# Top arXiv papers

• The cosmic radio-frequency spectrum is expected to show a strong absorption signal corresponding to the 21-centimetre-wavelength transition of atomic hydrogen around redshift 20, which arises from Lyman-alpha radiation from some of the earliest stars. By observing this 21-centimetre signal - either its sky-averaged spectrum or maps of its fluctuations, obtained using radio interferometers - we can obtain information about cosmic dawn, the era when the first astrophysical sources of light were formed. The recent detection of the global 21-centimetre spectrum reveals a stronger absorption than the maximum predicted by existing models, at a confidence level of 3.8 standard deviations. Here we report that this absorption can be explained by the combination of radiation from the first stars and excess cooling of the cosmic gas induced by its interaction with dark matter. Our analysis indicates that the spatial fluctuations of the 21-centimetre signal at cosmic dawn could be an order of magnitude larger than previously expected and that the dark-matter particle is no heavier than several proton masses, well below the commonly predicted mass of weakly interacting massive particles. Our analysis also confirms that dark matter is highly non-relativistic and at least moderately cold, and primordial velocities predicted by models of warm dark matter are potentially detectable. These results indicate that 21-centimetre cosmology can be used as a dark-matter probe.
• We prove a uniform C^alpha estimate for collapsing Calabi-Yau metrics on the total space of a proper holomorphic submersion over the unit ball in C^m. The usual methods of Calabi, Evans-Krylov, and Caffarelli do not apply to this setting because the background geometry degenerates. We instead rely on blowup arguments and on linear and nonlinear Liouville theorems on cylinders. In particular, as an intermediate step, we use such arguments to prove sharp new Schauder estimates for the Laplacian on cylinders. If the fibers of the submersion are pairwise biholomorphic, our method yields a uniform C^infinity estimate. We then apply these local results to the case of collapsing Calabi-Yau metrics on compact Calabi-Yau manifolds. In this global setting, the C^0 estimate required as a hypothesis in our new local C^alpha and C^infinity estimates is known to hold thanks to earlier work of the second-named author.
• A study of a new scheme to produce very low emittance muon beams using a positron beam of about 45 GeV interacting on electrons on target is presented. One of the innovative topics to be investigated is the behaviour of the positron beam stored in a low emittance ring with a thin target, that is directly inserted in the ring chamber to produce muons. Muons can be immediately collected at the exit of the target and transported to two mu+ and mu- accumulator rings and then accelerated and injected in muon collider rings. We focus in this paper on the simulation of the e+ beam interacting with the target, the effect of the target on the 6-D phase space and the optimization of the e+ ring design to maximize the energy acceptance. We will investigate the performances of this scheme, ring plus target system, comparing different multi-turn simulations. A preliminary review of the full scheme parameters is discussed in view of the results obtained on the ring plus target system. In addition, a first acceleration scheme is presented together with a possible 14 TeV collider layout.
• We discuss a manifestly covariant formulation of ideal relativistic magnetohydrodynamics, which has been recently used in astrophysical and heavy-ion contexts, and compare it to other similar frameworks. We show that the covariant equations allow for stationary vortex-like solutions that represent generalizations of the perfect-fluid solutions describing systems in global equilibrium with rotation. Such solutions are further used to demonstrate that inhomogeneous Maxwell equations, implicitly included in the covariant framework, may generate very large electric charge densities. This suggests that solutions of the covariant formulation may violate in some cases the assumptions of standard ideal magnetohydrodynamics. Furthermore, we show that the flow four-vector and conserved currents obtained in the covariant approach are usually not related to each other, which hinders kinetic-theory interpretation of the obtained results.
• We study asymptotical expansion as $\nu\to0$ for integrals over ${ \mathbb{R} }^{2d}=\{(x,y)\}$ of quotients of the form $F(x,y) \cos(\lambda x\cdot y) \big/ \big( (x\cdot y)^2+\nu^2\big)$, where $\lambda\ge 0$ and $F$ decays at infinity sufficiently fast. Integrals of this kind appear in the theory of wave turbulence.
• We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike traditional advection-dispersion-reaction models, the SADR model describes mechanical and diffusive mixing as two separate processes. In the SADR model, mechanical mixing is driven by random advective velocity with the variance given by the coefficient of mechanical dispersion. The diffusive mixing is modeled as a Fickian diffusion with the effective diffusion coefficient. We demonstrate that the sum of the two coefficients is equal to the dispersion coefficients, but only the effective diffusion coefficient contributes to the mixing-controlled reactions, indicating that such systems do not get fully mixed at the Representative Elementary Volume scale where the deterministic equations and dispersion coefficient are defined. We use the experimental results of Gramling et al. \citeGramling to show that for transport and bimolecular reactions in porous media, the SADR model is significantly more accurate than the traditional dispersion model, which overestimates the concentration of the reaction product by as much as 60\%.
• We give a characterisation of radial Schur multipliers on finite products of trees. The equivalent condition is that a certain generalised Hankel matrix involving the discrete derivatives of the radial function is a trace class operator. This extends Haagerup, Steenstrup and Szwarc's result for trees. The same condition can be expressed in terms of Besov spaces on the torus. We also prove a similar result for products of hyperbolic graphs and provide a sufficient condition for a function to define a radial Schur multiplier on a finite dimensional CAT(0) cube complex.
• Let $G$ be a finite solvable group. We show that $G$ does not have a normal nonabelian Sylow $p$-subgroup when its prime character degree graph $\Delta(G)$ satisfies a technical hypothesis.
• Non-reciprocal components, such as isolators and circulators, are critical to wireless communication and radar applications. Traditionally, non-reciprocal components have been implemented using ferrite materials, which exhibit non-reciprocity under the influence of an external magnetic field. However, ferrite materials cannot be integrated into IC fabrication processes, and consequently are bulky and expensive. In the recent past, there has been strong interest in achieving non-reciprocity in a non-magnetic IC-compatible fashion using spatio-temporal modulation. In this paper, we present a general approach to non-reciprocity based on switched transmission lines. Switched transmission lines enable broadband, lossless and compact non-reciprocity, and a wide range of non-reciprocal functionalities, including non-reciprocal phase shifters, ultra-broadband gyrators and isolators, frequency-conversion isolators, and high-linearity/high-frequency/ultra-broadband circulators. We present a detailed theoretical analysis of the various non-idealities that impact insertion loss and provide design guidelines. The theory is validated by experimental results from discrete-component-based gyrators and isolators, and a 25GHz circulator fabricated in 45nm SOI CMOS technology.
• We consider a network of n spin 1/2 systems which are pairwise interacting via Ising interaction and are controlled by the same electro-magnetic control field. Such a system presents symmetries since the Hamiltonian is unchanged if we permute two spins. This prevents full (operator) controllability in that not every unitary evolution can be obtained. We prove however that controllability is verified if we restrict ourselves to unitary evolutions which preserve the above permutation invariance. For low dimensional cases, n=2 and n=3, we provide an analysis of the Lie group of available evolutions and give explicit control laws to transfer between any two permutation invariant states. This class of states includes highly entangled states such as GHZ states and W states, which are of interest in quantum information.
• In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$. As a straightforward consequence, we announce a structure-type result for proper graphs defined on relatively compact domains.
• We study the time optimal control problem for the evolution operator of an n-level quantum system from the identity to any desired final condition. For the considered class of quantum systems the control couples all the energy levels to a given one and is assumed to be bounded in Euclidean norm. From a mathematical perspective, such a problem is a sub-Riemannian K-P problem, whose underlying symmetric space is SU(n)/S(U(n-1) x U(1)). Following the method of symmetry reduction, we consider the action of S(U(n-1) xU(1)) on SU(n) as a conjugation X ---> AXA^-1. This allows us to do a symmetry reduction and consider the problem on a quotient space. We give an explicit description of such a quotient space which has the structure of a stratified space. We prove several properties of sub-Riemannian problems with the given structure. We derive the explicit optimal control for the case of three level quantum systems where the desired operation is on the lowest two energy levels (Lambda-systems). We solve this latter problem by reducing it to an integer quadratic optimization problem with linear constraints.
• The purpose of this paper is to investigate shifted $(+1)$ Poisson structures in context of differential geometry. The relevant notion is shifted $(+1)$ Poisson structures on differentiable stacks. More precisely, we develop the notion of Morita equivalence of quasi-Poisson groupoids. Thus isomorphism classes of $(+1)$ Poisson stack correspond to Morita equivalence classes of quasi-Poisson groupoids. In the process, we carry out the following programs of independent interests: (1) We introduce a $\mathbb Z$-graded Lie 2-algebra of polyvector fields on a given Lie groupoid and prove that its homotopy equivalence class is invariant under Morita equivalence of Lie groupoids, thus can be considered as polyvector fields on the corresponding differentiable stack ${\mathfrak X}$. It turns out that shifted $(+1)$ Poisson structures on ${\mathfrak X}$ correspond exactly to elements of the Maurer-Cartan moduli set of the corresponding dgla. (2) We introduce the notion of tangent complex $T_{\mathfrak X}$ and cotangent complex $L_{\mathfrak X}$ of a differentiable stack ${\mathfrak X}$ in terms of any Lie groupoid $\Gamma{\rightrightarrows} M$ representing ${\mathfrak X}$. They correspond to homotopy class of 2-term homotopy $\Gamma$-modules $A[1]\rightarrow TM$ and $T^\vee M\rightarrow A^\vee[-1]$, respectively. We prove that a $(+1)$-shifted Poisson structure on a differentiable stack ${\mathfrak X}$, defines a morphism ${L_{{\mathfrak X}}}[1]\to {T_{{\mathfrak X}}}$. We rely on the tools of theory of VB-groupoids including homotopy and Morita equivalence of VB-groupoids.
• We prove a decomposition formula for Verlinde sums (rational trigonometric sums), as a discrete counterpart to the Boysal-Vergne decomposition formula for Bernoulli series. Motivated by applications to fixed point formulas in Hamiltonian geometry, we develop differential form valued version of Bernoulli series and Verlinde sums, and extend the decomposition formula to this wider context.
• Akyol M.A. [Conformal anti-invariant submersions from cosymplectic manifolds, Hacettepe Journal of Mathematics and Statistic, 46(2), (2017), 177-192.] defined and studied conformal anti-invariant submersions from cosymplectic manifolds. The aim of the present paper is to define and study the notion of conformal slant submersions (it means the Reeb vector field $\xi$ is a vertical vector field) from almost contact metric manifolds onto Riemannian manifolds as a generalization of Riemannian submersions, horizontally conformal submersions, slant submersions and conformal anti-invariant submersions. More precisely, we mention lots of examples and obtain the geometries of the leaves of $\ker\pi_{*}$ and $(\ker\pi_{*})^\perp,$ including the integrability of the distributions, the geometry of foliations, some conditions related to totally geodesicness and harmonicty of the submersions. Finally, we consider a decomposition theorem on total space of the new submersion.
• We propose a simple and transparent machine learning approach for recognition and classification of complex non-collinear magnetic structures in two-dimensional materials. It is based on the implementation of the single-hidden-layer neural network that only relies on the z projections of the spins. In this setup one needs a limited set of magnetic configurations to distiguish ferromagnetic, skyrmion and spin spiral phases, as well as their different combinations. The network trained on the configurations for square-lattice Heisenberg model with Dzyaloshinskii-Moriya interaction can classify the magnetic structures obtained from Monte Carlo calculations for triangular lattice. Our approach is also easy to use for analysis of the numerous experimental data collected with spin-polarized scanning tunneling experiments.
• In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane, with no-slip condition for velocity field, perfect conducting condition for magnetic field and Dirichlet boundary condition for temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer that is described by a Prandtl-type system. By applying a coordinate transformation in terms of stream function as motivated by the recent work \citeliu2016mhdboundarylayer on the incompressible MHD system, under the non-degeneracy condition on the tangential magnetic field, we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.
• We study the evolution of holographic subregion complexity under a thermal quench in this paper. From the subregion CV proposal in the AdS/CFT correspondence, the subregion complexity in the CFT is holographically captured by the volume of the codimension-one surface enclosed by the codimension-two extremal entanglement surface and the boundary subregion. Under a thermal quench, the dual gravitational configuration is described by a Vaidya-AdS spacetime. In this case we find that the holographic subregion complexity always increases at early time, and after reaching a maximum it decreases and gets to saturation. Moreover we notice that when the size of the strip is large enough and the quench is fast enough, in $AdS_{d+1}(d\geq3)$ spacetime the evolution of the complexity is discontinuous and there is a sudden drop due to the transition of the extremal entanglement surface. We discuss the effects of the quench speed, the strip size, the black hole mass and the spacetime dimension on the evolution of the subregion complexity in detail numerically.
• We show that in order to prove that every second countable locally compact groups with exact reduced group C*-algebra is exact in the dynamical sense (i.e. KW-exact) it suffices to show this for totally disconnected groups.
• Using the atmospheric structure from a 3D global radiation-hydrodynamic simulation of HD 189733b and the open-source BART code, we investigate the difference between the secondary-eclipse temperature structure produced with a 3D simulation and the best-fit 1D retrieved model. Synthetic data are generated by integrating the 3D models over the Spitzer, HST, and JWST bandpasses, covering the wavelength range between 1 and 11 um. Using the data from different observing instruments, we present detailed comparisons between the temperature-pressure profiles recovered by BART and those from the 3D simulations. We calculate several averages of the 3D thermal structure and implement two temperature parameterizations to investigate different thermal profile shapes. To assess which part of the thermal structure is best constrained by the data, we generate contribution functions for both our theoretical model and each of our retrieved models. Our conclusions are strongly affected by the spectral resolution of the instruments included, their wavelength coverage, and the number of data points combined. We also see some limitations in each of the temperature parametrizations. The results show that our 1D retrieval is recovering a temperature and pressure profile that most closely matches the arithmetic average of the 3D thermal structure. When we use a higher resolution, more data points, and a parametrized temperature profile that allows more flexibility in the middle part of the atmosphere, we find a better match between the retrieved temperature and pressure profile and the arithmetic average.
• Selberg and Morris integral probability distributions are long conjectured to be distributions of the total mass of the Bacry-Muzy Gaussian Multiplicative Chaos measures with non-random logarithmic potentials on the unit interval and circle, respectively. The construction and properties of these distributions are reviewed from three perspectives: analytic based on several representations of the Mellin transform, asymptotic based on low intermittency expansions, and probabilistic based on the theory of Barnes beta probability distributions. In particular, positive and negative integer moments, infinite factorizations and involution invariance of the Mellin transform, analytic and probabilistic proofs of infinite divisibility of the logarithm, factorizations into products of Barnes beta distributions, and Stieltjes moment problems of these distributions are presented in detail. Applications are given in the form of conjectured mod-Gaussian limit theorems, laws of derivative martingales, distribution of extrema of $1/f$ noises, and calculations of inverse participation ratios in the Fyodorov-Bouchaud model.
• Two-stage robust unit commitment (RUC) models have been widely used for day-ahead energy and reserve scheduling under high renewable integration. The current state of the art relies on budget-constrained polyhedral uncertainty sets to control the conservativeness of the solutions. The associated lack of interpretability and parameter specification procedures, as well as the high computational burden exhibited by available exact solution techniques call for new approaches. In this work, we use an alternative scenario-based framework whereby uncertain renewable generation is characterized by a polyhedral uncertainty set relying on the direct specification of its vertexes. Moreover, we present a simple, yet efficient, adaptive data-driven procedure to dynamically update the uncertainty set vertexes with observed daily renewable-output profiles. Within this setting, the proposed data-driven RUC ensures protection against the convex hull of realistic scenarios empirically capturing the complex and time-varying intra-day spatial and temporal interdependencies among units. The resulting counterpart features advantageous properties from a computational perspective and can be effectively solved by the column-and-constraint generation algorithm until $\epsilon$-global optimality. Out-of-sample experiments reveal that the proposed approach is capable of producing efficient solutions in terms of cost and robustness while keeping the model tractable and scalable.
• The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed slow convergence which often hinders the application of EM algorithms in high-dimensional problems or in other complex settings.To address the need for more rapidly convergent EM algorithms, we describe a new class of acceleration schemes that build on the Anderson acceleration technique for speeding fixed-point iterations. Our approach is effective at greatly accelerating the convergence of EM algorithms and is automatically scalable to high dimensional settings. Through the introduction of periodic algorithm restarts and a damping factor, our acceleration scheme provides faster and more robust convergence when compared to un-modified Anderson acceleration while also improving global convergence. Crucially, our method works as an "off-the-shelf" method in that it may be directly used to accelerate any EM algorithm without relying on the use of any model-specific features or insights. Through a series of simulation studies involving five representative problems, we show that our algorithm is substantially faster than the existing state-of-art acceleration schemes.
• Topologically engineered optical materials support robust light transport. Herein, the investigated non-Hermitian lattice is trimerized and inhomogeneously coupled using uniform intracell coupling. The topological properties of the coupled waveguide lattice are evaluated, the PT-symmetric phase of a PT-symmetric lattice can have different topologies; the edge states depend on the lattice size, boundary configuration, and competition between the coupling and degree of non-Hermiticity. The topologically nontrivial region extends in the presence of periodic gain and loss. The nonzero geometric phases accumulated by the Bloch bands indicate the existence of topologically protected edge states between the band gaps. The unidirectional amplification and attenuation zero modes appear above a threshold degree of non-Hermiticity, which facilitate the development of a robust optical diode.
• Mar 20 2018 math.LO arXiv:1803.06671v1
We continue the algebraic investigation of PBZ*-lattices, a notion introduced in [12] in order to obtain insights into the structure of certain algebras of effects of a Hilbert space, lattice-ordered under the spectral ordering.
• In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes' representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn duality and introduce the categories of 2spaces and 2spaces$^{\star}$. The categories of 2spaces and 2spaces$^{\star}$ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces with respect to the category of Boolean algebras. Actually, the aim of this work is to show that these categories are, in fact, dually equivalent.
• We present a novel method for testing the hypothesis of equality of two correlation matrices using paired high-dimensional datasets. We consider test statistics based on the average of squares, maximum and sum of exceedances of Fisher transform sample correlations and we derive approximate null distributions using asymptotic and non-parametric distributions. Theoretical results on the power of the tests are presented and backed up by a range of simulation experiments. We apply the methodology to a case study of colorectal tumour gene expression data with the aim of discovering biological pathway lists of genes that present significantly different correlation matrices on healthy and tumour samples. We find strong evidence for a large part of the pathway lists correlation matrices to change among the two medical conditions.
• We show that in the class of solvable Lie algebras there exist algebras which admit local derivations which are not ordinary derivation and also algebras for which every local derivation is a derivation. We found necessary and sufficient conditions under which any local derivation of solvable Lie algebras with abelian nilradical and one-dimensional complementary space is a derivation. Moreover, we prove that every local derivation on a finite-dimensional solvable Lie algebra with model nilradical and maximal dimension of complementary space is a derivation.
• Applying the method of light-cone sum rules with photon distribution amplitudes, we compute the subleading-power correction to the radiative leptonic $B \to \gamma \ell \nu$ decay, at next-to-leading order in QCD for the twist-two contribution and at leading order in $\alpha_s$ for the higher-twist contributions, induced by the hadronic component of the collinear photon. The leading-twist hadronic photon effect turns out to preserve the symmetry relation between the two $B \to \gamma$ form factors due to the helicity conservation, however, the higher-twist hadronic photon corrections can yield symmetry-breaking effect already at tree level in QCD. Using the conformal expansion of photon distribution amplitudes with the non-perturbative parameters estimated from QCD sum rules, the twist-two hadronic photon contribution can give rise to approximately 30\% correction to the leading-power "direct photon" effect computed from the perturbative QCD factorization approach. In contrast, the subleading-power corrections from the higher-twist two-particle and three-particle photon distribution amplitudes are estimated to be of ${\cal O} (3 \sim 5\%)$ with the light-cone sum rule approach. We further predict the partial branching fractions of $B \to \gamma \ell \nu$ with a photon-energy cut $E_{\gamma} \geq E_{\rm cut}$, which are of interest for determining the inverse moment of the leading-twist $B$-meson distribution amplitude thanks to the forthcoming high-luminosity Belle II experiment at KEK.
• In this paper, we address the problem of causality violation in the solutions of Einstein equations and seek possible causality restoration mechanisms in modifed theories of gravity. We choose for the above problem, the causality violation due to the existence of closed time-like curves in the context of Kerr-Newman black hole. We first revisit and quantify the details of the causality violation in the Kerr-Newman spacetime. We then show that the issue is also existent in two of the modified solutions to the Kerr Newman spacetime: The Non-Commutativity inspired solution and the f(R)-Gravity modifed solution. We explore the possibility of mechanisms present within the model that prevent causality violation. We show that, in both the models, the model parameters can be chosen such that the causality violating region is eliminated. We argue that in the context of non commutativity inspired solution, the non commutativity parameter can be chosen such that the causality violating region is eliminated and the inner horizon is no longer the Cauchy horizon. We then discuss the geodesic connectivity of the causality violating region in both the scenarios and quantify the geodesics that have points in the causality violating regions. We also discuss the causal aspects of Kerr Newman deSitter/antideSitter spacetimes.
• The purpose of the paper under review is to explain the main ideas and the main ingredients of the involved and delicate work of A. Eskin, M. Kontsevich and A. Zorich concerning the sum of the positive Lyapunov exponents of the so-called Kontsevich- Zorich cocycle acting on the first cohomology spaces of translation surfaces.
• Mar 20 2018 math.CO arXiv:1803.06664v1
This is an introduction to the Möbius function of a poset. The chief novelty is in the exposition. We show how order-preserving maps from one poset to another can be used to relate their Möbius functions. We derive the basic results on the Möbius function, applying them in particular to geometric lattices.
• Active plasma lenses have the potential to enable broad-ranging applications of plasma-based accelerators owing to their compact design and radially symmetric kT/m-level focusing fields, facilitating beam-quality preservation and compact beam transport. We report on the direct measurement of magnetic field gradients in active plasma lenses and demonstrate their impact on the emittance of a charged particle beam. This is made possible by the use of a well-characterized electron beam with 1.4mmmrad normalized emittance from a conventional accelerator. Field gradients of up to 823T/m are investigated. The observed emittance evolution is supported by numerical simulations, which demonstrate the conservation of the core beam emittance in such a plasma lens setup.
• The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the existence of fixed point can be proved in incomplete metric spaces with non-contraction map on it. We have reported an example in support our result.
• Mar 20 2018 math.FA arXiv:1803.06661v1
In this article, we discuss a new version of metric fixed point theory especially of Banach Contraction Principle, Ran-Reurings Theorem and others.
• A number of computer-generated models of water, methanol and ethanol are considered at room temperature and ambient pressure, and also as a function of temperature (for water and ethanol), and the potential model (for water only). The Laplace matrices are determined, and various characteristics of this, such as eigenvalues and eigenvectors, and the corresponding Laplace spectra are calculated. It is revealed how the width of the spectral gap in the Laplace matrix of H-bonded networks may be applied for characterising the stability of the network. A novel method for detecting the presence percolated network in these systems is also introduced.
• If $\sigma$ is a symmetric mean and $f$ is an operator monotone function on $[0, \infty)$, then $$f(2(A^-1+B^-1)^-1)\le f(A\sigma B)\le f((A+B)/2).$$ Conversely, Ando and Hiai showed that if $f$ is a function that satisfies either one of these inequalities for all positive operators $A$ and $B$ and a symmetric mean different than the arithmetic and the harmonic mean, then the function is operator monotone. In this paper, we show that the arithmetic and the harmonic means can be replaced by the geometric mean to obtain similar characterizations. Moreover, we give characterizations of operator monotone functions using self-adjoint means and general means subject to a constraint due to Kubo and Ando.
• Temperature dependent hydrogen bond energetics and dynamical features, such as the diffusion coefficient and reorientational times, have been determined for ethanol-water mixtures with 10, 20 and 30 mol % of ethanol. Concerning pairwise interaction energies between molecules, it is found that water-water interactions become stronger, while ethanol-ethanol ones become significantly weaker in the mixtures than the corresponding values characteristic to the pure substances. Concerning the diffusion processes, for all concentrations the activation barrier of water and ethanol molecule become very similar to each other. Reorientation motions of water and ethanol become slower as ethanol concentration is increasing. Characteristic reorientational times of water in the mixtures are substantially longer than these values in the pure substance. On the other hand, this change for ethanol is only moderate. The reorientation motions of water (especially the ones related to the H-bonded interaction) become very similar for those of ethanol in the mixtures.
• ZnO is co-doped with Na+ and Si4+ in the ratio 2:1. The ratio was intentionally chosen so that net valence state of dopant theoretically matches that of host. This is to avoid dependence in the amount of oxygen vacancies/interstitials arising out of cationic valence state of the dopant. With such a combination, modifications in structural and optical properties do not depend on excess or deficit of the dopant charge state. For lower doping, Na+ ions behave as interstitial sites which enhance strain, lattice disorder and thereby creating defects. Formation of interstitial defects leads to reduction in bandgap energy and produce orange-red luminescence. For higher doping, Na+ starts substituting at Zn2+ site which helps in reducing strain and lattice disorder and thereby increases bandgap. Inspite of presence of Si4+ with higher charge, there is a gradual increase in oxygen vacancies due to lattice disorder.
• We study scattering of propagating microwave fields by a DC-voltage-biased Josephson junction. At sub-gap voltages, a small Josephson junction works merely as a non-linear boundary that can absorb, amplify, and diversely convert propagating microwaves. We find that in the leading-order perturbation theory of the Josephson coupling energy, the spectral density and quadrature fluctuations of scattered thermal and coherent radiation can be described in terms of the well-known $P(E)$ function. Applying this, we show how thermal and coherent radiation can be absorbed and amplified in a circuit with a resonance frequency. We also show when a coherent input can create a two-mode squeezed output. In addition, we evaluate scattering amplitudes between arbitrary photon-number (Fock) states, describing individual photon multiplication and absorption processes occuring at the junction.
• There are two possible ways of interpreting the seemingly stochastic nature of financial markets: the Efficient Market Hypothesis (EMH) and a set of stylized facts that drive the behavior of the markets. We show evidence for some of the stylized facts such as memory-like phenomena in price volatility in the short term, a power-law behavior and non-linear dependencies on the returns. Given this, we construct a model of the market using Markov chains. Then, we develop an algorithm that can be generalized for any N-symbol alphabet and K-length Markov chain. Using this tool, we are able to show that it's, at least, always better than a completely random model such as a Random Walk. The code is written in MATLAB and maintained in GitHub.
• Mar 20 2018 math.CT arXiv:1803.06651v1
We develop a notion of limit for dagger categories, that we show is suitable in the following ways: it subsumes special cases known from the literature; dagger limits are unique up to unitary isomorphism; a wide class of dagger limits can be built from a small selection of them; dagger limits of a fixed shape can be phrased as dagger adjoints to a diagonal functor; dagger limits can be built from ordinary limits in the presence of polar decomposition; dagger limits commute with dagger colimits in many cases.
• Core helium-burning red clump (RC) stars are excellent standard candles in the Milky Way: beyond 3 kpc, RC stars may have more precise distance estimates from spectrophotometry than from Gaia parallaxes. However, RC stars have $T_{\rm eff}$ and $\log g$ very similar to some red giant branch (RGB) stars. Especially for low-resolution R=2000 spectroscopic studies with $T_{\rm eff}$, $\log g$, and [Fe/H] estimated of limited precision, separating RC stars from RGB through established method can incur ~20% contamination. Recently, Hawkins et al. (2018) demonstrated that the additional information in single-epoch spectra, such as the C/N ratio, can be exploited to cleanly differentiate RC and RGB stars. In this second paper of the series, we establish a data-driven mapping from spectral flux space to independently determined asteroseismic parameters, the frequency and the period separations. From this, we identify 210,371 RC stars from the publicly available LAMOST DR3 and APOGEE DR14 data, with ~9% of contamination. We provide an RC sample of 92,249 stars with a contamination of only ~3%, by restricting the combined analysis to LAMOST stars with${\rm S/N}_{\rm pix} \ge 75$. This demonstrates that high-S/N, low-resolution spectra covering a broad wavelength range can identify RC samples at least as pristine as their high-resolution counterparts. As coming and ongoing surveys such as TESS, DESI, and LAMOST will continue to improve the overlapping training spectroscopic-asteroseismic sample, the method presented in this study provides an efficient and straightforward way to derive a vast yet pristine RC stars to reveal the 3D structure of the Milky Way.
• We construct a model of cubical type theory with a univalent and impredicative universe in a category of cubical assemblies. We show that the cubical assembly model does not satisfy the propositional resizing axiom.
• Various charge migration mechanisms in the DNA are studied within the framework of the Peyrard-Bishop-Holstein model which has been widely used to address charge dynamics in this macromolecule. To analyze these mechanisms we consider characteristic size and time scales of the fluctuations of the electronic and vibrational subsystems. It is shown, in particular, that due to substantial differences in these timescales polaron formation is unlikely within a broad range of temperatures. We demonstrate that at low temperatures electronic transport can be quasi-ballistic. For high temperatures, we propose an alternative to polaronic charge migration mechanism: the fluctuation-assisted one, in which the electron dynamics is governed by relatively slow fluctuations of the vibrational subsystem. We argue also that the discussed methods and mechanisms can be relevant for other organic macromolecular systems, such as conjugated polymers and molecular aggregates.
• Mar 20 2018 math.DG hep-th arXiv:1803.06646v1
We consider $G_2$-manifolds with an effective torus action that is multi-Hamiltonian for one or more of the defining forms. The case of $T^3$-actions is found to be distinguished. For such actions multi-Hamiltonian with respect to both the three- and four-form, we derive a Gibbons-Hawking type ansatz giving the geometry on an open dense set in terms a symmetric $3\times 3$-matrix of functions. This leads to particularly simple examples of explicit metrics with holonomy equal to $G_2$. We prove that the multi-moment maps exhibit the full orbit space topologically as a smooth four-manifold containing a trivalent graph as the image of the set of special orbits and describe these graphs in some complete examples.
• Selecting a set of alternatives based on the preferences of agents is an important problem in committee selection and beyond. Among the various criteria put forth for the desirability of a committee, Pareto optimality is a minimal and important requirement. As asking agents to specify their preferences over exponentially many subsets of alternatives is practically infeasible, we assume that each agent specifies a weak order on single alternatives, from which a preference relation over subsets is derived using some preference extension. We consider five prominent extensions (responsive, downward lexicographic, upward lexicographic, best, and worst). For each of them, we consider the corresponding Pareto optimality notion, and we study the complexity of computing and verifying Pareto optimal outcomes. We also consider strategic issues: for four of the set extensions, we present a linear-time, Pareto optimal and strategyproof algorithm that even works for weak preferences.
• We study the photon blockade effect in a coupled cavity system, which is formed by a linear cavity coupled to a Kerr-type nonlinear cavity via a photon-hopping interaction. We explain the physical phenomenon from the viewpoint of the conventional and unconventional photon blockade effects. The corresponding physical mechanisms of these two photon blockade effects are based on the anharmonicity in eigenenergy spectrum and the destructive quantum interference between two different transition paths, respectively. We find that the quantum interference effect also exists in the conventional photon blockade regime. Our results are confirmed by analytically and numerically solving the quantum master equation and calculating the second-order correlation function of the cavity fields. This model is general and hence it can be implemented in various experimental setups such as coupled optical cavities, coupled photon-magnon systems, and coupled superconducting resonators. We present some discussions on the experimental implementation.
• We study the invariant Planck scale correction to the white dwarf dynamics. We have considered the modified dispersion relation and the cut-off to the maximum possible momentum/energy of the non-interacting Fermi gas particles as a signal of appearance of the effects of Quantum Gravity phenomena. With such a modification the expression for the degenerate pressure of white dwarf gets modified accordingly and so does the Chandrasekhar mass limit. The mass-radius M-R plot shows that the modified/ corrected radius of the white dwarf can be greater than, equal to and smaller than the usual special relativity (SR) value for particular masses. We found that the Chandrasekhar mass limit gets a positive correction i.e, the maximum possible mass for white dwarf increases in this formalism. The correction is purely perturbative in the SR limit which is quite unusual for a theory having an ultraviolet energy cut-off. Therefore this correction is solely because of the modified dispersion relation. The value of the obtained degenerate pressure for a given mass is found to be greater than, equal to and smaller than the usual special relativity (SR) value for particular masses as expected. It is shown by Mishra et al. that the Stefan-Boltzmann law gets a correction in such a theory with an ultraviolet cut-off. Using this result we have calculated the luminosity of the white dwarf by taking the model of partially degenerate gas and considering the modified radiative envelope equation. In such an analysis we observe that the pressure for a given mass and temperature value is less than that predicted by the usual SR theory. The luminosity also gets a negative correction. The correction to luminosity is nonperturbative as expected for such a theory.

Luis Cruz Mar 16 2018 15:34 UTC

Related Work:

- [Performance-Based Guidelines for Energy Efficient Mobile Applications](http://ieeexplore.ieee.org/document/7972717/)
- [Leafactor: Improving Energy Efficiency of Android Apps via Automatic Refactoring](http://ieeexplore.ieee.org/document/7972807/)

Dan Elton Mar 16 2018 04:36 UTC

Code is open source and available at :
[https://github.com/delton137/PIMD-F90][1]

[1]: https://github.com/delton137/PIMD-F90

Danial Dervovic Mar 01 2018 12:08 UTC

Hello again Māris, many thanks for your patience. Your comments and questions have given me much food for thought, and scope for an amended version of the paper -- please see my responses below.

Please if any of the authors of [AST17 [arXiv:1712.01609](https://arxiv.org/abs/1712.01609)] have any fu

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igorot Feb 28 2018 05:19 UTC

The Igorots built an [online community][1] that helps in the exchange, revitalization, practice, and learning of indigenous culture. It is the first and only Igorot community on the web.

[1]: https://www.igorotage.com/

Beni Yoshida Feb 13 2018 19:53 UTC

This is not a direct answer to your question, but may give some intuition to formulate the problem in a more precise language. (And I simplify the discussion drastically). Consider a static slice of an empty AdS space (just a hyperbolic space) and imagine an operator which creates a particle at some

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Abhinav Deshpande Feb 10 2018 15:42 UTC

I see. Yes, the epsilon ball issue seems to be a thorny one in the prevalent definition, since the gate complexity to reach a target state from any of a fixed set of initial states depends on epsilon, and not in a very nice way (I imagine that it's all riddled with discontinuities). It would be inte

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Elizabeth Crosson Feb 10 2018 05:49 UTC

Thanks for the correction Abhinav, indeed I meant that the complexity of |psi(t)> grows linearly with t.

Producing an arbitrary state |phi> exactly is also too demanding for the circuit model, by the well-known argument that given any finite set of gates, the set of states that can be reached i

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Abhinav Deshpande Feb 09 2018 20:21 UTC

Elizabeth, interesting comment! Did you mean to say that the complexity of $U(t)$ increases linearly with $t$ as opposed to exponentially?

Also, I'm confused about your definition. First, let us assume that the initial state is well defined and is $|\psi(0)\rangle$.
If you define the complexit

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Elizabeth Crosson Feb 08 2018 04:27 UTC

The complexity of a state depends on the dynamics that one is allowed to use to generate the state. If we restrict the dynamics to be "evolving according a specific Hamiltonian H" then we immediately have that the complexity of U(t) = exp(i H t) grows exponentially with t, up until recurrences that

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Danial Dervovic Feb 05 2018 15:03 UTC

Thank you Māris for the extremely well thought-out and articulated points here.

I think this very clearly highlights the need to think explicitly about the precompute time if using the lifting to directly simulate the quantum walk, amongst other things.

I wish to give a well-considered respons

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