ShantanuT01/DACTYL-Pretraining huggingface dataset:
We use finite-size scaling to investigate the critical behavior of the quasiespecies model of molecular evolution in the single-sharp-peak replication landscape. This model exhibits a sharp threshold phenomenon at Q=Q_c=1/a, where Q is the probability of exact replication of a molecule of length L and a is the selective advantage of the master string.   We investigate the sharpness of the threshold and find that its characteristic persist across a range of Q of order L^(-1) about Q_c. Furthermore, using the data collapsing method we show that the normalized mean Hamming distance between the master string and the entire population, as well as the properly scaled fluctuations around this mean value, follow universal forms in the critical region.
This document is the Habilitation Thesis (Habilitation \`a Diriger des Recherches) of Nicolas Trotignon. It presents his work in structural graph theory, from 2001 to 2009.
We study models of emergent space associated with the Coulomb branch, non-commutative and beta deformations of the N=4 super Yang-Mills theory, extending a previous work on the undeformed conformal case. The idea is to compute the effective action for D-instantons from the microscopic four-dimensional open-string description and to compare with the non-abelian D-instanton action in the dual ten-dimensional supergravity background. To linear order in the deformation parameter, the D-instantons can probe the full space-time geometry and we can derive all the supergravity fields in this way. We find a perfect match with the known supergravity solutions, including for the Neveu-Schwarz and Ramond-Ramond forms.
It has often been suggested that supernova remnants (SNRs) can trigger star formation. To investigate the relationship between SNRs and star formation, we have examined the known sample of 45 SNRs in the Large Magellanic Cloud to search for associated young stellar objects (YSOs) and molecular clouds. We find seven SNRs associated with both YSOs and molecular clouds, three SNRs associated with YSOs but not molecular clouds, and eight SNRs near molecular clouds but not associated with YSOs. Among the 10 SNRs associated with YSOs, the association between the YSOs and SNRs can be either rejected or cannot be convincingly established for eight cases. Only two SNRs have YSOs closely aligned along their rims; however, the time elapsed since the SNR began to interact with the YSOs' natal clouds is much shorter than the contraction timescales of the YSOs, and thus we do not see any evidence of SNR-triggered star formation in the LMC. The 15 SNRs that are near molecular clouds may trigger star formation in the future when the SNR shocks have slowed down to <45 km/s. We discuss how SNRs can alter the physical properties and abundances of YSOs.
Generically, the asymmetric interactions in asymmetric dark matter (ADM) models lead to decaying DM. We show that, for ADM that carries nonzero baryon number, the continuous flavor symmetries that generate the flavor structure in the quark sector also imply a looser lower bound on the mass scale of the asymmetric mediators between the dark and visible sectors. The mediators for $B=2$ ADM that can produce a signal in the future indirect dark matter searches can thus also be searched for at the LHC. For two examples of the mediator models, with either the MFV or Froggatt-Nielsen flavor breaking pattern, we derive the FCNC constraints and discuss the search strategies at the LHC.
For calculation of the single-channel nucleon-nucleon scattering a phase-functions method has been proposed. Using a phase-functions method the following phase shifts of a np- scattering numerically for 1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-, 1F3-, 3F3-, 1G4-, 3G4- states are calculated. The calculations has been performed using realistic nucleon-nucleon potentials Argonne group (Av18, Av14sscc, Av8', Av8'sscc, Av6', Av4', Av2'). Obtained phase shifts are in good agreement with the results obtained in the framework of other methods. Using the obtained phase shifts we have calculated the full cross-section np- scattering.
We present an original strategy for the calculation of direct and inverse photo-emission spectra from first principles. The main goal is to go beyond the standard Green's function approaches, such as the $GW$ method, in order to find a good description not only of the quasiparticles but also of the satellite structures, which are of particular importance in strongly correlated materials. To this end we use as a key quantity the three-body Green's function, or, more precisely, its hole-hole-electron and electron-electron-hole parts, and we show how the one-body Green's function, and hence the corresponding spectral function, can be retrieved from it. We show that, contrary to the one-body Green's function, information about satellites is already present in the non-interacting three-body Green's function. Therefore, simple approximations to the three-body self-energy, which is defined by the Dyson equation for the three-body Green's function and which contains many-body effects, can still yield accurate spectral functions. In particular, the self-energy can be chosen to be static which could simplify a self-consistent solution of the Dyson equation. We give a proof of principle of our strategy by applying it to the Hubbard dimer, for which the exact self-energy is available.
We present a theoretical analysis aimed at understanding electrical conduction in molecular tunnel junctions. We focus on discussing the validity of coherent versus incoherent theoretical formulations for single-level tunneling to explain experimental results obtained under a wide range of experimental conditions, including measurements in individual molecules connecting the leads of electromigrated single-electron transistors and junctions of self-assembled monolayers (SAM) of molecules sandwiched between two macroscopic contacts. We show that the restriction of transport through a single level in solid state junctions (no solvent) makes coherent and incoherent tunneling formalisms indistinguishable when only one level participates in transport. Similar to Marcus relaxation processes in wet electrochemistry, the thermal broadening of the Fermi distribution describing the electronic occupation energies in the electrodes accounts for the exponential dependence of the tunneling current on temperature. We demonstrate that a single-level tunnel model satisfactorily explains experimental results obtained in three different molecular junctions (both single-molecule and SAM-based) formed by ferrocene-based molecules. Among other things, we use the model to map the electrostatic potential profile in EGaIn-based SAM junctions in which the ferrocene unit is placed at different positions within the molecule, and we find that electrical screening gives rise to a strongly non-linear profile across the junction.
Strong gravity and magnetic fields are key ingredients that power processes of accretion and ejection near compact objects. While the particular mechanisms that operate here are still discussed, it seems that the presence of an ordered magnetic field is crucial for the acceleration and collimation of relativistic jets of electrically charged particles on superhorizon length scales. In this context, we further study the effect of a large-scale magnetic field on the dynamics of charged particles near a rotating black hole. We consider a scenario in which the initially neutral particles on regular geodesic orbits in the equatorial plane are destabilized by a charging process (e.g., by photoionization). Some charged particles are accelerated out of the equatorial plane, and they follow jetlike trajectories with relativistic velocities. In our previous paper, we investigated this scenario for the case of perfect alignment of the magnetic field with the axis of rotation; i.e., the system was considered axisymmetric. Here we relax this assumption and investigate nonaxisymmetric systems in which the magnetic field is arbitrarily inclined with respect to the black hole spin. We study the system numerically in order to locate the zones of escaping trajectories and compute the maximum (terminal) escape velocity. It appears that breaking the axial symmetry (even by small inclination angles) substantially increases the fraction of escaping orbits and allows the acceleration to ultrarelativistic velocities that were excluded in the axisymmetric setup. The presence of transient chaotic dynamics in the launching region of the relativistic outflow is confirmed with chaotic indicators.
In this paper we give a proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudo-differential operators is equivalent to condition ($\Psi$). This condition rules out certain sign changes of the imaginary part of the principal symbol along the bicharacteristics of the real part. We obtain local solvability by proving a localizable estimate of the adjoint operator with a loss of two derivatives (compared with the elliptic case).   The proof involves a new metric in the Weyl (or Beals-Fefferman) calculus which makes it possible to reduce to the case when the gradient of the imaginary part is non-vanishing, so that the zeroes forms a smooth submanifold. The estimate uses a new type of weight, which measures the changes of the distance to the zeroes of the imaginary part along the bicharacteristics of the real part between the minima of the curvature of this submanifold. By using condition ($\Psi$) and this weight, we can construct a multiplier giving the estimate.
We use the anomaly cancellation of the M-theory fivebrane to derive the R-symmetry anomalies of the $A_{N}$ $(0,2)$ tensor-multiplet theories. This result leads to a simple derivation of black hole entropy in $d=4, \mathcal{N}=2$ compactifications of $M$-theory. We also show how the formalism of normal bundle anomaly cancellation clarifies the Kaluza-Klein origin of Chern-Simons terms in gauged supergravity theories. The results imply the existence of interesting 1/N corrections in the AdS/CFT correspondence.
An approach to experimentally exploring electronic correlation functions in mesoscopic regimes is proposed. The idea is to monitor the mesoscopic fluctuations of a tunneling current flowing between the two layers of a semiconductor double-quantum-well structure. From the dependence of these fluctuations on external parameters, such as in-plane or perpendicular magnetic fields, external bias voltages, etc., the temporal and spatial dependence of various prominent correlation functions of mesoscopic physics can be determined. Due to the absence of spatially localized external probes, the method provides a way to explore the interplay of interaction and localization effects in two-dimensional systems within a relatively unperturbed environment. We describe the theoretical background of the approach and quantitatively discuss the behavior of the current fluctuations in diffusive and ergodic regimes. The influence of both various interaction mechanisms and localization effects on the current is discussed. Finally a proposal is made on how, at least in principle, the method may be used to experimentally determine the relevant critical exponents of localization-delocalization transitions.
The growth of Fe nanoclusters on the Ge(001) surface has been studied using lowtemperature scanning tunnelling microscopy (STM) and density functional theory (DFT) calculations. STM results indicate that Fe nucleates on the Ge(001) surface, forming wellordered nanoclusters of uniform size. Depending on the preparation conditions, two types of nanoclusters were observed having either four or sixteen Fe atoms within a nanocluster. The results were confirmed by DFT calculations. Annealing the nanoclusters at 420 K leads to the formation of nanorow structures, due to cluster mobility at such temperature. The Fe nanoclusters and nanorow structures formed on the Ge(001) surface show a superparamagnetic behaviour as measured by X-ray magnetic circular dichroism.
We investigate the relation between the optical extinction ($A_V$) and the hydrogen column density ($N_H$) determined from X-ray observations of a large sample of Galactic sightlines toward 35 supernova remnants, 6 planetary nebulae, and 70 X-ray binaries for which $N_H$ was determined in the literature with solar abundances. We derive an average ratio of ${N_H}/{A_V}=(2.08\pm0.02)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the whole Galaxy. We find no correlation between ${N_H}/{A_V}$ and the number density of hydrogen, the distance away from the Galactic centre, and the distance above or below the Galactic plane. The ${N_H}/{A_V}$ ratio is generally invariant across the Galaxy, with ${N_H}/{A_V}=(2.04\pm0.05)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the 1st and 4th Galactic quadrants and ${N_H}/{A_V}=(2.09\pm0.03)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ for the 2nd and 3rd Galactic quadrants. We also explore the distribution of hydrogen in the Galaxy by enlarging our sample with additional 74 supernova remnants for which both $N_H$ and distances are known. We find that, between the Galactic radius of 2 kpc to 10 kpc, the vertical distribution of hydrogen can be roughly described by a Gaussian function with a scale height of $h=75.5\pm12.4\,{\rm pc}$ and a mid-plane density of $n_{H}(0)=1.11\pm0.15\,{\rm cm^{-3}}$, corresponding to a total gas surface density of ${\sum}_{gas}{\sim}7.0\,{M_{\bigodot}}\,{\rm pc^{-2}}$. We also compile $N_H$ from 19 supernova remnants and 29 X-ray binaries for which $N_H$ was determined with subsolar abundances. We obtain ${N_H}/{A_V}=(2.47\pm0.04)\times10^{21}{\rm H\, cm^{-2}\, mag^{-1}}$ which exceeds that derived with solar abundances by $\sim$20%. We suggest that in future studies one may simply scale $N_H$ derived from subsolar abundances by a factor of $\sim$1.2 when converting to $N_H$ of solar abundances.
We study a non local approximation of the Gaussian perimeter, proving the Gamma convergence to the local one. Surprisingly, in contrast with the local setting, the halfspace turns out to be a volume constrained stationary point if and only if the boundary hyperplane passes through the origin. In particular, this implies that Ehrhard symmetrization can in general increase the considered non local Gaussian perimeter.
We study algebraic fiber spaces $f:X \longrightarrow Y$ where $Y$ is of maximal Albanese dimension. In particular we give an effective version a theorem of Kawamata: If $P_m(X)=1$ for some $m \ge 2$, then the Albanese map of $X$ is surjective. Combining this with \cite{CH} it follows that $X$ is birational to an abelian variety if and only if $P_2(X)=1$ and $q(X)= \text{\rm dim} (X)$.
Lifting the valley degeneracy is an efficient way to achieve valley polarization for further valleytronics operations. In this work, we demonstrate that a large valley splitting can be obtained in monolayer transition metal dichalcogenides by magnetic proximity coupling to an insulating antiferromagnetic substrate. As an example, we perform first-principles calculations to investigate the electronic structures of monolayer WS$_2$ on the MnO(111) surface. Our calculation results suggest that a large valley splitting of 214 meV, which corresponds to a Zeeman magnetic field of 1516 T, is induced in the valence band of monolayer WS$_2$. The magnitude of valley splitting relies on the strength of interfacial orbital hybridization, and can be continually tuned by applying an external out-of-plane pressure and in-plane strain. More interestingly, we find that both spin and valley index will flip when the magnetic ordering of MnO is reversed. Besides, owing to the sizeable Berry curvature and time-reversal symmetry breaking in the WS$_2$/MnO heterostructure, a spin and valley polarized anomalous Hall current can be generated in the presence of an in-plane electric field, which allow one to detect valleys by the electrical approach. Our results shed light on the realization of valleytronic devices using the antiferromagnetic insulator as the substrate.
We use the moduli space of stable curves to determine the stable (in the sense of Koll\'{a}r-Shepherd-Barron) degenerations of surfaces isogenous to a product of stable curves. A recent family of examples of Catanese show that the moduli space of such smooth surfaces may have two components. The main result of this note is that these components do not meet in the stable compactification. To the best of my knowledge this gives the first example of a moduli space of stable surfaces with multiple connected components parameterizing diffeomorphic smooth surfaces. Comments are appreciated.
We provide estimates of the rate of strong approximation and bounds for probabilities of moderate deviations in the CLT for the $L_1$-norm of the kernel density estimator without any assumptions on the density and assuming that the kernel is bounded and has bounded support.
In certain models of gauge-mediated supersymmetry breaking with messenger fields in incomplete GUT multiplets, the radiative corrections to the Higgs potential cancel out during renormalization group running. This allows for relatively heavy superpartners and for a 125 GeV Higgs while the fine-tuning remains modest. In this paper, we show that such gauge mediation models with "focus point" behaviour can be naturally embedded into a model of SU(5) x U(3) product group unification.
We study the anomalous transport in systems of random walks (RW's) on comb-like lattices with fractal sidebranches, showing subdiffusion, and in a system of Brownian particles driven by a random shear along the x-direction, showing a superdiffusive behavior. In particular, we discuss whether scaling and universality are present or not in the shapes of the particle distribution along the preferential transport direction (x-axis).
The spectra of Wolf-Rayet (WR) stars exhibit strong, broad emission lines that originate in the wind. These winds are radiatively driven and are susceptible to hydrodynamic instabilities that result in the formation of clumps. When modelling spectra of WR stars the volume-filling factor (VFF) approach is usually employed to treat clumpy winds. However, it is based on the assumption that the entire wind mass resides in optically thin clumps, which is not necessarily justifiable in dense winds. To test the validity of the VFF approach we use a previously described method of treating clumping, the ``Shell'' approach, to study line and continuum formation in the dense wind of the WN4 star, HD 50896. Our models indicate that fully intact spherical shells are in tension with observed spectra; a persistent ``dip'' in emission lines occurs at line centre. Removing this dip requires our models to use ``broken'' shells -- shells that are highly decoherent laterally. This insinuates that the wind of HD 50896, and by extension the winds of other WR stars, are comprised of small laterally confined and radially compressed clumps -- clumps smaller than the Sobolev length. We discuss some of the conditions necessary for the VFF approach to be valid.
We consider 1-D Laplace operator with short range potential V(x), such that $$(1+|x|)^\gamma V(x) \in L^1(R), \ \ \gamma > 1.$$ We study the equivalence of classical homogeneous Besov type spaces $\dot{B}^s_p(R)$, $p \in (1,\infty)$ and the corresponding perturbed homogeneous Besov spaces associated with the perturbed Hamiltonian $\mathcal{H}= -\partial_x^2 + V(x)$ on the real line. It is shown that the assumptions $1/p < \gamma -1$ and zero is not a resonance guarantee that the perturbed and unperturbed homogeneous Besov norms of order $s \in [0,1/p)$ are equivalent. As a corollary, the corresponding wave operators leave classical homogeneous Besov spaces of order $s \in [0,1/p)$ invariant.
Over the last twenty years of research on quantum game theory have given us many ideas of how quantum games could be played. One of the most prominent ideas in the field is a model of quantum playing a 2x2 game introduced by J. Eisert, M. Wilkens and M. Lewenstein. The scheme assumes that players' strategies are unitary operations the players act on the maximally entangled two-qubit state. The quantum nature of the scheme has been under discussion since the article by Eisert et al. came out. The aim of our paper is to identify some of non-classical features of the quantum scheme.
Non-perturbative methods of effective field theory such like Lattice QCD have allowed to establish connection between the QCD Lagrangian and quark potential models, a prominent outcome being the Cornell (linear plus Coulomb) potential. In being quite successful in explaining properties of heavy flavor hadrons, be them quarkonia or baryons, this potential has been found less spectacular in the description of the non-strange baryons, the nucleon and the Delta. This behavior indicates that the one-gluon exchange and the flux-tube interaction do not fully account for the complexity of the dynamics of three light quarks. Very recently, the Cornell potential which is of infinte range has been upgraded by us toward an exactly solvable trigonometric potential of finite range that interpolates between the inverse-distance potential and the infinite wells while passing through a region of linear growth, a reason for which it contains the inverse distance and the linear potentials as first terms in its Taylor series decomposition. We here first make the point that the upgraded Cornell potential can be viewed as the exact counterpart on a curved space to a flat space 1/r potential, a circumstance that equips it by two simultaneous symmetries, SO(4), and SO(2,1). These allow to place the trigonometric confinement potential in the context of AdS_5/CFT correspondence and thus to establish the link of the algebraic aspects of the latter to QCD potentiology. Next we report that the above potential when employed in the quark-diquark system, provides a remarkably adequate description of both nucleon and Delta spectra and the proton mean square charge radius as well, and moreover implies an intriguing venue toward quark deconfinement as shut-down of the curvature considered as temperature dependent.
The method of the optical parameter estimations of the nonisothermal giant planet atmospheres by using intensity data of Raman scattering features was used. We applied this method to the observational data of Uranus' geometric albedo spectra from 1981, 1993 and 1995 and obtained the spectral values of the optical depth, namely, $\tau_a/\tau_R$ and $\tau_\kappa/\tau_S$ (where $\tau_a$, $\tau_R$ are aerosol and gas components, $\tau_S=\tau_a+\tau_R$ and $\tau_\kappa$ is absorption component of the effective optical depth of the intensity of diffuse - reflected irradiation forming). We showed that these ratios are different for the three years. The conclusion is that this effect can be due to the horizontal inhomogeneity of aerosol component of optical depth over the Uranus' disk.
This paper is concerned with the nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any time t, the sigma-algebra generated by the observation process Y provides all the available information about the signal X. The central goal of stochastic filtering is to characterize the filter which is the conditional distribution of X, given the observed data. It has been proved in Ceci-Colaneri (2012) that the filter is the unique probability measure-valued process satisfying a nonlinear stochastic equation, the so-called Kushner-Stratonovich equation (KS-equation). In this paper the aim is to describe the filter in terms of the unnormalized filter, which is solution to a linear stochastic differential equation, called the Zakai equation. We prove equivalence between strong uniqueness for the solution to the Kushner Stratonovich equation and strong uniqueness for the solution to the Zakai one and, as a consequence, we deduce pathwise uniqueness for the solutions to the Zakai equation by applying the Filtered Martingale Problem approach (Kurtz-Ocone (1988), Kurtz-Nappo (2011), Ceci-Colaneri (2012)). To conclude, we discuss some particular cases.