependent solution is suppressed by consideration of low-energy relativistic effects. Hence at a distance $x_0$ from the potential the probability density rises after a time $t_0=x_0/c$ restoring Einstein causality. This implies that the tunneling time of a particle can never be zero.
We re-examine the Peierls insulator to Mott insulator transition scenario in the one-dimensional Holstein-Hubbard model where, at half-filling, electron-phonon and electron-electron interactions compete for establishing charge- and spin-density-wave states, respectively. By means of large-scale density-matrix renormalization group calculations we determine the spin, single-particle and two-particle excitation gaps and prove--in the course of a careful finite-size scaling analysis--recent claims for an intervening metallic phase in the weak-coupling regime. We show that for large phonon frequencies the metallic region is even more extended than previously expected, and subdivided into ordinary Luttinger liquid and bipolaronic liquid phases.
We point out that the quasiparticle spectrum of the Landau Fermi liquid theory has an extra $Z_2$ symmetry, local in momentum space, which is not generic to the Hamiltonian with interactions. Thus the Fermi liquid is in this sense a (quantum) zero-temperature critical point.
We present a method to automatically learn to segment dynamic objects using SLAM outliers. It requires only one monocular sequence per dynamic object for training and consists in localizing dynamic objects using SLAM outliers, creating their masks, and using these masks to train a semantic segmentation network. We integrate the trained network in ORB-SLAM 2 and LDSO. At runtime we remove features on dynamic objects, making the SLAM unaffected by them. We also propose a new stereo dataset and new metrics to evaluate SLAM robustness. Our dataset includes consensus inversions, i.e., situations where the SLAM uses more features on dynamic objects that on the static background. Consensus inversions are challenging for SLAM as they may cause major SLAM failures. Our approach performs better than the State-of-the-Art on the TUM RGB-D dataset in monocular mode and on our dataset in both monocular and stereo modes.
Different to semantic segmentation, instance segmentation assigns unique labels to each individual instance of the same class. In this work, we propose a novel recurrent fully convolutional network architecture for tracking such instance segmentations over time. The network architecture incorporates convolutional gated recurrent units (ConvGRU) into a stacked hourglass network to utilize temporal video information. Furthermore, we train the network with a novel embedding loss based on cosine similarities, such that the network predicts unique embeddings for every instance throughout videos. Afterwards, these embeddings are clustered among subsequent video frames to create the final tracked instance segmentations. We evaluate the recurrent hourglass network by segmenting left ventricles in MR videos of the heart, where it outperforms a network that does not incorporate video information. Furthermore, we show applicability of the cosine embedding loss for segmenting leaf instances on still images of plants. Finally, we evaluate the framework for instance segmentation and tracking on six datasets of the ISBI celltracking challenge, where it shows state-of-the-art performance.
The photometric light curve of PG1302-102 shows periodic variability which makes this object one of the most plausible supermassive black hole binary candidate. Interestingly, the most recent study of its updated optical light curve reports a decrease in significance of periodicity which may suggest that the binary model is less favorable. Here, we model the PG 1302-102 light curve, spanning almost 20 years, with a supermassive black hole binary system in which a perturbation in the accretion disk of more massive component is present. Our model reproduces well the observed light curve with a slight perturbation of a sinusoidal feature and predicts that a slightly larger period than previously reported, of about 1899 days, could arise due to a cold spot in the disk of {\bf more massive} component of a close, unequal-mass ($\frac{\mathrm{m}_{1}}{\mathrm{m}_{2}}=0.1$) black hole binary system. The light curve resembles the pattern of sinusoid-like shape within a few years, which could be confirmed by future observations. In addition, using our hybrid method for periodicity detection, we show that the periods in the observed ($1972\pm 254$ days) and modeled ($1873 \pm \ 250$ days) light curves are within one-sigma, which is also consistent with our physical model prediction and with previous findings. Thus, both the periodic nature and its slight fluctuation of the light curve of PG1302-102 is evident from our physical model and confirmed by the hybrid method for periodicity detection.