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In this paper we systematically classify and describe bosonic symmetry protected topological (SPT) phases in all physical spatial dimensions using semiclassical nonlinear Sigma model (NLSM) field theories. All the SPT phases on a $d-$dimensional lattice discussed in this paper can be described by the same NLSM, which is an O(d+2) NLSM in $(d+1)-$dimensional space-time, with a topological $\Theta-$term. The field in the NLSM is a semiclassical Landau order parameter with a unit length constraint. The classification of SPT phases discussed in this paper based on their NLSMs is consistent with the more mathematical classification based on group cohomology. Besides the classification, the formalism used in this paper also allows us to explicitly discuss the physics at the boundary of the SPT phases, and it reveals the relation between SPT phases with different symmetries. For example, it gives many of these SPT states a natural "decorated defect" construction.
With a particular focus on Scipy's minimize function the eclipse mapping method is thoroughly researched and implemented utilizing Python and essential libraries. Many optimization techniques are used, including Sequential Least Squares Programming (SLSQP), Nelder-Mead, and Conjugate Gradient (CG). However, for the purpose of examining photometric light curves these methods seek to solve the maximum entropy equation under a chi-squared constraint. Therefore, these techniques are first evaluated on two-dimensional Gaussian data without a chi-squared restriction, and then they are used to map the accretion disc and uncover the Gaussian structure of the Cataclysmic Variable KIC 201325107. Critical analysis is performed on the code structure to find possible faults and design problems. Additionally, the analysis shows how several factors impacting computing time and image quality are included including the variance in Gaussian weighting, disc image resolution, number of data points in the light curve, and degree of constraint.
We study the quench dynamics of non-Hermitian topological models with non-Hermitian skin effects. Adopting the non-Bloch band theory and projecting quench dynamics onto the generalized Brillouin zone, we find that emergent topological structures, in the form of dynamic skyrmions, exist in the generalized momentum-time domain, and are correlated with the non-Bloch topological invariants of the static Hamiltonians. The skyrmion structures anchor on the fixed points of dynamics whose existence are conditional on the coincidence of generalized Brillouin zones of the pre- and post-quench Hamiltonians. Global signatures of dynamic skyrmions, however, persist well beyond such a condition, thus offering a general dynamic detection scheme for non-Bloch topology in the presence of non-Hermitian skin effects. Applying our theory to an experimentally relevant, non-unitary quantum walk, we explicitly demonstrate how the non-Bloch topological invariants can be revealed through the non-Bloch quench dynamics.
We investigate the constraints imposed by the first-year WMAP CMB data extended to higher multipole by data from ACBAR, BOOMERANG, CBI and the VSA and by the LSS data from the 2dF galaxy redshift survey on the possible amplitude of primordial isocurvature modes. A flat universe with CDM and Lambda is assumed, and the baryon, CDM (CI), and neutrino density (NID) and velocity (NIV) isocurvature modes are considered. Constraints on the allowed isocurvature contributions are established from the data for various combinations of the adiabatic mode and one, two, and three isocurvature modes, with intermode cross-correlations allowed. Since baryon and CDM isocurvature are observationally virtually indistinguishable, these modes are not considered separately. We find that when just a single isocurvature mode is added, the present data allows an isocurvature fraction as large as 13+-6, 7+-4, and 13+-7 percent for adiabatic plus the CI, NID, and NIV modes, respectively. When two isocurvature modes plus the adiabatic mode and cross-correlations are allowed, these percentages rise to 47+-16, 34+-12, and 44+-12 for the combinations CI+NID, CI+NIV, and NID+NIV, respectively. Finally, when all three isocurvature modes and cross-correlations are allowed, the admissible isocurvature fraction rises to 57+-9 per cent. The sensitivity of the results to the choice of prior probability distribution is examined.
These notes rigorously construct the stochastic integral of a Hilbert Space valued process driven by a Cylindrical Brownian Motion. We expand upon this stochastic calculus to present an introduction to stochastic differential equations in infinite dimensions, with a particular focus on Stratonovich equations due to their physical importance as well as unbounded noise operators (with applications to transport noise). Furthermore we explore techniques in the existence theory for nonlinear stochastic partial differential equations.
We employ population synthesis method to model the double neutron star (DNS) population and test various possibilities on natal kick velocities gained by neutron stars after their formation. We first choose natal kicks after standard core collapse SN from a Maxwellian distribution with velocity dispersion of sigma=265 km/s as proposed by Hobbs et al. (2005) and then modify this distribution by changing the velocity dispersion towards smaller and larger kick values. We also take into account the possibility of NS formation through electron capture supernova. In this case we test two scenarios: zero natal kick or small natal kick, drawn from Maxwellian distribution with sigma = 26.5 km/s. We calculate the present-day orbital parameters of binaries and compare the resulting eccentricities with those known for observed DNSs. As an additional test we calculate Galactic merger rates for our model populations and confront them with observational limits. We do not find any model unequivocally consistent with both observational constraints simultaneously.The models with low kicks after CCSN for binaries with the second NS forming through core collapse SN are marginally consistent with the observations. This means that either 14 observed DNSs are not representative of the intrinsic Galactic population, or that our modeling of DNS formation needs revision.
The proportional hazards model has been extensively used in many fields such as biomedicine to estimate and perform statistical significance testing on the effects of covariates influencing the survival time of patients. The classical theory of maximum partial-likelihood estimation (MPLE) is used by most software packages to produce inference, e.g., the coxph function in R and the PHREG procedure in SAS. In this paper, we investigate the asymptotic behavior of the MPLE in the regime in which the number of parameters p is of the same order as the number of samples n. The main results are (i) existence of the MPLE undergoes a sharp 'phase transition'; (ii) the classical MPLE theory leads to invalid inference in the high-dimensional regime. We show that the asymptotic behavior of the MPLE is governed by a new asymptotic theory. These findings are further corroborated through numerical studies. The main technical tool in our proofs is the Convex Gaussian Min-max Theorem (CGMT), which has not been previously used in the analysis of partial likelihood. Our results thus extend the scope of CGMT and shed new light on the use of CGMT for examining the existence of MPLE and non-separable objective functions.
We point out that the ability of some models of inflation, such as Higgs inflation and the universal attractor models, in reproducing the available data is due to their relation to the Starobinsky model of inflation. For large field values, where the inflationary phase takes place, all these classes of models are indeed identical to the Starobinsky model. Nevertheless, the inflaton is just an auxiliary field in the Jordan frame of the Starobinsky model and this leads to two important consequences: first, the inflationary predictions of the Starobinsky model and its descendants are slightly different (albeit not measurably); secondly the theories have different small-field behaviour, leading to different ultra-violet cut-off scales. In particular, one interesting descendant of the Starobinsky model is the non-minimally- coupled quadratic chaotic inflation. Although the standard quadratic chaotic inflation is ruled out by the recent Planck data, its non-minimally coupled version is in agreement with observational data and valid up to Planckian scales.
Non-standard .sty file `equations.sty' now included inline. The critical exponents of the metal--insulator transition in disordered systems have been the subject of much published work containing often contradictory results. Values ranging between $\half$ and $2$ can be found even in the recent literature. In this paper the results of a long term study of the transition are presented. The data have been calculated with sufficient accuracy (0.2\%) that the calculated exponent can be quoted as $s=\nu=1.54 \pm 0.08$ with confidence. The reasons for the previous scatter of results is discussed.
We study the stellar and gas kinematics of the brightest group galaxies (BGGs) in dynamically relaxed and unrelaxed galaxy groups for a sample of 154 galaxies in the SAMI galaxy survey. We characterize the dynamical state of the groups using the luminosity gap between the two most luminous galaxies and the BGG offset from the luminosity centroid of the group. We find that the misalignment between the rotation axis of gas and stellar components is more frequent in the BGGs in unrelaxed groups, although with quite low statistical significance. Meanwhile galaxies whose stellar dynamics would be classified as `regular rotators' based on their kinemetry are more common in relaxed groups. We confirm that this dependency on group dynamical state remains valid at fixed stellar mass and Sersic index. The observed trend could potentially originate from a differing BGG accretion history in virialised and evolving groups. Amongst the halo relaxation probes, the group BGG offset appears to play a stronger role than the luminosity gap on the stellar kinematic differences of the BGGs. However, both the group BGG offset and luminosity gap appear to roughly equally drive the misalignment between the gas and stellar component of the BGGs in one direction. This study offers the first evidence that the dynamical state of galaxy groups may influence the BGG's stellar and gas kinematics and calls for further studies using a larger sample with higher signal-to-noise.
The Large Hadron Collider (LHC) is expected to provide proton-proton collisions at a centre-of-mass energy of 14 TeV, yielding millions of of top quark events. The top-physics potential of the two general purpose experiments, ATLAS and CMS, is discussed according to state-of-the-art simulation of both physics and detectors. An overview is given of the most important results with emphasis on the expected improvements in our understanding of physics connected to the top quark.
Assuming hierarchical neutrino masses we calculate the heavy neutrino mass scale in the seesaw mechanism from experimental data on oscillations of solar and atmospheric neutrinos and quark-lepton symmetry. The resulting scale is around or above the unification scale, unless the two lightest neutrinos have masses of opposite sign, in which case the resulting scale can be intermediate.
Despite their great success in recent years, deep neural networks (DNN) are mainly black boxes where the results obtained by running through the network are difficult to understand and interpret. Compared to e.g. decision trees or bayesian classifiers, DNN suffer from bad interpretability where we understand by interpretability, that a human can easily derive the relations modeled by the network. A reasonable way to provide interpretability for humans are logical rules. In this paper we propose neural logic rule layers (NLRL) which are able to represent arbitrary logic rules in terms of their conjunctive and disjunctive normal forms. Using various NLRL within one layer and correspondingly stacking various layers, we are able to represent arbitrary complex rules by the resulting neural network architecture. The NLRL are end-to-end trainable allowing to learn logic rules directly from available data sets. Experiments show that NLRL-enhanced neural networks can learn to model arbitrary complex logic and perform arithmetic operation over the input values.
In this paper, we quantify the non-linear effects from $k$-essence dark energy through an effective parameter $\mu$ that encodes the additional contribution of a dark energy fluid or a modification of gravity to the Poisson equation. This is a first step toward quantifying non-linear effects of dark energy/modified gravity models in a more general approach. We compare our $N$-body simulation results from $k$-evolution with predictions from the linear Boltzmann code $\texttt{CLASS}$, and we show that for the $k$-essence model one can safely neglect the difference between the two potentials, $ \Phi -\Psi$, and short wave corrections appearing as higher order terms in the Poisson equation, which allows us to use single parameter $\mu$ for characterizing this model. We also show that for a large $k$-essence speed of sound the $\texttt{CLASS}$ results are sufficiently accurate, while for a low speed of sound non-linearities in matter and in the $k$-essence field are non-negligible. We propose a $\tanh$-based parameterisation for $\mu$, motivated by the results for two cases with low ($c_s^2=10^{-7}$) and high ($c_s^2=10^{-4}$) speed of sound, to include the non-linear effects based on the simulation results. This parametric form of $\mu$ can be used to improve Fisher forecasts or Newtonian $N$-body simulations for $k$-essence models.
In this work, we investigate the current flaws with identifying network-related errors, and examine how K-Means and Long-Short Term Memory Networks solve these problems. We demonstrate that K-Means is able to classify messages, but not necessary provide meaningful clusters. However, Long-Short Term Memory Networks are able to meet our goals of providing an intelligent clustering of messages by grouping messages that are temporally related. Additionally, Long-Short Term Memory Networks can provide the ability to understand and visualize temporal causality, which unlocks the ability to warn about errors before they happen. We show that LSTMs have a 70% accuracy on classifying network errors, and provide some suggestions on future work.
We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model. In the strong-coupling limit, this method can be applied directly, while in the weak-coupling limit we change the variables from compact to noncompact ones in order to cast the Schwinger-Dyson equations in the stochastic form. This leads to a new action with an infinite number of higher-order interaction terms. Nevertheless, such an action can be efficiently handled. This suggests the way to apply the method of ArXiv:1009.4033 to field theories with U(N) field variables as well as to effective field theories in the large-N limit.
We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space is not Martin-Lof random, there is a computable measure-preserving transformation and a computable set that witness that x is not typical with respect to the ergodic theorem, which gives us the converse of a theorem by V'yugin. We further show that if x is weakly 2-random, then it satisfies the ergodic theorem for all computable measure-preserving transformations and all lower semi-computable functions.
Class-Incremental Learning (CIL) aims to build classification models from data streams. At each step of the CIL process, new classes must be integrated into the model. Due to catastrophic forgetting, CIL is particularly challenging when examples from past classes cannot be stored, the case on which we focus here. To date, most approaches are based exclusively on the target dataset of the CIL process. However, the use of models pre-trained in a self-supervised way on large amounts of data has recently gained momentum. The initial model of the CIL process may only use the first batch of the target dataset, or also use pre-trained weights obtained on an auxiliary dataset. The choice between these two initial learning strategies can significantly influence the performance of the incremental learning model, but has not yet been studied in depth. Performance is also influenced by the choice of the CIL algorithm, the neural architecture, the nature of the target task, the distribution of classes in the stream and the number of examples available for learning. We conduct a comprehensive experimental study to assess the roles of these factors. We present a statistical analysis framework that quantifies the relative contribution of each factor to incremental performance. Our main finding is that the initial training strategy is the dominant factor influencing the average incremental accuracy, but that the choice of CIL algorithm is more important in preventing forgetting. Based on this analysis, we propose practical recommendations for choosing the right initial training strategy for a given incremental learning use case. These recommendations are intended to facilitate the practical deployment of incremental learning.
In a recent Nature Materials article, Brown et al. reported a generality of shear thickening in dense suspensions and demonstrated that shear thickening can be masked by a yield stress and can be recovered when the yield stress is decreased to below a threshold. However, the generality of the shear thickening reported in the article may not be necessary true when a high electric/magnetic field is applied on an ER/MR fluid. Shear thickening of ER fluid and MR fluid under high electric/magnetic fields at low shear rates, indicating an obvious phase change inside the dense suspensions has been observed.
Hyperbolic metamaterials were initially proposed in optics to boost radiation efficiencies of quantum emitters. Adopting this concept for antenna design can allow approaching long-standing challenges in radio physics. For example, impedance matching and gain are among the most challenging antenna parameters to achieve in case when a broadband operation is needed. Here we pro-pose and numerically analyse a new compact antenna design, based on hyperbolic metamaterial slab with a patterned layer on top. Energy from a subwavelength loop antenna is shown to be efficiently harvested into bulk modes of the metamaterial over a broad frequency range. Highly localized propagating waves within the medium have a well-resolved spatial-temporal separation owing to the hyperbolic type of effective permeability tensor. This strong interplay between chromatic and modal dispersions enables routing different frequencies into different spatial locations within compact subwavelength geometry. An array of non-overlapping resonant elements is placed on the metamaterial layer and provides a superior matching of localized electromagnetic energy to the free space radiation. As the result, two-order of magnitude improvement in linear gain of the device is predicted. The proposed new architecture can find a use in applications, where multiband or broadband compact devices are required.
We study solutions of high codimension mean curvature flow defined for all negative times, usually referred to as ancient solutions. We show that any compact ancient solution whose second fundamental form satisfies a certain natural pinching condition must be a family of shrinking spheres. Andrews and Baker have shown that initial submanifolds satisfying this pinching condition, which generalises the notion of convexity, converge to round points under the flow. As an application, we use our result to simplify their proof.
Grassmann (or anti-commuting) variables are extensively used in theoretical physics. In this paper we use Grassmann variable calculus to give new proofs of celebrated combinatorial identities such as the Lindstr\"om-Gessel-Viennot formula for graphs with cycles and the Jacobi-Trudi identity. Moreover, we define a one parameter extension of Schur polynomials that obey a natural convolution identity.
We present deep, large area B and r' imaging for a sample of 49 brightest cluster galaxies (BCGs). The clusters were selected by their x-ray luminosity and redshift to form two volume limited samples, one with mean redshift ~ 0.07 and one at a mean redshift ~ 0.17. For each cluster the data cover 41' by 41'. We discuss our data reduction techniques in detail, and show that we can reliably measure the surface brightness at the levels of mu_B ~ 29 and mu_r' ~ 28. For each galaxy we present the B and r' images together with the surface brightness profile, B-r' colour, eccentricity and position angle as a function of radius. We investigate the distribution of positional offsets between the optical centroid of the BCG and the centre of the X-ray emission, and conclude that the mass profiles are cuspy, and do not have extended cores. We also introduce a method to objectively identify the transition from BCG to extended envelope of intra-cluster light, using the Petrosian index as a function of radius.
The inequivalence of thermodynamical ensembles related by a Legendre transformation is manifest in self-gravitating systems and in black hole thermodynamics. Using the Poincare's method of the linear series, we describe the mathematical reasons which lead to this inequivalence which in turn induces a hierarchy of ensembles: the most stable ensemble describes the most isolated system. Moreover, we prove that one can obtain the degree of stability of all equilibrium configurations in any ensensemble related by Legendre transformations to the most stable if one knows the degree of stability in the most stable ensemble.
We investigate the possibility of the gravitational-wave event GW170817 being a light, solar-mass black hole (BH) - neutron star (NS) merger. We explore two exotic scenarios involving primordial black holes (PBH) that could produce such an event, taking into account available observational information on NGC 4993. First, we entertain the possibility of dynamical NS-PBH binary formation where a solar-mass PBH and a NS form a binary through gravitational interaction. We find that while dynamical NS-PBH formation could account for the GW170817 event, the rate is highly dependent on unknown density contrast factors and could potentially be affected by galaxy mergers. We also find that PBH-PBH binaries would likely have a larger merger rate, assuming the density contrast boost factor of an order similar to the NS-PBH case. These exotic merger formations could provide new channels to account for the volumetric rate of compact-object mergers reported by LIGO/Virgo. Secondly, we consider the case where one of the NS's in a binary NS system is imploded by a microscopic PBH. We find that the predicted rate for NS implosion into a BH is very small, at least for the specific environment of NGC 4993. We point out that similar existing (e.g. GW190425 and GW190814) and future observations will shed additional light on these scenarios.
As a maintainer of an open source software project, you are usually happy about contributions in the form of pull requests that bring the project a step forward. Past studies have shown that when reviewing a pull request, not only its content is taken into account, but also, for example, the social characteristics of the contributor. Whether a contribution is accepted and how long this takes therefore depends not only on the content of the contribution. What we only have indications for so far, however, is that pull requests from bots may be prioritized lower, even if the bots are explicitly deployed by the development team and are considered useful. One goal of the bot research and development community is to design helpful bots to effectively support software development in a variety of ways. To get closer to this goal, in this GitHub mining study, we examine the measurable differences in how maintainers interact with manually created pull requests from humans compared to those created automatically by bots. About one third of all pull requests on GitHub currently come from bots. While pull requests from humans are accepted and merged in 72.53% of all cases, this applies to only 37.38% of bot pull requests. Furthermore, it takes significantly longer for a bot pull request to be interacted with and for it to be merged, even though they contain fewer changes on average than human pull requests. These results suggest that bots have yet to realize their full potential.
Let \Gamma be the convex set consisting of all marginal tracial states on the tensor product B \otimes B of the algebra B of nxn matrices over the complex numbers. We find necessary and sufficient conditions for such a state to be extremal in \Gamma. We also give a characterization of those extreme points in \Gamma which are pure states. We conjecture that all extremal marginal tracial states are pure states.
For the standard symplectic forms on Jacobi and CMV matrices, we compute Poisson brackets of OPRL and OPUC, and relate these to other basic Poisson brackets and to Jacobians of basic changes of variable.
The expressive power of neural networks is important for understanding deep learning. Most existing works consider this problem from the view of the depth of a network. In this paper, we study how width affects the expressiveness of neural networks. Classical results state that depth-bounded (e.g. depth-$2$) networks with suitable activation functions are universal approximators. We show a universal approximation theorem for width-bounded ReLU networks: width-$(n+4)$ ReLU networks, where $n$ is the input dimension, are universal approximators. Moreover, except for a measure zero set, all functions cannot be approximated by width-$n$ ReLU networks, which exhibits a phase transition. Several recent works demonstrate the benefits of depth by proving the depth-efficiency of neural networks. That is, there are classes of deep networks which cannot be realized by any shallow network whose size is no more than an exponential bound. Here we pose the dual question on the width-efficiency of ReLU networks: Are there wide networks that cannot be realized by narrow networks whose size is not substantially larger? We show that there exist classes of wide networks which cannot be realized by any narrow network whose depth is no more than a polynomial bound. On the other hand, we demonstrate by extensive experiments that narrow networks whose size exceed the polynomial bound by a constant factor can approximate wide and shallow network with high accuracy. Our results provide more comprehensive evidence that depth is more effective than width for the expressiveness of ReLU networks.
In this paper, we present an equitable partition theorem of tensors, which gives the relations between $H$-eigenvalues of a tensor and its quotient equitable tensor and extends the equitable partitions of graphs to hypergraphs. Furthermore, with the aid of it, some properties and $H$-eigenvalues of the generalized power hypergraphs are obtained, which extends some known results, including some results of Yuan, Qi and Shao.
Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however statistical methods have been limited by the high dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with Sparse Principal Component Analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene "relationship" matrices that are of practical interest, such as the weighted adjacency matrices.
Plasma jets belong to the category remote plasma. This means that the discharge conditions and the chemical effect on samples can be tuned separately, this being a big advantage compared to standard low-pressure reactors. The inductive coupling brings the advantage of a pure and dense plasma. The microwave excitation allows furthermore miniaturization and generation of low temperature plasmas. The present paper shows the state of the art of the research on such sources, demonstrating their work up to atmospheric pressure.
We found that three types of tethered surface model undergo a first-order phase transition between the smooth and the crumpled phase. The first and the third are discrete models of Helfrich, Polyakov, and Kleinert, and the second is that of Nambu and Goto. These are curvature models for biological membranes including artificial vesicles. The results obtained in this paper indicate that the first-order phase transition is universal in the sense that the order of the transition is independent of discretization of the Hamiltonian for the tethered surface model.
Nanoscale systems offer key capabilities for quantum technologies that include single qubit control and readout, multiple qubit gate operation, extremely sensitive and localized sensing and imaging, as well as the ability to build hybrid quantum systems. To fully exploit these functionalities, multiple degrees of freedom are highly desirable: in this respect, nanoscale systems that coherently couple to light and possess spins, allow for storage of photonic qubits or light-matter entanglement together with processing capabilities. In addition, all-optical control of spins can be possible for faster gate operations and higher spatial selectivity compared to direct RF excitation. Such systems are therefore of high interest for quantum communications and processing. However, an outstanding challenge is to preserve properties, and especially optical and spin coherence lifetimes, at the nanoscale. Indeed, interactions with surfaces related perturbations strongly increase as sizes decrease, although the smallest objects present the highest flexibility for integration with other systems. Here, we demonstrate optically controlled nuclear spins with long coherence lifetimes (T2) in rare earth doped nanoparticles. We observed spins echoes and measured T2 of 2.9 +/- 0.3 ms at 5 K and under a magnetic field of 9 mT, a value comparable to those obtained in bulk single crystals. Moreover, we achieve, for the first time, spin T2 extension using all-optical spin dynamical decoupling and observe high fidelity between excitation and echo phases. Rare-earth doped nanoparticles are thus the only reported nano-materials in which optically controlled spins with millisecond coherence lifetimes have been observed. These results open the way to providing quantum light-atom-spin interfaces with long storage time within hybrid architectures.
We perform coupled-cluster and diffusion Monte Carlo calculations of the energies of circular quantum dots up to 20 electrons. The coupled-cluster calculations include triples corrections and a renormalized Coulomb interaction defined for a given number of low-lying oscillator shells. Using such a renormalized Coulomb interaction brings the coupled-cluster calculations with triples correlations in excellent agreement with the diffusion Monte Carlo calculations. This opens up perspectives for doing ab initio calculations for much larger systems of electrons.
In recent years, deep learning has been at the center of analytics due to its impressive empirical success in analyzing complex data objects. Despite this success, most of the existing tools behave like black-box machines, thus the increasing interest in interpretable, reliable, and robust deep learning models applicable to a broad class of applications. Feature-selected deep learning has emerged as a promising tool in this realm. However, the recent developments do not accommodate ultra-high dimensional and highly correlated features, in addition to the high noise level. In this article, we propose a novel screening and cleaning method with the aid of deep learning for a data-adaptive multi-resolutional discovery of highly correlated predictors with a controlled error rate. Extensive empirical evaluations over a wide range of simulated scenarios and several real datasets demonstrate the effectiveness of the proposed method in achieving high power while keeping the false discovery rate at a minimum.
Given a compact and H-convex subset $K$ of the Heisenberg group ${\mathbb H}$, with the origin $e$ in its interior, we are interested in finding a homogeneous H-convex function $f$ such that $f(e)=0$ and $f\bigl|_{\partial K}=1$; we will call this function $f$ the ${\mathbb H}$-cone-function of vertex $e$ and base $\partial K$. While the equivalent version of this problem in the Euclidean framework has an easy solution, in our context this investigation turns out to be quite entangled, and the problem can be unsolvable. The approach we follow makes use of an extension of the notion of convex family introduced by Fenchel. We provide the precise, even if awkward, condition required to $K$ so that $\partial K$ is the base of an ${\mathbb H}$-cone-function of vertex $e.$ Via a suitable employment of this condition, we prove two interesting binding constraints on the shape of the set $K,$ together with several examples.
The unbound nature of pure neutron matter (PNM) requires intrinsic correlations between the symmetric nuclear matter (SNM) EOS parameters (incompressibility $K_0$, skewness $J_0$ and kurtosis $I_0$) and those (slope $L$, curvature $K_{\rm{sym}}$ and skewness $J_{\rm{sym}}$) characterizing the symmetry energy independent of any nuclear many-body theory. We investigate these intrinsic correlations and their applications in better constraining the poorly known high-density behavior of nuclear symmetry energy. Several novel correlations connecting the characteristics of SNM EOS with those of nuclear symmetry energy are found. In particular, at the lowest-order of approximations, the bulk parts of the slope $L$, curvature $K_{\rm{sym}}$ and skewness $J_{\rm{sym}}$ of the symmetry energy are found to be $L\approx K_0/3, K_{\rm{sym}}\approx LJ_0/2K_0$ and $J_{\rm{sym}}\approx I_0L/3K_0$, respectively. High-order corrections to these simple relations can be written in terms of the small ratios of high-order EOS parameters. The resulting intrinsic correlations among some of the EOS parameters reproduce very nicely their relations predicted by various microscopic nuclear many-body theories and phenomenological models constrained by available data of terrestrial experiments and astrophysical observations in the literature. The unbound nature of PNM is fundamental and the required intrinsic correlations among the EOS parameters characterizing both the SNM EOS and symmetry energy are universal. These intrinsic correlations provide a novel and model-independent tool not only for consistency checks but also for investigating the poorly known high-density properties of neutron-rich matter by using those with smaller uncertainties.
Limit cycles of planar polynomial vector fields have been an active area of research for decades; the interest in periodic-orbit related dynamics comes from Hilbert's 16th problem and the fact that oscillatory states are often found in applications. We study the existence of limit cycles and their coexistence with invariant algebraic curves in two families of Kukles systems, via Lyapunov quantities and Melnikov functions of first and second order. We show center conditions, as well as a connection between small- and large-amplitude limit cycles arising in one of the families, in which the first coefficients of the Melnikov function correspond to the first Lyapunov quantities. We also provide an example of a planar polynomial system in which the cyclicity is not fully controlled by the first nonzero Melnikov function.
Local and long range structure, optical and photoluminescence properties of sol-gel synthesized Ce1-xNixO2 nanostructures have been studied. The crystal structure, lattice strain and crystallite size have been analyzed. A decrease in lattice parameter may be attributed to substitution of Ce with smaller Ni ion. UV-Vis measurement is used for studying the effect of Ni substitution on bandgap and disorder. The bandgap decreases with Ni substitution and disorder increases. The PL spectra show five major peaks attributed to various defect states. The PL emission decreases with Ni substitution owing to increase in defects which acts as emission quenching centers. The lattice disorder and defects have been studied using Raman spectroscopy. Raman measurement shows that oxygen vacancies related defects are increasing with Ni substitution which causes changes in optical and PL properties. Local structure measurements show that Ni substitution leads to oxygen vacancies which does change host lattice structure notably. Ce4+ to Ce3+ conversion increases with Ni substitution.
When a novel treatment has successfully passed phase I, different options to design subsequent phase II trials are available. One approach is a single-arm trial, comparing the response rate in the intervention group against a fixed proportion. Another alternative is to conduct a randomized phase II trial, comparing the new treatment with placebo or the current standard. A significant problem arises in both approaches when the investigated patient population is very heterogeneous regarding prognostic factors. For the situation that a substantial dataset of historical controls exists, we propose an approach to enhance the classic single-arm trial design by including matched control patients. The outcome of the observed study population can be adjusted based on the matched controls with a comparable distribution of known confounders. We propose an adaptive two-stage design with the options of early stopping for futility and recalculation of the sample size taking the matching rate, number of matching partners, and observed treatment effect into account. The performance of the proposed design in terms of type I error rate, power, and expected sample size is investigated via simulation studies based on a hypothetical phase II trial investigating a novel therapy for patients with acute myeloid leukemia.
A case is made that in encounters with the earth's atmosphere, astrophysical little black holes (LBH) can manifest themselves as the core energy source of balllightning (BL). Relating the LBH incidence rate on earth to BL occurrence has the potential of shedding light on the distribution of LBH in the universe, and their velocities relative to the earth. Most BL features can be explained by a testable LBH model. Analyses are presented to support this model. LBH produce complex and many-faceted interactions in air directly and via their exhaust, resulting in excitation, ionization, and radiation due to processes such as gravitational and electrostatic tidal force, bremsstrahlung, pair production and annihilation, orbital electron near-capture by interaction with a charged LBH. Gravitational interaction of atmospheric atoms with LBH can result in an enhanced cross-section for polarization and ionization. An estimate for the power radiated by BL ~ Watts is in agreement with observation. An upper limit is found for the largest masses that can produce ionization and polarization excitation. It is shown that the LBH high power exhaust radiation is not prominent and its effects are consistent with observations.
Video frame interpolation aims to synthesize one or multiple frames between two consecutive frames in a video. It has a wide range of applications including slow-motion video generation, frame-rate up-scaling and developing video codecs. Some older works tackled this problem by assuming per-pixel linear motion between video frames. However, objects often follow a non-linear motion pattern in the real domain and some recent methods attempt to model per-pixel motion by non-linear models (e.g., quadratic). A quadratic model can also be inaccurate, especially in the case of motion discontinuities over time (i.e. sudden jerks) and occlusions, where some of the flow information may be invalid or inaccurate. In our paper, we propose to approximate the per-pixel motion using a space-time convolution network that is able to adaptively select the motion model to be used. Specifically, we are able to softly switch between a linear and a quadratic model. Towards this end, we use an end-to-end 3D CNN encoder-decoder architecture over bidirectional optical flows and occlusion maps to estimate the non-linear motion model of each pixel. Further, a motion refinement module is employed to refine the non-linear motion and the interpolated frames are estimated by a simple warping of the neighboring frames with the estimated per-pixel motion. Through a set of comprehensive experiments, we validate the effectiveness of our model and show that our method outperforms state-of-the-art algorithms on four datasets (Vimeo, DAVIS, HD and GoPro).
We have obtained broad-band near-infrared photometry for seven Galactic star clusters (M92, M15, M13, M5, NGC1851, M71 and NGC6791) using the WIRCam wide-field imager on the Canada-France-Hawaii Telescope, supplemented by images of NGC1851 taken with HAWK-I on the VLT. In addition, 2MASS observations of the [Fe/H] ~ 0.0 open cluster M67 were added to the cluster database. From the resultant (V-J)-V and (V-Ks)-V colour-magnitude diagrams (CMDs), fiducial sequences spanning the range in metallicity, -2.4 < [Fe/H] < +0.3, have been defined which extend (for most clusters) from the tip of the red-giant branch (RGB) to ~ 2.5 magnitudes below the main-sequence turnoff. These fiducials provide a valuable set of empirical isochrones for the interpretation of stellar population data in the 2MASS system. We also compare our newly derived CMDs to Victoria isochrones that have been transformed to the observed plane using recent empirical and theoretical colour-Teff relations. The models are able to reproduce the entire CMDs of clusters more metal rich than [Fe/H] ~ -1.4 quite well, on the assumption of the same reddenings and distance moduli that yield good fits of the same isochrones to Johnson-Cousins BV(RI)C photometry. However, the predicted giant branches become systematically redder than the observed RGBs as the cluster metallicity decreases. Possible explanations for these discrepancies are discussed.
The detection of a nuclear spin in an individual molecule represents a key challenge in physics and biology whose solution has been pursued for many years. The small magnetic moment of a single nucleus and the unavoidable environmental noise present the key obstacles for its realization. Here, we demonstrate theoretically that a single nitrogen-vacancy (NV) center in diamond can be used to construct a nano-scale single molecule spectrometer that is capable of detecting the position and spin state of a single nucleus and can determine the distance and alignment of a nuclear or electron spin pair. The proposed device will find applications in single molecule spectroscopy in chemistry and biology, such as in determining protein structure or monitoring macromolecular motions and can thus provide a tool to help unravelling the microscopic mechanisms underlying bio-molecular function.
Let $\mathcal{L}$ be a pencil of plane curves defined over $\mathbb{F}_q$ with no $\mathbb{F}_q$-points in its base locus. We investigate the number of curves in $\mathcal{L}$ whose $\mathbb{F}_q$-points form a blocking set. When the degree of the pencil is allowed to grow with respect to $q$, we show that the geometric problem can be translated into a purely combinatorial problem about disjoint blocking sets. We also study the same problem when the degree of the pencil is fixed.
We pursue a classification of low-rank super-modular categories parallel to that of modular categories. We classify all super-modular categories up to rank=$6$, and spin modular categories up to rank=$11$. In particular, we show that, up to fusion rules, there is exactly one non-split super-modular category of rank $2,4$ and $6$, namely $PSU(2)_{4k+2}$ for $k=0,1$ and $2$. This classification is facilitated by adapting and extending well-known constraints from modular categories to super-modular categories, such as Verlinde and Frobenius-Schur indicator formulae.
In effective models of loop quantum cosmology, the holonomy corrections are associated with deformations of space-time symmetries. The most evident manifestation of the deformations is the emergence of an Euclidean phase accompanying the non-singular bouncing dynamics of the scale factor. In this article, we compute the power spectrum of scalar perturbations generated in this model, with a massive scalar field as the matter content. Instantaneous and adiabatic vacuum-type initial conditions for scalar perturbations are imposed in the contracting phase. The evolution through the Euclidean region is calculated based on the extrapolation of the time direction pointed by the vectors normal to the Cauchy hypersurface in the Lorentzian domains. The obtained power spectrum is characterized by a suppression in the IR regime and oscillations in the intermediate energy range. Furthermore, the speculative extension of the analysis in the UV reveals a specific rise of the power.
This paper deals with the classical problem of density estimation on the real line. Most of the existing papers devoted to minimax properties assume that the support of the underlying density is bounded and known. But this assumption may be very difficult to handle in practice. In this work, we show that, exactly as a curse of dimensionality exists when the data lie in $\R^d$, there exists a curse of support as well when the support of the density is infinite. As for the dimensionality problem where the rates of convergence deteriorate when the dimension grows, the minimax rates of convergence may deteriorate as well when the support becomes infinite. This problem is not purely theoretical since the simulations show that the support-dependent methods are really affected in practice by the size of the density support, or by the weight of the density tail. We propose a method based on a biorthogonal wavelet thresholding rule that is adaptive with respect to the nature of the support and the regularity of the signal, but that is also robust in practice to this curse of support. The threshold, that is proposed here, is very accurately calibrated so that the gap between optimal theoretical and practical tuning parameters is almost filled.
In this paper we introduce and study a categorical action of the positive part of the Heisenberg Lie algebra on categories of modules over rational Cherednik algebras associated to symmetric groups. We show that the generating functor for this action is exact. We then produce a categorical Heisenberg action on the categories $\mathcal{O}$ and show it is the same as one constructed by Shan and Vasserot. Finally, we reduce modulo a large prime $p$. We show that the functors constituting the action of the positive half of the Heisenberg algebra send simple objects to semisimple ones, and we describe these semisimple objects.
Creating sound zones has been an active research field since the idea was first proposed. So far, most sound zone control methods rely on either an optimization of physical metrics such as acoustic contrast and signal distortion or a mode decomposition of the desired sound field. By using these types of methods, approximately 15 dB of acoustic contrast between the reproduced sound field in the target zone and its leakage to other zone(s) has been reported in practical set-ups, but this is typically not high enough to satisfy the people inside the zones. In this paper, we propose a sound zone control method shaping the leakage errors so that they are as inaudible as possible for a given acoustic contrast. The shaping of the leakage errors is performed by taking the time-varying input signal characteristics and the human auditory system into account when the loudspeaker control filters are calculated. We show how this shaping can be performed using variable span trade-off filters, and we show theoretically how these filters can be used for trading signal distortion in the target zone for acoustic contrast. The proposed method is evaluated based on physical metrics such as acoustic contrast and perceptual metrics such as STOI. The computational complexity and processing time of the proposed method for different system set-ups are also investigated. Lastly, the results of a MUSHRA listening test are reported. The test results show that the proposed method provides more than 20% perceptual improvement compared to existing sound zone control methods.
We calculate the operating parameters of a transition edge sensor that is mounted on a thin dielectric membrane with the assumption that the phononic heat transport in the membrane is ballistic. Our treatment uses the correct phonon modes from elasticity theory (Lamb-modes), and spans the transition from 3D to 2D behavior. The phonon cooling power and conductance have a global minimum as function of membrane thickness, which leads to an optimal value for the membrane thickness with respect to noise equivalent power at a fixed operating temperature. The energy resolution of a calorimeter will not be affected strongly, but, somewhat counterintuitively, the effective time constant can be reduced by decreasing the membrane thickness in the 2D limit.
We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.
Pulsar Wind Nebulae (PWNe) shine at multi-wavelengths and are expected to constitute the largest class of gamma-ray sources in our Galaxy. They are known to be very efficient particle accelerators: the Crab nebula, the PWNe class prototype, is the unique firmly identified leptonic PeVatron of the Galaxy to date, and most of the PeVatrons recently detected by LHAASO appear to be compatible with a pulsar origin. PWNe have been proved to be associated with the formation of misaligned X-ray tails and TeV halos, as sign of an efficient escape of energetic particles from the PWN into the surrounding medium. With the advent of the Cherenkov Telescope Array we expect that ~200 new PWNe will be detected. Being able to correctly model their multi-wavelength spectral properties, spatial and spectral morphology at gamma-rays is then topical today. This in particular means we should be able to account for their different evolutionary phases, and to correctly determine the influence they have on the spectral properties of the source. This indeed reflects directly on the expectation of how many PWNe will be detected at gamma-rays. Finally, the identification of PWNe in future gamma-ray data, not only is relevant for their scientific importance, but also to allow for the identification of less prominent sources that might be hidden by the background of non-identified PWNe.
The antiProton Unstable Matter Annihilation experiment (PUMA) at CERN aims at investigating the nucleon composition in the matter density tail of radioactive as well as stable isotopes by use of low-energy antiproton-nucleon annihilation processes. For this purpose, antiprotons provided by the Extra Low ENergy Antiproton (ELENA) facility will be trapped together with the ions of interest. While exotic ions will be obtained by the Isotope mass Separator On-Line DEvice (ISOLDE), stable ions will be delivered from an offline ion source setup designed for this purpose. This allows the proposed technique to be applied to a variety of stable nuclei and for reference measurements. For beam purification, the ion source setup includes a multi-reflection time-of-flight mass spectrometer (MR-ToF MS). Supported by SIMION simulations, an earlier MR-ToF MS design has been modified to meet the requirements of PUMA. During commissioning of the new MR-ToF device with Ar$^+$ ions, mass resolving powers in excess of 50,000 have been obtained after 150 revolutions, limited by the chopping of the continuous beam from an electron impact ionisation source.
Negative index metamaterials (NIMs) give rise to unusual and intriguing properties and phenomena, which may lead to important applications such as superlens, subwavelength cavity and slow light devices. However, the negative refractive index in metamaterials normally requires a stringent condition of simultaneously negative permittivity and negative permeability. A new class of negative index metamaterials - chiral NIMs, have been recently proposed. In contrast to the conventional NIMs, chiral NIMs do not require the above condition, thus presenting a very robust route toward negative refraction. Here we present the first experimental demonstration of a chiral metamaterial exhibiting negative refractive index down to n=-5 at terahertz frequencies, with only a single chiral resonance. The strong chirality present in the structure lifts the degeneracy for the two circularly polarized waves and relieves the double negativity requirement. Chiral NIM are predicted to possess intriguing electromagnetic properties that go beyond the traditional NIMs, such as opposite signs of refractive indices for the two circular polarizations and negative reflection. The realization of terahertz chiral NIMs offers new opportunities for investigations of their novel electromagnetic properties, as well as important terahertz device applications.
We give a new proof, independent of Lin's theorem, of the Segal conjecture for the cyclic group of order two. The key input is a calculation, as a Hopf algebroid, of the Real topological Hochschild homology of $\mathbb{F}_2$. This determines the $\mathrm{E}_2$-page of the descent spectral sequence for the map $\mathrm{N}\mathbb{F}_2 \to \mathbb{F}_2$, where $\mathrm{N}\mathbb{F}_2$ is the $C_2$-equivariant Hill--Hopkins--Ravenel norm of $\mathbb{F}_2$. The $\mathrm{E}_2$-page represents a new upper bound on the $RO(C_2)$-graded homotopy of $\mathrm{N}\mathbb{F}_2$, from which the Segal conjecture is an immediate corollary.
For first order differential equations of the form $y'=\sum_{p=0}^P F_p(x)y^p$ and second order homogeneous linear differential equations $y''+a(x)y'+b(x)y=0$ with locally integrable coefficients having asymptotic (possibly divergent) power series when $|x|\to\infty$ on a ray $\arg(x)=$const, under some further assumptions, it is shown that, on the given ray, there is a one-to-one correspondence between true solutions and (complete) formal solutions. The correspondence is based on asymptotic inequalities which are required to be uniform in $x$ and optimal with respect to certain weights.
Finite smooth digraphs, that is, finite directed graphs without sources and sinks, can be partially ordered via pp-constructability. We give a complete description of this poset and, in particular, we prove that it is a distributive lattice. Moreover, we show that in order to separate two smooth digraphs in our poset it suffices to show that the polymorphism clone of one of the digraphs satisfies a prime cyclic loop condition that is not satisfied by the polymorphism clone of the other. Furthermore, we prove that the poset of cyclic loop ordered by their strength for clones is a distributive lattice, too.
We systematically investigated the phonon and electron transport properties of monolayer InSe and its Janus derivatives including monolayer In2SSe and In2SeTe by first-principles calculations. The breaking of mirror symmetry produce a distinguishable A1 peak in the Raman spectra of monolayer In2SSe and In2SeTe. The room-temperature thermal conductivity (\k{appa}) of monolayer InSe, In2SSe and In2SeTe is 44.6, 46.9, and 29.9 W/(m K), respectively. There is a competition effect between atomic mass, phonon group velocity and phonon lifetime. The \k{appa} can be further effectively modulated by sample size for the purpose of thermoelectric applications. Meanwhile, monolayer In2SeTe exhibits a direct band and higher electron mobility than that of monolayer InSe, due to the smaller electron effective mass caused by tensile strain on the Se side. These results indicate that 2D Janus group-III chalcogenides can provide a platform to design the new electronic, optoelectronic and thermoelectric devices.
Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and their dynamical evolution. Using a hitherto largest sample of lensing clusters drawn from literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is an excellent agreement between the weak lensing, X-ray and isothermal sphere model determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2--4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters as well as an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.
We present an analysis of the ENEAR sample of peculiar velocities of elliptical galaxies, obtained with D_n-\sigma distances. We use the velocity correlation function to analyze the statistics of the field-object's velocities, while the analysis of the cluster data is based on the estimate of their rms peculiar velocity, Vrms. The statistics of the model velocity field is parameterized by the amplitude, \eta_8=\sigma_8 \Omega_m^{0.6}, and by the shape parameter, \Gamma. From the velocity correlation statistics we obtain \eta_8=0.51{-0.09}{+0.24} for \Gamma=0.25 at the 2\sigma level. Even though less constraining, a consistent result is obtained by comparing the measured Vrms of clusters to linear theory predictions. For \Gamma=0.25 we find \eta_8=0.63{-0.19}{+0.22}$ at 1\sigma. Overall, our results point toward a statistical concordance of the cosmic flows traced by spirals and early-type galaxies, with galaxy distances estimated using TF and D_n-\sigma distance indicators, respectively.
We collect in one place a variety of known and folklore results in enriched model category theory and add a few new twists. The central theme is a general procedure for constructing a Quillen adjunction, often a Quillen equivalence, between a given V-model category and a category of enriched presheaves in V, where V is any good enriching category. For example, we rederive the result of Schwede and Shipley that reasonable stable model categories are Quillen equivalent to presheaf categories of spectra (alias categories of module spectra) under more general hypotheses. The technical improvements and modifications of general model categorical results given here are applied to equivariant contexts in a pair of sequels, where we indicate various directions of application.
We show in this Letter that the spectral details of the FUV radiation fields have a large impact on the chemistry of protoplanetary disks surrounding T Tauri stars. We show that the strength of a realistic stellar FUV field is significantly lower than typically assumed in chemical calculations and that the radiation field is dominated by strong line emission, most notably Lyman alpha radiation. The effects of the strong Lyman alpha emission on the chemical equilibrium in protoplanetary disks has previously been unrecognized. We discuss the impact of this radiation on molecular observations in the context of a radiative transfer model that includes both direct attenuation and scattering. In particular, Lyman alpha radiation will directly dissociate water vapor and may contribute to the observed enhancements of CN/HCN in disks.
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.
In this work, we investigate the spectra of gravitational waves produced by chiral symmetry breaking in dark quantum chromodynamics (dQCD) sector. The dark pion ($\pi$) can be a dark matter candidate as weakly interacting massive particle (WIMP) or strongly interacting massive particle (SIMP). For a WIMP scenario, we introduce the dQCD sector coupled to the standard model (SM) sector with classical scale invariance and investigate the annihilation process of the dark pion via the $2\pi \to 2\,\text{SM}$ process. For a SIMP scenario, we investigate the $3\pi \to 2\pi$ annihilation process of the dark pion as a SIMP using chiral perturbation theory. We find that in the WIMP scenario the gravitational wave background spectra can be observed by future space gravitational wave antennas. On the other hand, when the dark pion is the SIMP dark matter with the constraints for the chiral perturbative limit and pion-pion scattering cross section, the chiral phase transition becomes crossover and then the gravitational waves are not produced.
Radio frequency (RF) wireless power transfer (WPT) is a promising technology for sustainable support of massive Internet of Things (IoT). However, RF-WPT systems are characterized by low efficiency due to channel attenuation, which can be mitigated by precoders that adjust the transmission directivity. This work considers a multi-antenna RF-WPT system with multiple non-linear energy harvesting (EH) nodes with energy demands changing over discrete time slots. This leads to the charging scheduling problem, which involves choosing the precoders at each slot to minimize the total energy consumption and meet the EH requirements. We model the problem as a Markov decision process and propose a solution relying on a low-complexity beamforming and deep deterministic policy gradient (DDPG). The results show that the proposed beamforming achieves near-optimal performance with low computational complexity, and the DDPG-based approach converges with the number of episodes and reduces the system's power consumption, while the outage probability and the power consumption increase with the number of devices.
The Higgs boson couplings to bottom and top quarks have been measured and agree well with the Standard Model predictions. Decays to lighter quarks and gluons, however, remain elusive. Observing these decays is essential to complete the picture of the Higgs boson interactions. In this work, we present the perspectives for the 14 TeV LHC to observe the Higgs boson decay to gluon jets assembling convolutional neural networks, trained to recognize abstract jet images constructed embodying particle flow information, and boosted decision trees with kinetic information from Higgs-strahlung $ZH\to \ell^+\ell^- + gg$ events. We show that this approach might be able to observe Higgs to gluon decays with a significance of around $2.4\sigma$ improving significantly previous prospects based on cut-and-count analysis. An upper bound of $BR(H\to gg)\leq 1.74\times BR^{SM}(H\to gg)$ at 95\% confidence level after 3000 fb$^{-1}$ of data is obtained using these machine learning techniques.
We have made experimental measurements of electrical conductivity, pH and relative magnetic susceptibility of the aqueous solutions of 24 indian spices. The measured values of electrical conductance of these spices are found to be linearly related to their ash content and bulk calorific values reported in literature. The physiological relevance of the pH and diamagnetic susceptibility of spices when consumed as food or medicine will be also discussed.
We studied the hydration of a single methanol molecule in aqueous solution by first-principle DFT-based molecular dynamics simulation. The calculations show that the local structural and short-time dynamical properties of the water molecules remain almost unchanged by the presence of the methanol, confirming the observation from recent experimental structural data for dilute solutions. We also see, in accordance with this experimental work, a distinct shell of water molecules that consists of about 15 molecules. We found no evidence for a strong tangential ordering of the water molecules in the first hydration shell.
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding of Dyson-Schwinger equations and their solutions is of high interest. To this end we consider combinatorial Dyson-Schwinger equations manifestly relying on the Hopf-algebraic structure of perturbative renormalization. We find that these equations are fully compatible with renormalization, relying only on the superficially divergent diagrams which are planar ribbon graphs, i.e. decompleted dual combinatorial maps. Still, they are of a similar kind as in realistic models of local QFT, featuring in particular an infinite number of primitive diagrams as well as graph-dependent combinatorial factors.
Most representation learning algorithms for language and image processing are local, in that they identify features for a data point based on surrounding points. Yet in language processing, the correct meaning of a word often depends on its global context. As a step toward incorporating global context into representation learning, we develop a representation learning algorithm that incorporates joint prediction into its technique for producing features for a word. We develop efficient variational methods for learning Factorial Hidden Markov Models from large texts, and use variational distributions to produce features for each word that are sensitive to the entire input sequence, not just to a local context window. Experiments on part-of-speech tagging and chunking indicate that the features are competitive with or better than existing state-of-the-art representation learning methods.
We discuss and derive the continuous Becchi-Rouet-Stora-Tyutin (BRST)and anti-BRST symmetry transformations for the Jackiw-Pi (JP) model of three (2 + 1)-dimensional (3D) massive non-Abelian 1-form gauge theory by exploiting the standard technique of (anti-)chiral superfield approach (ACSA) to BRST formalism where a few appropriate and specific sets of (anti-)BRST invariant quantities (i. e. physical quantities at quantum level) play a very important role. We provide the explicit derivation of the nilpotency and absolute anticommutativity properties of (anti-)BRST conserved charges and the existence of the Curci-Ferrari (CF) condition within the realm of ACSA to BRST formalism where we take only a single Grassmannian variable into account. We also provide clear proof of (anti-) BRST invariances of the coupled (but equivalent) Lagrangian densities within the framework of ACSA to BRST approach where the emergence of the CF-condition is observed.
Composites of the type: metal - dielectrics and superconductor - dielectrics are studied in the quasistatic approximation. The dielectric response is described by the spectral function $G(n,x)$, which contains effects of the concentration x (of metallic resp. superconductive particles) on the dielectric function,and effects of the shape. The parameter n plays the role of the depolarisation factor for dielectric materials, in metals it is a factor which includes effects like shape, and a topology of the composite. There exists a percolation transition at $ x_{c}= \frac{1}{3} $ which leads to a metallic-like for the composite with the concentration $ x > x_{c}$. At low frequencies divergence with frequency remains even when there are present dielectric particles above the percolation concentration. In superconductor case the spectral function $G(n,x)$ may include also Josephson junction effects. We assume in both cases of composites two types of spheroidal particles, metal (superconducting) ones and dielectric ones. A dielectric function is constant in both cases for the dielectric material, and a dielectric function for the metal and for the superconductor are used with well known form for metals and a classical superconductor. A percolation transition at $ x_{c}$ leads to a metallic-like absorption for the composite with $x>x_{c}$. Note that at low frequencies divergence in frequency remains even when there are present dielectric particles above $x_{c}$. Below the percolation threshold dielectric properties are modified by metalic particles. We obtain at very low temperatures and low concentrations x of the superconductor the effective dielectric constant. The absorption part is zero in our simple case. The real part of the dielectric function increases with the concentration of the superconducting spheres. The frequency dependence is quadratic, it gives low frequency tail.
The construction of a new detector is proposed to extend the capabilities of ALICE in the high transverse momentum (pT) region. This Very High Momentum Particle Identification Detector (VHMPID) performs charged hadron identification on a track-by-track basis in the 5 GeV/c < p < 25 GeV/c momentum range and provides ALICE with new opportunities to study parton-medium interactions at LHC energies. The VHMPID covers up to 30% of the ALICE central barrel and presents sufficient acceptance for triggered- and tagged-jet studies, allowing for the first time identified charged hadron measurements in jets. This Letter of Intent summarizes the physics motivations for such a detector as well as its layout and integration into ALICE.
This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.
We study the geometry of 4d N=1 SCFT's arising from compactification of 6d (1,0) SCFT's on a Riemann surface. We show that the conformal manifold of the resulting theory is characterized, in addition to moduli of complex structure of the Riemann surface, by the choice of a connection for a vector bundle on the surface arising from flavor symmetries in 6d. We exemplify this by considering the case of 4d N=1 SCFT's arising from M5 branes probing Z_k singularity compactified on a Riemann surface. In particular, we study in detail the four dimensional theories arising in the case of two M5 branes on Z_2 singularity. We compute the conformal anomalies and indices of such theories in 4d and find that they are consistent with expectations based on anomaly and the moduli structure derived from the 6 dimensional perspective.
Light-fidelity (LiFi) is a wireless communication technology that employs both infrared and visible light spectra to support multiuser access and user mobility. Considering the small wavelength of light, the optical channel is affected by the random orientation of a user equipment (UE). In this paper, a random process model for changes in the UE orientation is proposed based on data measurements. We show that the coherence time of the random orientation is in the order of hundreds of milliseconds. Therefore, an indoor optical wireless channel can be treated as a slowly-varying channel as its delay spread is typically in the order of nanoseconds. A study of the orientation model on the performance of direct-current-biased orthogonal frequency-division multiplexing (DC-OFDM) is also presented. The performance analysis of the DC-OFDM system incorporates the effect of diffuse link due to reflection and blockage by the user. The results show that the diffuse link and the blockage have significant effects, especially if the UE is located relatively far away from an access point (AP). It is shown that the effect is notable if the horizontal distance between the UE and the AP is greater than $1.5$ m in a typical $5\times3.5\times3$ m$^3$ indoor room.
In this note, we show that any distributive lattice is isomorphic to the set of reachable configurations of an Edge Firing Game. Together with the result of James Propp, saying that the set of reachable configurations of any Edge Firing Game is always a distributive lattice, this shows that the two concepts are equivalent.
I use Bridgeland's definition of a stability condition on a triangulated category to investigate the stability of D-branes on Calabi-Yau cones given by the canonical line bundle over a del Pezzo surface. In this context, I prove the existence of the decay of a D3-brane into a set of fractional branes. This is an important aspect of the derivation of quiver gauge theories from branes at singularities via the technique of equivalences of categories. Some important technical aspects of this equivalence are discussed. I also prove that the representations corresponding to skyscraper sheaves supported off the zero section are simple.
The small but measurable effect of weak gravitational lensing on the cosmic microwave background radiation provide information about the large-scale distribution of matter in the universe. We use the all sky distribution of matter, as represented by the {\em convergence map} that is inferred from CMB lensing measurement by Planck survey, to test the fundamental assumption of Statistical Isotropy (SI) of the universe. For the analysis we use the $\alpha$ statistic that is devised from the contour Minkowski tensor, a tensorial generalization of the scalar Minkowski functional, the contour length. In essence, the $\alpha$ statistic captures the ellipticity of isofield contours at any chosen threshold value of a smooth random field and provides a measure of anisotropy. The SI of the observed convergence map is tested against the suite of realistic simulations of the convergence map provided by the Planck collaboration. We first carry out a global analysis using the full sky data after applying the galactic and point sources mask. We find that the observed data is consistent with SI. Further we carry out a local search for departure from SI in small patches of the sky using $\alpha$. This analysis reveals several sky patches which exhibit deviations from simulations with statistical significance higher than 95\% confidence level (CL). Our analysis indicates that the source of the anomalous behaviour of most of the outlier patches is inaccurate estimation of noise. We identify two outlier patches which exhibit anomalous behaviour originating from departure from SI at higher than 95\% CL. Most of the anomalous patches are found to be located roughly along the ecliptic plane or in proximity to the ecliptic poles.
Segmentation algorithms based on an energy minimisation framework often depend on a scale parameter which balances a fit to data and a regularising term. Irregular pyramids are defined as a stack of graphs successively reduced. Within this framework, the scale is often defined implicitly as the height in the pyramid. However, each level of an irregular pyramid can not usually be readily associated to the global optimum of an energy or a global criterion on the base level graph. This last drawback is addressed by the scale set framework designed by Guigues. The methods designed by this author allow to build a hierarchy and to design cuts within this hierarchy which globally minimise an energy. This paper studies the influence of the construction scheme of the initial hierarchy on the resulting optimal cuts. We propose one sequential and one parallel method with two variations within both. Our sequential methods provide partitions near the global optima while parallel methods require less execution times than the sequential method of Guigues even on sequential machines.
We present a new realization of inverted neutrino mass hierarchy based on $S_3 \times {\cal U}(1)$ flavor symmetry. In this scenario, the deviation of the solar oscillation angle from $\pi/4$ is correlated with the value of $\theta_{13}$, as they are both induced by a common mixing angle in the charged lepton sector. We find several interesting predictions: $\te_{13}\geq 0.13$, $\sin^2\te_{12}\geq 0.31$, $\sin^2\te_{23}\simeq 0.5$ and $0\leq \cos \de \leq 0.7$ for the neutrino oscillation parameters and $0.01 {\rm eV}\stackrel{<}{_\sim}m_{\bt \bt}\stackrel{<}{_\sim} 0.02 {\rm eV}$ for the effective neutrino mass in neutrino-less double $\bt $-decay. We show that our scenario can also explain naturally the observed baryon asymmetry of the universe via resonant leptogenesis. The masses of the decaying right--handed neutrinos can be in the range $(10^3 - 10^7)$ GeV, which would avoid the generic gravitino problem of supersymmetric models.
In this work, we present and study a new framework for online learning in systems with multiple users that provide user anonymity. Specifically, we extend the notion of bandits to obey the standard $k$-anonymity constraint by requiring each observation to be an aggregation of rewards for at least $k$ users. This provides a simple yet effective framework where one can learn a clustering of users in an online fashion without observing any user's individual decision. We initiate the study of anonymous bandits and provide the first sublinear regret algorithms and lower bounds for this setting.
We present the first determination of the hadronic decays of the lightest exotic $J^{PC}=1^{-+}$ resonance in lattice QCD. Working with SU(3) flavor symmetry, where the up, down and strange quark masses approximately match the physical strange-quark mass giving $m_\pi \sim 700$ MeV, we compute finite-volume spectra on six lattice volumes which constrain a scattering system featuring eight coupled channels. Analytically continuing the scattering amplitudes into the complex energy plane, we find a pole singularity corresponding to a narrow resonance which shows relatively weak coupling to the open pseudoscalar--pseudoscalar, vector--pseudoscalar and vector--vector decay channels, but large couplings to at least one kinematically-closed axial-vector--pseudoscalar channel. Attempting a simple extrapolation of the couplings to physical light-quark mass suggests a broad $\pi_1$ resonance decaying dominantly through the $b_1 \pi$ mode with much smaller decays into $f_1 \pi$, $\rho \pi$, $\eta' \pi$ and $\eta \pi$. A large total width is potentially in agreement with the experimental $\pi_1(1564)$ candidate state, observed in $\eta \pi$, $\eta' \pi$, which we suggest may be heavily suppressed decay channels.
The IceCube Neutrino Observatory, which instruments 1$\,$km$^3$ of clear ice at the geographic South Pole, was mainly designed to detect particles with energies in the multi-GeV to PeV range. Due to ice temperatures between $-20^\circ$C to $-43^\circ$C and the low radioactivity of the ice, the dark noise rates of the 5160 photomultiplier tubes forming the IceCube lattice are of order 500 Hz, which is particularly low for 10 inch photomultipliers. Therefore, IceCube can extend its searches to bursts of $\mathcal{O}$(10$\,$MeV) neutrinos lasting several seconds, which are expected to be produced by Galactic core collapse supernovae. By observing a uniform rise in all photomultiplier rates, IceCube can provide a particularly high statistical precision for the neutrino rate from supernovae in the inner part of our Galaxy ($<$ 20 kpc). In this paper, the tools and the method to study potential obscured or failed core collapse supernovae in our Galaxy are presented. The analysis will be based on 3911 days of IceCube data taken between April 17, 2008 and December 31, 2018.
This is an overview of mathematical heritage of Sergey Naboko in the area of functional models of non-self-adjoint operators. It covers the works by Sergey in model construction, the analysis of absolutely continuous and singular spectra and the construction of the scattering theory in model terms.
With the rise of geospatial big data, new narratives of cities based on spatial networks and flows have replaced the traditional focus on locations. While plenty of research have empirically analyzed network structures, there lacks a state-of-the-art synthesis of applicable insights and methods of spatial networks in the planning context. In this chapter, we reviewed the theories, concepts, methods, and applications of spatial network analysis in cities and their insights for planners from four areas of concern: spatial structures, urban infrastructure optimizations, indications of economic wealth, social capital, and residential mobility, and public health control (especially COVID-19). We also outlined four challenges that planners face when taking the planning knowledge from spatial networks to actions: data openness and privacy, linkage to direct policy implications, lack of civic engagement, and the difficulty to visualize and integrate with GIS. Finally, we envisioned how spatial networks can be integrated into a collaborative planning framework.
We present {\AE}THEL, a semantic compositionality dataset for written Dutch. {\AE}THEL consists of two parts. First, it contains a lexicon of supertags for about 900 000 words in context. The supertags correspond to types of the simply typed linear lambda-calculus, enhanced with dependency decorations that capture grammatical roles supplementary to function-argument structures. On the basis of these types, {\AE}THEL further provides 72 192 validated derivations, presented in four formats: natural-deduction and sequent-style proofs, linear logic proofnets and the associated programs (lambda terms) for meaning composition. {\AE}THEL's types and derivations are obtained by means of an extraction algorithm applied to the syntactic analyses of LASSY Small, the gold standard corpus of written Dutch. We discuss the extraction algorithm and show how `virtual elements' in the original LASSY annotation of unbounded dependencies and coordination phenomena give rise to higher-order types. We suggest some example usecases highlighting the benefits of a type-driven approach at the syntax semantics interface. The following resources are open-sourced with {\AE}THEL: the lexical mappings between words and types, a subset of the dataset consisting of 7 924 semantic parses, and the Python code that implements the extraction algorithm.
With the growing prevalence of large language models, it is increasingly common to annotate datasets for machine learning using pools of crowd raters. However, these raters often work in isolation as individual crowdworkers. In this work, we regard annotation not merely as inexpensive, scalable labor, but rather as a nuanced interpretative effort to discern the meaning of what is being said in a text. We describe a novel, collaborative, and iterative annotator-in-the-loop methodology for annotation, resulting in a 'Bridging Benchmark Dataset' of comments relevant to bridging divides, annotated from 11,973 textual posts in the Civil Comments dataset. The methodology differs from popular anonymous crowd-rating annotation processes due to its use of an in-depth, iterative engagement with seven US-based raters to (1) collaboratively refine the definitions of the to-be-annotated concepts and then (2) iteratively annotate complex social concepts, with check-in meetings and discussions. This approach addresses some shortcomings of current anonymous crowd-based annotation work, and we present empirical evidence of the performance of our annotation process in the form of inter-rater reliability. Our findings indicate that collaborative engagement with annotators can enhance annotation methods, as opposed to relying solely on isolated work conducted remotely. We provide an overview of the input texts, attributes, and annotation process, along with the empirical results and the resulting benchmark dataset, categorized according to the following attributes: Alienation, Compassion, Reasoning, Curiosity, Moral Outrage, and Respect.
The RHESSI experiment uses rotational modulation for x- and gamma ray imaging of solar eruptions. In order to disentangle rotational modulation from intrinsic time variation, an unbiased linear estimator for the spatially integrated photon flux is proposed. The estimator mimics a flat instrumental response under a gaussian prior, with achievable flatness depending on the counting noise. The amount of regularization is primarily given by the modulation-to-Poisson levels of fluctuations, and is only weakly affected by the Bayesian prior. Monte Carlo simulations demonstrate that the mean relative error of the estimator reaches the Poisson limit, and real-data applications are shown.
We show that the stress-energy tensor for a superstring in the AdS5xS5 background is written in a supersymmetric generalized "Sugawara" form. It is the "supertrace" of the square of the right-invariant current which is the Noether current satisfying the flatness condition. The Wess-Zumino term is taken into account through the supersymmetric gauge connection in the right-invariant currents, therefore the obtained stress-energy tensor is kappa invariant. The integrability of the AdS superstring provides an infinite number of the conserved "local" currents which are supertraces of the n-th power of the right-invariant current. For even n the "local" current reduces to terms proportional to the Virasoro constraint and the kappa symmetry constraint, while for odd n it reduces to a term proportional to the kappa symmetry constraint .
Theoretical remarks are offered regarding recent hadron collider results on the mixing and decays of $B_s$ mesons. Topics covered include: (1) CP-violating mixing in $B_s(\ob_s) \to J/\psi \phi$, (2) the D0 dimuon charge asymmetry, (3) information from triple products, (4) $B_s \to J/\psi f_0$, (5) new physics constraints, (6) some illustrative new physics scenarios.
Answering science questions posed in natural language is an important AI challenge. Answering such questions often requires non-trivial inference and knowledge that goes beyond factoid retrieval. Yet, most systems for this task are based on relatively shallow Information Retrieval (IR) and statistical correlation techniques operating on large unstructured corpora. We propose a structured inference system for this task, formulated as an Integer Linear Program (ILP), that answers natural language questions using a semi-structured knowledge base derived from text, including questions requiring multi-step inference and a combination of multiple facts. On a dataset of real, unseen science questions, our system significantly outperforms (+14%) the best previous attempt at structured reasoning for this task, which used Markov Logic Networks (MLNs). It also improves upon a previous ILP formulation by 17.7%. When combined with unstructured inference methods, the ILP system significantly boosts overall performance (+10%). Finally, we show our approach is substantially more robust to a simple answer perturbation compared to statistical correlation methods.
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the Schroedinger equation of a harmonic oscillator. In this way we derive the discrete oscillator spectrum from classical dynamics. The model is then generalized to an arbitrary potential. This opens up the possibility of efficiently simulating quantum computers with the help of classical systems.
A cover of an associative (not necessarily commutative nor unital) ring $R$ is a collection of proper subrings of $R$ whose set-theoretic union equals $R$. If such a cover exists, then the covering number $\sigma(R)$ of $R$ is the cardinality of a minimal cover, and a ring $R$ is called $\sigma$-elementary if $\sigma(R) < \sigma(R/I)$ for every nonzero two-sided ideal $I$ of $R$. If $R$ is a ring with unity, then we define the unital covering number $\sigma_u(R)$ to be the size of a minimal cover of $R$ by subrings that contain $1_R$ (if such a cover exists), and $R$ is $\sigma_u$-elementary if $\sigma_u(R) < \sigma_u(R/I)$ for every nonzero two-sided ideal of $R$. In this paper, we classify all $\sigma$-elementary unital rings and determine their covering numbers. Building on this classification, we are further able to classify all $\sigma_u$-elementary rings and prove $\sigma_u(R) = \sigma(R)$ for every $\sigma_u$-elementary ring $R$. We also prove that, if $R$ is a ring without unity with a finite cover, then there exists a unital ring $R'$ such that $\sigma(R) = \sigma_u(R')$, which in turn provides a complete list of all integers that are the covering number of a ring. Moreover, if \[\mathscr{E}(N) := \{m : m \le N, \sigma(R) = m \text{ for some ring } R\},\] then we show that $|\mathscr{E}(N)| = \Theta(N/\log(N))$, which proves that almost all integers are not covering numbers of a ring.
The devil's staircase is a fractal structure that characterizes the ground state of one-dimensional classical lattice gases with long-range repulsive convex interactions. Its plateaus mark regions of stability for specific filling fractions which are controlled by a chemical potential. Typically such staircase has an explicit particle-hole symmetry, i.e., the staircase at more than half-filling can be trivially extracted from the one at less than half filling by exchanging the roles of holes and particles. Here we introduce a quantum spin chain with competing short-range attractive and long-range repulsive interactions, i.e. a non-convex potential. In the classical limit the ground state features generalized Wigner crystals that --- depending on the filling fraction --- are either composed of dimer particles or dimer holes which results in an emergent complete devil's staircase without explicit particle-hole symmetry of the underlying microscopic model. In our system the particle-hole symmetry is lifted due to the fact that the staircase is controlled through a two-body interaction rather than a one-body chemical potential. The introduction of quantum fluctuations through a transverse field melts the staircase and ultimately makes the system enter a paramagnetic phase. For intermediate transverse field strengths, however, we identify a region, where the density-density correlations suggest the emergence of quasi long-range order. We discuss how this physics can be explored with Rydberg-dressed atoms held in a lattice.
The competing nature of the app market motivates us to shift our focus on apps that provide similar functionalities and directly compete with each other (i.e., peer apps). In this work, we study the ratings and the review text of 100 Android apps across 10 peer app groups. We highlight the importance of performing peer-app analysis by showing that it can provide a unique perspective over performing a global analysis of apps (i.e., mixing apps from multiple categories). First, we observe that comparing user ratings within peer groups can provide very different results from comparing user ratings from a global perspective. Then, we show that peer-app analysis provides a different perspective to spot the dominant topics in the user reviews, and to understand the impact of the topics on user ratings. Our findings suggest that future efforts may pay more attention to performing and supporting app analysis from a peer group context. For example, app store owners may consider an additional rating mechanism that normalizes app ratings within peer groups, and future research may help developers understand the characteristics of specific peer groups and prioritize their efforts.
We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay $n_1$, and coupling acts with a delay $n_2$. Depending on the sign of the difference $n_1-n_2$, the slave map can synchronize to a future or a past state of the master system. The stability properties of the synchronized state are studied analytically, and we find that they are independent of the coupling delay $n_2$. These results are compared with numerical simulations of a delayed map that arises from discretization of the Ikeda delay-differential equation. We show that the critical value of the coupling strength above which synchronization is stable becomes independent of the delay $n_1$ for large delays.
It is argued that if cosmic rays penetrate into molecular clouds, the total energy they lose can exceed the energy from galactic supernovae shocks. It is shown that most likely galactic cosmic rays interacting with the surface layers of molecular clouds are efficiently reflected and do not penetrate into the cloud interior. Low-energy cosmic rays ($E<1$ GeV) that provide the primary ionization of the molecular cloud gas can be generated inside such clouds by multiple shocks arising due to supersonic turbulence.