ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we investigate the set of sizes of induced subgraphs of bipartite graphs. We introduce the definition of $C$-$Bipartite$-$Ramsey$ graphs, which is closely related to Ramsey graphs and prove that in `most' cases, these graphs have multiplication tables of $\Omega(e(G))$ in size. We apply our result to give direct evidence to the conjecture that the complete bipartite graph $K_{n,n}$ is the minimiser of the multiplication table on $n^2$ edges raised by Narayanan, Sahasrabudhe and Tomon.
RGB-infrared person re-identification is a challenging task due to the intra-class variations and cross-modality discrepancy. Existing works mainly focus on learning modality-shared global representations by aligning image styles or feature distributions across modalities, while local feature from body part and relationships between person images are largely neglected. In this paper, we propose a Dual-level (i.e., local and global) Feature Fusion (DF^2) module by learning attention for discriminative feature from local to global manner. In particular, the attention for a local feature is determined locally, i.e., applying a learned transformation function on itself. Meanwhile, to further mining the relationships between global features from person images, we propose an Affinities Modeling (AM) module to obtain the optimal intra- and inter-modality image matching. Specifically, AM employes intra-class compactness and inter-class separability in the sample similarities as supervised information to model the affinities between intra- and inter-modality samples. Experimental results show that our proposed method outperforms state-of-the-arts by large margins on two widely used cross-modality re-ID datasets SYSU-MM01 and RegDB, respectively.
A new numerical method to construct binary black hole/neutron star initial data is presented. The method uses three spherical coordinate patches; Two of these are centered at the binary compact objects and cover a neighborhood of each object; the third patch extends to the asymptotic region. As in the Komatsu-Eriguchi-Hachisu method, nonlinear elliptic field equations are decomposed into a flat space Laplacian and a remaining nonlinear expression that serves in each iteration as an effective source. The equations are solved iteratively, integrating a Green's function against the effective source at each iteration. Detailed convergence tests for the essential part of the code are performed for a few types of selected Green's functions to treat different boundary conditions. Numerical computation of the gravitational potential of a fluid source, and a toy model for a binary black hole field are carefully calibrated with the analytic solutions to examine accuracy and convergence of the new code. As an example of the application of the code, an initial data set for binary black holes in the Isenberg-Wilson-Mathews formulation is presented, in which the apparent horizons are located using a method described in Appendix A.
We study the problem of quantization of thin shells in a Weyl-Dirac theory by deriving a Wheeler-DeWitt equation from the dynamics. Solutions are found which have interpretations in both cosmology and particle physics.
We consider UL (and LU) decompositions of the one-step transition probability matrix of a random walk with state space the nonnegative integers, with the condition that both upper and lower triangular matrices in the factorization are also stochastic matrices. We give conditions on the free parameter of the UL factorization in terms of certain continued fraction such that this stochastic factorization is possible. By inverting the order of multiplication (also known as a Darboux transformation) we get a new family of random walks where it is possible the identify the spectral measures in terms of a Geronimus transformation. The same can be done for the LU factorization but now without a free parameter. Finally, we apply our results in two examples, the random walk with constant transition probabilities and the random walk generated by the Jacobi orthogonal polynomials. In both situations we give urn models associated with all the random walks in question.
The proportional elections held in Brazil in 1998 and 2002 display identical statistical signatures. In particular, the distribution of votes among candidates includes a power-law regimen. We suggest that the rationale behind this robust scaling invariance is a multiplicative process in which the voter's choice for a candidate is governed by a product of probabilities.
The inclusion of electromagnetism in a low energy effective theory is worth further study in view of the present high precision experiments (muon g-2, pi_0->2 gamma, tau decays, etc.). In particular in many applications of chiral perturbation theory, one has to purify physical matrix elements from electromagnetic effects. The theoretical problems that I want to point out here are following: the splitting of a pure QCD and a pure electromagnetic part in a hadronic process is model dependent: is it possible to parametrise in a clear way this splitting? What kind of information (scale dependence, gauge dependence,..) is actually included in the parameters of the low energy effective theory? I will attempt to answer these questions introducing a possible convention to perform the splitting between strong and electromagnetic parts in some examples.
Let $\Omega$ be a matrix with entries $a_{i,j}=\omega^{ij},$ $1\leq i,j \leq n,$ where $\omega=e^{2\pi \sqrt{-1}/n},$ $n\in \mathbb N.$ The Chebotarev theorem states that if $n$ is a prime then any minor of $\Omega$ is non-zero. In this note we provide an analogue of this statement for composite $n.$
It is shown that in the 70 and 700 SU(6) irreducible spaces, the SU(6) extension of the Weinberg-Tomozawa (WT) s-wave meson-baryon interaction incorporating vector mesons ({\it hep-ph/0505233}) scales as ${\cal O}(N_c^0)$, instead of the well known ${\cal O}(N_c^{-1})$ behavior for its SU(3) counterpart. However, the WT interaction behaves as order ${\cal O}(N_c^{-1})$ within the 56 and 1134 meson-baryon spaces. Explicit expressions for the WT couplings (eigenvalues) in the irreducible SU(2$N_F$) spaces, for arbitrary $N_F$ and $N_c$, are given. This extended interaction is used as a kernel of the Bethe-Salpeter equation, to study the large $N_c$ scaling of masses and widths of the lowest--lying negative parity s-wave baryon resonances. Analytical expressions are found in the $N_c\to \infty$ limit, from which it can be deduced that resonance widths and excitation energies $(M_R-M)$ behave as order ${\cal O} (N^0_c)$, in agreement with model independent arguments, and moreover they fall in the 70-plet, as expected in constituent quark models for an orbital excitation. For the 56 and 1134 spaces, excitation energies and widths grow ${\cal O} (N_c^{1/2})$ indicating that such resonances do not survive in the large $N_c$ limit. The relation of this latter $N_c$ behavior with the existence of exotic components in these resonances is discussed. The interaction comes out repulsive in the 700.
In this this paper we introduce entanglement among the points in a non-commutative scheme, in addition to the tangent directions. A diagram of $A$-modules is a pair $\uc=(|\uc|,\Gamma)$ where $|\uc|={V_1,...,V_r}$ is a set of $A$-modules, and $\Gamma=\{\gamma_{ij}(l)\}$ is a set of $A$-module homomorphisms $\gamma_{ij}(l):V_i\rightarrow V_j$, seen as the 0'th order tangent directions. This concludes the discussion on non-commutative schemes by defining the deformation theory for diagrams, making these the fundamental points of the non-commutative algebraic geometry, which means that the construction of non-commutative schemes is a closure operation. Two simple examples of the theory are given: The space of a line and a point, which is a non-commutative but untangled example, and the space of a line and a point on the line, in which the condition of the point on the line gives an entanglement between the point and the line.
We derive two-sided bounds for moments and tails of random quadratic forms (random chaoses of order $2$), generated by independent symmetric random variables such that $\lVert X \rVert_{2p} \leq \alpha \lVert X \rVert_p$ for any $p\geq 1$ and some $\alpha\geq 1$. Estimates are deterministic and exact up to some multiplicative constants which depend only on $\alpha$.
Despite of its huge successes in vast amount of applications, the Kohn-Sham scheme of density functional theory (DFT-Kohn-Sham) has not been able to get reliable ionization potentials (IP) for semiconductors, due to self-interaction error in the local density approximation (LDA) and generalized gradient approximations (GGA), and the difficulty of using asymptotically long-ranged potentials for surface calculations. An approximate optimize effective potential (OEP), the Becke-Johnson'06 exchange, is used to explore the capability of OEP to calculate semiconductor IP with a surface technique suitable for both short- and long-ranged potentials. Combined with the LDA correlation, the approximate OEP has achieved an IP accuracy for 17 semiconductors which is similar to the much more sophisticated $GW$ approximation (GWA), with the computational cost of only LDA/GGA. For the first time, this opens the way for systematic calculation of semiconductor IP's by the DFT-Kohn-Sham scheme. The long-range part of the $v_{xc}$ is not as important for solid surface as for atoms and molecules since the wave functions are mainly bound to the slab while less exposed to the asymptotic region. Nevertheless, it contributes significantly to the total IP and therefore shall not be simply ignored. Without including its effects, it is unlikely that the same GWA procedure could achieve universally accurate band gaps and accurate IP's at the same time, as is indeed seen in practical calculations.
We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the J\"uttner function -- originally derived for a flat spacetime -- via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified J\"uttner function, which was initially proposed as an alternative to the J\"uttner function.
We solve the site-site Ornstein-Zernike equation using the Percus-Yevick closure for binary hard-sphere mixture. We calculate an excess chemical potential for the mixture's diameter ratios of 0.3, 0.5, 0.6 and 0.9, and at packing fraction of 0.49 using the analytical expression. Our numerical results are in good agreement with those in the literature.
We propose a subconjecture that implies the semiampleness conjecture for quasi-numerically positive log canonical divisors and prove the semiampleness in some elementary cases.
We have examined the correlations between the large-scale environment of galaxies and their physical properties, using a sample of 28,354 nearby galaxies drawn from the Sloan Digital Sky Survey, and the large-scale tidal field reconstructed in real space from the 2Mass Redshift Survey and smoothed over a radius of $\sim 6 h^{-1}$Mpc. The large-scale environment is expressed in terms of the overdensity, the ellipticity of the shear and the type of the large-scale structure. The physical properties analyzed include $r$-band absolute magnitude $M_{^{0.1}r}$, stellar mass $M_\ast$, $g-r$ colour, concentration parameter $R_{90}/R_{50}$ and surface stellar mass density $\mu_\ast$.   Both luminosity and stellar mass are found to be statistically linked to the large-scale environment, regardless of how the environment is quantified. More luminous (massive) galaxies reside preferentially in the regions with higher densities, lower ellipticities and halo-like structures. At fixed luminosity, the large-scale overdensity depends strongly on parameters related to the recent star formation history, that is colour and D(4000), but is almost independent of the structural parameters $R_{90}/R_{50}$ and $\mu_\ast$. All the physical properties are statistically linked to the shear of the large-scale environment even when the large-scale density is constrained to a narrow range. This statistical link has been found to be most significant in the quasi-linear regions where the large-scale density approximates to an order of unity, but no longer significant in highly nonlinear regimes with $\delta_{\rm LS}\gg 1$.
We discuss abelian equivariant Iwasawa theory for elliptic curves over $\mathbb{Q}$ at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the Beilinson-Kato element to the equivariant $p$-adic $L$-functions. Then we propose equivariant main conjectures and, under certain assumptions, prove one divisibility via Euler system machinery. As an application, we prove a case of a conjecture of Mazur-Tate.
We present deep spectroscopy of 17 very low mass (M* ~ 2.0x10^6 Msun to 1.4x10^9 Msun) and low luminosity (M_UV ~ -13.7 to -19.9) gravitationally lensed galaxies in the redshift range z~1.5-3.0. Deep rest-frame ultraviolet spectra reveal large equivalent width emission from numerous lines (NIV], OIII], CIV, Si III], CIII]) which are rarely seen in individual spectra of more massive star forming galaxies. CIII] is detected in 16 of 17 low mass star forming systems with rest-frame equivalent widths as large as 13.5 Angstroms. Nebular CIV emission is present in the most extreme CIII] emitters, requiring an ionizing source capable of producing a substantial component of photons with energies in excess of 47.9 eV. Photoionization models support a picture whereby the large equivalent widths are driven by the increased electron temperature and enhanced ionizing output arising from metal poor gas and stars, young stellar populations, and large ionization parameters. The young ages implied by the emission lines and continuum SEDs indicate that the extreme line emitters in our sample are in the midst of a significant upturn in their star formation activity. The low stellar masses, blue UV colors, and large sSFRs of our sample are similar to those of typical z>6 galaxies. Given the strong attenuation of Ly-alpha in z>6 galaxies we suggest that CIII] is likely to provide our best probe of early star forming galaxies with ground-based spectrographs and one of the most efficient means of confirming z>10 galaxies with the James Webb Space Telescope.
We investigate the development of the red sequence (RS) of cluster galaxies by using a semi-analytic model of galaxy formation. Results show good agreement between the general trend of the simulated RS and the observed relation in early-type galaxies. However, the most luminous galaxies ($M_V \lesssim -20$) depart from the linear fit to observed data, displaying almost constant colours. We analyze the dependence with redshift of the fraction of stellar mass contributed to each galaxy by different processes (i.e., quiescent star formation, disc instability and mergers), finding that the evolution of the bright end, since $z\approx 2$, is mainly driven by minor and major dry mergers. Since the most luminous galaxies have a narrow spread in ages ($1.0\times 10^{10}$ yr $<t<1.2\times 10^{10}$ yr), their metallicities are the main factor that affects their colours. Galaxies in the bright end reach an upper limit in metallicity as a result of the competition of the mass of stars and metals provided by the star formation within the galaxies and by the accretion of merging satellites. Star formation activity in massive galaxies (M_\star \gtrsim 10^{10} M_{\odot}$) contribute with stellar components of high metallicity, but this fraction of stellar mass is negligible. Mergers contribute with a larger fraction of stellar mass ($\approx 10-20$ per cent), but the metallicity of the accreted satellites is lower by $\approx 0.2$ dex than the mean metallicity of galaxies they merge with. The effect of dry mergers is to increase the mass of galaxies in the bright end, without significantly altering their metallicities, and hence,their colours, giving rise to the break in the RS. These results are found for clusters with different virial masses, supporting the idea of the universality of the CMR in agreement with observational results.
Let S be a complex smooth projective surface and L be a line bundle on S. G\"ottsche conjectured that for every integer r, the number of r-nodal curves in |L| is a universal polynomial of four topological numbers when L is sufficiently ample. We prove G\"ottsche's conjecture using the algebraic cobordism group of line bundles on surfaces and degeneration of Hilbert schemes of points. In addition, we prove the the G\"ottsche-Yau-Zaslow Formula which expresses the generating function of the numbers of nodal curves in terms of quasi-modular forms and two unknown series.
Within the framework of the relativistic distorted wave impulse approximation (DWIA), we investigate the sensitivity of complete sets of polarization transfer observables for exclusive proton knockout from the 3s$_{1/2}$, 2d$_{3/2}$ and 2d$_{5/2}$ states in $^{208}$Pb, at an incident laboratory kinetic energy of 202 MeV, and for coincident coplanar scattering angles ($28.0^{\circ}$, $-54.6^{\circ}$), to different distorting optical potentials, finite-range (FR) versus zero-range (ZR) approximations to the DWIA, as well as medium-modified meson-nucleon coupling constants and meson masses. Results are also compared to the nonrelativistic DWIA predictions based on the Schr\"{o}dinger equation.
We discuss asymptotics for large random planar maps under the assumption that the distribution of the degree of a typical face is in the domain of attraction of a stable distribution with index $\alpha\in(1,2)$. When the number $n$ of vertices of the map tends to infinity, the asymptotic behavior of distances from a distinguished vertex is described by a random process called the continuous distance process, which can be constructed from a centered stable process with no negative jumps and index $\alpha$. In particular, the profile of distances in the map, rescaled by the factor $n^{-1/2\alpha}$, converges to a random measure defined in terms of the distance process. With the same rescaling of distances, the vertex set viewed as a metric space converges in distribution as $n\to\infty$, at least along suitable subsequences, toward a limiting random compact metric space whose Hausdorff dimension is equal to $2\alpha$.
We report on the discovery of a z=1.58 mature cluster around the high-redshift radio galaxy 7C1753+6311, first identified in the Clusters Around Radio-Loud AGN survey. Two-thirds of the excess galaxies within the central 1Mpc lie on a red sequence with a colour that is consistent with an average formation redshift of zf~3. We show that 80+/-6% of the red sequence galaxies in the cluster core are quiescent, while the remaining 20% are red due to dusty star formation. We demonstrate that the cluster has an enhanced quiescent galaxy fraction that is three times that of the control field. We also show that this enhancement is mass dependent: 91+/-9% of the M* >10^{10.5}Msun cluster galaxies are quiescent, compared to only 36+/-2% of field galaxies, whereas the fraction of quiescent galaxies with lower masses is the same in the cluster and field environments. The presence of a dense core and a well-formed, quiescent red sequence suggest that this is a mature cluster. This means that distant radio galaxies do not solely reside in young, uncollapsed protoclusters, rather they can be found in clusters in a wide range of evolutionary states.
We present Spitzer photometric data for a complete sample of 19 low redshift (z<0.1) 3CRR radio galaxies as part of our efforts to understand the origin of the prodigious mid- to far-infrared (MFIR) emission from radio-loud AGN. Our results show a correlation between AGN power (indicated by [OIII] 5007 emission line luminosity) and 24 micron luminosity. This result is consistent with the 24 micron thermal emission originating from warm dust heated directly by AGN illumination. Applying the same correlation test for 70 micron luminosity against [OIII] luminosity we find this relation to suffer from increased scatter compared to that of 24 micron. In line with our results for the higher-radio-frequency-selected 2Jy sample, we are able to show that much of this increased scatter is due to heating by starbursts which boost the far-infrared emission at 70 micron in a minority of objects (17-35%). Overall this study supports previous work indicating AGN illumination as the dominant heating mechanism for MFIR emitting dust in the majority of low to intermediate redshift radio galaxies (0.03<z<0.7), with the advantage of strong statistical evidence. However, we find evidence that the low redshift broad-line objects (z<0.1) are distinct in terms of their positions on the MFIR vs. [OIII] correlations.
We present a trace formula for a Witten type Index for superconformal field theories in d=3,5 and 6 dimensions, generalizing a similar recent construction in d=4. We perform a detailed study of the decomposition of long representations into sums of short representations at the unitarity bound to demonstrate that our trace formula yields the most general index (i.e. quantity that is guaranteed to be protected by superconformal symmetry alone) for the corresponding superalgebras. Using the dual gravitational description, we compute our index for the theory on the world volume of N M2 and M5 branes in the large N limit. We also compute our index for recently constructed Chern Simons theories in three dimensions in the large N limit, and find that, in certain cases, this index undergoes a large N phase transition as a function of chemical potentials.
We draw parallels between the recently introduced ``Immirzi ambiguity'' of the Ashtekar-like formulation of canonical quantum gravity and other ambiguities that appear in Yang-Mills theories, like the $\theta$ ambiguity. We also discuss ambiguities in the Maxwell case, and implication for the loop quantization of these theories.
We are interested in finding an explicit bijection between two families of combinatorial objects: Gog and Magog triangles. These two families are particular classes of Gelfand-Tsetlin triangles and are respectively in bijection with alternating sign matrices (ASM) and totally symmetric self complementary plane partitions (TSSCPP). For this purpose, we introduce left Gog and GOGAm trapezoids. We conjecture that these two families of trapezoids are equienumerated and we give an explicit bijection between the trapezoids with one or two diagonals.
High-energy neutrinos are unique messengers of the high-energy universe, tracing the processes of cosmic-ray acceleration. This paper presents analyses focusing on time-dependent neutrino point-source searches. A scan of the whole sky, making no prior assumption about source candidates, is performed, looking for a space and time clustering of high-energy neutrinos in data collected by the IceCube Neutrino Observatory between 2012 and 2017. No statistically significant evidence for a time-dependent neutrino signal is found with this search during this period since all results are consistent with the background expectation. Within this study period, the blazar 3C 279, showed strong variability, inducing a very prominent gamma-ray flare observed in 2015 June. This event motivated a dedicated study of the blazar, which consists of searching for a time-dependent neutrino signal correlated with the gamma-ray emission. No evidence for a time-dependent signal is found. Hence, an upper limit on the neutrino fluence is derived, allowing us to constrain a hadronic emission model.