ShantanuT01/DACTYL-Pretraining huggingface dataset:
A planar semimodular lattice $L$ is \emph{slim} if $\mathbf{M}_3$ is not a sublattice of $L$. In a recent paper, G. Cz\'edli introduced a very powerful diagram type for slim, planar, semimodular lattices. This short note proves the existence of such diagrams.
Gribov theory is applied to investigate the shadowing effects in the structure functions of nuclei. In this approach these effects are related to the process of diffractive dissociation of a virtual photon. A model for this diffractive process, which describes well the HERA data, is used to calculate the shadowing in nuclear structure functions. A reasonable description of the x, Q^2 and A-dependence of nuclear shadowing is achieved.
This is a pedagogical review of the subject of linear polymers on deterministic finitely ramified fractals. For these, one can determine the critical properties exactly by real-space renormalization group technique. We show how this is used to determine the critical exponents of self-avoiding walks on different fractals. The behavior of critical exponents for the $n$-simplex lattice in the limit of large $n$ is determined. We study self-avoiding walks when the fractal dimension of the underlying lattice is just below 2. We then consider the case of linear polymers with attractive interactions, which on some fractals leads to a collapse transition. The fractals also provide a setting where the adsorption of a linear chain near on attractive substrate surface and the zipping-unzipping transition of two mutually interacting chains can be studied analytically. We also discuss briefly the critical properties of branched polymers on fractals.
We find the number $s_k(p,\Omega)$ of cuspidal automorphic representations of $\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}})$ with trivial central character such that the archimedean component is a holomorphic discrete series representation of weight $k\ge 3$, and the non-archimedean component at $p$ is an Iwahori-spherical representation of type $\Omega$ and unramified otherwise. Using the automorphic Plancherel density theorem, we show how a limit version of our formula for $s_k(p,\Omega)$ generalizes to the vector-valued case and a finite number of ramified places.
In this letter, we report on high performance depletion/enhancement (D/E)-mode beta-Ga2O3 on insulator (GOOI) field-effect transistors (FETs) with record high drain currents (ID) of 600/450 mA/mm, which are nearly one order of magnitude higher than any other reported ID values. The threshold voltage (VT) can be modulated by varying the thickness of the beta-Ga2O3 films and the E-mode GOOI FET can be simply achieved by shrinking the beta-Ga2O3 film thickness. Benefiting from the good interface between beta-Ga2O3 and SiO2 and wide bandgap of beta-Ga2O3, a negligible transfer characteristic hysteresis, high ID on/off ratio of 10^10, and low subthreshold swing of 140 mV/dec for a 300 nm thick SiO2 are observed. E-mode GOOI FET with source to drain spacing of 0.9 um demonstrates a breakdown voltage of 185 V and an average electric field (E) of 2 MV/cm, showing the great promise of GOOI FET for future power devices.
We explore a generalized Seceder Model with variable size selection groups and higher dimensional genotypes, uncovering its well-defined mean-field limiting behavior. Mapping to a discrete, deterministic version, we pin down the upper critical size of the multiplet selection group, characterize all relevant dynamically stable fixed points, and provide a complete analytical description of its self-similar hierarchy of multiple branch solutions.
The influence of isolated impurity atoms on the electron energy spectrum in a parabolic quantum dot in quantizing magnetic field is studied. The impurity potential is approximated by a Gaussian separable operator which allows one to obtain the exact solution of the problem. We demonstrate that in the electron energy spectrum there is a set of local levels which are split from the Landau zone boundaries in the upward or downward direction depending on the impurity type. We have calculated the local level positions, the wave functions of electrons in bound states, and the residues of the electron scattering amplitudes by impurity atoms at the poles.
The Olkin-Baker functional equation is closely related to the celebrated Lukacs characterization of the gamma distribution. Its deeper understanding is essential to settle a challenging question of multivariate extensions of the Lukacs theorem. In this paper, first, we provide a new approach to the additive Olkin-Baker equation which holds almost everywhere on (0,\infinity)^2 (with respect to the Lebesgue measure on R^2) under measurability assumption. Second, this new approach is adapted to the case when unknown functions are allowed to be non-measurable and the complete solution is given in such a general case. Third, the Olkin-Baker equation holding outside of a set from proper linearly invariant ideal of subsets of R^2 is considered.
In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.
For a loopless multigraph $G$, the fractional arboricity $Arb(G)$ is the maximum of $\frac{|E(H)|}{|V(H)|-1}$ over all subgraphs $H$ with at least two vertices. Generalizing the Nash-Williams Arboricity Theorem, the Nine Dragon Tree Conjecture asserts that if $Arb(G)\le k+\frac{d}{k+d+1}$, then $G$ decomposes into $k+1$ forests with one having maximum degree at most $d$. The conjecture was previously proved for $d=k+1$ and for $k=1$ when $d \le 6$. We prove it for all $d$ when $k \le 2$, except for $(k,d)=(2,1)$.
In "Global regularity for vortex patches" (Commun. Math. Phys. 1993), Bertozzi and Constantin formulate the vortex patch problem in the level-set framework and prove a priori estimates for this active scalar equation. By extending the tools used to prove these estimates, we construct solutions and show propagation of higher H\"older regularity. This constitutes a proof of the regularity of vortex patches, carried out solely in the level-set framework.
A plane quartic curve is called L\"uroth if it contains the ten vertices of a complete pentalateral. White and Miller constructed in 1909 a covariant quartic 4-fold, associated to any plane quartic. We review their construction and we show how it gives a computational tool to detect if a plane quartic is L\"uroth. As a byproduct, the 28 bitangents of a general plane quartic correspond to 28 singular points of the associated White-Miller quartic 4-fold.
It has been proved by Bovier & Hartung [Elect. J. Probab. 19 (2014)] that the maximum of a variable-speed branching Brownian motion (BBM) in the weak correlation regime converges to a randomly shifted Gumbel distribution. The random shift is given by the almost sure limit of McKean's martingale, and captures the early evolution of the system. In the Bovier-Hartung extremal process, McKean's martingale thus plays a role which parallels that of the derivative martingale in the classical BBM. In this note, we provide an alternative interpretation of McKean's martingale in terms of a law of large numbers for high-points of BBM, i.e. particles which lie at a macroscopic distance from the edge. At such scales, 'McKean-like martingales' are naturally expected to arise in all models belonging to the BBM-universality class.
We present a detailed analysis of 17,852 quiescent, Luminous Red Galaxies (LRGs) selected from Sloan Digital Sky Survey (SDSS) Data Release Seven (DR7) spanning a redshift range of 0.0 < z < 0.4. These galaxies are co-added into four equal bins of velocity dispersion and luminosity to produce high signal-to-noise spectra (>100A^{-1}), thus facilitating accurate measurements of the standard Lick absorption-line indices. In particular, we have carefully corrected and calibrated these indices onto the commonly used Lick/IDS system, thus allowing us to compare these data with other measurements in the literature, and derive realistic ages, metallicities ([Z/H]) and alpha-element abundance ratios ([alpha/Fe]) for these galaxies using Simple Stellar Population (SSP) models. We use these data to study the relationship of these galaxy parameters with redshift, and find little evidence for evolution in metallicity or alpha-elements (especially for our intermediate mass samples). This demonstrates that our subsamples are consistent with pure passive evolving (i.e. no chemical evolution) and represent a homogeneous population over this redshift range. We also present the age-redshift relation for these LRGs and clearly see a decrease in their age with redshift (5 Gyrs over the redshift range studied here) which is fully consistent with the cosmological lookback times in a concordance Lambda CDM universe. We also see that our most massive sample of LRGs is the youngest compared to the lower mass galaxies. We provide these data now to help future cosmological and galaxy evolution studies of LRGs, and provide in the appendices of this paper the required methodology and information to calibrate SDSS spectra onto the Lick/IDS system.
Applying newly developed dynamical density matrix renormalization group techniques at zero and finite temperatures to a Hubbard-Holstein model at half-filling, we examine the optical conductivity of a typical one-dimensional Mott insulator Sr_2CuO_3. We find a set of parameters in the Hubbard-Holstein model, which can describe optical conductivity for both Mott-gap excitation in the high-energy region and phonon-assisted spin excitation in the low-energy region. We also find that electron-phonon interaction gives additional broadening in the temperature dependence of the Mott-gap excitation.
Consider an external product of a higher cycle and a usual cycle which is algebraically equivalent to zero. Assume there exists an algebraically closed subfield k such that the higher cycle and its ambient variety are defined over k, but the image of the usual cycle by the Abel-Jacobi map is not. Then we prove that the external product is nonzero if the image of the higher cycle by the cycle map to the reduced Deligne cohomology does not vanish. We also give examples of indecomposable higher cycles on even dimensional hypersurfaces of degree at least four in a projective space such that the last condition is satisfied.
We present a systematic study of the shape function for inclusive B-meson decays in the heavy-quark limit, which is based on the QCD equations of motion and heavy-quark symmetry, and takes into account the cusp divergence due to radiative corrections.
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent.
A majority of shape correspondence frameworks are based on devising pointwise and pairwise constraints on the correspondence map. The functional maps framework allows for formulating these constraints in the spectral domain. In this paper, we develop a functional map framework for the shape correspondence problem by constructing pairwise constraints using point-wise descriptors. Our core observation is that, every point-wise descriptor allows for the construction a pairwise kernel operator whose low frequency eigenfunctions depict regions of similar descriptor values at various scales of frequency. By aggregating the pairwise information from the descriptor and the intrinsic geometry of the surface encoded in the heat kernel, we construct a hybrid kernel and call it the bilateral operator. Analogous to the edge preserving bilateral filter in image processing, the action of the bilateral operator on a function defined over the manifold yields a descriptor dependent local smoothing of that function. By forcing the correspondence map to commute with the Bilateral operator, we show that we can maximally exploit the information from a given set of pointwise descriptors in a functional map framework.
The identity j/n {kn}\choose{n+j} =(k-1) {kn-1}\choose{n+j-1}- {kn-1}\choose{n+j} shows that j/n {kn}\choose{n+j} is always an integer. Here we give a combinatorial interpretation of this integer in terms of lattice paths, using a uniformly distributed statistic. In particular, the case j=1,k=2 gives yet another manifestation of the Catalan numbers.
The effective one-loop action for general dilaton theories with arbitrary dilaton-dependent measure and nonminimal coupling to scalar matter is computed. As an application we determine the Hawking flux to infinity from black holes in d-dimensions. We resolve the recently resurrected problem of an apparent negative flux for nonminimally coupled scalars: For any $D \geq 4$ Black Hole the complete flux turns out to be precisely the one of minimal coupling. This result is obtained from a Christensen-Fulling type argument involving the (non-)conservation of energy-momentum. It is compared with approaches using the effective action.
In this paper, we consider the holograph principle emergent from noncommutative geometry, based on the spectral action principle. We show that under some appropriate conditions, the gravity theory on a manifold with boundary could be equivalent to a gauge theory $SU(N)$ on the boundary. Then an expression for $N$ with the geometrical quantities of the manifold is given. Based on this result, we find that the volume of the manifold and the boundary have some discrete structure. Applying the result to the black hole, we get that the radium of the Schwarzschild black hole is quantized. We also find an explanation why the extremal RN-black hole has zero temperature but with finite entropy.
I review recent advances in our understanding of accretion disks in transient systems - the dwarf novae and the soft X-ray transients. The primary theme will be the ongoing development of theory in response to the observations. The accretion disk limit cycle model appears to provide a unifying framework within which we may begin to understand what is seen in different types of interacting binary stars, and also to constrain parameters which enter into the theory.
We find formulas for the macroscopic Minkowski and Hausdorff dimensions of the range of an arbitrary transient walk in Z^d. This endeavor solves a problem of Barlow and Taylor (1991).
Background subtraction (BGS) is a common choice for performing motion detection in video. Hundreds of BGS algorithms are released every year, but combining them to detect motion remains largely unexplored. We found that combination strategies allow to capitalize on this massive amount of available BGS algorithms, and offer significant space for performance improvement. In this paper, we explore sets of performances achievable by 6 strategies combining, pixelwise, the outputs of 26 unsupervised BGS algorithms, on the CDnet 2014 dataset, both in the ROC space and in terms of the F1 score. The chosen strategies are representative for a large panel of strategies, including both deterministic and non-deterministic ones, voting and learning. In our experiments, we compare our results with the state-of-the-art combinations IUTIS-5 and CNN-SFC, and report six conclusions, among which the existence of an important gap between the performances of the individual algorithms and the best performances achievable by combining them.
Using the instant form dynamics of Poincar\'e invariant quantum mechanics and the modified relativistic impulse approximation proposed previously we calculate asymptotics of electromagnetic form factors for the deuteron considered as two--nucleon system. We show that today experiment on the elastic $ed$-scattering has reached asymptotic regime. The possible range of momentum transfer when the quark degrees of freedom could be seen in future JLab experiments is estimated. The explicit relation between the behavior of deuteron wave function at $r=0$ and the form factors asymptotics is obtained. The conditions on wave functions to give the asymptotics predicted by QCD and quark counting rules are formulated.
Quantum dot lattices (QDLs) have the potential to allow for the tailoring of optical, magnetic and electronic properties of a user-defined artificial solid. We use a dual gated device structure to controllably tune the potential landscape in a GaAs/AlGaAs two-dimensional electron gas, thereby enabling the formation of a periodic QDL. The current-voltage characteristics, I(V), follow a power law, as expected for a QDL. In addition, a systematic study of the scaling behavior of I(V) allows us to probe the effects of background disorder on transport through the QDL. Our results are particularly important for semiconductor-based QDL architectures which aim to probe collective phenomena.
We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of integers with j<k, and assume that they are i.i.d. copies of v. The set of edges of the graph is the set (j,k), j<k. A path in the graph from vertex j to vertex k, j<k, is a finite sequence of edges (j(0), j(1)), (j(1), j(2)), ..., (j(m-1), j(m)) with j(0)=j and j(m)=j; the weight of this path is taken to be the sum v(j(0),j(1))+v(j(1),j(2))+...+v(j(m-1),j(m)) of the weights of its edges. Let w(0,n) be the maximal weight of all paths from 0 to n. We study the asymptotic behaviour of the sequence w(0,n), n=1, 2, ..., as n tends to infinity, under the assumptions that P(v>0)>0, the conditional distribution of v, given v>0, is not degenerate, and that E exp(Cv) is finite, for some C>0. We derive local limit theorems in the normal and moderate large deviations regimes in the case where v has an arithmetic distribution. We also derive an integro-local theorem in the case where v has a non-lattice distribution.
Grassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view-spaces of varying dimensions, generalise the classical notion of fundamental matrices. In this paper we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is declined both from an algebraic and geometric point of view, e.g., the duality between the view spaces and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann tensors, thus showing that this variety is both birational to a suitable homogeneous space and endowed with a dominant rational map to a Grassmannian.
The HII regions are all studied employing the same general prescriptions, despite the possible influence of their environment in their star formation processes. Through the analysis of two samples of 725 inner and 671 outer disk HII region observed spectra, we explore possible systematic differences between their ionising clusters physical properties (metallicity, mass, and age), comparing observations and predictions by photoionisation models. Higher metallicities are confirmed for inner regions, although there are important discrepancies between the diagnostic diagrams. Calibrations based on the N2 index may underestimate inner regions O/H due to the [NII] saturation at solar metallicities. The degeneracy between the age and ionisation parameter affects O/H calibrations based on the O3N2 index. Innermost regions have enhanced N/O ratios, indicating an increase in the slope of the relation between N/O and O/H. Ionisation parameter calibrations based on the [SII]/H{\alpha} ratio are not valid for inner regions due to the bivalued behaviour of this ratio with O/H. Innermost regions have lower [OII]/[OIII] ratios than expected, indicating a possible non-linear relation between u and Z. Ionising and non-ionising populations are present in both inner and outer regions. Inner regions show larger ionising cluster masses that possibly compose star-forming complexes. Outer regions might be affected by stochastic effects. Equivalent widths indicate younger ages for outer regions, but degeneracy between evolution and underlying population effects prevent a quantitative determination. Inner regions have larger angular sizes, lower filling factors, and larger ionised hydrogen masses. The confirmed systematic differences between ionising clusters of inner and outer HII regions condition the validity and range of reliability of O/H and u calibrations commonly applied to the study of HII regions.
Recent observations have successfully detected [O III] $88.3\,{\rm \mu m}$ and [C II] $157.6\,{\rm \mu m}$ lines from galaxies in the early Universe with the Atacama Large Millimeter Array (ALMA). Combining cosmological hydrodynamic simulations and radiative transfer calculations, we present relations between the metal line emission and galaxy evolution at $z=6-15$. We find that galaxies during their starburst phases have high [O III] luminosity of $\sim 10^{42}~\rm erg~s^{-1}$. Once supernova feedback quenches star formation, [O III] luminosities rapidly decrease and continue to be zero for $\sim 100\,{\rm Myr}$. The slope of the relation between $\log{(\rm SFR/M_{\odot}~yr^{-1})}$ and $\log{(L_{\rm [O_{III}]}/{\rm L_{\odot}})}$ at $z=6-9$ is 1.03, and 1.43 for $\log{(L_{\rm [C_{II}]}/{\rm L_{\odot}})}$. As gas metallicity increases from sub-solar to solar metallicity by metal enrichment from star formation and feedback, the line luminosity ratio $L_{\rm [O_{III}]} / L_{\rm [C_{II}]}$ decreases from $\sim 10$ to $\sim 1$ because the O/C abundance ratio decreases due to carbon-rich winds from AGB stars and the mass ratio of {\sc H\,ii} to {\sc H\,i} regions decreases due to rapid recombination. Therefore, we suggest that the combination of [O III] and [C II] lines is a good probe to investigate the relative distribution of ionized and neutral gas in high-$z$ galaxies. In addition, we show that deep [C II] observations with a sensitivity of $\sim 10^{-2}~{\rm mJy~arcsec^{-2}}$ can probe the extended neutral gas disks of high-$z$ galaxies.