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We link the appearance of universal kernels in random matrix ensembles to the phenomenon of shock formation in some fluid dynamical equations. Such equations are derived from Dyson's random walks after a proper rescaling of the time. In the case of the Gaussian Unitary Ensemble, on which we focus in this letter, we show that the orthogonal polynomials, and their Cauchy transforms, evolve according to a viscid Burgers equation with an effective "spectral viscosity" $\nu_s=1/2N$, where $N$ is the size of the matrices. We relate the edge of the spectrum of eigenvalues to the shock that naturally appears in the Burgers equation for appropriate initial conditions, thereby obtaining a new perspective on universality. | Universal shocks in random matrix theory |
Suppose that X is a Fano manifold that corresponds under Mirror Symmetry to a Laurent polynomial f, and that P is the Newton polytope of f. In this setting it is expected that there is a family of algebraic varieties over the unit disc with general fiber X and special fiber the toric variety defined by the spanning fan of P. Building on recent work and conjectures by Corti--Hacking--Petracci, who construct such families of varieties, we determine the topology of the general fiber from combinatorial data on P. This provides evidence for the Corti--Hacking--Petracci conjectures, and verifies that their construction is compatible with expectations from Mirror Symmetry. | On the Topology of Fano Smoothings |
We examine the system where a string stretches between pair of D-branes, and study the bending of the D-brane caused by the tension of the string. If the distance between the pair of D-branes is sent to infinity, the tension of the string stretching between them is strong enough to pull the spike all the way to infinity. We study the shape of these spikes when the branes are finite distance apart using two different methods. First, we consider a string stretched between a pair of D2-branes in type IIA theory by going to the M-theory limit in which all of these branes are M-theory 2-branes embedded along a holomorphic curve. Second, we consider a D-string stretched between a pair of D3-branes in type IIB theory and infer the geometry of the D3-brane embeddings from the configuration of the adjoint scalar field in the magnetic monopole solution of Prasad and Sommerfield. The case of fundamental string stretching between a pair of D3-branes follows from S-duality. The energy of these configurations matches the expected value based on fundamental string and D-string tensions. | The Shape of Branes Pulled by Strings |
Correctly assessing a scientist's past research impact and potential for future impact is key in recruitment decisions and other evaluation processes. While a candidate's future impact is the main concern for these decisions, most measures only quantify the impact of previous work. Recently, it has been argued that linear regression models are capable of predicting a scientist's future impact. By applying that future impact model to 762 careers drawn from three disciplines: physics, biology, and mathematics, we identify a number of subtle, but critical, flaws in current models. Specifically, cumulative non-decreasing measures like the h-index contain intrinsic autocorrelation, resulting in significant overestimation of their "predictive power". Moreover, the predictive power of these models depend heavily upon scientists' career age, producing least accurate estimates for young researchers. Our results place in doubt the suitability of such models, and indicate further investigation is required before they can be used in recruiting decisions. | On the Predictability of Future Impact in Science |
The effects of a large-scale shear on the energy spectrum of a passively advected scalar field are investigated. The shear is superimposed on a turbulent isotropic flow, yielding an Obukhov-Corrsin $k^{-5/3}$ scalar spectrum at small scales. Shear effects appear at large scales, where a different, anisotropic behavior is observed. The scalar spectrum is shown to behave as $k^{-4/3}$ for a shear fixed in intensity and direction. For other types of shear characteristics, the slope is generally intermediate between the -5/3 Obukhov-Corrsin's and the -1 Batchelor's values. The physical mechanisms at the origin of this behaviour are illustrated in terms of the motion of Lagrangian particles. They provide an explanation to the scalar spectra shallow and dependent on the experimental conditions observed in shear flows at moderate Reynolds numbers. | Shear effects on passive scalar spectra |
Image registration plays an important role in medical image analysis. Conventional optimization based methods provide an accurate estimation due to the iterative process at the cost of expensive computation. Deep learning methods such as learn-to-map are much faster but either iterative or coarse-to-fine approach is required to improve accuracy for handling large motions. In this work, we proposed to learn a registration optimizer via a multi-scale neural ODE model. The inference consists of iterative gradient updates similar to a conventional gradient descent optimizer but in a much faster way, because the neural ODE learns from the training data to adapt the gradient efficiently at each iteration. Furthermore, we proposed to learn a modal-independent similarity metric to address image appearance variations across different image contrasts. We performed evaluations through extensive experiments in the context of multi-contrast 3D MR images from both public and private data sources and demonstrate the superior performance of our proposed methods. | Multi-scale Neural ODEs for 3D Medical Image Registration |
Numerical simulations are important when assessing the many characteristics of field emission related phenomena. In small simulation domains, the electrostatic effect from the boundaries is known to influence the calculated apex field enhancement factor (FEF) of the emitter, but no established dependence has been reported at present. In this work, we report the dependence of the lateral size, $L$, and the height, $H$, of the simulation domain on the apex-FEF of a single conducting ellipsoidal emitter. Firstly, we analyze the error, $\varepsilon$, in the calculation of the apex-FEF as a function of $H$ and $L$. Importantly, our results show that the effects of $H$ and $L$ on $\varepsilon$ are scale invariant, allowing one to predict $\varepsilon$ for ratios $L/h$ and $H/h$, where $h$ is the height of the emitter. Next, we analyze the fractional change of the apex-FEF, $\delta$, from a single emitter, $\gamma_1$, and a pair, $\gamma_2$. We show that small relative errors in $\gamma_1$ (i.e., $\varepsilon\approx0.5\%$), due to the finite domain size, are sufficient to alter the functional dependence $\delta(c)$, where $c$ is the distance from the emitters in the pair. We show that $\delta(c)$ obeys a recently proposed power law decay in the limit of infinite domain size ($\varepsilon=0$, say), in contrast to a long time established exponential decay. Thus, power law functional dependence, $-\delta \sim c^{-n}$, with $n=3$, is suggested to be a universal signature of the charge-blunting effect, at sufficient large distances between similar emitters with any shape. These results explain the origin of the discrepancies in the literature and improves the scientific understanding of the field electron emission theory, for accurate characterization of emitters in small clusters or arrays. | Origin of the literature discrepancies in the fractional reduction of the apex-field enhancement factor considering small clusters of field emitters |
For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but gapless, and its spectrum is $\R^+$. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit. | Frustration free gapless Hamiltonians for Matrix Product States |
Hawkes processes are a class of simple point processes that are self-exciting and have clustering effect, with wide applications in finance, social networks and many other fields. This paper considers a self-exciting Hawkes process where the baseline intensity is time-dependent, the exciting function is a general function and the jump sizes of the intensity process are independent and identically distributed non-negative random variables. This Hawkes model is non-Markovian in general. We obtain closed-form formulas for the Laplace transform, moments and the distribution of the Hawkes process. To illustrate the applications of our results, we use the Hawkes process to model the clustered arrival of trades in a dark pool and analyze various performance metrics including time-to-first-fill, time-to-complete-fill and the expected fill rate of a resting dark order. | Transform Analysis for Hawkes Processes with Applications in Dark Pool Trading |
A generic feature of inflationary models in supergravity/string constructions is vacuum misalignment for the moduli fields. The associated production of moduli particles leads to an epoch in the post-inflationary history in which the energy density is dominated by cold moduli particles. This modification of the post-inflationary history implies that the preferred range for the number of e-foldings between horizon exit of the modes relevant for CMB observations and the end of inflation $(N_k)$ depends on moduli masses. This in turn implies that the precision CMB observables $n_s$ and $r$ are sensitive to moduli masses. We analyse this sensitivity for some representative models of inflation and find the effect to be highly relevant for confronting inflationary models with observations. | Inflationary Predictions and Moduli Masses |
We study a polynomial sequence $C_n(x|q)$ defined as a solution of a $q$-difference equation. This sequence, evaluated at $q$-integers, interpolates Carlitz-Riordan's $q$-ballot numbers. In the basis given by some kind of $q$-binomial coefficients, the coefficients are again some $q$-ballot numbers. We obtain in a combinatorial way another curious recurrence relation for these polynomials. | A curious polynomial interpolation of Carlitz-Riordan's $q$-ballot numbers |
Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter $F_{\ell} \le -1$ in the angular momentum $\ell=2$ channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters $F_\ell$ of the composite fermion Fermi liquid with a finite layer width. We consider $F_{\ell}$ in different Landau levels $n=0,1,2$ as a function of layer width parameter $\eta$. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of $\eta$. Furthermore, the critical value $\eta_c$ is higher for the $n=2$ Landau level, which is consistent with observation of nematic order in ambient conditions only in the $n=2$ Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability. | Pomeranchuk Instability of Composite Fermi Liquids |
With an aim to study whether the close correlation between [Na/H] and [Fe/H] recently found in A-type stars further persists in the regime of B-type stars, the abundances of Na were determined for 30 selected sharp-lined late B-type stars (10000K < T_eff < 14000K) from the Na I 5890/5896 doublet. These Na abundances were then compared with the O and Fe abundances (derived from the O I 6156-8 and Fe II 6147/6149 lines) showing anti-correlated peculiarities. It turned out that, unlike the case of A-type stars, [Na/H] is roughly constant at a slightly subsolar level ([Na/H] ~ -0.2 (+/-0.2)) without any significant correlation with [Fe/H] which shows considerable dispersion ranging from ~ -0.6 to ~ +1.0. This may serve as an important observational constraint for understanding the abundance peculiarities along with the physical mechanism of atomic diffusion in upper main-sequence stars of late A through late B-type including Am and HgMn stars. | On the Sodium versus Iron Correlation in Late B-Type Stars |
In the last years, various extensions of {\omega}-regular languages have been proposed in the literature, including {\omega}B-regular ({\omega}-regular languages extended with boundedness), {\omega}S-regular ({\omega}-regular languages extended with strict unboundedness), and {\omega}BS-regular languages (the combination of {\omega}B- and {\omega}S-regular ones). While the first two classes satisfy a generalized closure property, namely, the complement of an {\omega}B-regular (resp., {\omega}S-regular) language is an {\omega}S-regular (resp., {\omega}B-regular) one, the last class is not closed under complementation. The existence of non-{\omega}BS-regular languages that are the complements of some {\omega}BS-regular ones and express fairly natural properties of reactive systems motivates the search for other well-behaved classes of extended {\omega}-regular languages. In this paper, we introduce the class of {\omega}T-regular languages, that includes meaningful languages which are not {\omega}BS-regular. We first define it in terms of {\omega}T-regular expressions. Then, we introduce a new class of automata (counter-check automata) and we prove that (i) their emptiness problem is decidable in PTIME and (ii) they are expressive enough to capture {\omega}T-regular languages (whether or not {\omega}T-regular languages are expressively complete with respect to counter-check automata is still an open problem). Finally, we provide an encoding of {\omega}T-regular expressions into S1S+U. | Beyond $\omega$BS-regular Languages: $\omega$T-regular Expressions and Counter-Check Automata |
An exactly solvable electron model of a confined system with inverse-square interaction is presented. The ground state is given by the Jastrow-product wavefunction of power-law form. We discuss the results in connection with conductance oscillations observed in semiconductor nanostructures, for which single-electron charging effects play a crucial role. Due to the internal spin degrees of freedom, there appear two independent periods of the conductance oscillations in very narrow channels even at zero temperature. | Confined quantum systems in one dimension and conductance oscillations in narrow channels |
We report on the observation of the reststrahl band assisted photocurrents in epitaxial graphene on SiC excited by infrared radiation. The peculiar spectral dependence for frequencies lying within the reststrahl band of the SiC substrate provides a direct and noninvasive way to probe the electric field magnitude at atomic distances from the material's surface. Furthermore our results reveal that nonlinear optical and optoelectronic phenomena in 2D crystals and other atomic scale structures can be giantly enhanced by a proper combination of the spectral range and substrate material. | Probing of electromagnetic fields on atomic scale by photoelectric phenomena in graphene |
In previous work, Ohno conjectured, and Nakagawa proved, relations between the counting functions of certain cubic fields. These relations may be viewed as complements to the Scholz reflection principle, and Ohno and Nakagawa deduced them as consequences of `extra functional equations' involving the Shintani zeta functions associated to the prehomogeneous vector space of binary cubic forms. In the present paper we generalize their result by proving a similar identity relating certain degree l fields with Galois groups D_l and F_l respectively, for any odd prime l, and in particular we give another proof of the Ohno-Nakagawa relation without appealing to binary cubic forms. | Identities for field extensions generalizing the Ohno-Nakagawa relations |
A simple burning or epidemic type of algorithm is developed in order to test whether any loops in percolation clusters link a fixed reference loop, a problem considered recently by Gliozzi, Lottini, Panero, and Rago in the context of gauge theory. We test our algorithm at criticality in both 2d, where the behavior agrees with a theoretical prediction, and in 3d. | A simple algorithm to test for linking to Wilson loops in percolation |
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the conditions of the measurement define the type of quantization (Weyl, normal, antinormal, etc.). The quantum states and quantum operators are obtained by means of the projection, defined from the system of generalized coherent states. | Geometric Quantization, Coherent States and Stochastic Measurements |
The standard $SU(2) \times U(1)$ fields are considered in 4D plus one extra compact dimension. As a result two basic effects are obtained. First, four Goldstone-like scalars are produced, three of them are used to create longitudinal modes of the $W,Z$ fields, while the fourth becomes the Higgs-like scalar. Second, $W$ and $Z$ get their masses from the extra compact dimension with the standard pattern of symmetry violation. The resulting theory has the same fields as in the standard model, but without the Higgs vacuum average. The properties of the new Higgs scalar and its interaction with fermions are briefly discussed. | The Higgs Mechanism from an extra dimension |
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting nonlinear quantum logic gates. It is argued that virtually any deterministic nonlinear quantum theory will include such gates, and the method is explicitly demonstrated using the Weinberg model of nonlinear quantum mechanics. | Nonlinear quantum mechanics implies polynomial-time solution for NP-complete and #P problems |
The combination of the surface science techniques (STM, XPS, ARPES) and density-functional theory calculations was used to study the decoupling of graphene from Ni(111) by oxygen intercalation. The formation of the antiferromagnetic (AFM) NiO layer at the interface between graphene and ferromagnetic (FM) Ni is found, where graphene protects the underlying AFM/FM sandwich system. It is found that graphene is fully decoupled in this system and strongly $p$-doped via charge transfer with a position of the Dirac point of $(0.69\pm0.02)$ eV above the Fermi level. Our theoretical analysis confirms all experimental findings, addressing also the interface properties between graphene and AFM NiO. | Decoupling of graphene from Ni(111) via oxygen intercalation |
The second law of thermodynamics states that a system in contact with a heat bath can undergo a transformation if and only if its free energy decreases. However, the "if" part of this statement is only true when the effective heat bath is infinite. In this article we remove this idealization and derive corrections to the second law in the case where the bath has a finite size, or equivalently finite heat capacity. This can also be translated to processes lasting a finite time, and we show that thermodynamical reversibility is lost in this regime. We do so in full generality, that is without assuming any particular model for the bath, the only parameters defining the bath are its temperature and heat capacity. We find connections with second order Shannon information theory, in particular in the case of Landauer erasure. We also consider the case of non-fluctuating work, and derive finite-bath corrections to the min and max free energies employed in single-shot thermodynamics. | Finite-bath corrections to the second law of thermodynamics |
In this paper we give a completely new approach to the problem of covariate selection in linear regression. A covariate or a set of covariates is included only if it is better in the sense of least squares than the same number of Gaussian covariates consisting of i.i.d. $N(0,1)$ random variables. The Gaussian P-value is defined as the probability that the Gaussian covariates are better. It is given in terms of the Beta distribution, it is exact and it holds for all data. The covariate selection procedures based on this require only a cut-off value $\alpha$ for the Gaussian P-value: the default value in this paper is $\alpha=0.01$. The resulting procedures are very simple, very fast, do not overfit and require only least squares. In particular there is no regularization parameter, no data splitting, no use of simulations, no shrinkage and no post selection inference is required. The paper includes the results of simulations, applications to real data sets and theorems on the asymptotic behaviour under the standard linear model. Here the stepwise procedure performs overwhelmingly better than any other procedure we are aware of. An R-package {\it gausscov} is available. | Covariate Selection Based on a Assumpton-free Approach to Linear Regression with Exact Probabilities |
A non-LTE (NLTE) abundance analysis was carried out for three extreme helium stars (EHes): BD+10 2179, BD-9 4395, and LS IV+6 002, from their optical spectra with NLTE model atmospheres. NLTE TLUSTY model atmospheres were computed with H, He, C, N, O, and Ne treated in NLTE. Model atmosphere parameters were chosen from consideration of fits to observed He I line profiles and ionization equilibria of C and N ions. The program SYNSPEC was then used to determine the NLTE abundances for Ne as well as H, He, C, N, and O. LTE neon abundances from Ne I lines in the EHes: LSE 78, V1920 Cyg, HD 124448, and PV Tel, are derived from published models and an estimate of the NLTE correction applied to obtain the NLTE Ne abundance. We show that the derived abundances of these key elements, including Ne, are well matched with semi-quantitative predictions for the EHe resulting from a cold merger (i.e., no nucleosynthesis during the merger) of a He white dwarf with a C-O white dwarf. | Neon and CNO Abundances for Extreme Helium Stars -- A Non-LTE Analysis |
We study Lagrangians with the minimal amount of gauge symmetry required to propagate spin-two particles without ghosts or tachyons. In general, these Lagrangians also have a scalar mode in their spectrum. We find that, in two cases, the symmetry can be enhanced to a larger group: the whole group of diffeomorphisms or a enhancement involving a Weyl symmetry. We consider the non-linear completions of these theories. The intuitive completions yield the usual scalar-tensor theories except for the pure spin-two cases, which correspond to two inequivalent Lagrangians giving rise to Einstein's equations. A more constructive self-consistent approach yields a background dependent Lagrangian. | Gauge Symmetry and Consistent Spin-Two Theories |
We present two observational campaigns performed with the RXTE satellite on the black hole transient H 1743-322. The source was observed in outburst on two separate occasions between October-November 2008 and May-July 2009. We have carried out timing and spectral analysis of the data set, obtaining a complete state classification of all the observations. We find that all the observations are well described by using a spectral model consisting of a disk-blackbody, a powerlaw + reflection + absorption and a gaussian emission component. During the 2009 outburst the system followed the canonical evolution through all the states seen in black hole transients. In the 2008 outburst only the hard states were reached. The early evolution of the spectral parameters is consistent between the two epochs, and it does not provide clues about the subsequent behavior of the source. The variation of the flux associated to the two main spectral components (i.e. disk and powerlaw) allows us to set a lower limit to the orbital inclination of the system of >= 43{\deg}. | On the outburst evolution of H1743-322: a 2008/2009 comparison |
We investigate a phase-field version of the Faber--Krahn theorem based on a phase-field optimization problem introduced in Garcke et al. [ESAIM Control Optim. Calc. Var. 29 (2023), Paper No. 10] formulated for the principal eigenvalue of the Dirichlet--Laplacian. The shape, that is to be optimized, is represented by a phase-field function mapping into the interval $[0,1]$. We show that any minimizer of our problem is a radially symmetric-decreasing phase-field attaining values close to $0$ and $1$ except for a thin transition layer whose thickness is of order $\varepsilon>0$. Our proof relies on radially symmetric-decreasing rearrangements and corresponding functional inequalities. Moreover, we provide a $\Gamma$-convergence result which allows us to recover a variant of the Faber--Krahn theorem for sets of finite perimeter in the sharp-interface limit. | A phase-field version of the Faber--Krahn theorem |
CoRoT and Kepler high-precision photometric data allowed the detection and characterization of the oscillation parameters in stars other than the Sun. Moreover, thanks to the scaling relations, it is possible to estimate masses and radii for thousands of solar-type oscillating stars. Recently, a \Delta\nu - \rho relation has been found for \delta Scuti stars. Now, analyzing several hundreds of this kind of stars observed with CoRoT and Kepler, we present an empiric relation between their frequency at maximum power of their oscillation spectra and their effective temperature. Such a relation can be explained with the help of the \kappa-mechanism and the observed dispersion of the residuals is compatible with they being caused by the gravity-darkening effect. | The envelope of the power spectra of over a thousand \delta Scuti stars. The $\bar{T}_{eff}$-$\nu_{max}$ scaling relation |
We present LTE chemical abundances for five red giants and one AGB star in the Galactic globular cluster (GC) M5 based on high resolution spectroscopy using the MIKE spectrograph on the Magellan 6.5-m Clay telescope. Our results are based on a line-by-line differential abundance analysis relative to the well-studied red giant Arcturus. The stars in our sample that overlap with existing studies in the literature are consistent with published values for [Fe/H] and agree to within typically 0.04 dex for the alpha-elements. Most deviations can be assigned to varying analysis techniques in the literature. This strengthens our newly established differential GC abundance scale and advocates future use of this method. In particular, we confirm a mean [Fe I/H] of -1.33 +- 0.03 (stat.) +- 0.03 (sys.) dex and also reproduce M5's enhancement in the alpha-elements (O,Mg,Si,Ca,Ti) at +0.4 dex, rendering M5 a typical representative of the Galactic halo. Over-ionization of Fe I in the atmospheres of these stars by non-LTE effects is found to be less than 0.07 dex. Five of our six stars show O-Na-Al-Mg abundance patterns consistent with pollution by proton-capture nucleosynthesis products. | A differential chemical abundance scale for the globular cluster M5 |
[Abridged] The aim of this work is to search for an absorption signal from exospheric sodium (Na) and singly ionized calcium (Ca$^+$) in the optical transmission spectrum of the hot rocky super-Earth 55 Cancri e. Although the current best-fitting models to the planet mass and radius require a possible atmospheric component, uncertainties in the radius exist, making it possible that 55 Cancri e could be a hot rocky planet without an atmosphere. High resolution (R$\sim$110000) time-series spectra of five transits of 55 Cancri e, obtained with three different telescopes (UVES/VLT, HARPS/ESO 3.6m & HARPS-N/TNG) were analysed. Targeting the sodium D lines and the calcium H and K lines, the potential planet exospheric signal was filtered out from the much stronger stellar and telluric signals, making use of the change of the radial component of the orbital velocity of the planet over the transit from -57 to +57 km/sec. Combining all five transit data sets, we detect a signal potentially associated with sodium in the planet exosphere at a statistical significance level of 3$\sigma$. Combining the four HARPS transits that cover the calcium H and K lines, we also find a potential signal from ionized calcium (4.1 $\sigma$). Interestingly, this latter signal originates from just one of the transit measurements - with a 4.9$\sigma$ detection at this epoch. Unfortunately, due to the low significance of the measured sodium signal and the potentially variable Ca$^+$ signal, we estimate the p-values of these signals to be too high (corresponding to <4$\sigma$) to claim unambiguous exospheric detections. By comparing the observed signals with artificial signals injected early in the analysis, the absorption by Na and Ca$^+$ are estimated to be at a level of approximately 2.3$\times 10^{-3}$ and 7.0$\times 10^{-2}$ respectively, relative to the stellar spectrum. | Search for an exosphere in sodium and calcium in the transmission spectrum of exoplanet 55 Cancri e |
We study total and partial supersymmetry breaking by freely acting orbifolds, or equivalently by Scherk-Schwarz compactifications, in type I string theory. In particular, we describe a four-dimensional chiral compactification with spontaneously broken N=1 supersymmetry, some models with partial $N=4\to N=2$ and $N=4\to N=1$ supersymmetry breaking and their heterotic and M-theory duals. A generic feature of these models is that in the gravitational sector and in the spectrum of D-branes parallel to the breaking coordinate, all mass splittings are proportional to the compactification scale, while global (extended) supersymmetry remains unbroken at tree level for the massless excitations of D-branes transverse to the breaking direction. | Partial breaking of supersymmetry, open strings and M-theory |
Fatigue failure in ferroelectrics has been intensively investigated in the past few decades. Most of the mechanisms discussed for ferroelectric fatigue have been built on the "hypothesis of variation in charged defects", which however are rarely evidenced by experimental observation. Here, using a combination of complex impedance spectra techniques, piezoresponse force microscopy and first-principles theory, we examine the microscopic evolution and redistribution of charged defects during the electrical cycling in BiFeO3 thin films. The dynamic formation and melting behaviors of oxygen vacancy (VO) order are identified during the fatigue process. It reveals that the isolated VO tend to self-order along grain boundaries to form a planar-aligned structure, which blocks the domain reversals. Upon further electrical cycling, migration of VO within vacancy clusters is accommodated with a lower energy barrier (~0.2 eV) and facilitates the formation of nearby-electrode layer incorporated with highly concentrated VO. The interplay between the macroscopic fatigue and microscopic evolution of charged defects clearly demonstrates the role of ordered VO cluster in the fatigue failure of BiFeO3 thin films. | Microstructural Evolution of Charged Defects in the Fatigue Process of Polycrystalline BiFeO3 Thin Films |
Comet 67P/Churyumov-Gerasimenko was selected in 2003 as the new target of the Rosetta mission. It has since been the subject of a detailed campaign of observations to characterise its nucleus and activity. Here we present previously unpublished data taken around the start of activity of the comet in 2007/8, before its last perihelion passage. We constrain the time of the start of activity, and combine this with other data taken throughout the comet's orbit to make predictions for its likely behaviour during 2014/5 while Rosetta is operating. A considerable difficulty in observing 67P during the past years has been its position against crowded fields towards the Galactic centre for much of the time. The 2007/8 data presented here were particularly difficult, and the comet will once again be badly placed for Earth-based observations in 2014/5. We make use of the difference image analysis (DIA) technique, which is commonly used in variable star and exoplanet research, to remove background sources and extract images of the comet. In addition, we reprocess a large quantity of archival images of 67P covering its full orbit, to produce a heliocentric lightcurve. By using consistent reduction, measurement and calibration techniques we generate a remarkably clean lightcurve, which can be used to measure a brightness-distance relationship and to predict the future brightness of the comet. We determine that the comet was active around November 2007, at a pre-perihelion distance from the Sun of 4.3 AU. The comet will reach this distance, and probably become active again, in March 2014. We find that the dust brightness can be well described by Af\rho \propto r^-3.2 pre-perihelion and r^-3.4 post-perihelion, and that the comet has a higher dust-to-gas ratio than average. A model fit to the photometric data suggests that only a small fraction (1.4%) of the surface is active. | Beginning of activity in 67P/Churyumov-Gerasimenko and predictions for 2014/5 |
We analyze a chain of coupled nonlinear optical cavities driven by a coherent source of light localized at one end and subject to uniform dissipation. We characterize photon transport by studying the populations and the photon correlations as a function of position. When complemented with input-output theory, these quantities provide direct information about photon transmission through the system. The position of single- and multi-photon resonances directly reflect the structure of the many-body energy levels. This shows how a study of transport along a coupled cavity array can provide rich information about the strongly correlated (many-body) states of light even in presence of dissipation. By means of a numerical algorithm based on the time-evolving block decimation scheme adapted to mixed states, we are able to simulate arrays up to sixty cavities. | Photon transport in a dissipative chain of nonlinear cavities |
In this work we generalize the Stefan-Boltzmann and Wien's displacement laws for a $D$-dimensional manifold composed by 4 non-compact dimensions and $D-4$ compact dimensions, $ R^{1,3}$ x $T^{D-4} $. The electromagnetic field is assumed to pervade all compact and non-compact dimensions. In particular, the total radiated power becomes $ R(T) = \sigma_B T^4 + \sigma_D (a) \, T^D $, where $a$ is the size of the compact extra dimensions. For $D=10$, predicted from String Theory, and $D=11$, from M-Theory, the outcomes agree with available experimental data for $a$ as high as 2 x $10^{-7}$m. | The Size of Compact Extra Dimensions from Blackbody Radiation Laws |
We present a high-contrast imaging survey of intermediate-mass (1.75--4.5 $M_\odot$) stars to search for the most extreme stellar binaries, i.e., for the lowest mass stellar companions. Using adaptive optics at the Lick and Gemini observatories, we observed 169 stars and detected 24 candidates companions, 16 of which are newly discovered and all but three are likely or confirmed physical companions. Despite obtaining sensitivity down to the substellar limit for 75\% of our sample, we do not detect any companion below 0.3 $M_\odot$, strongly suggesting that the distribution of stellar companions is truncated at a mass ratio of $q_\mathrm{min} \gtrsim0.075$. Combining our results with known brown dwarf companions, we identify a low-mass companion desert to intermediate mass stars in the range $0.02\lesssim q \lesssim0.05$, which quantitatively matches the known brown dwarf desert among solar-type stars. We conclude that the formation mechanism for multiple systems operates in a largely scale-invariant manner and precludes the formation of extremely uneven systems, likely because the components of a proto-binary accrete most of their mass after the initial cloud fragmentation. Similarly, the mechanism to form "planetary" ($q \lesssim 0.02$) companions likely scales linearly with stellar mass, probably as a result of the correlation between the masses of stars and their protoplanetary disks. Finally, we predict the existence of a sizable population of brown dwarf companions to low-mass stars and of a rising population of planetary-mass objects towards $\approx 1\,M_\mathrm{Jup}$ around solar-type stars. Improvements on current instrumentation will test these predictions. | A low-mass companion desert among intermediate-mass visual binaries: The scaled-up counterpart to the brown dwarf desert |
In a metastable de Sitter space any object has a finite life expectancy beyond which it undergoes vacuum decay. However, by spreading into different parts of the universe which will fall out of causal contact of each other in future, a civilization can increase its collective life expectancy, defined as the average time after which the last settlement disappears due to vacuum decay. We study in detail the collective life expectancy of two comoving objects in de Sitter space as a function of the initial separation, the horizon radius and the vacuum decay rate. We find that even with a modest initial separation, the collective life expectancy can reach a value close to the maximum possible value of 1.5 times that of the individual object if the decay rate is less than 1% of the expansion rate. Our analysis can be generalized to any number of objects, general trajectories not necessarily at rest in the comoving coordinates and general FRW space-time. As part of our analysis we find that in the current state of the universe dominated by matter and cosmological constant, the vacuum decay rate is increasing as a function of time due to accelerated expansion of the volume of the past light cone. Present decay rate is about 3.7 times larger than the average decay rate in the past and the final decay rate in the cosmological constant dominated epoch will be about 56 times larger than the average decay rate in the past. This considerably weakens the lower bound on the half-life of our universe based on its current age. | Surviving in a Metastable de Sitter Space-Time |
Infrared Imaging Surveyor (IRIS) is a satellite which will be launched in the beginning of 2003. One of the main purposes of the IRIS mission is an all-sky survey at far-infrared (FIR) with a flux limit much deeper than that of IRAS. In order to examine the performance of the survey, we estimated the FIR galaxy counts in four (50, 70, 120, and 150 $\mu$m) bands based on some models. We adopted a multicomponent model which consists of cirrus and starburst components for galaxy spectra, and the nearby FIR luminosity function derived from that of IRAS galaxies. We derived the number counts, redshift distributions, and infrared diffuse background radiation spectra for i) no evolution, ii) pure luminosity evolution, iii) pure density evolution with $q_0 = 0.1$ and 0.5. We found that a large number of galaxies ($\sim {\rm a few} \times 10^6$ in the whole sky) will be detected in this survey. With the aid of a vast number of detection, we will detect the effect of galaxy evolution, and evaluate the amplitude of evolution at least in the nearby universe in the IRIS survey, though it will be still difficult to constrain which type of evolution takes place from the number count alone. We also studied the estimation of redshifts of detected galaxies by their infrared colors alone. Although significant contamination takes place among nearby faint galaxies and high-$z$ ones, we found that rough estimation of galaxy redshift can be practicable by jointly using present and future optical surveys. | The IRIS Far-Infrared Galaxy Survey : Expected Number Count, Redshift, and Perspective |
The performance of the emerging petaflops-scale supercomputers of the nearest future (hypercomputers) will be governed not only by the clock frequency of the processing nodes or by the width of the system bus, but also by such factors as the overall power consumption and the geometric size. In this paper, we study the influence of such parameters on one of the most important characteristics of a general purpose computer - on the degree of multithreading that must be present in an application to make the use of the hypercomputer justifiable. Our major finding is that for the class of applications with purely random memory access patterns "super-fast computing" and "high-performance computing" are essentially synonyms for "massively-parallel computing." | Parametric Estimation of the Ultimate Size of Hypercomputers |
We discuss the effect of the stationarity on the avalanche statistics of Barkhuasen noise signals. We perform experimental measurements on a Fe$_{85}$B$_{15}$ amorphous ribbon and compare the avalanche distributions measured around the coercive field, where the signal is stationary, with those sampled through the entire hysteresis loop. In the first case, we recover the scaling exponents commonly observed in other amorphous materials ($\tau=1.3$, $\alpha=1.5$). while in the second the exponents are significantly larger ($\tau=1.7$, $\alpha=2.2$). We provide a quantitative explanation of the experimental results through a model for the depinning of a ferromagnetic domain wall. The present analysis shed light on the unusually high values for the Barkhausen noise exponents measured by Spasojevic et al. [Phys. Rev. E 54 2531 (1996)]. | The role of stationarity in magnetic crackling noise |
Binary image segmentation plays an important role in computer vision and has been widely used in many applications such as image and video editing, object extraction, and photo composition. In this paper, we propose a novel interactive binary image segmentation method based on the Markov Random Field (MRF) framework and the fast bilateral solver (FBS) technique. Specifically, we employ the geodesic distance component to build the unary term. To ensure both computation efficiency and effective responsiveness for interactive segmentation, superpixels are used in computing geodesic distances instead of pixels. Furthermore, we take a bilateral affinity approach for the pairwise term in order to preserve edge information and denoise. Through the alternating direction strategy, the MRF energy minimization problem is divided into two subproblems, which then can be easily solved by steepest gradient descent (SGD) and FBS respectively. Experimental results on the VGG interactive image segmentation dataset show that the proposed algorithm outperforms several state-of-the-art ones, and in particular, it can achieve satisfactory edge-smooth segmentation results even when the foreground and background color appearances are quite indistinctive. | Interactive Binary Image Segmentation with Edge Preservation |
We propose an entanglement sharing protocol based on separable states. Initially, two parties, Alice and Bob, share a two-mode separable Gaussian state. Alice then splits her mode into two separable modes and distributes them between two players. Bob is separable from the players but he can create entanglement with either of the players if the other player moves to his location and collaborates with him. Any two parties are separable and the creation of entanglement is thus mediated by transmission of a mode which is separable from individual modes on Alice's and Bob's side. For the state shared by the players and Bob one cannot establish entanglement between any two modes even with the help of operation on the third mode provided that Bob is restricted to Gaussian measurements and the state thus carries a nontrivial signature of bound entanglement. The present protocol also demonstrates switching between different separability classes of tripartite systems by coherent operations on its bipartite parts and complements studies on protocols utilizing mixed partially entangled multipartite states. | Entanglement sharing with separable states |
Two simple mathematical models of electric neuro-stimulation are derived and discussed. It is found that the common injected-charge model is less realistic than a model, in which a latency period, which follows after a short electric pulse, plays a role as important as the electric pulse. A stimulation signal is proposed that takes advantage of these findings and calls for experimental testing. | Comparison of two models of electric neuro-stimulation and consequences for the design of retinal prostheses |
This paper is a companion of [Phys. Rev. D 95, 124041 (2017)] in which, following a program on black hole nonmodal linear stability initiated in Phys. Rev. Lett. 112 (2014) 191101, odd perturbations of the Einstein-Maxwell equations around a Reissner-Nordstr\"om (A)dS black hole were analyzed. Here we complete the proof of the nonmodal linear stability of this spacetime by analyzing the even sector of the linear perturbations. We show that all the gauge invariant information in the metric and Maxwell field even perturbations is encoded in two spacetime scalars: ${\mathcal S}$, which is a gauge invariant combination of $\delta (C_{\alpha \beta \gamma \epsilon}C^{\alpha \beta \gamma \epsilon})$ and $\delta (C_{\alpha \beta \gamma \delta} F_{\alpha \beta} F^{\gamma \delta})$, and ${\mathcal T}$, a gauge invariant combination of $\delta ( \nabla _\mu F_{\alpha \beta} \nabla^\mu F^{\alpha \beta })$ and $\delta ( \nabla_{\mu} C_{\alpha \beta \gamma \delta} \nabla^{\mu}C^{\alpha \beta \gamma \delta})$. Here $C_{\alpha \beta \gamma \delta}$ is the Weyl tensor, $F_{\alpha \beta}$ the Maxwell field and $\delta$ means first order variation. We prove that $\mathcal{S}$ and $\mathcal{T}$ are are in one-one correspondence with gauge classes of even linear perturbations, and that the linearized Einstein-Maxwell equations imply that these scalar fields are pointwise bounded on the outer static region. | Black hole nonmodal linear stability: even perturbations in the Reissner-Nordstr\"om case |
For the Higgs boson mass of $\sim 220$ GeV expected to arise from radiative electroweak symmetry breaking, we find the same lowest-order expressions as would be obtained from conventional electroweak symmetry breaking, given the same Higgs boson mass, for Higgs-Goldstone sector scattering processes identified with $W_L^ + W_L^- \to W_L^+ W_L^-$, $W_L^+ W_L^- \to Z_L Z_L$, as well as for Higgs boson decay widths $H \to W_L^+ W_L^-$, $H \to Z_L Z_L$. The radiatively broken case, however, leads to an order of magnitude enhancement over lowest-order conventional symmetry breaking for scattering processes $W_L^+ W_L^+ \to H H$, $Z_L Z_L \to H H$, as well as a factor of $\sim 30$ enhancement for $H H \to H H$. | Startling Equivalences in the Higgs-Goldstone Sector between Radiative and Lowest-Order Conventional Electroweak Symmetry Breaking |
In terms of spin-charge separated variables, the Minkowski space Yang-Mills BPST instanton describes a locally conformally flat doubly-wrapped cigar manifold that can be viewed as a Euclidean quantum black hole. An ensemble of instantons then corresponds to a ``spacetime foam'' that creates a locally conformally flat spacetime from ``nothing'' as a quantum fluctuation. | Yang-Mills instanton as a quantum black hole |
We characterise the evolution of a dynamical system by combining two well-known complex systems' tools, namely, symbolic ordinal analysis and networks. From the ordinal representation of a time-series we construct a network in which every node weights represents the probability of an ordinal patterns (OPs) to appear in the symbolic sequence and each edges weight represents the probability of transitions between two consecutive OPs. Several network-based diagnostics are then proposed to characterize the dynamics of different systems: logistic, tent and circle maps. We show that these diagnostics are able to capture changes produced in the dynamics as a control parameter is varied. We also apply our new measures to empirical data from semiconductor lasers and show that they are able to anticipate the polarization switchings, thus providing early warning signals of abrupt transitions. | Quantifying sudden changes in dynamical systems using symbolic networks |
In this paper, we consider the voter model with popularity bias. The influence of each node on its neighbors depends on its degree. We find the consensus probabilities and expected consensus times for each of the states. We also find the fixation probability, which is the probability that a single node whose state differs from every other node imposes its state on the entire system. In addition, we find the expected fixation time. Then two extensions to the model are proposed and the motivations behind them are discussed. The first one is confidence, where in addition to the states of neighbors, nodes take their own state into account at each update. We repeat the calculations for the augmented model and investigate the effects of adding confidence to the model. The second proposed extension is irreversibility, where one of the states is given the property that once nodes adopt it, they cannot switch back. The dynamics of densities, fixation times and consensus times are obtained. | Voter Model with Arbitrary Degree Dependence: Clout, Confidence and Irreversibility |
We analyse photometry of $\sim$2000 Galactic Cepheids available in the OGLE Collection of Variable Stars. We analyse both Galactic disk and Galactic bulge fields; stars classified both as single- and multi-periodic. Our goal was to search for additional low-amplitude variability. We extend the sample of multi-mode radial pulsators by identifying ten new candidates for double-mode and six new candidates for triple-mode pulsation. In the first overtone OGLE sample, we found twelve Cepheids with additional periodicity having period ratio $P_{\rm x}/P_{\rm 1O}\in (0.60,\, 0.65)$. These periodicities do not correspond to any other radial mode. While such variables are abundant in the Magellanic Clouds, only one Cepheid of this class was known in the Galaxy before our analysis. Comparing our sample with the Magellanic Cloud Cepheids we note a systematic shift towards longer pulsation periods for more metal rich Galactic stars. Moreover in eleven stars we find one more type of additional variability, with characteristic frequencies close to half of that reported in the group with (0.60,\, 0.65) period ratios. Two out of the above inventory show simultaneous presence of both signals. Most likely, origin of these signals is connected to excitation of non-radial pulsation modes. We report three Cepheids with low-amplitude periodic modulation of pulsation: two stars are single-mode fundamental and first overtone Cepheids and one is a double-mode Cepheid pulsating simultaneously in fundamental and in first overtone modes. Only the former mode is modulated. It is a first detection of periodic modulation of pulsation in this type of double-mode Cepheids. | Frequency analysis of OGLE-IV photometry for classical Cepheids in Galactic fields: non-radial modes and modulations |
We present an analysis of production and signature of neutral Higgs boson ($H_{2}^{0}$) on the version of the 3-3-1 model containing heavy leptons at the Large Hadron Collider. We studied the possibility to identify it using the respective branching ratios. Cross section are given for the collider energy, $\sqrt{s} =$ 14 TeV. Event rates and significances are discussed for two possible values of integrated luminosity, 300 fb$^{-1}$ and 3000 fb$^{-1}$. | Search for the Higgs Boson $H_2^0$ at LHC in 3-3-1 Model |
Recent searches for physics beyond the standard model at high-energy colliders are reviewed, with emphasis on supersymmetry, additional space dimensions, extra gauge bosons, leptoquarks, and model-independent searches. The results reported are based on data samples of up to 0.5 and 2.5 fb-1 collected at HERA and at the Tevatron, respectively. | Searches beyond the standard model at high-energy colliders |
We show that the `erasing-larger-loops-first' (ELLF) method, which was first introduced for erasing loops from the simple random walk on the Sierpinski gasket, does work also for non-Markov random walks, in particular, self-repelling walks to construct a new family of self-avoiding walks on the Sierpinski gasket. The one-parameter family constructed in this method continuously connects the loop-erased random walk and a self-avoiding walk which has the same asymptotic behavior as the `standard' self-avoiding walk. We prove the existence of the scaling limit and study some path properties: The exponent governing the short-time behavior of the scaling limit varies continuously in the parameter. The limit process is almost surely self-avoiding, while its path Hausdorff dimension is the reciprocal of the exponent above, which is strictly greater than 1. | A family of self-avoiding random walks interpolating the loop-erased random walk and a self-avoiding walk on the Sierpinski gasket |
We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies. | Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns |
Although the bandits framework is a classical and well-suited approach for optimal bidding strategies in sponsored search auctions, industrial attempts are rarely documented. This paper outlines the development process at Zalando, a leading fashion e-commerce company, and describes the promising outcomes of a bandits-based approach to increase profitability in sponsored search auctions. We discuss in detail the technical and theoretical challenges that were overcome during the implementation, as well as the mechanisms that led to increased profitability. | Learning Optimal Bidding Strategy: Case Study in E-Commerce Advertising |
We show that no distillation protocol for Gaussian quantum states exists that relies on (i) arbitrary local unitary operations that preserve the Gaussian character of the state and (ii) homodyne detection together with classical communication and postprocessing by means of local Gaussian unitary operations on two symmetric identically prepared copies. This is in contrast to the finite-dimensional case, where entanglement can be distilled in an iterative protocol using two copies at a time. The ramifications for the distribution of Gaussian states over large distances will be outlined. We also comment on the generality of the approach and sketch the most general form of a Gaussian local operation with classical communication in a bipartite setting. | On the impossibility of distilling Gaussian states with Gaussian operations |
We develop a non-perturbative numerical method to study a single electron tunneling through an Aharonov-Bohm ring in the presence of bound, interacting electrons. Inelastic processes and spin-flip scattering are properly taken into account. We show that electron-electron interactions described by the Hubbard Hamiltonian lead to strong dephasing and we obtain high transmission probability at Phi=pi even at small interaction strength. Depending on the many-electron state on the ring, dephasing can occur in elastic or inelastic channels with or without changing the spin of the scattering electron. | Tunneling through an Aharonov-Bohm ring -- effects of dephasing by electron-electron interactions |
Two families of SO(2n) Higgs models in $2n$ dimensional spacetime are presented. One family arises from the {\it dimensional reduction} of higher dimensional Yang-Mills systems while the construction of the other one is {\it ad hoc}, the $n=2$ member of each family coinciding with the usual SU(2) Yang-Mills--Higgs system without Higgs potential. All models support BPS 'monopole' solutions. The 'dyons' of the {\it dimensionally descended} models are also BPS, while the electrically charged solutions of the {\it ad hoc} models are not BPS. | Static BPS 'monopoles' in all even spacetime dimensions |
Vision Transformer (ViT) extracts the final representation from either class token or an average of all patch tokens, following the architecture of Transformer in Natural Language Processing (NLP) or Convolutional Neural Networks (CNNs) in computer vision. However, studies for the best way of aggregating the patch tokens are still limited to average pooling, while widely-used pooling strategies, such as max and GeM pooling, can be considered. Despite their effectiveness, the existing pooling strategies do not consider the architecture of ViT and the channel-wise difference in the activation maps, aggregating the crucial and trivial channels with the same importance. In this paper, we present Group Generalized Mean (GGeM) pooling as a simple yet powerful pooling strategy for ViT. GGeM divides the channels into groups and computes GeM pooling with a shared pooling parameter per group. As ViT groups the channels via a multi-head attention mechanism, grouping the channels by GGeM leads to lower head-wise dependence while amplifying important channels on the activation maps. Exploiting GGeM shows 0.1%p to 0.7%p performance boosts compared to the baselines and achieves state-of-the-art performance for ViT-Base and ViT-Large models in ImageNet-1K classification task. Moreover, GGeM outperforms the existing pooling strategies on image retrieval and multi-modal representation learning tasks, demonstrating the superiority of GGeM for a variety of tasks. GGeM is a simple algorithm in that only a few lines of code are necessary for implementation. | Group Generalized Mean Pooling for Vision Transformer |
Current CoVID-19 pandemic is spreading rapidly worldwide, and it may become one of the largest pandemic events in modern history if out of control. It appears most of the SARS-CoV2 virus infection resulted deaths are mainly due to dysfunctions or failures of the lung or multiple organs that could be attributed to hosts immunodysfunctions particularly hyperinflammatory type disorders. In this brief review and study, a math model is proposed to correlate the Pathogen Infection Recovery Probability (PIRP) versus Proinflammatory Anti-Pathogen Species (PIAPS) levels within a host unit, where a maximum PIRP is exhibited when the PIAPS levels are equal to or around PIAPS equilibrium levels at the pathogen elimination or clearance onset. Based on this model, rational or effective therapeutic strategies at right stages or timing, with right type of agents (immuno-stimulators or immuno-suppressors), and right dosages, may be designed and implemented that are expected to effectively achieve maximum PIRP or reduce the mortality. | Pathogen Infection Recovery Probability (PIRP) Versus Proinflammatory Anti-Pathogen Species (PIAPS) Levels: Modelling and Therapeutic Strategies |
Recent advances in metasurfaces and optical nanostructures have enabled complex control of incident light with optically thin devices. However, it has thus far been unclear whether it is possible to achieve complete linear control of coherent light transmission, i.e., independent control of polarization, amplitude, and phase for both input polarization states, with just a single, thin nanostructure array. Here we prove that it is possible and propose a universal metasurface, a bilayer array of high-index elliptic cylinders, that possesses a complete degree of optical freedom with fully designable chirality and anisotropy. We mathematically show the completeness of achievable light control with corresponding Jones matrices, experimentally demonstrate new types of three-dimensional holographic schemes that were formerly impossible, and present a systematic way of realizing any input-state-sensitive vector linear optical device. Our results unlock previously inaccessible degrees of freedom in light transmission control. | Universal metasurfaces for complete linear control of coherent light transmission |
We investigate in detail the asymptotic properties of tachyon cosmology for a broad class of self-interaction potentials. The present approach relies in an appropriate re-definition of the tachyon field, which, in conjunction with a method formerly applied in the bibliography in a different context, allows to generalize the dynamical systems study of tachyon cosmology to a wider class of self-interaction potentials beyond the (inverse) square-law one. It is revealed that independent of the functional form of the potential, the matter-dominated solution and the ultra-relativistic (also matter-dominated) solution, are always associated with equilibrium points in the phase space of the tachyon models. The latter is always the past attractor, while the former is a saddle critical point. For inverse power-law potentials $V\propto\phi^{-2\lambda}$ the late-time attractor is always the de Sitter solution, while for sinh-like potentials $V\propto\sinh^{-\alpha}(\lambda\phi)$, depending on the region of parameter space, the late-time attractor can be either the inflationary tachyon-dominated solution or the matter-scaling (also inflationary) phase. In general, for most part of known quintessential potentials, the late-time dynamics will be associated either with de Sitter inflation, or with matter-scaling, or with scalar field-dominated solutions. | Study Of Tachyon Dynamics For Broad Classes of Potentials |
Excess energy method is used in searches of gravitational waves (GWs) produced from sources with poorly modeled characteristics. It identifies GW events by searching for a coincidence appearance of excess energy in a GW detector network. While it is sensitive to a wide range of signal morphologies, the energy outliers can be populated by background noise events (background), thereby reducing the statistical confidence of a true signal. However, if the physics of the source is partially understood, weak model dependent constraints can be imposed to suppress the background. This letter presents a novel idea of using the reconstructed chirp mass along with two goodness of fit parameters for suppressing background when search is focused on GW produced from the compact binary coalescence. | Reconstruction of Chirp Mass in the Search of Compact Binaries |
We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a version of the one-sided Huber losses. The smoothness properties of these functions allow us to choose time-varying penalty parameters in such a way that the incremental procedure with the diminishing step-size converges to the exact solution with the rate $O(1/{\sqrt k})$. To the best of our knowledge, we present the first result on the convergence rate for the penalty-based gradient method, in which the penalty parameters vary with time. | Convergence Rate of a Penalty Method for Strongly Convex Problems with Linear Constraints |
As an indicator of the stability of spectral clustering of an undirected weighted graph into $k$ clusters, the $k$th spectral gap of the graph Laplacian is often considered. The $k$th spectral gap is characterized in this paper as an unstructured distance to ambiguity, namely as the minimal distance of the Laplacian to arbitrary symmetric matrices with vanishing $k$th spectral gap. As a conceptually more appropriate measure of stability, the structured distance to ambiguity of the $k$-clustering is introduced as the minimal distance of the Laplacian to Laplacians of graphs with the same vertices and edges but with weights that are perturbed such that the $k$th spectral gap vanishes. To compute a solution to this matrix nearness problem, a two-level iterative algorithm is proposed that uses a constrained gradient system of matrix differential equations in the inner iteration and a one-dimensional optimization of the perturbation size in the outer iteration. The structured and unstructured distances to ambiguity are compared on some example graphs. The numerical experiments show, in particular, that selecting the number $k$ of clusters according to the criterion of maximal stability can lead to different results for the structured and unstructured stability indicators. | Measuring the stability of spectral clustering |
We investigate the phase diagram of the compact $U(1)$ lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. The topological action offers an algorithmic advantage for the computation of the free energy. | U(1) lattice gauge theory with a topological action |
Assume that $G$ is a graph with edge ideal $I(G)$. We provide sharp lower bounds for the depth of $I(G)^2$ in terms of the star packing number of $G$. | Lower bounds for the depth of second power of edge ideals |
Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affine parabolic category O of type A. In this paper we reduce their conjecture to some purely combinatorial conjecture. Our principal tool for the reduction is the theory of categorical sl_2-actions on highest weight categories. Then we prove our combinatorial conjecture in some cases. | Towards multiplicities for categories O of cyclotomic rational Cherednik algebras |
Numerical calculations are performed and compared to the experimental data for the electromagnetic form factor of the kaon, which is extracted from both components of the electromagnetic current, $J^{+}$ and $J^{-}$, with a pseudo-scalar coupling of the quarks to the kaon. In the case of $J^{+}$ there is no pair term contribution in the Drell-Yan frame ($q^{+}=0$). However, for $J^{-}$, the pair term contribution is different from zero and necessary in order to preserve the rotational symmetry of the current. The free parameters are the quark masses and the regulator mass. | Kaon Eletromagnetic Form Factor in the Light-Front Formalism |
The power graph of a group is the simple graph with vertices as the group elements, in which two distinct vertices are adjacent if and only if one of them can be obtained as an integral power of the other. We study (minimal) cut-sets of the power graph of a (finite) non-cyclic (nilpotent) group which are associated with its maximal cyclic subgroups. Let $G$ be a finite non-cyclic nilpotent group whose order is divisible by at least two distinct primes. If $G$ has a Sylow subgroup which is neither cyclic nor a generalized quaternion $2$-group and all other Sylow subgroups of $G$ are cyclic, then under some conditions we prove that there is only one minimum cut-set of the power graph of $G$. We apply this result to find the vertex connectivity of the power graphs of certain finite non-cyclic abelian groups whose order is divisible by at most three distinct primes. | Minimal cut-sets in the power graphs of certain finite non-cyclic groups |
In this paper we study the fully nonlinear stochastic Hamilton-Jacobi-Bellman (HJB) equation for the optimal stochastic control problem of stochastic differential equations with random coefficients. The notion of viscosity solution is introduced, and we prove that the value function of the optimal stochastic control problem is the maximal viscosity solution of the associated stochastic HJB equation. For the superparabolic cases when the diffusion coefficients are deterministic functions of time, states and controls, the uniqueness is addressed as well. | Viscosity Solutions of Stochastic Hamilton-Jacobi-Bellman Equations |
[Abridged] Clumping in the radiation-driven winds of hot, massive stars affects the derivation of synthetic observables across the electromagnetic spectrum. We implement a formalism for treating wind clumping - in particular the light-leakage effects associated with a medium that is porous in physical and velocity space - into the global (photosphere+wind) NLTE model atmosphere code FASTWIND. We assume a stochastic, two-component wind consisting of a mixture of optically thick and thin clumps embedded in a rarefied inter-clump medium. We account fully for the reductions in opacity associated with porosity in physical and velocity-space, and for the well-known effect that opacities depending on rho^2 are higher in clumpy winds than in smooth ones of equal mass-loss rate. By formulating our method in terms of suitable mean and effective opacities for the clumpy wind, we are able to compute models with the same speed (~15 min. on a modern laptop) as in previous code-generations. Some first, generic results of the new models include: i) Confirming earlier results that velocity-space porosity is critical for analysis of UV wind lines in O-stars; ii) for the optical Halpha line, optically thick clumping effects are small for O-stars, but potentially very important for late B and A-supergiants; iii) spatial porosity is a marginal effect for absorption of high-energy X-rays in O-stars, as long as the mean-free path between clumps are kept at realistic values; iv) porosity is negligible at typical O-star radio-photosphere radii; v) regarding the wind ionization balance, a general trend is that increased rates of recombination in simulations with optically thin clumps lead to overall lower degrees of ionization than in corresponding smooth models, but that this effect now is counteracted by the increased levels of light-leakage associated with porosity in physical and velocity space. | Atmospheric NLTE-models for the spectroscopic analysis of blue stars with winds. IV. Porosity in physical and velocity space |
We study the renormalization of the matrix elements of the twist-two non-singlet bilinear quark operators, contributing to the $n=2$ and $n=3$ moments of the structure functions, at next-to-next-to-next-to-leading order in QCD perturbation theory at the symmetric subtraction point. This allows us to obtain conversion factors between the $\overline{\rm MS}$ scheme and the regularization-invariant symmetric momentum subtraction (RI/SMOM, RI${}'$/SMOM) schemes. The obtained results can be used to reduce errors in determinations of moments of structure functions from lattice QCD simulations. The results are given in Landau gauge. | Moments $n=2$ and $n=3$ of the Wilson twist-two operators at three loops in the RI${}'$/SMOM scheme |
Let $\Sigma_{g,n}$ be an orientable surface of genus $g$ with $n$ punctures. We study actions of the mapping class group of $\Sigma_{g,n}$ via Hodge-theoretic and arithmetic techniques. We show that if $$\rho: \pi_1(\Sigma_{g,n})\to GL_r(\mathbb{C})$$ is a representation whose conjugacy class has finite orbit under the mapping class group, and $r<\sqrt{g+1}$, then $\rho$ has finite image. This answers questions of Junho Peter Whang and Mark Kisin. We give applications of our methods to the Putman-Wieland conjecture, the Fontaine-Mazur conjecture, and a question of Esnault-Kerz. The proofs rely on non-abelian Hodge theory, our earlier work on semistability of isomonodromic deformations, and recent work of Esnault-Groechenig and Klevdal-Patrikis on Simpson's integrality conjecture for cohomologically rigid local systems. | Canonical representations of surface groups |
A formula for the structure constants of the multiplication of Schubert classes is obtained in arXiv:1909.05283. In this note, we prove analogous formulae for the Chern--Schwartz--MacPherson (CSM) classes and Segre--Schwartz--MacPherson (SSM) classes of Schubert cells in the flag variety. By the equivalence between the CSM classes and the stable basis elements for the cotangent bundle of the flag variety, a formula for the structure constants for the latter is also deduced. | Structure constants for Chern classes of Schubert cells |
We calculate the entanglement and the universal boundary entropy (BE) in the critical quantum spin chains, such as the transverse field Ising chain and the XXZ chain, with arbitrary direction of the boundary magnetic field (ADBMF). We determine the boundary universality class that an ADBMF induces. In particular, we show that the induced boundary conformal field theory (BCFT) depends on the point on the Bloch sphere where the boundary magnetic field directs. We show that the classification of the directions boils down to the simple fact that the boundary field breaks the bulk symmetry or does not. We present a procedure to estimate the universal BE, based on the finite-size corrections of the entanglement entropy, that apply to the ADBMF. To calculate the universal BE in the XXZ chain, we use the density matrix renormalization group (DMRG). The transverse field XY chain with ADBMF after Jordan-Wigner (JW) transformation is not a quadratic free fermion Hamiltonian. We map this model to a quadratic free fermion chain by introducing two extra ancillary spins coupled to the main chain at the boundaries, which makes the problem {\it{integrable}}. The eigenstates of the transverse field XY chain can be obtained by proper projection in the enlarged chain. Using this mapping, we are able to calculate the entanglement entropy of the transverse field XY chain using the usual correlation matrix technique up to relatively large sizes. | Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields |
We show that for any dimension t>2(1+alpha K)/(1+K) there exists a compact set E of dimension t and a function alpha-Holder continuous on the plane, which is K-quasiregular only outside of E. To do this, we construct an explicit K-quasiconformal mapping that gives, by one side, extremal dimension distortion on a Cantor-type set, and by the other, more Holder continuity than the usual 1/K. | Nonremovable sets for H\"older continuous quasiregular mappings in the plane |
The spin-resolved non-equilibrium real-time electron transport through a double-quantum-dot (DQD) Aharonov-Bohm (AB) interferometer with spin-orbit interaction (SOI) is explored. The SOI and AB interference in the real-time dynamics of spin transport is expressed by effective magnetic fluxes. Analytical formulae for the time-dependent currents, for initially unpolarized spins, are presented. In many cases, there appear spin currents in the electrodes, for which the spins in each electrode are polarized along characteristic directions, pre-determined by the SOI parameters and by the geometry of the system. Special choices of the system parameters yield steady-state currents in which the spins are fully polarized along these characteristic directions. The time required to reach this steady state depends on the couplings of the DQD to the leads. The magnitudes of the currents depend strongly on the SOI-induced effective fluxes. Without the magnetic flux, the spin-polarized current cannot be sustained to the steady states, due to the phase rigidity for this system. For a non-degenerate DQD, transient spin transport can be produced by the sole effects of SOI. We also show that one can extract the spin-resolved currents from measurements of the total charge current. | Real-time dynamics of spin-dependent transport through a double-quantum-dot Aharonov-Bohm interferometer with spin-orbit interaction |
We have measured the spin injection efficiency and spin lifetime in Co$_2$FeSi/$n$-GaAs lateral nonlocal spin valves from 20 to 300 K. We observe large ($\sim$40 $\mu$V) spin valve signals at room temperature and injector currents of $10^3~$A/cm$^2$, facilitated by fabricating spin valve separations smaller than the 1 $\mu$m spin diffusion length and applying a forward bias to the detector contact. The spin transport parameters are measured by comparing the injector-detector contact separation dependence of the spin valve signal with a numerical model accounting for spin drift and diffusion. The apparent suppression of the spin injection efficiency at the lowest temperatures reflects a breakdown of the ordinary drift-diffusion model in the regime of large spin accumulation. A theoretical calculation of the D'yakonov-Perel spin lifetime agrees well with the measured $n$-GaAs spin lifetime over the entire temperature range. | Spin injection and detection up to room temperature in Heusler~alloy/$n$-GaAs spin valves |
We revisit the construction of topological Yang-Mills theories of the Witten type with arbitrary space-time dimension and number of ``shift supersymmetry'' generators, using a superspace formalism. The super-BF structure of these theories is exploited in orderto determine their actions uniquely, up to the ambiguities due to the fixing of the Yang-Mills and BF gauge invariance. UV finiteness to all orders of perturbation theory is proved in a gauge of the Landau type. | Superspace Gauge Fixing of Topological Yang-Mills Theories |
Third-order harmonic generation (THG) plays a vital role in microscopy, optical communications etc. Conventional methods of obtaining efficient THG in macroscopic crystal is already mature; however, they will finally limit the miniaturization and integration of on-chip laser sources. To date, THG from either photonic crystals or metamaterials provide compact photonic platforms, however selection of materials remains elusive. Herein, we experimentally demonstrate a giant enhancement of THG efficiency from an air/high index Ge2Sb2Te5 (GST225) /gold multi-layered Fabry-Perot cavity. At cavity resonant wavelength in near-infrared regime, the efficiency of THG from a 50 nm thick amorphous GST225 planar film is boosted by 422 times compared to that of nonresonant conditions. Interestingly, the THG efficiency has a dramatic decrease of three orders when the structural state of GST225 is transformed from amorphous to crystalline. Our findings have a potential for achieving ultra-compact nonlinear optical source with high efficiency and switchable functionality. | Giant Enhancement of Third Harmonic Generation from Ge2Sb2Te5 based Fabry-Perot Cavity |
We establish precise counts of cubic $\mathbb{F}_q[t]$-algebras and quartic $\mathbb{F}_q[t]$-algebras with cubic resolvent of discriminant $q^b$. To get these counts, the main geometric input is our construction of smooth compactifications of simply branched degree $d$ Hurwitz stacks in mixed characteristic for $d \in \{3,4,5\}$ as stacks of orbifold quasimaps to $B\mathbf{S}_d$, which is presented as a GIT quotient stack $[V_d^{ss}/G_d]$ for a prehomogeneous vector space $(G_d,V_d)$. The main number-theoretic input is Igusa's computations of the Igusa zeta functions for $(G_3,V_3)$ and $(G_4,V_4)$. Our compactifications of Hurwitz stacks of a curve $C$ admit proper extensions of the branch map to $\mathrm{Sym}^n(C)$. Because these extensions are small, we can compute the intersection cohomology of certain local systems on $\mathrm{Conf}^n(C) \subset \mathrm{Sym}^n(C)$ as the cohomology of our compactifications, answering questions of Ellenberg-Tran-Westerland and Kapranov-Schechtman. Using a comparison theorem of Kapranov-Schechtman, we compute the part of the cohomology of a 576-dimensional Nichols algebra $\mathfrak{B}_4$ that is invariant under a natural $\mathbf{S}_4$-action. Because our counts are precise, we obtain two answers to Venkatesh's question about the topological origin of secondary terms in arithmetic counts. | Hurwitz spaces, Nichols algebras, and Igusa zeta functions |
We present a mathematically rigorous analysis of the superfluid properties of a Bose-Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential. | Superfluidity and BEC in a Model of Interacting Bosons in a Random Potential |
In the context of big data analysis, the divide-and-conquer methodology refers to a multiple-step process: first splitting a data set into several smaller ones; then analyzing each set separately; finally combining results from each analysis together. This approach is effective in handling large data sets that are unsuitable to be analyzed entirely by a single computer due to limits either from memory storage or computational time. The combined results will provide a statistical inference which is similar to the one from analyzing the entire data set. This article reviews some recently developments of divide-and-conquer methods in a variety of settings, including combining based on parametric, semiparametric and nonparametric models, online sequential updating methods, among others. Theoretical development on the efficiency of the divide-and-conquer methods is also discussed. | Divide-and-conquer methods for big data analysis |
The isospin breaking effect plays an essential role in generating hadronic molecular states with a very tiny binding energy. Very recently, the LHCb Collaboration observed a very narrow doubly charmed tetraquark $T_{cc}^+$ in the $D^0D^0\pi$ mass spectrum, which lies just below the $D^0D^{*+}$ threshold around 273 keV. In this work, we study the $D^0D^{*+}/D^+D^{*0}$ interactions with the one-boson-exchange effective potentials and consider the isospin breaking effect carefully. We not only reproduce the mass of the newly observed $T_{cc}^+$ very well in the doubly charmed molecular tetraquark scenario, but also predict the other doubly charmed partner resonance $T_{cc}^{\prime+}$ with $m=3876~\text{MeV}$, and $\Gamma= 412~\text{keV}$. The prime decay modes of the $T_{cc}^{\prime+}$ are $D^0D^+\gamma$ and $D^+D^0\pi^0$. The peculiar characteristic mass spectrum of the $D^0D^{*+}/D^+D^{*0}$ molecular systems can be applied to identify the doubly charmed molecular states. | Predicting another doubly charmed molecular resonance $T_{cc}^{\prime+}(3876)$ |
In this paper, we first define the quantum discrete logarithm problem (QDLP)which is similar to classical discrete logarithm problem. But, this problem cannot be solved by Shor's quantum algorithm. Based on quantum discrete logarithm problem, we present a novel quantum secret key encryption algorithm. The receiver constructs his quantum channel using their secret key. Then, the sender can use the receiver's quantum channel to encrypt the message. Finally, the receiver dencrypts the ciphertext by using secret key. In our algorithm, the quantum system will be broken after transferring messages. But, the secret key can still be used repeatedly in our algorithm. | Quantum secret key encryption algorithm based on quantum discrete logarithm problem |
The Lov\'{a}sz Local Lemma (LLL) says that, given a set of bad events that depend on the values of some random variables and where each event happens with probability at most $p$ and depends on at most $d$ other events, there is an assignment of the variables that avoids all bad events if the LLL criterion $ep(d+1)<1$ is satisfied. In this paper, we study the dependency of the distributed complexity of the LLL problem on the chosen LLL criterion. We show that for the fundamental case of each random variable of the considered LLL instance being associated with an edge of the input graph, that is, each random variable influences at most two events, a sharp threshold phenomenon occurs at $p = 2^{-d}$: we provide a simple deterministic (!) algorithm that matches a known $\Omega(\log^* n)$ lower bound in bounded degree graphs, if $p < 2^{-d}$, whereas for $p \geq 2^{-d}$, a known $\Omega(\log \log n)$ randomized and a known $\Omega(\log n)$ deterministic lower bounds hold. In many applications variables affect more than two events; our main contribution is to extend our algorithm to the case where random variables influence at most three different bad events. We show that, surprisingly, the sharp threshold occurs at the exact same spot, providing evidence for our conjecture that this phenomenon always occurs at $p = 2^{-d}$, independent of the number $r$ of events that are affected by a variable. Almost all steps of the proof framework we provide for the case $r=3$ extend directly to the case of arbitrary $r$; consequently, our approach serves as a step towards characterizing the complexity of the LLL under different exponential criteria. | A Sharp Threshold Phenomenon for the Distributed Complexity of the Lov\'asz Local Lemma |
Recent strides have been made developing dust evolution models for galaxy formation simulations but these approaches vary in their assumptions and degree of complexity. Here we introduce and compare two separate dust evolution models (labelled 'Elemental' and 'Species'), based on recent approaches, incorporated into the GIZMO code and coupled with FIRE-2 stellar feedback and ISM physics. Both models account for turbulent dust diffusion, stellar production of dust, dust growth via gas-dust accretion, and dust destruction from time-resolved supernovae, thermal sputtering in hot gas, and astration. The "Elemental" model tracks the evolution of generalized dust species and utilizes a simple, 'tunable' dust growth routine, while the "Species" model tracks the evolution of specific dust species with set chemical compositions and incorporates a physically motivated, two-phase dust growth routine. We test and compare these models in an idealized Milky Way-mass galaxy and find that while both produce reasonable galaxy-integrated dust-to-metals (D/Z) ratios and predict gas-dust accretion as the main dust growth mechanism, a chemically motivated model is needed to reproduce the observed scaling relation between individual element depletions and D/Z with column density and local gas density. We also find the inclusion of theoretical metallic iron and O-bearing dust species are needed in the case of specific dust species in order to match observations of O and Fe depletions, and the integration of a sub-resolution dense molecular gas/CO scheme is needed to both match observed C depletions and ensure carbonaceous dust is not overproduced in dense environments. | The Galactic Dust-Up: Modeling Dust Evolution in FIRE |
We consider a closed Riemannian manifold $M$ of negative curvature and dimension at least 3 with marked length spectrum sufficiently close (multiplicatively) to that of a locally symmetric space $N$. Using the methods of Hamenst\"adt, we show the volumes of $M$ and $N$ are approximately equal. We then show the Besson-Courtois-Gallot map $F: M \to N$ is a diffeomorphism with derivative bounds close to 1 and depending on the ratio of the two marked length spectrum functions. Thus, we refine the results of Hamenst\"adt and Besson-Courtois-Gallot, which show $M$ and $N$ are isometric if their marked length spectra are equal. We also prove a similar result for compact negatively curved surfaces using the methods of Otal together with a version of the Gromov compactness theorem due to Greene--Wu and Pugh. | Quantitative marked length spectrum rigidity |
The Echellette Spectrograph and Imager (ESI) is a multipurpose instrument which has been delivered by the Instrument Development Laboratory of Lick Observatory for use at the Cassegrain focus of the Keck II telescope. ESI saw first light on August 29, 1999. ESI is a multi-mode instrument that enables the observer to seamlessly switch between three modes during an observation. The three modes of ESI are: An R=13,000-echellette mode; Low-dispersion prismatic mode; Direct imaging mode. ESI contains a unique flexure compensation system which reduces the small instrument flexure to negligible proportions. Long-exposure images on the sky show FWHM spot diameters of 34 microns (0.34") averaged over the entire field of view. These are the best non-AO images taken in the visible at Keck Observatory to date. Maximum efficiencies are measured to be 28% for the echellette mode and greater than 41% for low-dispersion prismatic mode including atmospheric, telescope and detector losses. In this paper we describe the instrument and its development. We also discuss the performance-testing and some observational results. | ESI, a new Keck Observatory echellette spectrograph and imager |
Tests of CPT and Lorentz symmetry using neutral-meson oscillations are studied within a formalism that allows for indirect CPT and T violation of arbitrary size and is independent of phase conventions. The analysis is particularly appropriate for studies of CPT and T violation in oscillations of the heavy neutral mesons D, B_d, and B_s. The general Lorentz- and CPT-breaking standard-model extension is used to derive an expression for the parameter for CPT violation. It varies in a prescribed way with the magnitude and orientation of the meson momentum and consequently also with sidereal time. Decay probabilities are presented for both uncorrelated and correlated mesons, and some implications for experiments are discussed. | CPT, T, and Lorentz Violation in Neutral-Meson Oscillations |
In this article we give the definitions of log Fano varieties and log Calabi-Yau varieties in the framework of theory of log schemes of Fontain-Illusie-Kato and give congruences of the cardinalities of rational points of them over the log points of finite fields. | Congruences of the cardinalities of rational points of log Fano varieties and log Calabi-Yau varieties over the log points of finite fields |
Results from initial helioseismic observations by Solar Optical Telescope onboard Hinode are reported. It has been demonstrated that intensity oscillation data from Broadband Filter Imager can be used for various helioseismic analyses. The k-omega power spectra, as well as corresponding time-distance cross-correlation function that promises high-resolution time-distance analysis below 6-Mm travelling distance, were obtained for G-band and CaII-H data. Subsurface supergranular patterns have been observed from our first time-distance analysis. The results show that the solar oscillation spectrum is extended to much higher frequencies and wavenumbers, and the time-distance diagram is extended to much shorter travel distances and times than they were observed before, thus revealing great potential for high-resolution helioseismic observations from Hinode. | Initial Helioseismic Observations by Hinode/SOT |
We report measurements of the effects of a random vector potential generated by applying an in-plane magnetic field to a graphene flake. Magnetic flux through the ripples cause orbital effects: phase-coherent weak localization is suppressed, while quasi-random Lorentz forces lead to anisotropic magnetoresistance. Distinct signatures of these two effects enable an independent estimation of the ripple amplitude and correlation length. | Rippled Graphene in an In-Plane Magnetic Field: Effects of a Random Vector Potential |
Minimum Bayes Risk (MBR) decoding is a method for choosing the outputs of a machine learning system based not on the output with the highest probability, but the output with the lowest risk (expected error) among multiple candidates. It is a simple but powerful method: for an additional cost at inference time, MBR provides reliable several-point improvements across metrics for a wide variety of tasks without any additional data or training. Despite this, MBR is not frequently applied in NLP works, and knowledge of the method itself is limited. We first provide an introduction to the method and the recent literature. We show that several recent methods that do not reference MBR can be written as special cases of MBR; this reformulation provides additional theoretical justification for the performance of these methods, explaining some results that were previously only empirical. We provide theoretical and empirical results about the effectiveness of various MBR variants and make concrete recommendations for the application of MBR in NLP models, including future directions in this area. | It's MBR All the Way Down: Modern Generation Techniques Through the Lens of Minimum Bayes Risk |
The quantum anomalous Hall (QAH) effect - a macroscopic manifestation of chiral band topology at zero magnetic field - has only been experimentally realized by magnetic doping of topological insulators (1 - 3) and delicate design of Moire heterostructures (4 - 8). However, the seemingly simple bilayer graphene without magnetic doping or Moire engineering has long been predicted to host competing ordered states with QAH effects (9 - 11). Here, we explore states in bilayer graphene with conductance of 2 e2/h that not only survive down to anomalously small magnetic fields and up to temperatures of 5 K, but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital magnetism driven QAH behavior with a Chern number tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations due to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley, and spin-valley Hall behavior. | Tunable quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene |
The article considers arrowhead and diagonal-plus-rank-one matrices in F^(nxn) where F in R,C or H. H is a non-commutative field of quaternions. We give unified formulas for fast matrix-vector multiplications, determinants, and inverses for considered matrices. The formulas are unified in the sense that the same formula holds in both, commutative and noncommutative algebras. Each formula requires O(n) arithmetic operations. Most of the formulas hold for block matrices, as well. | Fast multiplication, determinants, and inverses of arrowhead and diagonal-plus-rank-one matrices over associative fields |
In this paper, we propose a new integrable fractional Fokas--Lenells equation by using the completeness of the squared eigenfunctions, dispersion relation, and inverse scattering transform. To solve this equation, we employ the Riemann-Hilbert approach. Specifically, we focus on the case of the reflectionless potential with a simple pole for the zero boundary condition. And we provide the fractional $N$-soliton solution in determinant form. Additionally, we prove the fractional one-soliton solution rigorously. Notably, we demonstrate that as $|t|\to\infty$, the fractional $N$-soliton solution can be expressed as a linear combination of $N$ fractional single-soliton solutions. | The Riemann-Hilbert approach for the integrable fractional Fokas--Lenells equation |
A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f(u) and f(v) of H whenever there is an edge between vertices u and v of G. The H-Colouring problem is to decide whether or not a graph G allows a homomorphism to a fixed graph H. We continue a study on a variant of this problem, namely the Surjective H-Colouring problem, which imposes the homomorphism to be vertex-surjective. We build upon previous results and show that this problem is NP-complete for every connected graph H that has exactly two vertices with a self-loop as long as these two vertices are not adjacent. As a result, we can classify the computational complexity of Surjective H-Colouring for every graph H on at most four vertices. | Surjective H-Colouring: New Hardness Results |
SXP 15.6 is a recently established Be star X-ray binary system (BeXRB) in the Small Magellanic Cloud (SMC). Like many such systems the variable X-ray emission is driven by the underlying behaviour of the mass donor Be star. It is shown here that the neutron star in this system is exceptionally close to spin equilibrium averaged over several years, with the angular momentum gain from mass transfer being almost exactly balanced by radiative losses. This makes SXP 15.6 exceptional compared to all other known members of its class in the SMC, all of whom exhibit much higher spin period changes. In this paper we report on X-ray observations of the brightest known outburst from this system. These observations are supported by contemporaneous optical and radio observations, as well as several years of historical data. | SXP 15.6 -- an accreting pulsar close to spin equilibrium? |
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