ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $\D_{v,b,k}$ denote the family of all connected block designs with $v$ treatments and $b$ blocks of size $k$. Let $d\in\D_{v,b,k}$. The replication of a treatment is the number of times it appears in the blocks of $d$. The matrix $C(d)=R(d)-\frac{1}{k}N(d)N(d)^\top$ is called the information matrix of $d$ where $N(d)$ is the incidence matrix of $d$ and $R(d)$ is a diagonal matrix of the replications. Since $d$ is connected, $C(d)$ has $v-1$ nonzero eigenvalues $\mu_1(d),...,\mu_{v-1}(d)$. Let $\D$ be the class of all binary designs of $\D_{v,b,k}$. We prove that if there is a design $d^*\in\D$ such that (i) $C(d^*)$ has three distinct eigenvalues, (ii) $d^*$ minimizes trace of $C(d)^2$ over $d\in\D$, (iii) $d^*$ maximizes the smallest nonzero eigenvalue and the product of the nonzero eigenvalues of $C(d)$ over $d\in\D$, then for all $p>0$, $d^*$ minimizes $(\sum_{i=1}^{v-1}\mu_i(d)^{-p})^{1/p}$ over $d\in\D$. In the context of optimal design theory, this means that if there is a design $d^*\in\D$ such that its information matrix has three distinct eigenvalues satisfying the condition (ii) above and that $d^*$ is E- and D-optimal in $\D$, then $d^*$ is $\Phi_p$-optimal in $\D$ for all $p>0$. As an application, we demonstrate the $\Phi_p$-optimality of certain group divisible designs. Our proof is based on the method of KKT conditions in nonlinear programming.
The robustness of stellar-dynamical black hole (BH) mass measurements is illustrated using 7 galaxies that have results from independent groups. Derived masses have remained constant to a factor of about 2 as spatial resolution has improved by factors of 2 - 330 and as the analysis has improved from spherical, isotropic models to axisymmetric, three-integral models. This gives us confidence that the masses are reliable and that the galaxies do not indulge in a wide variety of perverse orbital structures. Constraints on BH alternatives are also improving. In M31, Hubble Space Telescope (HST) spectroscopy shows that the central massive dark object (MDO) is in a tiny cluster of blue stars embedded in the P2 nucleus of the galaxy. The MDO must be less than about 0.06 arcsec in radius. M31 becomes the third galaxy in which dark clusters of brown dwarf stars or stellar remnants can be excluded. In our Galaxy, observations of almost-complete stellar orbits show that the MDO radius is less than about 0.0006 pc. Among BH alternatives, this excludes even neutrino balls. Therefore, measurements of central dark masses and the conclusion that these are BHs have both stood the test of time. Confidence in the BH paradigm for active galactic nuclei is correspondingly high. Compared to the radius of the BH sphere of influence, BHs are discovered at similar spatial resolution with HST as in ground-based work. The reason is that HST is used to observe more distant galaxies. Large, unbiased samples are accessible. As a result, HST has revolutionized the study of BH demographics.
We introduce a deterministic self-organized critical system that is one dimensional and bulk driven. We find that there is no universality class associated with the system. That is, the critical exponents change as the parameters of the system are changed. This is in contrast with the boundary driven version of the model [M. de Sousa Vieira, Phys. Rev. E 61 (2000) 6056] in which the exponents are unique. This model can be seen as a discretized version of the conservative limit of the Burridge-Knopoff model for earthquakes.
We discuss two theoretical motivations of precision measurements of oscillation parameters. One is the guidance for flavour model building with flavour symmetries, and the other is the connection with the origin of matter-antimatter asymmetry. We also present our recent progress in these aspects, a new approach of flavour model building based on cross coupling in the flavon potential and a novel mechanism of leptogenesis via phase transition.
We present a conjectural formula for the principal minors and the characteristic polynomial of Gross's regulator matrix associated to a totally odd character of a totally real field. The formula is given in terms of the Eisenstein cocycle, which was defined and studied earlier by the authors and collaborators. For the determinant of the regulator matrix, our conjecture follows from recent work of Kakde, Ventullo and the first author. For the diagonal entries, our conjecture overlaps with the conjectural formula presented in our prior work. The intermediate cases are new and provide a refinement of the Gross--Stark conjecture.
We compute the effects of soft gluon resummation for the production of high mass systems in hadronic collisions. We carefully analyse the growth of the perturbative expansion coefficients of the resummation formula. We propose an expression consistent with the known leading and next-to-leading resummation results, in which the coefficients grow much less than factorially. We apply our formula to Drell--Yan pair production, heavy flavour production, and the production of high invariant mass jet pairs in hadronic collisions. We find that, with our formula, resummation effects become important only fairly close to the threshold region. In the case of heavy flavour production we find that resummation effects are small in the experimental configurations of practical interest.
In the present work we classify the relatively minimal 3-dimensional quasihomogeneous complex projective varieties under the assumption that the automorphism group is not solvable. By relatively minimal we understand varieties X having at most Q-factorial terminal singularities and allowing an extremal contraction X to Y, where dim Y <3.
We enlighten relations between the K\"all\'en function, allowing in a simple way to distinguish between virtual and real processes involving massive particles, and the dilogarithms occurring as results of loop calculations for such kind of processes.
We discuss the QCD and leading electroweak corrections to the hadronic width of the charged Higgs boson of the MSSM. In our renormalization framework, tan(beta) is defined through Gamma(H^+ -> tau^+ nu_{tau}). We show that a measurement of the hadronic width of H^\pm and/or of the branching ratio of its tau-decay mode with a modest precision of ~20% could be sufficient to unravel the supersymmetric nature of H^\pm in full consistency with the low-energy data from radiative B-meson decays.
The constraints imposed on heterotic compactifications by global consistency and phenomenology seem to be very finely balanced. We show that weakening these constraints, as was proposed in some recent works, is likely to lead to frivolous results. In particular, we construct an infinite set of such frivolous models having precisely the massless spectrum of the MSSM and other quasi-realistic features. Only one model in this infinite collection (the one constructed in arXiv:hep-th/0512149) is globally consistent and supersymmetric. The others might be interpreted as being anomalous, or as non-supersymmetric models, or as local models that cannot be embedded in a global one. We also show that the strongly coupled model of arXiv:hep-th/0512149 can be modified to a perturbative solution with stable SU(4) or SU(5) bundles in the hidden sector. We finally propose a detailed exploration of heterotic vacua involving bundles on Calabi-Yau threefolds with Z_6 Wilson lines; we obtain many more frivolous solutions, but none that are globally consistent and supersymmetric at the string scale.
We report an efficient technique to induce gate-tunable two-dimensional superlattices in graphene by the combined action of a back gate and a few-layer graphene patterned bottom gate complementary to existing methods. The patterned gates in our approach can be easily fabricated and implemented in van der Waals stacking procedures allowing flexible use of superlattices with arbitrary geometry. In transport measurements on a superlattice with lattice constant $a=40$ nm well pronounced satellite Dirac points and signatures of the Hofstadter butterfly including a non-monotonic quantum Hall response are observed. Furthermore, the experimental results are accurately reproduced in transport simulations and show good agreement with features in the calculated band structure. Overall, we present a comprehensive picture of graphene-based superlattices, featuring a broad range of miniband effects, both in experiment and in theoretical modeling. The presented technique is suitable for studying more advanced geometries which are not accessible by other methods.
The goal of this paper is to develop the theory of weighted Diophantine approximation of rational numbers to $p$-adic numbers. Firstly, we establish complete analogues of Khintchine's theorem, the Duffin-Schaeffer theorem and the Jarn\'ik-Besicovitch theorem for `weighted' simultaneous Diophantine approximation in the $p$-adic case. Secondly, we obtain a lower bound for the Hausdorff dimension of weighted simultaneously approximable points lying on $p$-adic manifolds. This is valid for very general classes of curves and manifolds and have natural constraints on the exponents of approximation. The key tools we use in our proofs are the Mass Transference Principle, including its recent extension due to Wang and Wu, and a Zero-One law for weighted $p$-adic approximations established in this paper.
This note for the Proceedings of the International Congress of Mathematical Physics gives an account of a construction of an ``elliptic quantum group'' associated with each simple classical Lie algebra. It is closely related to elliptic face models of statistical mechanics, and, in its semiclassical limit, to the Wess-Zumino-Witten model of conformal field theory on tori.
In this note we show that $k$-convex functions on $\Bbb R^n$ are twice differentiable almost everywhere for every positive integer $k>n/2$. This generalizes the classical Alexsandrov's theorem for convex functions.
We calculate the cross section for the production of a Z boson in association with heavy quarks. We suggest that this cross section can be measured using an inclusive heavy-quark tagging technique. This could be used as a feasibility study for the search for a Higgs boson produced in association with bottom quarks. We argue that the best formalism for calculating that cross section is based on the leading-order process b b -> h, and that it is valid for all Higgs masses of interest at both the Fermilab Tevatron and the CERN Large Hadron Collider.
Let $f$ and $g$, of weights $k'>k\geq 2$, be normalised newforms for $\Gamma_0(N)$, for square-free $N>1$, such that, for each Atkin-Lehner involution, the eigenvalues of $f$ and $g$ are equal. Let $\lambda\mid\ell$ be a large prime divisor of the algebraic part of the near-central critical value $L(f\otimes g,\frac{k+k'-2}{2})$. Under certain hypotheses, we prove that $\lambda$ is the modulus of a congruence between the Hecke eigenvalues of a genus-two Yoshida lift of (Jacquet-Langlands correspondents of) $f$ and $g$ (vector-valued in general), and a non-endoscopic genus-two cusp form. In pursuit of this we also give a precise pullback formula for a genus-four Eisenstein series, and a general formula for the Petersson norm of a Yoshida lift.   Given such a congruence, using the 4-dimensional $\lambda$-adic Galois representation attached to a genus-two cusp form, we produce, in an appropriate Selmer group, an element of order $\lambda$, as required by the Bloch-Kato conjecture on values of $L$-functions.
In the first part we study deviation of a polynomial from its mathematical expectation. This deviation can be estimated from above by Carbery--Wright inequality, so we investigate estimates of the deviation from below. We obtain such estimates in two different cases: for Gaussian measures and a polynomial of an arbitrary degree and for an arbitrary log-concave measure but only for polynomials of the second degree. In the second part we deals with isoperimetric inequality and the Poincar\'e inequality for probability measures on the real line that are images of the uniform distributions on convex compact sets in $\mathbb{R}^n$ under polynomial mappings.
The YN results are presented from the Extended-soft-core (ESC) interactions. They consist of local- and non-local-potentials due to (i) One-boson-exchange (OBE), with pseudoscalar-, vector-, scalar-, and axial-vector-nonets, (ii) Diffractive exchanges, (iii) Two-pseudoscalar exchange, and (iv) Meson-pair-exchange (MPE). This model, called ESC04, describes NN and YN in a unified way using broken flavor SU(3)-symmetry. Novel ingredients are the inclusion of (i) the axial-vector-mesons, (ii) a zero in the scalar- and axial-vector meson form factors. We describe simultaneous fits to the NN- and YN-data, using four options in the ESC-model. Very good fits were obtained. G-matrix calculations with these four options are also reported. The obtained well depths (U_\Lambda, U_\Sigma, U_\Xi) reveal distinct features of ESC04a-d. The \Lambda\Lambda-interactions are demonstrated to be consistent with the observed data of_{\Lambda\Lambda}^6He. The possible three-body effects are investigated by considering phenomenologically the changes of the vector-meson masses in a nuclear medium.
We study a sample of 48127 galaxies selected from the SDSS MPA-JHU catalogue, with $\log M_{\star}/M_{\odot} = 10.73 - 11.03$ and $z<0.1$. Local galaxies in this stellar mass range have been shown to have systematically shorter assembly times within their inner regions ($<0.5~R_{50}$) when compared to that of the galaxy as a whole, contrary to lower or higher mass galaxies which show consistent assembly times at all radii. Hence, we refer to these galaxies as Inside-Out Assembled Galaxy (IOAG) candidates. We find that the majority of IOAG candidates with well-detected emission lines are classified as either AGN (40%) or composite (40%) in the BPT diagram. We also find that the majority of our sources are located below the main sequence of star formation, and within the green valley or red sequence. Most BPT-classified star-forming IOAG candidates have spiral morphologies and are in the main sequence, whereas Seyfert 2 and composites have mostly spiral morphologies but quiescent star formation rates (SFRs). We argue that a high fraction of IOAG candidates seem to be in the process of quenching, moving from the blue cloud to the red sequence. Those classified as AGN have systematically lower SFRs than star-forming galaxies suggesting that AGN activity may be related to this quenching. However, the spiral morphology of these galaxies remains in place, suggesting that the central star-formation is suppressed before the morphological transformation occurs.
Statistical parameters of the ISM driven by thermal energy injections from supernova explosions have been obtained from 3D, nonlinear, magnetohydrodynamic, shearing-box simulations for spiral arm and interarm regions. The density scale height obtained for the interarm regions is 50% larger than within the spiral arms because of the higher gas temperature. The filling factor of the hot gas is also significantly larger between the arms and depends sensitively on magnetic field strength.
For open systems described by the quantum Markovian master equation, we study a possible extension of the Clausius equality to quasistatic operations between nonequilibrium steady states (NESSs). We investigate the excess heat divided by temperature (i.e., excess entropy production) which is transferred into the system during the operations. We derive a geometrical expression for the excess entropy production, which is analogous to the Berry phase in unitary evolution. Our result implies that in general one cannot define a scalar potential whose difference coincides with the excess entropy production in a thermodynamic process, and that a vector potential plays a crucial role in the thermodynamics for NESSs. In the weakly nonequilibrium regime, we show that the geometrical expression reduces to the extended Clausius equality derived by Saito and Tasaki (J. Stat. Phys. {\bf 145}, 1275 (2011)). As an example, we investigate a spinless electron system in quantum dots. We find that one can define a scalar potential when the parameters of only one of the reservoirs are modified in a non-interacting system, but this is no longer the case for an interacting system.
In a recent paper, Michalowicz et al. provide an extension of Isserlis theorem to the case of a Bernoulli location mixture of a Gaussian vector. We extend here this result to the case of any location mixture of Gaussian vector; we also provide an example of the Isserlis theorem for a "scale location" mixture of Gaussian, namely the d-dimensional generalized hyperbolic distribution.
In this article, we report emergence of topological phase in XMR material TmSb under hydrostatic pressure using first principles calculations. We find that TmSb, a topologically trivial semimetal, undergoes a topological phase transition with band inversion at X point without breaking any symmetry under a hydrostatic pressure of 12 GPa. At 15 GPa, it again becomes topologically trivial with band inversion at $\Gamma$ as well as X point. We find that the pressures corresponding to the topological phase transitions are far below the pressure corresponding to structural phase transition at 25.5 GPa. The reentrant behaviour of topological quantum phase with hydrostatic pressure would help in finding a correlation between topology and XMR effect through experiments.
We study the full set of solutions to the ADHM equation as an affine algebraic set, the ADHM variety. We gather the points of the ADHM variety into subvarieties according to the dimension of the stabilizing subspace. We compute dimension, and analyze singularity and reducibility of all of these varieties. We also connect representations of the ADHM quiver to coherent perverse sheaves on $\mathbb{P}^2$ in the sense of Kashiwara.
Spin polarized current is the main ingredient of diluted magnetic oxides due to its potential manipulation in spintronic devices. However, most research has focused on ferromagnetic properties rather than polarization of electric current, because direct measurements were difficult and the origin of spin polarized currents has yet to be fully understood. The method to increase the spin polarized current percentage is beyond practical consideration at the present status. To target this problem, we focus on the role of oxygen vacancies and nano grain size on the spin polarized current, which are controlled by growing the Co-doped ZnO thin-films at room temperature in a reducing atmosphere [Ar + (1% ~ 30%) H2]. We found that the conductivity increases with an increase in oxygen vacancies via two independent channels: the variable range hopping (VRH) within localized states and the itinerant transport in the conduction band. The Andreev Reflection measurements prove that the VRH conduction is equivalent to spin polarized current. Transport measurements show that the best way to increase the VRH content, or the percentage of spin polarized current, is to increase oxygen vacancy concentration and to reduce grain size and lattice constants of the films.
In this paper we show a lethargy result in the non-Arquimedian context, for general ultrametric approximation schemes and, as a consequence, we prove the existence of p-adic transcendental numbers whose best approximation errors by algebraic p-adic numbers of degree less than or equal to n decays slowly.
RXCJ0232.2-4420, at $z$ = 0.28, is a peculiar system hosting a radio halo source around the cool-core of the cluster. To investigate its formation and nature, we used archival {\it Chandra} and XMM-\textit{Newton} X-ray data to study the dynamical state of the cluster and detect possible substructures in the hot gas. Its X-ray surface brightness distribution shows no clear disruption except an elongation in the North-East to South-West direction. We perform the unsharp masking technique and compute morphology parameters (Gini, $M_{20}$ and concentration) to characterise the degree of disturbance in the projected X-ray emission. Both of these methods revealed a substructure, which is located at $\sim$ 1$'$ from the cluster core in the South-West direction. Previous spectral analysis conducted for RXCJ0232.2-4420 concluded that there are a short cooling time and low entropy at the cluster centre, indicating that the cluster has a cool core. Thus, we suggest that RXCJ0232.2-4420 may be a system where the core of the cluster is not showing any sign of disturbance, but the South-West substructure could be pumping energy to the detected radio halo via turbulence.
We study, in the ensemble of constant particle number, processes in which a cluster of particles is annihilated and particles are created catalytically in active sites. In this ensemble, particles belonging to a cluster of $\ell$ particles jump to $\ell$ distinct active sites. As examples of our prescription, we analyze numerically three nonequilibrium systems that annihilate cluster of particles that are identified as conserved versions of the pair annihilation contact model, triplet annihilation contact model and pair contact process. We show also how to set up the constant particle number ensemble from the constant rate ensemble.
We present a systematic investigation of molecule-metal interactions for transition-metal phthalocyanines (TMPc, with TM = Fe, Co, Ni, Cu) adsorbed on Ag(100). Scanning tunneling spectroscopy and density functional theory provide insight into the charge transfer and hybridization mechanisms of TMPc as a function of increasing occupancy of the 3d metal states. We show that all four TMPc receive approximately one electron from the substrate. Charge transfer occurs from the substrate to the molecules, inducing a charge reorganization in FePc and CoPc, while adding one electron to ligand \pi-orbitals in NiPc and CuPc. This has opposite consequences on the molecular magnetic moment: in FePc and CoPc the interaction with the substrate tends to reduce the TM spin, whereas in NiPc and CuPc an additional spin is induced on the aromatic Pc ligand, leaving the TM spin unperturbed. In CuPc, the presence of both TM and ligand spins leads to a triplet ground state arising from intramolecular exchange coupling between d and \pi electrons. In FePc and CoPc the magnetic moment of C and N atoms is antiparallel to that of the TM. The different character and symmetry of the frontier orbitals in the TMPc series leads to varying degrees of hybridization and correlation effects, ranging from the mixed-valence (FePc, CoPc) to the Kondo regime (NiPc, CuPc). Coherent coupling between Kondo and inelastic excitations induces finite-bias Kondo resonances involving vibrational transitions in both NiPc and CuPc and triplet-singlet transitions in CuPc.
The existence of nonnegative radially symmetric eternal solutions of exponential self-similar type $u(t,x)=e^{-p\beta t/(2-p)} f_\beta(|x|e^{-\beta t};\beta)$ is investigated for the singular diffusion equation with critical gradient absorption \partial_{t} u-\Delta_{p} u+|\nabla u|^{p/2}=0 \quad \;\;\hbox{in}\;\; (0,\infty)\times\real^N where $2N/(N+1) < p < 2$. Such solutions are shown to exist only if the parameter $\beta$ ranges in a bounded interval $(0,\beta_*]$ which is in sharp contrast with well-known singular diffusion equations such as $\partial_{t}\phi-\Delta_{p} \phi=0$ when $p=2N/(N+1)$ or the porous medium equation $\partial_{t}\phi-\Delta\phi^m=0$ when $m=(N-2)/N$. Moreover, the profile $f(r;\beta)$ decays to zero as $r\to\infty$ in a faster way for $\beta=\beta_*$ than for $\beta\in (0,\beta_*)$ but the algebraic leading order is the same in both cases. In fact, for large $r$, $f(r;\beta_*)$ decays as $r^{-p/(2-p)}$ while $f(r;\beta)$ behaves as $(\log r)^{2/(2-p)} r^{-p/(2-p)}$ when $\beta\in (0,\beta_*)$.