ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider almost minimizers to the one-phase energy functional and we prove their optimal Lipschitz regularity and partial regularity of their free boundary. These results were recently obtained by David and Toro, and David, Engelstein, and Toro. Our proofs provide a different method based on a non-infinitesimal notion of viscosity solutions.
In this note, we establish an analog of the Mallows-Sloane bound for Type III formal weight enumerators. This completes the bounds for all types (Types I through IV) in synthesis of our previous results. Next we show by using the binomial moments that there exists a family of polynomials divisible by three, which are not related to linear codes but are invariant under the MacWilliams transform for the value 3/2. We also discuss some properties of the zeta functions for such polynomials.
We report sample preparation, structure, electrical resistivity, magnetic susceptibility and heat capacity studies of a new compound Yb$_2$Ir$_3$Ge$_5$. We find that this compound crystallizes in an orthorhombic structure with a space group PMMN unlike the compound Ce$_2$Ir$_3$Ge$_5$ which crystallizes in the tetragonal IBAM (U$_2$Co$_3$Si$_5$ type) structure. Our resistivity measurements indicate that the compound Yb$_2$Ir$_3$Ge$_5$ behaves like a typical Kondo lattice system with no ordering down to 0.4 K. However, a Curie-Weiss fit of the inverse magnetic susceptibility above 100 K gives an effective moment of only 3.66 $\mu$$_B$ which is considerably less than the theoretical value of 4.54 $\mu$$_B$ for magnetic Yb$^3+$ ions. The value of $\theta_{P}$ = -15.19 K is also considerably higher indicating the presence of strong hybridization. An upturn in the low temperature heat capacity gives an indication that the system may order magnetically just below the lowest temperature of our heat capacity measurements (0.4 K). The structure contains two sites for Yb ions and the present investigation suggests that Yb may be trivalent in one site while it may be significantly lower (close to divalent) in the other.
Synthesizing high-quality, realistic images from text-descriptions is a challenging task, and current methods synthesize images from text in a multi-stage manner, typically by first generating a rough initial image and then refining image details at subsequent stages. However, existing methods that follow this paradigm suffer from three important limitations. Firstly, they synthesize initial images without attempting to separate image attributes at a word-level. As a result, object attributes of initial images (that provide a basis for subsequent refinement) are inherently entangled and ambiguous in nature. Secondly, by using common text-representations for all regions, current methods prevent us from interpreting text in fundamentally different ways at different parts of an image. Different image regions are therefore only allowed to assimilate the same type of information from text at each refinement stage. Finally, current methods generate refinement features only once at each refinement stage and attempt to address all image aspects in a single shot. This single-shot refinement limits the precision with which each refinement stage can learn to improve the prior image. Our proposed method introduces three novel components to address these shortcomings: (1) An initial generation stage that explicitly generates separate sets of image features for each word n-gram. (2) A spatial dynamic memory module for refinement of images. (3) An iterative multi-headed mechanism to make it easier to improve upon multiple image aspects. Experimental results demonstrate that our Multi-Headed Spatial Dynamic Memory image refinement with our Multi-Tailed Word-level Initial Generation (MSMT-GAN) performs favourably against the previous state of the art on the CUB and COCO datasets.
By means of an envelope function analysis, we perform a numerical investigation of the conductance behavior of a graphene structure consisting of two regions (dots) connected to the entrance and exit leads through constrictions and separated by a potential barrier. We show that the conductance of the double dot depends on the symmetry of the structure and that this effect survives also in the presence of a low level of disorder, in analogy of what we had previously found for a double dot obtained in a semiconductor heterostructure. In graphene, this phenomenon is less dramatic and, in particular, conductance is not enhanced by the addition of symmetric constrictions with respect to that of the barrier alone.
We prove global well-posedness of the two-dimensional exterior Navier-Stokes equations for bounded initial data with a finite Dirichlet integral, subject to the non-slip boundary condition. As an application, we construct global solutions for asymptotically constant initial data and arbitrary large Reynolds numbers.
We consider a two-dimensional motion of a thin film flowing down an inclined plane under the influence of the gravity and the surface tension. In order to investigate the stability of such flow, it is hard to treat the Navier--Stokes equations directly, so that a thin film approximation is often used. It is an approximation obtained by the perturbation expansion with respect to the aspect ratio $\delta$ of the film under the thin film regime $\delta\ll1$. Our purpose is to give a mathematically rigorous justification of the thin film approximation by establishing an error estimate between the solution of the Navier--Stokes equations and those of approximate equations. To this end, in this paper we derive a uniform estimate for the solution of the Navier--Stokes equations with respect to $\delta$ under appropriate assumptions.
Electric Scanning Probe Microscopies are used to characterize the surface behavior of ferroelectric materials. The effects of local charge density on the chemistry and physics of ferroelectric surfaces are investigated. The kinetics and thermodynamics parameters of adsorption are assessed by variable temperature Scanning Surface Potential Microscopy. Contrast formation mechanism of Piezoresponse Force Microscopy (PFM) is analyzed in detail, and the contributions of electroelastic constants of the material to response amplitude are determined. The effect of experimental conditions including indentation force and tip radius of curvature is elucidated using PFM Contrast Mechanism Maps. Simple quantitative criterion for non-local cantilever-surface interactions in PFM is developed.
The ESA Cornerstone Mission GAIA, to be launched prior to 2012 and with a nominal lifetime of 5 years, will improve the accuracy of Hipparcos astrometry by more than two orders of magnitude. GAIA high-precision global astrometric measurements will provide deep insights on the science of extra-solar planets. The GAIA contribution is primarily understood in terms of the number and spectral type of targets available for investigation, and characteristics of the planets to be searched for. Several hundreds of thousands of solar-type stars (F-G-K) within a sphere of $\sim 200$ pc centered on our Sun will be observed. GAIA will be particularly sensitive to giant planets (M$_\mathrm{p}$$\sim$M$_\mathrm{J}$) on wide orbits, up to periods twice as large as the mission duration, the potential signposts of the existence of rocky planets in the Habitable Zone. Thousands of new planets might be discovered, and a significant fraction of those which will be detected will have orbital parameters measured to better than 30% accuracy. By measuring to a few degrees the relative inclinations of planets in multiple systems with favorable configurations, GAIA will also make measurements of unique value towards a better understanding of the formation and evolution processes of planetary systems.
A Bayesian analysis of the world's p(gamma,K+)Lambda data is presented. We adopt a Regge-plus-resonance framework featuring consistent couplings for nucleon resonances up to spin J=5/2, and evaluate 2048 model variants considering all possible combinations of 11 candidate resonances. The best model, labeled RPR-2011, is discussed with special emphasis on nucleon resonances in the 1900-MeV mass region.
Recent development of mixed-state encoding (MSE) allows pure-state logical information to be encoded by a bosonic (continuous-variable) system in mixed physical state. Despite interest due to its counter-intuitiveness, the utility of the current MSE scheme is limited due to several operational drawbacks, namely redundant information carrier, probabilistic initialisation, and requirement of discrete-variable measurement. In this work, we present a simplified MSE that does not suffer from any of these drawbacks. Specifically, our protocol encodes each qubit by only one mixed-state bosonic mode, and the logical basis can be deterministically initialised from thermal equilibrium. All logical operations of this encoding can be performed with continuous-variable interaction and measurement only. Without the necessity of ground state cooling, our proposal could broaden the set of candidate systems for implementing quantum computers, and reduce the reliance on demanding refrigerating facility for current quantum computing architectures. Additionally, our protocol can enhance the noise tolerance of logical qubit even if the system can be efficiently cooled.
The crystal structure of hexagonal-Sr0.6Ba0.4MnO3 allows various competing superexchange interactions, leading to intriguing magnetic properties. Local structural changes modify overlapping between Mn and oxygen ions with temperature. Calculations based on our model spin-Hamiltonian reveal that the dominant linear antiferromagnetic superexchange interaction between the oxygen-linked Mn4+ ions results in short range correlations (SRC), manifesting a smooth drop in magnetization below 325K. Dominance of superexchange interaction changes its allegiance towards the non-linear oxygen-linked Mn-O-Mn interactions, onsetting long-range correlations (LRC) below 225K. Below the SRC-LRC crossover temperature, electrical response arising from the interacting dipoles exhibits power-law divergent behaviour of relaxation time, upon cooling. Non-ergodic character of the dipole-cluster glass state is examined via the indispensable aging and rejuvenation effects, similar to the spin glasses. Competitive-frustration among spin-exchange and local-strain is reckoned as responsible for the electrical glass origin.
In this article, we provide a Stein type characterization for $G$-normal distributions: Let $\mathcal{N}[\varphi]=\max_{\mu\in\Theta}\mu[\varphi],\ \varphi\in C_{b,Lip}(\mathbb{R}),$ be a sublinear expectation. $\mathcal{N}$ is $G$-normal if and only if for any $\varphi\in C_b^2(\mathbb{R})$, we have \[\int_\mathbb{R}[\frac{x}{2}\varphi'(x)-G(\varphi"(x))]\mu^\varphi(dx)=0,\] where $\mu^\varphi$ is a realization of $\varphi$ associated with $\mathcal{N}$, i.e., $\mu^\varphi\in \Theta$ and $\mu^\varphi[\varphi]=\mathcal{N}[\varphi]$.
We introduce a new four-parameters sequence that simultaneously generalizes some well-known integer sequences, including Fibonacci, Padovan, Jacobsthatl, Pell, and Lucas numbers. Combinatorial interpretations are discussed and many identities for this general sequence are derived. As a consequence, a number of identities for Fibonacci, Lucas, Pell, Jacobsthal, Padovan, and Narayana numbers as well as some of their generalizations are obtained. We also present the Cassini formula for the new sequence.
Mordell-Weil groups of different abelian fibrations of a hyperk\"ahler manifold may have non-trivial relation even among elements of infinite order, but have essentially no relation, as its birational transformation. Precise definition of the terms "essentially no relation" will be given in Introduction.
Let $C$ be a smooth curve which is complete intersection of a quadric and a degree $k>2$ surface in $\mathbb{P}^3$ and let $C^{(2)}$ be its second symmetric power. In this paper we study the finite generation of the extended canonical ring $R(\Delta,K) := \bigoplus_{(a,b)\in\mathbb{Z}^2}H^0(C^{(2)},a\Delta+bK)$, where $\Delta$ is the image of the diagonal and $K$ is the canonical divisor. We first show that $R(\Delta,K)$ is finitely generated if and only if the difference of the two $g_k^1$ on $C$ is torsion non-trivial and then show that this holds on an analytically dense locus of the moduli space of such curves.
We introduce and present preliminary results from COCOA (Cluster simulatiOn Comparison with ObservAtions) code for a star cluster after 12 Gyrs of evolution simulated using the MOCCA code. The COCOA code is being developed to quickly compare results of numerical simulations of star clusters with observational data. We use COCOA to obtain parameters of the projected cluster model. For comparison, a FITS file of the projected cluster was provided to observers so that they could use their observational methods and techniques to obtain cluster parameters. The results show that the similarity of cluster parameters obtained through numerical simulations and observations depends significantly on the quality of observational data and photometric accuracy.
The full metric describing two counter-rotating identical Kerr black holes separated by a massless strut is derived in the explicit analytical form. It contains three arbitrary parameters which are the Komar mass M, Komar angular momentum per unit mass a of one of the black holes (the other has the same mass and equal but opposite angular momentum) and the coordinate distance R between the centers of the horizons. In the limit of extreme black holes, the metric becomes a special member of the Kinnersly-Chitre five-parameter family of vacuum solutions generalizing the Tomimatsu-Sato delta=2 spacetime, and we present the complete set of metrical fields defining this limit.
We analyse the clustering of 22,361 quasars between redshift 2.2 < z < 2.9 observed with the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS), which are included in the ninth data release (DR9). We fit the clustering results with a {\Lambda}CDM model to calculate the linear bias of the quasar sample, b=3.74\pm 0.12. The measured value of bias is consistent with the findings of White et al. (2012), where they analyse almost the same quasar sample, although only in the range, s<40 Mpc/h. At large scales we observe an excess or plateau in the clustering correlation function. By fitting a model that incorporates a scale dependent additional term in the bias introduced by primordial non-Gaussianity of the local type, we calculate the amplitude of the deviation from the Gaussian initial conditions as 70<f_NL< 190 at the 95% confidence level. We correct the sample from systematics according to the methods of Ross et al. (2011); Ho et al. (2012) and Ross et al. (2011,2012b), with the f_NL measurements after the application of the two methods being consistent with each other. Finally we use cross-correlations across redshift slices to test the corrected sample for any remaining unknown sources of systematics, but the results give no indication of any such further errors. We consider as our final results on non-Gaussianity of the local type, 46<f_NL< 158 at 95% confidence, after correcting the sample with the weights method of Ross et al. (2011, 2012b). These results are consistent with previous tight constraints on non-Gaussianity from other LSS surveys, but are in tension with the latest results from the CMB.
We establish several results concerning the expected general phenomenon that, given a multiplicative function $f:\mathbb{N}\to\mathbb{C}$, the values of $f(n)$ and $f(n+a)$ are "generally" independent unless $f$ is of a "special" form. First, we classify all bounded completely multiplicative functions having uniformly large gaps between its consecutive values. This implies the solution of the following folklore conjecture: for any completely multiplicative function $f:\mathbb{N}\to\mathbb{T}$ we have $$\liminf_{n\to\infty}|f(n+1)-f(n)|=0.$$ Second, we settle an old conjecture due to N.G. Chudakov [Actes du ICM ({N}ice, 1970), {T}. 1, p. 487] that states that any completely multiplicative function $f:\mathbb{N}\to\mathbb{C}$ that: a) takes only finitely many values, b) vanishes at only finitely many primes, and c) has bounded discrepancy, is a Dirichlet character. This generalizes previous work of Tao on the Erd\H{o}s Discrepancy Problem. Finally, we show that if many of the binary correlations of a 1-bounded multiplicative function are asymptotically equal to those of a Dirichlet character $\chi$ mod $q$ then $f(n) = \chi'(n)n^{it}$ for all $n$, where $\chi'$ is a Dirichlet character modulo $q$ and $t \in \mathbb{R}$. This establishes a variant of a conjecture of H. Cohn for multiplicative arithmetic functions. The main ingredients include the work of Tao on logarithmic Elliott conjecture, correlation formulas for \emph{pretentious} multiplicative functions developed earlier by the first author and Szemeredi's theorem for long arithmetic progressions.
Let $\varphi:\mathbb{P}^1(\mathbb F_q)\to\mathbb{P}^1(\mathbb F_q)$ be a rational map of degree $d>1$ on a fixed finite field. We give asymptotic formulas for the size of image sets $\varphi^n(\mathbb{P}^1(\mathbb F_q))$ as a function of $n$. This is done using properties of Galois groups of iterated maps, whose connection to the size of image sets is established via the Chebotarev Density Theorem. We apply our results in the following setting. For a rational map defined over a number field, consider the reduction of the map modulo each prime of the number field. We use our results to give explicit bounds on the proportion of periodic points in the residue fields.
Systematic measurements of stress-impedance (SI) have been carried out using Co-rich amorphous ribbons of nominal composition Co71-xFexCr7Si8B14 (x = 0, 2) at various excitation frequencies and bias fields and at room temperature. The impedance, Z for both the samples was found to be very sensitive functions of applied tensile stresses (up to 100MPa) exhibiting a maximum SI ratio as much as 80% at low frequency ~ 0.1MHz. The nature of variation of SI changes with the excitation frequency especially at higher frequencies in MHz region where it exhibits a peak. Magnetization measurements were also performed to observe the effects of applied stresses and magnetization decreased with the application of stress confirming the negative magnetostriction co-efficient of both the samples. Both the samples exhibited negative magneto-impedance (MI) when the variation of Z is observed with the applied bias magnetic field, H. The impedance as functions of applied magnetic field, Z(H), decreases with the application of stress thus making the MI curves broader. Maximum MI ratio as large as 99% has been observed for both the samples at low fields ~ 27Oe.
The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseudospin, or both intertwined. In this article, we present a comprehensive numerical study of the collective excitations of these textured crystals using the GRPA. For the pure spin case, at finite Zeeman coupling the state is a Skyrmion crystal with a gapless phonon mode, and a separate Goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent Skyrmions break up, and the resulting state is a meron crystal with 4 gapless modes. In contrast, a pure pseudospin Skyrme crystal at finite tunneling has only the phonon mode. For Delta_SAS=0, the state evolves into a meron crystal and supports an extra gapless U(1) mode in addition to the phonon. For a CP(3) Skyrmion crystal, we find a U(1) gapless mode in the presence of the symmetry-breaking fields. In addition, a second mode with a very small gap is present in the spectrum.
The local environment and the charge state of a nickel impurity in cubic Ba$_{0.8}$Sr$_{0.2}$TiO$_3$ are studied by XAFS spectroscopy. According to the XANES data, the mean Ni charge state is $\sim$2.5+. An analysis of the EXAFS spectra and their comparison with the results of first-principle calculations of the defect geometry suggest that Ni$^{2+}$ ions are in a high-spin state at the $B$ sites of the perovskite structure and the difference of the Ni$^{2+}$ and Ti$^{4+}$ charges is mainly compensated by distant oxygen vacancies. In addition, a considerable amount of nickel in the sample is in a second phase BaNiO$_{3-\delta}$. The measurements of the lattice parameter show a decrease in the unit cell volume upon doping, which can indicate the existence of a small amount of Ni$^{4+}$ ions at the $B$ sites.
We present a general field-theoretic strategy to analyze three connected families of continuous phase transitions which occur in nonequilibrium steady-states. We focus on transitions taking place between an active state and one absorbing state, when there exist an infinite number of such absorbing states. In such transitions the order parameter is coupled to an auxiliary field. Three situations arise according to whether the auxiliary field is diffusive and conserved, static and conserved, or finally static and not conserved.
Algorithms for searching and sorting data sets on quantum annealing systems are presented. Search algorithms for unordered data sets are developed. A sorting algorithm for data sets is provided, with a consideration of sort stability. Scalability of the algorithms, considering both the number of qubits required and the qubit connectivity, is characterized as a function of problem size.
An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical' properties are asymptotically equivalent and, thus, a graph $G$ possessing one such property automatically satisfies the others.   In recent years, work in this area has focused on uncovering more quasirandom graph properties and on extending the known results to other discrete structures. In the context of hypergraphs, however, one may consider several different notions of quasirandomness. A complete description of these notions has been provided recently by Towsner, who proved several central equivalences using an analytic framework. We give short and purely combinatorial proofs of the main equivalences in Towsner's result.
One of the most appealing results of metric-affine gauge theory of gravity is a close parallel between the Riemann curvature two-form and the Cartan torsion two-form: While the former is the field strength of the Lorentz-group connection one-form, the latter can be understood as the field strength of the coframe one-form. This parallel, unfortunately, is not fully established until one adopts Trautman's idea of introducing an affine-vector-valued zero-from, the meaning of which has not been satisfactorily clarified. This paper aims to derive this parallel from first principles without any ad hoc prescriptions. We propose a new mathematical framework of an associated affine-vector bundle as a more suitable arena for the affine group than a conventional vector bundle, and rigorously derive the covariant derivative of a local section on the affine-vector bundle in the formal Ehresmann-connection approach. The parallel between the Riemann curvature and the Cartan torsion arises naturally on the affine-vector bundle, and their geometric and physical meanings become transparent. The clear picture also leads to a conjecture about a kinematical effect of the Cartan torsion that in principle can be measured \`{a} la the Aharonov-Bohm effect.