ShantanuT01/DACTYL-Pretraining huggingface dataset:
This paper presents the link between stochastic approximation and clinical trials based on randomized urn models investigated in Bai and Hu (1999,2005) and Bai, Hu and Shen (2002). We reformulate the dynamics of both the urn composition and the assigned treatments as standard stochastic approximation (SA) algorithms with remainder. Then, we derive the a.s. convergence and the asymptotic normality (CLT) of the normalized procedure under less stringent assumptions by calling upon the ODE and SDE methods. As a second step, we investigate a more involved family of models, known as multi-arm clinical trials, where the urn updating depends on the past performances of the treatments. By increasing the dimension of the state vector, our SA approach provides this time a new asymptotic normality result.
We show that the one-way channel formalism of quantum optics has a physical realisation in electronic systems. In particular, we show that magnetic edge states form unidirectional quantum channels capable of coherently transporting electronic quantum information. Using the equivalence between one-way photonic channels and magnetic edge states, we adapt a proposal for quantum state transfer to mesoscopic systems using edge states as a quantum channel, and show that it is feasible with reasonable experimental parameters. We discuss how this protocol may be used to transfer information encoded in number, charge or spin states of quantum dots, so it may prove useful for transferring quantum information between parts of a solid-state quantum computer.
The BKMP Remodeling Conjecture \cite{Ma,BKMP09,BKMP10} predicts all genus open-closed Gromov-Witten invariants for a toric Calabi-Yau $3$-orbifold by Eynard-Orantin's topological recursion \cite{EO07} on its mirror curve. The proof of the Remodeling Conjecture by the authors \cite{FLZ1,FLZ3} relies on comparing two Feynman-type graph sums in both A and B-models. In this paper, we will survey these graph sum formulae and discuss their roles in the proof of the conjecture.
We construct a one-particle TOA operator $\mathcal{\hat{T}}$ canonically conjugate with the Hamiltonian describing a free, charged, spin-$0$, relativistic particle in one spatial dimension and show that it is maximally symmetric. We solve for its eigenfunctions and show that they form a complete and non-orthogonal set. Plotting the time evolution of their corresponding probability densities, it implies that the eigenfunctions become more localized at the origin at the time equal to their eigenvalues. That is, a particle being described by an eigenfunction of $\mathcal{\hat{T}}$ is in a state of definite arrival time at the origin and at the corresponding eigenvalue. We also calculate the TOA probability distribution of a particle in some initial state.
We have presented the role of the Coulomb interaction ($U$) and the magnetic field ($\vec{B}$) on the ground state properties of the quasi-one dimensional graphite ribbon structures at half-filling. Mean field Hartree-Fock Approximation is used to study the systems. To understand the boundary effects in graphite structures, we have compared the results of these systems with those of the square lattice ribbon structures. Studying the density of states, the Drude weight and the charge gap, we have drawn the $U-B$ phase diagrams for the zigzag and the armchair graphite ribbons.
We extend our recent work on the two-fluid hydrodynamics of the condensate and non-condensate in a trapped Bose gas by including the dissipation associated with viscosity and thermal conduction. For purposes of illustration, we consider the hydrodynamic modes in the case of a uniform Bose gas. A finite thermal conductivity and shear viscosity give rise to a damping of the first and second sound modes in addition to that found previously due to the lack of diffusive equilibrium between the condensate and non-condensate. The relaxational mode associated with this equilibration process is strongly coupled to thermal fluctuations and reduces to the usual thermal diffusion mode above the Bose-Einstein transition. In contrast to the standard Landau two-fluid hydrodynamics, we predict a damped mode centered at zero frequency, in addition to the usual second sound doublet.
In this paper we analyse time change equations (TCEs) for L\'evy-type processes in detail. To this end we establish a connection between TCEs and classical one-dimensional initial value problems (IVPs) which are easier to handle. Properties of the IVPs are linked with properties of the TCEs. We show in a general setting existence and uniqueness of solutions of the TCEs. Our main result is based on the general path properties for L\'evy-type processes found in Schnurr (2013). Applications include an existence result for processes which correspond to a certain class of given symbols.
The surface and bulk properties of the two-dimensional Q > 4 state Potts model in the vicinity of the first order bulk transition point have been studied by exact calculations and by density matrix renormalization group techniques. For the surface transition the complete analytical solution of the problem is presented in the $Q \to \infty$ limit, including the critical and tricritical exponents, magnetization profiles and scaling functions. According to the accurate numerical results the universality class of the surface transition is independent of the value of Q > 4. For the bulk transition we have numerically calculated the latent heat and the magnetization discontinuity and we have shown that the correlation lengths in the ordered and in the disordered phases are identical at the transition point.
What is the momentum spectrum of a particle moving in an infinite deep square well? Einstein, Pauli and Yukawa had adopted different point of view than that in usual text books. The theoretical and experimental implication of this problem is discussed.
The magic nature of the $^{54}$Ca nucleus is investigated in the light of the recent experimental results. We employ both HFB and HF+BCS methods using Skyrme-type SLy5, SLy5+T and T44 interactions. The evolution of the single-particle spectra is studied for the N=34 isotones: $^{60}$Fe, $^{58}$Cr, $^{56}$Ti and $^{54}$Ca. An increase is obtained in the neutron spin-orbit splittings of $p$ and $f$ states due to the effect of the tensor force which also makes $^{54}$Ca a magic nucleus candidate. QRPA calculations on top of HF+BCS are performed to investigate the first $J^{\pi}$=$2^{+}$ states of the calcium isotopic chain. A good agreement for excitation energies is obtained when we include the tensor force in the mean-field part of the calculations. The first $2^{+}$ states indicate a subshell closure for both $^{52}$Ca and $^{54}$Ca nuclei. We confirm that the tensor part of the interaction is quite essential in explaining the neutron subshell closure in $^{52}$Ca and $^{54}$Ca nuclei.
In a quantum system that is bounded by past and future conditions, weak continuous monitoring forward-evolving and backward-evolving quantum states are usually carried out separately. Therefore, measured signals at a given time t cannot be monitored continuously. Here, we propose an enlarged-quantum-system method to combine these two processes together. Therein, we introduce an enlarged quantum state that contains both the forward- and backward-evolving quantum states. The enlarged state is governed by an enlarged master equation and propagates one-way forward in time. As a result, the measured signals at time t can be monitored continuously and can provide advantages in the signals amplification and signal processing techniques. Our proposal can be implemented on various physical systems, such as superconducting circuits, NMR systems, ion-traps, quantum photonics, and among others.
Her X-1, one of the brightest and best studied X-ray binaries, shows a cyclotron resonant scattering feature (CRSF) near 37 keV. This makes it an ideal target for detailed study with the Nuclear Spectroscopic Telescope Array (NuSTAR), taking advantage of its excellent hard X-ray spectral resolution. We observed Her X-1 three times, coordinated with Suzaku, during one of the high flux intervals of its 35d super-orbital period. This paper focuses on the shape and evolution of the hard X-ray spectrum. The broad-band spectra can be fitted with a powerlaw with a high-energy cutoff, an iron line, and a CRSF. We find that the CRSF has a very smooth and symmetric shape, in all observations and at all pulse-phases. We compare the residuals of a line with a Gaussian optical depth profile to a Lorentzian optical depth profile and find no significant differences, strongly constraining the very smooth shape of the line. Even though the line energy changes dramatically with pulse phase, we find that its smooth shape does not. Additionally, our data show that the continuum is only changing marginally between the three observations. These changes can be explained with varying amounts of Thomson scattering in the hot corona of the accretion disk. The average, luminosity-corrected CRSF energy is lower than in past observations and follows a secular decline. The excellent data quality of NuSTAR provides the best constraint on the CRSF energy to date.
We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces $R^d$ with $d\ge1$ and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on $R^d$, their local times exist when $d\le3$. A Tanaka formula of the local time is also derived.
Deep neural networks with alternating convolutional, max-pooling and decimation layers are widely used in state of the art architectures for computer vision. Max-pooling purposefully discards precise spatial information in order to create features that are more robust, and typically organized as lower resolution spatial feature maps. On some tasks, such as whole-image classification, max-pooling derived features are well suited; however, for tasks requiring precise localization, such as pixel level prediction and segmentation, max-pooling destroys exactly the information required to perform well. Precise localization may be preserved by shallow convnets without pooling but at the expense of robustness. Can we have our max-pooled multi-layered cake and eat it too? Several papers have proposed summation and concatenation based methods for combining upsampled coarse, abstract features with finer features to produce robust pixel level predictions. Here we introduce another model --- dubbed Recombinator Networks --- where coarse features inform finer features early in their formation such that finer features can make use of several layers of computation in deciding how to use coarse features. The model is trained once, end-to-end and performs better than summation-based architectures, reducing the error from the previous state of the art on two facial keypoint datasets, AFW and AFLW, by 30\% and beating the current state-of-the-art on 300W without using extra data. We improve performance even further by adding a denoising prediction model based on a novel convnet formulation.
Type 0A string theory in the (2,4k) superconformal minimal model backgrounds and the bosonic string in the (2,2k-1) conformal minimal models, while perturbatively identical in some regimes, may be distinguished non-perturbatively using double scaled matrix models. The resolvent of an associated Schrodinger operator plays three very important interconnected roles, which we explore perturbatively and non-perturbatively. On one hand, it acts as a source for placing D-branes and fluxes into the background, while on the other, it acts as a probe of the background, its first integral yielding the effective force on a scaled eigenvalue. We study this probe at disc, torus and annulus order in perturbation theory, in order to characterize the effects of D-branes and fluxes on the matrix eigenvalues. On a third hand, the integrated resolvent forms a representation of a twisted boson in an associated conformal field theory. The entire content of the closed string theory can be expressed in terms of Virasoro constraints on the partition function, which is realized as wavefunction in a coherent state of the boson. Remarkably, the D-brane or flux background is simply prepared by acting with a vertex operator of the twisted boson. This generates a number of sharp examples of open-closed duality, both old and new. We discuss whether the twisted boson conformal field theory can usefully be thought of as another holographic dual of the non-critical string theory.
We reconsider the dynamics of stochastic or thermal tunneling in theories like Dirac-Born-Infeld inflation that have non-minimal kinetic terms and, as a result, strongly non-Gaussian perturbations. We first describe a local description of the tunneling process which gives results consistent with the standard Hawking-Moss tunneling. This result is under perturbative control as long as the fluctuation determinant is well approximated by a one-loop integral. We then move to a global description, using the methodology of stochastic inflation and the in-in path integral formalism. This approach shows clearly that the tunneling process becomes strongly coupled whenever the sound speed of the tunneling trajectory departs sufficiently from unity. We argue that these two very different perspectives are nevertheless consistent, and may imply the existence of a simple resummation of the strongly coupled interactions of the field.
The amplitude of the Compton-Getting (CG) anisotropy contains the power-law index of the cosmic-ray energy spectrum. Based on this relation and using the Tibet air-shower array data, we measure the cosmic-ray spectral index to be $-3.03 \pm 0.55_{stat} \pm < 0.62_{syst}$ between 6 TeV and 40 TeV, consistent with $-$2.7 from direct energy spectrum measurements. Potentially, this CG anisotropy analysis can be utilized to confirm the astrophysical origin of the ``knee'' against models for non-standard hadronic interactions in the atmosphere.
The two papers referred to in the title, claiming the detection of a large-scale massive hot gaseous halo around the Galaxy, have generated a lot of confusion and unwarranted excitement (including public news coverage). However, the papers are seriously flawed in many aspects, including problematic analysis and assumptions, as well as mis-reading and mis-interpreting earlier studies, which are inconsistent with the claim. Here we show examples of such flaws.
We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify the relation between different renormalizations at non-positive values appearing in the recent literature.
Extremal problems involving independent sets are much studied. Two of the most important extremal problems in this context are concerned with the sharp upper bounds for the number of independent sets of fixed size and the independence number. In literature, these sharp upper bounds are derived in completely different contexts. In this paper, we show that both of these sharp upper bounds can be derived by considering Lex graphs. More exactly, they depend on two parameters of a sequence defined on them.
Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent single particle potential of nucleons in isospin-symmetric nuclear matter. The contributions from one- and two-pion exchange diagrams give rise to a potential depth for a nucleon at rest of $U(0,k_{f0}) = -53.2 $MeV at saturation density. The momentum dependence of the real part of the single particle potential $U(p,k_{f0})$ is non-monotonic and can be translated into a mean effective nucleon mass of $\bar M^* \simeq 0.8 M$. The imaginary part of the single particle potential $W(p,k_f)$ is generated to that order entirely by iterated one-pion exchange. The resulting half width of a nucleon hole-state at the bottom of the Fermi sea comes out as $W(0,k_{f0})=29.7 $MeV. The basic theorems of Hugenholtz-Van-Hove and Luttinger are satisfied in our perturbative two-loop calculation of the nuclear mean field.
In a nanoscale molecular junction at finite bias voltage,the intra-molecular distribution of vibrational energy can strongly deviate from the thermal equilibrium distribution and specific vibrational modes can be selectively excited in a controllable way,regardless of the corresponding mode frequency. This is demonstrated for generic models of asymmetric molecular junctions with localized electronic states, employing a master equation as well as a nonequilibrium Green's function approach. It is shown that the applied bias voltage controls the excitation of specific vibrational modes coupled to these states, by tuning their electronic population,which influences the efficiency of vibrational cooling processes due to energy exchange with the leads.
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static solutions.
We present results from high--resolution cosmological hydrodynamical simulations of a Milky--Way-sized halo, aimed at studying the effect of feedback on the nature of gas accretion. Simulations include a model of inter-stellar medium and star formation, in which SN explosions provide effective thermal feedback. We distinguish between gas accretion onto the halo, which occurs when gas particles cross the halo virial radius, and gas accretion onto the central galaxy, which takes place when gas particles cross the inner one-tenth of the virial radius. Gas particles can be accreted through three different channels, depending on the maximum temperature value, $T_{\rm max}$, reached during the particles' past evolution: a cold channel for $T_{\rm max}<2.5 \times 10^5$ K, a hot one for $T>10^6$K, and a warm one for intermediate values of $T_{\rm max}$. We find that the warm channel is at least as important as the cold one for gas accretion onto the central galaxy. This result is at variance with previous findings that the cold mode dominates gas accretion at high redshift. We ascribe this difference to the different supernova feedback scheme implemented in our simulations. While results presented so far in the literature are based on uneffective SN thermal feedback schemes and/or the presence of a kinetic feedback, our simulations include only effective thermal feedback. We argue that observational detections of a warm accretion mode in the high--redshift circum-galactic medium would provide useful constraints on the nature of the feedback that regulates star formation in galaxies.
This paper develops algebraic geometry over Henselian real valued (i.e. of rank 1) fields $K$, being a sequel to our paper about that over Henselian discretely valued fields. Several results are given including: a certain concept of fiber shrinking (a relaxed version of curve selection) for definable sets, the canonical projection $K^{n} \times K\mathbb{P}^{m} \to K^{n}$ and blow-ups of the $K$-points of smooth $K$-varieties are definably closed maps, a descent property for blow-ups, a version of the Lojasiewicz inequality for continuous rational functions and the theorem on extending continuous hereditarily rational functions, established for the real and $p$-adic varieties in our joint paper with J. Kollar. The descent property enables application of desingularization and transformation to a normal crossing by blowing up in much the same way as over the locally compact ground field. Our approach applies quantifier elimination due to Pas.
We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling range differs in both quantities and allow to investigate the effect.
In the currently popular orientation-based unified scheme, a radio galaxy appears as a quasar when its principal radio-axis happens to be oriented within a certain cone opening angle around the observer's line of sight. Due to geometrical projection, the observed sizes of quasars should therefore appear smaller than those of radio galaxies. We show that this simple, unambiguous prediction of the unified scheme is not borne out by the actually observed angular sizes of radio galaxies and quasars. Except in the original 3CR sample, based on which the unified scheme was proposed, in other much larger samples no statistically significant difference is apparent in the size distributions of radio galaxies and quasars. The population of low-excitation radio galaxies with apparently no hidden quasars inside, which might explain the observed excess number of radio galaxies at low redshifts, cannot still account for the absence of any foreshortening of the sizes of quasars at large redshifts. On the other hand from infrared and X-ray studies there is evidence of hidden quasar within a dusty torus in many RGs, at $z>0.5$. It seems difficult how to reconcile this with the absence of foreshortening of quasar sizes at even these redshifts, and perhaps one has to allow that the major radio axis may not have anything to do with the optical axis of the torus. Otherwise to resolve the dichotomy of radio galaxies and quasars, a scheme quite different from the present might be required.
We study the compatibility of large quasar groups with the concordance cosmological model. Large Quasar Groups are very large spatial associations of quasars in the cosmic web, with sizes of 50-250h^-1 Mpc. In particular, the largest large quasar group known, named Huge-LQG, has a longest axis of ~860h^-1 Mpc, larger than the scale of homogeneity (~260 Mpc), which has been noted as a possible violation of the cosmological principle. Using mock catalogues constructed from the Horizon Run 2 cosmological simulation, we found that large quasar groups size, quasar member number and mean overdensity distributions in the mocks agree with observations. The Huge-LQG is found to be a rare group with a probability of 0.3 per cent of finding a group as large or larger than the observed, but an extreme value analysis shows that it is an expected maximum in the sample volume with a probability of 19 per cent of observing a largest quasar group as large or larger than Huge-LQG. The Huge-LQG is expected to be the largest structure in a volume at least 5.3 +- 1 times larger than the one currently studied.
A many-flavor electron gas (MFEG) in a semiconductor with a valley degeneracy ranging between 6 and 24 was analyzed using diffusion Monte Carlo (DMC) calculations. The DMC results compare well with an analytic expression derived by one of us [Phys. Rev. B 78, 035111 (2008)] for the total energy to within 1% over an order of magnitude range of density, which increases with valley degeneracy. For Bi2Te3 (six-fold valley degeneracy) the applicable charge carrier densities are between 7*10^19cm^{-3} and 2*10^20cm^{-3}. DMC calculations distinguished between an exact and a useful approximate expression for the 24-fold degenerate MFEG polarizability for wave numbers 2p_F<q<7p_F. The analytical result for the MFEG is generalized to inhomogeneous systems by means of a gradient correction, the validity range of this approach is obtained. Employed within a density functional theory calculation this approximation compares well with DMC results for a quantum dot.
In this work we study the geodesic motion on a noncommutative space-time. As a result we find a non-commutative geodesic equation and then we derive corrections of the deviation angle per revolution in terms of the non-commutative parameter when we specify the problem of Mercury's perihelion. In this way, we estimate the noncommutative parameter based in experimental data.