ShantanuT01/DACTYL-Pretraining huggingface dataset:
Two-dimensional (2D) Janus transitional metal dichalcogenides (TMDCs) have great potential for photocatalytic water splitting due to their novel properties induced by the unique out-of-plane asymmetric structures. Here, we systematically investigate the geometric, electronic and optical properties of 2D Janus MoSSe with titanium doping and vacancies to explore their synergistic effects on photocatalytic activity. We find that there are effective attractions between the substituted or adsorbed Ti atoms and S/Se vacancies. The Ti adatoms dramatically extend the light absorption range to infrared region. The S/Se vacancies coexisting with Ti adatoms will modulate the transition of photo-excited electrons, thereby enhancing the sunlight absorption. The Ti adatoms either existing alone or coexisting with vacancies introduce smaller lattice distortion compared to substituted Ti atoms and these Ti adatoms induce smaller effective mass of charge carriers. The configuration of S vacancy coexisting with Ti adatoms on Se-surface exhibits the most significant synergistic effects and best overall photocatalytic performance. Our work reveals the mechanism and effects induced by doping and vacancies coexisting in 2D Janus TMDCs, also propose a new practical strategy to improve the performance of 2D photocatalysts.
Globular clusters (GCs) can be considered discrete, long-lived, dynamical tracers that retain crucial information about the assembly history of their parent galaxy. In this paper, we present a new catalogue of GC velocities and colours for the lenticular galaxy NGC 1023, we study their kinematics and spatial distribution, in comparison with the underlying stellar kinematics and surface brightness profile, and we test a new method for studying GC properties. Specifically, we decompose the galaxy light into its spheroid (assumed to represent the bulge + halo components) and disk components and use it to assign to each GC a probability of belonging to one of the two components. Then we model the galaxy kinematics, assuming a disk and spheroidal component, using planetary nebulae (PNe) and integrated stellar light. We use this kinematic model and the probability previously obtained from the photometry to recalculate for each GC its likelihood of being associated with the disk, the spheroid, or neither. We find that the reddest GCs are likely to be associated with the disk, as found for faint fuzzies in this same galaxy, suggesting that the disk of this S0 galaxy originated at z ~ 2. The majority of blue GCs are found likely to be associated with the spheroidal (hot) component. The method also allows us to identify objects that are unlikely to be in equilibrium with the system. In NGC1023 some of the rejected GCs form a substructure in phase space that is connected with NGC 1023 companion galaxy.
Uncertainty in the mass-observable scaling relations is currently the limiting factor for galaxy cluster based cosmology. Weak gravitational lensing can provide a direct mass calibration and reduce the mass uncertainty. We present new ground-based weak lensing observations of 19 South Pole Telescope (SPT) selected clusters at redshifts $0.29 \leq z \leq 0.61$ and combine them with previously reported space-based observations of 13 galaxy clusters at redshifts $0.576 \leq z \leq 1.132$ to constrain the cluster mass scaling relations with the Sunyaev-Zel'dovich effect (SZE), the cluster gas mass \mgas, and \yx, the product of \mgas\ and X-ray temperature. We extend a previously used framework for the analysis of scaling relations and cosmological constraints obtained from SPT-selected clusters to make use of weak lensing information. We introduce a new approach to estimate the effective average redshift distribution of background galaxies and quantify a number of systematic errors affecting the weak lensing modelling. These errors include a calibration of the bias incurred by fitting a Navarro-Frenk-White profile to the reduced shear using $N$-body simulations. We blind the analysis to avoid confirmation bias. We are able to limit the systematic uncertainties to 5.6% in cluster mass (68% confidence). Our constraints on the mass--X-ray observable scaling relations parameters are consistent with those obtained by earlier studies, and our constraints for the mass--SZE scaling relation are consistent with the simulation-based prior used in the most recent SPT-SZ cosmology analysis. We can now replace the external mass calibration priors used in previous SPT-SZ cosmology studies with a direct, internal calibration obtained on the same clusters.
We discuss a progress in calculation of Feynman integrals which has been done with help of the Gegenbauer Polynomial Technique and demonstrate the results for most complicated parts of O(1/N^3) contributions to critical exponents of \phi^4 -theory, for any spacetime dimensionality D.
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo process) with a variable jumping rate. Both the exponential and the algebraic form of the covariance -- defined for the truncated distribution -- are considered. It is demonstrated by numerical calculations that the stationary solution of the master equation for the case of power-law correlations decays with time, but a simple modification of the process makes the tails stable. The main result of the paper is a finding that -- in contrast to the velocity fluctuations -- the position variance may be finite. It rises with time faster than linearly: the diffusion is anomalously enhanced. On the other hand, a process which follows from a superposition of the Ornstein-Uhlenbeck-L\'evy processes always leads to position distributions with a divergent variance which means accelerated diffusion.
Rio gave a concise bound for the central limit theorem in the Vaserstein distances, which is a ratio between some higher moments and some powers of the variance. As a corollary, it gives an estimate for the normal approximation of the small jumps of the L\'evy processes, and Fournier applied that to the Euler approximation of L\'evy-driven stochastic differential equations. However both results are restricted to the one-dimensional case. It will be shown in this article that, following Davie's idea, one can generalise Rio's result to multidimensional case, and the number of moments required is independent of the dimension. Also two different approaches are developed to simulate multidimensional L\'evy SDEs: one as a corollary to the central limit bound, the other directly derived from the L\'evy-Khinchine formula.
In this paper, we consider a cosmological model of the flat and homogeneous universe for the Starobinsky model $F(R)=\alpha R + \beta R^{2}$, which is non-minimally coupled with f-essence. For this model we obtained the field equations and considered particular solutions of the coupling and fermionic field functions. It is shown that the fermionic field can describe a nature of the universe.
We extend techniques employed by Garibaldi to construct various new injections involving the half-spin group, $\textbf{HSpin}$, induced by lifting the Kronecker tensor product to simply connected groups. We calculate the Rost multipliers of the maps we have constructed. Furthermore, we utilize our new map $\textbf{PSp}_{2n}\times \textbf{PSp}_{2m} \hookrightarrow \textbf{HSpin}_{4nm}$ to describe the structure of the normalized degree three cohomological invariants of $\textbf{HSpin}_{4n}$.
In this paper, we extend the resource theory of magic to the channel case by considering completely stabilizer preserving operations (CSPOs) as free. We introduce and characterize the set of CSPO preserving and completely CSPO preserving superchannels. We quantify the magic of quantum channels by extending the generalized robustness and the min relative entropy of magic from the state to the channel domain and show that they bound the single-shot dynamical magic cost and distillation. We also provide analytical conditions for qubit interconversion under CSPOs and show that it is a linear programming feasibility problem and hence can be efficiently solved. Lastly, we give a classical simulation algorithm whose runtime is related to the generalized robustness of magic for channels. Our algorithm depends on some pre-defined precision, and if there is no bound on the desired precision then it achieves a constant runtime.
A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations. Special attention is paid to equivalence with respect to local unitaries and stochastic local operations, invariants along these orbits, momentum map and spectra of partial traces. We discuss absolutely maximally entangled states and their relation to quantum error correction codes. An important case of a large number of parties is also analysed and entanglement in spin systems is briefly reviewed.
We investigate the origin of the observed scaling $j\sim R^{3/2}$ between the specific angular momentum $j$ and the radius $R$ of molecular clouds (MCs) and their their substructures, and of the observed near independence of $\beta$, the ratio of rotational to gravitational energy, from $R$. To this end, we measure the angular momentum (AM) of sets of particles in an SPH simulation of the formation, collapse and fragmentation of giant MCs. The sets of SPH particles are defined either as ``clumps'' (connected particle sets), or as lagrangian sets that conform a connected clump only at a certain time $\tdef$. We find that: {\it i)} Clumps evolve along the observed \jR\ relation at all times, {\it ii)} Lagrangian particle sets evolve along the observed relation when the volume containing them also contains a large number of other ``intruder'' particles. Otherwise, they evolve with $j\sim$ cst. {\it iii)} Tracking lagrangian sets to the future, we find that a subset of the SPH particles participates in the collapse, while another disperses away. {\it iv)} Noting that, under AM conservation, $\beta$ increases during contraction, we suggest that its near independence of radius may arise from the competition between this increase and an increase in the AM exchange rate at higher rotational energy density gradient. {\it v)} We suggest that, if MCs are globally dominated by gravity, the observed \jR\ relation arises because the observational selection of its dense structures amounts to selecting the fragments that have lost AM via Reynolds stresses from their neighbors.
Gabber deduced his theorem of independence of $l$ of intersection cohomology from a general stability result over finite fields. In this article, we prove an analogue of this general result over local fields. More precisely, we introduce a notion of independence of $l$ for systems of complexes of $l$-adic sheaves on schemes of finite type over a local field, equivariant under finite groups. We establish its stability by Grothendieck's six operations and the nearby cycle functor. Our method leads to a new proof of Gabber's theorem. We also give a generalization to algebraic stacks.   -----   Gabber a d\'eduit son th\'eor\`eme d'ind\'ependance de $l$ de la cohomologie l'intersection d'un r\'esultat g\'en\'eral de stabilit\'e sur les corps finis. Dans cet article, nous d\'emontrons un analogue sur les corps locaux de ce r\'esultat g\'en\'eral. Plus pr\'ecis\'ement, nous introduisons une notion d'ind\'ependance de $l$ pour les syst\`emes de complexes de faisceaux $l$-adiques sur les sch\'emas de type fini sur un corps local \'equivariants sous des groupes finis et nous \'etablissons sa stabilit\'e par les six op\'erations de Grothendieck et le foncteur des cycles proches. Notre m\'ethode permet d'obtenir une nouvelle d\'emonstration du th\'eor\`eme de Gabber. Nous donnons aussi une g\'en\'eralisation aux champs alg\'ebriques.
By considering even functions (mod $n$) we generalize a Menon-type identity by Li and Kim involving additive characters of the group ${\Bbb Z}_n$. We use a different approach, based on certain convolutional identities. Some other applications, including related formulas for Ramanujan sums, are discussed, as well.
We report on calculations of the total gravitational energy radiated in the head-on black hole collision, where we use the geometry of the Robinson-Trautman metrics.
We aim to provide spectroscopic evidence regarding the nature of the putative star cluster in Eridanus 2 and to place constraints on the mass and abundance of massive astrophysical compact halo objects (MACHOs) as a constituent of dark matter. Methods. We present spectroscopic observations of the central square arcminute of Eridanus 2 from MUSE-Faint, a survey of ultra-faint dwarf galaxies with the Multi Unit Spectroscopic Explorer on the Very Large Telescope. We derive line-of-sight velocities for possible member stars of the putative cluster and for stars in the centre of Eridanus 2. We discuss the existence of the cluster and determine new constraints for MACHOs using the Fokker-Planck diffusion approximation. Results. Out of 182 extracted spectra, we identify 26 member stars of Eridanus 2, seven of which are possible cluster members. We find intrinsic mean line-of-sight velocities of $79.7^{+3.1}_{-3.8}\,\mathrm{km}\,\mathrm{s}^{-1}$ and $76.0^{+3.2}_{-3.7}\,\mathrm{km}\,\mathrm{s}^{-1}$ for the cluster and the bulk of Eridanus 2, respectively, and intrinsic velocity dispersions of ${<}7.6\,\mathrm{km}\,\mathrm{s}^{-1}$ (68-$\%$ upper limit) and $10.3^{+3.9}_{-3.2}\,\mathrm{km}\,\mathrm{s}^{-1}$, respectively. This indicates the cluster most likely exists as a distinct dynamical population hosted by Eridanus 2, without surplus of dark matter over the background distribution. Among the member stars in the bulk of Eridanus 2, we find possible carbon stars, alluding to the existence of an intermediate-age population. We derive constraints on the fraction of dark matter that can consist of MACHOs with a given mass between $1$-$10^5\,M_\mathrm{sun}$. For dark matter consisting purely of MACHOs, the mass of the MACHOs must be less than ${\sim}7.6\,M_\mathrm{sun}$ and ${\sim}44\,M_\mathrm{sun}$ at a $68$- and $95$-$\%$ confidence level, respectively. (Abridged)
We propose a spin field-effect transistor based on spin-orbit (s-o) coupling of both the Rashba and the Dresselhaus types. Differently from earlier proposals, spin transport through our device is tolerant against spin-independent scattering processes. Hence the requirement of strictly ballistic transport can be relaxed. This follows from a unique interplay between the Dresselhaus and the (gate-controlled) Rashba interactions; these can be tuned to have equal strengths thus yielding k-independent eigenspinors even in two dimensions. We discuss implementations with two-dimensional devices and quantum wires. In the latter, our setup presents strictly parabolic dispersions which avoids complications arising from anticrossings of different bands.
The statistical analysis of parsec scale region of radio galaxies is crucial to obtain information on the nature of their central engine. To this purpose, we defined and observed the Bologna Complete Sample (BCS) which is unbiased with respect to the orientation of the nuclear relativistic jet being selected from low-frequency samples. The BCS is a complete sample of 94 nearby (z<0.1) radio galaxies that are well studied targets with literature kiloparsec data. For all of them, we collected parsec scale information asking new VLBI (VLBA and EVN) observations. Statistical results on their properties in radio band are presented. From the estimates of the Doppler factor and viewing angles, we discuss the connection with the available gamma-ray data. Finally, we show how future observations with Fermi could reveal new important detections of some of the BCS sources.
Very High Energy (VHE) gamma-ray emission from the flat spectrum radio quasar (FSRQ) PKS 1222+21 (4C 21.35, z=0.432) was detected with the MAGIC Cherenkov telescopes during a short observation (~0.5 hr) performed on 2010 June 17. The MAGIC detection coincides with high energy MeV/GeV gamma-ray activity measured by the Large Area Telescope (LAT) on board the Fermi satellite. The VHE spectrum measured by MAGIC extends from about 70 GeV up to at least 400 GeV and can be well described by a power law dN/dE \propto E^-Gamma with a photon index Gamma= 3.75+/-0.27stat +/-0.2syst. The averaged integral flux above 100 GeV is (4.56+/-0.46)x10^(-10) cm^-2 s^-1 (~1 Crab Nebula flux). The VHE flux measured by MAGIC varies significantly within the 30 min exposure implying a flux doubling time of about 10 min. The VHE and MeV/GeV spectra, corrected for the absorption by the extragalactic background light (EBL), can be described by a single power law with photon index 2.72+/-0.34 between 3 GeV and 400 GeV, and is consistent with emission belonging to a single component in the jet. The absence of a spectral cutoff constrains the gamma-ray emission region outside the Broad Line Region, which would otherwise absorb the VHE gamma-rays. Together with the detected fast variability, this challenges present emission models from jets in FSRQ. Moreover, the combined Fermi/LAT and MAGIC spectral data yield constraints on the density of the Extragalactic Background Light in the UV-optical to near-infrared range that are compatible with recent models.
In this article, we define the Pauli Hamiltonian function for twist-deformed N-enlarged Newton-Hooke space-time provided in article [12]. Further, we derive its energy spectrum, i.e., we find the corresponding eigenvalues as well as the proper eigenfunctions.
We establish the existence and uniqueness for a one-dimensional stochastic differential equation driven by a Brownian motion and a pure jump {\levy} process. It is shown that under fairly general conditions on the coefficients, pathwise uniqueness holds based on the methods of weak uniqueness and local time technique.
This is the second part of a work dedicated to the study of Bernstein-Sato polynomials for several analytic functions depending on parameters. In this part, we give constructive results generalizing previous ones obtained by the author in the case of one function. We also make an extensive study of an example for which we give an expression of a generic (and under some conditions, a relative) Bernstein-Sato polynomial.
The spontaneous magnetization of a two-dimensional lattice model can be expressed in terms of the partition function $W$ of a system with fixed boundary spins and an extra weight dependent on the value of a particular central spin. For the superintegrable case of the chiral Potts model with cylindrical boundary conditions, W can be expressed in terms of reduced hamiltonians H and a central spin operator S. We conjectured in a previous paper that W can be written as a determinant, similar to that of the Ising model. Here we generalize this conjecture to any Hamiltonians that satisfy a more general Onsager algebra, and give a conjecture for the elements of S.
We employ a ghost model of interacting dark energy to obtain the equation of state \omega for ghost energy density in an FRW universe in complex quintessence theory. We reconstruct the potential and study the dynamics of the scalar field that describes complex quintessence cosmology. We perform \omega-\omega' analysis and stability analysis for both non-interacting and interacting cases and find that the same basic conclusion as for the real model, where \omega' = d\omega/dlna. Taking account of the effect of the complex part and assuming the real part of the quintessence field to be a "slow-rolling" field, we conclude that the non-interacting model cannot describe the real universe since this will lead to fractional energy density \Omega_D > 1, where \Omega_D can be defined as the ratio of \rho_D to \rho_{cr}. However, for the interacting case, if we take present \Omega_D = 0.73, then we can determine that b^2 = 0.0849, where b^2 is the interaction coupling parameter between matter and dark energy. In the real quintessence model, \Omega_D and b^2 are independent parameters, whereas in the complex quintessence model, we conclude that there is a relationship between these two parameters.
The recently developed atom-bond sum-connection (ABS) index is a variation of the well-studied graph-based molecular descriptors connectivity (Randic), atom-bond connectivity, and sum-connectivity indices.We present the minimum ABS index of trees with a given number of pendent vertices in this paper, which provides a solution to the problem proposed by A. Ali, I. Gutman and I. Redzepovic, Atom-Bond Sum-Connectivity Index of Unicyclic Graphs and Some Applications, Electron. J. Math.(2023) 1-7
We develop a theory for spin transported by coherent Neel dynamics through an antiferromagnetic insulator coupled to a ferromagnetic insulator on one side and a current-carrying normal metal with strong spin-orbit coupling on the other. The ferromagnet is considered within the mono-domain limit and we assume its coupling to the local antiferromagnet Neel order at the ferromagnet|antiferromagnet interface through exchange coupling. Coupling between the charge current and the local Neel order at the other interface is described using spin Hall phenomenology. Spin transport through the antiferromagnet, assumed to possess an easy-axis magnetic anisotropy, is solved within the adiabatic approximation and the effect of spin current flowing into the ferromagnet on its resonance linewidth is evaluated. Onsager reciprocity is used to evaluate the inverse spin Hall voltage generated across the metal by a dynamic ferromagnet as a function the antiferromagnet thickness.
Weakly Supervised Semantic Segmentation (WSSS) based on image-level labels has been greatly advanced by exploiting the outputs of Class Activation Map (CAM) to generate the pseudo labels for semantic segmentation. However, CAM merely discovers seeds from a small number of regions, which may be insufficient to serve as pseudo masks for semantic segmentation. In this paper, we formulate the expansion of object regions in CAM as an increase in information. From the perspective of information theory, we propose a novel Complementary Patch (CP) Representation and prove that the information of the sum of the CAMs by a pair of input images with complementary hidden (patched) parts, namely CP Pair, is greater than or equal to the information of the baseline CAM. Therefore, a CAM with more information related to object seeds can be obtained by narrowing down the gap between the sum of CAMs generated by the CP Pair and the original CAM. We propose a CP Network (CPN) implemented by a triplet network and three regularization functions. To further improve the quality of the CAMs, we propose a Pixel-Region Correlation Module (PRCM) to augment the contextual information by using object-region relations between the feature maps and the CAMs. Experimental results on the PASCAL VOC 2012 datasets show that our proposed method achieves a new state-of-the-art in WSSS, validating the effectiveness of our CP Representation and CPN.
The exact operator solution for quantum Liouville theory constructed for the generic quantum deformation parameter $q$ is extended to the case with $q$ being a root of unity. The screening charge operator becomes nilpotent in such cases and arbitrary Liouville exponentials can be obtained in finite polynomials of the screening charge.
If E is an elliptic curve over Q and K is an imaginary quadratic field, there is an Iwasawa main conjecture predicting the behavior of the Selmer group of E over the anticyclotomic Z_p-extension of K. The main conjecture takes different forms depending on the sign of the functional equation of L(E/K,s). In the present work we combine ideas of Bertolini and Darmon with those of Mazur and Rubin to shown that the main conjecture, regardless of the sign of the functional equation, can be reduced to proving the nonvanishing of sufficiently many p-adic L-functions attached to a family of congruent modular forms.