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    The sign problem appears in lattice QCD as soon as a non-zero chemical potential is introduced. This prevents direct simulations to determine the phase structure of the strongly interacting matter. Complex Langevin methods have been successfully used for various models or approximations of QCD. However, in some scenarios it converges to incorrect results. We present developments of our new method that helps to improve the convergence by keeping the system closer to the SU(3) manifold and discuss preliminary tests and results.
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    We argue that the requirement of a finite entanglement entropy of quantum degrees of freedom across a boundary surface is closely related to the phenomenon of running spectral dimension, universal in approaches to quantum gravity. If quantum geometry hinders diffusion, for instance when its structure at some given scale is discrete or too rough, then the spectral dimension of spacetime vanishes at that scale and the entropy density blows up. A finite entanglement entropy is a key ingredient in deriving Einstein gravity in a semi-classical regime of a quantum-gravitational theory and, thus, our arguments strengthen the role of running dimensionality as an imprint of quantum geometry with potentially observable consequences.
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    We propose a scheme for preparation of large-scale entangled $W$ states based on the fusion mechanism via quantum Zeno dynamics. By sending two atoms belonging to an $n$-atom $W$ state and an $m$-atom $W$ state, respectively, into a vacuum cavity (or two separate cavities), we may obtain a ($n+m-2$)-atom $W$ state via detecting the two-atom state after interaction. The present scheme is robust against both spontaneous emission of atoms and decay of cavity, and the feasibility analysis indicates that it can also be realized in experiment.
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    Modern bandgap engineered electronic devices are typically made of multi-semiconductor multi-layer heterostructures that pose a major challenge to silicon-era characterization methods. As a result, contemporary bandgap engineering relies mostly on simulated band structures that are hardly ever verified experimentally. Here, we present a method that experimentally evaluates bandgap, band offsets, and electric fields, in complex multi-semiconductor layered structures and it does so simultaneously in all the layers. The method uses a modest optical photocurrent spectroscopy setup at ambient conditions. The results are analyzed using a simple model for electro-absorption. As an example, we apply the method to a typical GaN high electron mobility transistor structure. Measurements under various external electric fields allow us to experimentally construct band diagrams, not only at equilibrium, but also under any other working conditions of the device. The electric fields are then used to obtain the charge carrier density and mobility in the quantum well as a function of the gate voltage over the entire range of operating conditions of the device. The principles exemplified here may serve as guidelines for the development of methods for simultaneous characterization of all the layers in complex, multi-semiconductor structures.
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    Assembly of quantum nanophotonic systems with plasmonic resonators are important for fundamental studies of single photon sources as well as for on-chip information processing. In this work, we demonstrate controllable nanoassembly of gold nanospheres with ultra-bright quantum emitters in 2D layered hexagonal boron nitride (hBN). We utilize an atomic force microscope (AFM) tip to precisely position gold nanospheres to close proximity of the quantum emitters and observe the resulting emission enhancement and fluorescence lifetime reduction. A fluorescence enhancement of over 300% is achieved experimentally for quantum emitters in hBN, with a radiative quantum efficiency of up to 40% and a saturated count rate in excess of 5 million counts/s. Our results are promising for future employment of quantum emitters in hBN for integrated nanophotonic devices and plasmonic based nanosensors.
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    The tremendous advances in computer science in the last few decades have provided the platform to address and solve complex problems using interdisciplinary research. In this paper, we investigate how the extent of interdisciplinarity in computer science domain (which is further divided into 24 research fields) has changed over the last 50 years. To this end, we collect a massive bibliographic dataset with rich metadata information. We start with quantifying interdisciplinarity of a field in terms of the diversity of topics and citations. We then analyze the effect of interdisciplinary research on the scientific impact of individual fields and observe that highly disciplinary and highly interdisciplinary papers in general have a low scientific impact; remarkably those that are able to strike a balance between the two extremes eventually land up having the highest impact. Further, we study the reciprocity among fields through citation interactions and notice that links from one field to related and citation-intensive fields (fields producing large number of citations) are reciprocated heavily. A systematic analysis of the citation interactions reveals the life trajectory of a research field, which generally undergoes three phases -- a growing phase, a matured phase and an interdisciplinary phase. The combination of metrics and empirical observations presented here provides general benchmarks for future studies of interdisciplinary research activities in other domains of science.
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    We study a system of atoms that are laser-driven to $nD_{3/2}$ Rydberg states and assess how accurately they can be mapped onto spin-$1/2$ particles for the quantum simulation of anisotropic Ising magnets. Using non-perturbative calculations of the pair interaction potentials between two atoms in the presence of both electric and magnetic fields, we emphasize the importance of a careful selection of the experimental parameters in order to maintain the Rydberg blockade and avoid excitation of unwanted Rydberg states. We then benchmark these theoretical observations against experiments using two atoms. Finally, we show that in these conditions, the experimental dynamics observed after a quench is in good agreement with numerical simulations of spin-1/2 Ising models in systems with up to 49 spins, for which direct numerical simulations become intractable.
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    One dimensional Cherenkov processes in ferromagnetic isolators have been studied with perturbation theory under the constraint condition of conservation of energy and momentum. It is shown that the magnon-phonon interaction channels are limited and wave number dependent, which result in respectively the $k^{2}$ and $k^{4}$ dependence of the transition probabilities and the relaxation times of the long wavelength magnons. The reciprocal of relaxation time between the magnons and phonons, $1/\tau_{pm}$, is found to be a linearly increasing function of the temperature as $T>$ 70 K. Based on the Sanders and Walton (SW) model, we further show that the difference of temperature distributions of $k$-magnons becomes pronounced once the wavelength is below the critical wave vector $k_{mc}$, which in YIG is estimated as $0.066\pi/a$.
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    Time evolution of initially prepared entangled state in the system of coupled quantum dots has been analyzed by means of two different theoretical approaches: equations of motion for the all orders localized electron correlation functions, considering interference effects, and kinetic equations for the pseudo-particle occupation numbers with constraint on the possible physical states. Results obtained by means of different approaches were carefully analyzed and compared with each other. Revealed direct link between concurrence (degree of entanglement) and quantum dots pair correlation functions allowed us to follow the changes of entanglement during time evolution of the coupled quantum dots system. It was demonstrated that the degree of entanglement can be controllably tuned during the time evolution of quantum dots system.
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    We study the nodal length of random toral Laplace eigenfunctions ("arithmetic random waves") restricted to decreasing domains ("shrinking balls"), all the way down to Planck scale. We find that, up to a natural scaling, for "generic" energies the variance of the restricted nodal length obeys the same asymptotic law as the total nodal length, and these are asymptotically fully correlated. This, among other things, allows for a statistical reconstruction of the full toral length based on partial information. One of the key novel ingredients of our work, borrowing from number theory, is the use of bounds for the so-called spectral Quasi-Correlations, i.e. unusually small sums of lattice points lying on the same circle.
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    With rotating-wave approximation (RWA), we show in this paper that exciton transmission in a one-dimensional two-level molecule chain embedded in a cavity can be enhanced or suppressed by strong cavity-chain couplings. This exciton transmission is closely related to the number of molecules and the distribution of molecular exciton energy. In addition, we propose a proposal to enhance the exciton transmission by quantum-jump-based feedback. These results may find applications in experiments of exciton transmission in organic materials.
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    Let $M$ be a compact connected smooth Riemannian $n$-manifold with boundary. We combine Gromov's amenable localization technique with the Poincaré duality to study the traversally generic geodesic flows on $SM$, the space of the spherical tangent bundle. Such flows generate stratifications of $SM$, governed by rich universal combinatorics. The stratification reflects the ways in which the geodesic flow trajectories interact with the boundary $\d(SM)$. Specifically, we get lower estimates of the numbers of connected components of these flow-generated strata of any given codimension $k$. These universal bounds are expressed in terms of the normed homology $H_k(M; \R)$ and $H_k(DM; \R)$, where $DM = M\cup_{\d M} M$ denotes the double of $M$. The norms here are the Gromov simplicial semi-norms in homology. The more complex the metric on $M$ is, the more numerous the strata of $SM$ and $S(DM)$ are. So one may regard our estimates as analogues of the Morse inequalities for the geodesics on manifolds with boundary. It turns out that some close relatives of the normed homology spaces form obstructions to the existence of globally $k$-convex traversally generic metrics on $M$.
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    A negative reflecting mirror converts a wave of positive phase velocity into its negative counterpart and vice versa. Whatever the complexity of the propagation medium, the negatively reflected wave field focuses back towards the initial source location, thereby mimicking a phase conjugation operation while being a fully passive process. In this paper, we experimentally demonstrate this phenomenon with elastic waves in a 2D billiard and in a disordered plate by means of laser interferometry. These proof-of-concept experiments show that negative reflection can be a tool of choice for the control and focusing of waves in complex environments.
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    The Conformal Standard Model (CSM) is a minimal extension of the Standard Model of Particle Physics based on the assumed absence of large intermediate scales between the TeV scale and the Planck scale, which incorporates only right-chiral neutrinos and a new complex scalar in addition to the usual SM degrees of freedom, but no other features such as supersymmetric partners. In this paper, we present a comprehensive quantitative analysis of this model, and show that all outstanding issues of particle physics proper can in principle be solved `in one go' within this framework. This includes in particular the stabilization of the electroweak scale, `minimal' leptogenesis and the explanation of Dark Matter, with a small mass and very weakly interacting Majoron as the Dark Matter candidate (for which we propose to use the name `minoron'). The main testable prediction of the model is a new and almost sterile scalar boson that would manifest itself as a narrow resonance in the TeV region. We give a representative range of parameter values consistent with our assumptions and with observation.
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    In this work we apply reduced basis methods for parametric PDEs to an isogeometric formulation based on NURBS. The motivation for this work is an integrated and complete work pipeline from CAD to parametrization of domain geometry, then from full order to certified reduced basis solution. IsoGeometric Analysis (IGA) is a growing research theme in scientific computing and computational mechanics, as well as reduced basis methods for parametric PDEs. Their combination enhances the solution of some class of problems, especially the ones characterized by parametrized geometries we introduced in this work. This work wants to demonstrate that it is also possible for some class of problems to deal with affine geometrical parametrization combined with a NURBS IGA formulation. This is what this work brings as original ingredients with respect to other works dealing with reduced order methods and IGA. In this work we show a certification of accuracy and a complete integration between IGA formulation and parametric certified greedy RB formulation.
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    Both direct and HAL QCD methods are currently used to study the hadron interactions in lattice QCD. In the direct method, the eigen-energy of two-particle is measured from the temporal correlation. Due to the contamination of excited states, however, the direct method suffers from the fake eigen-energy problem, which we call the "mirage problem," while the HAL QCD method can extract information from all elastic states by using the spatial correlation. In this work, we further investigate systematic uncertainties of the HAL QCD method such as the quark source operator dependence, the convergence of the derivative expansion of the non-local interaction kernel, and the single baryon saturation, which are found to be well controlled. We also confirm the consistency between the HAL QCD method and the Lüscher's finite volume formula. Based on the HAL QCD potential, we quantitatively confirm that the mirage plateau in the direct method is indeed caused by the contamination of excited states.
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    For a proper, smooth scheme $X$ over a $p$-adic field $K$, we show that any proper, flat, semistable $\mathcal{O}_K$-model $\mathcal{X}$ of $X$ whose logarithmic de Rham cohomology is torsion free determines the same $\mathcal{O}_K$-lattice inside $H^i_{dR}(X/K)$ and, moreover, that this lattice is functorial in $X$. For this, we extend the results of Bhatt--Morrow--Scholze on the construction and the analysis of an $A_{inf}$-valued cohomology theory of $p$-adic formal, proper, smooth $\mathcal{O}_{\overline{K}}$-schemes $\mathfrak{X}$ to the semistable case. The relation of the $A_{inf}$-cohomology to the $p$-adic étale and the logarithmic crystalline cohomologies allows us to reprove the semistable conjecture of Fontaine--Jannsen.
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    For some theoretical and experimental considerations, the relatively light Majorana neutrinos at the GeV scale have been attracting some interest. In this article we consider a scenario with only one Majorana neutrino $N$, negligible mixing with the active neutrinos $\nu_{L}$, where the Majorana neutrino interactions could be described in a model independent approach based on an effective theory. Under such a framework, we particularly study the feasibility of observing the $N$ with mass in the range 0$-$30 GeV via the process $e^+ e^- \to \nu N \to\gamma + \slashed E$ in the future Belle-II and ILC experiments. The results show that it is unpromising for Belle-II to observe the signal, while ILC may easily make a discovery for the Majorana neutrino.
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    A modulated wideband converter (MWC) has been introduced as a sub-Nyquist sampler that exploits a set of fast alternating pseudo random (PR) signals. Through parallel sampling branches, an MWC compresses a multiband spectrum by mixing it with PR signals in the time domain, and acquires its sub-Nyquist samples. Previously, the ratio of compression was fully dependent on the specifications of PR signals. That is, to further reduce the sampling rate without information loss, faster and longer-period PR signals were needed. However, the implementation of such PR signal generators results in high power consumption and large fabrication area. In this paper, we propose a novel aliased modulated wideband converter (AMWC), which can further reduce the sampling rate of MWC with fixed PR signals. The main idea is to induce intentional signal aliasing at the analog-to-digital converter (ADC). In addition to the first spectral compression by the signal mixer, the intentional aliasing compresses the mixed spectrum once again. We demonstrate that AMWC reduces the number of sampling branches and the rate of ADC for lossless sub-Nyquist sampling without needing to upgrade the speed or period of PR signals. Conversely, for a given fixed number of sampling branches and sampling rate, AMWC improves the performance of signal reconstruction.
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    We investigate the simultaneous effect of a static homogeneous external magnetic field and a background gas medium on the quasi-localization of the dust particles -- characterized quantitatively by cage correlation functions -- in strongly coupled two-dimensional Yukawa systems. We apply the Langevin dynamics computer simulation method in which the frictional and Lorentz forces are taken into account. Both the presence of the magnetic field or the friction originating from the background gas, when acting alone, increase the caging time. When present simultaneously, however, we find that their effects combine in a nontrivial manner and act against each other within a window of the parameter values.
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    We report on the development of MPI-AMRVAC version 2.0, which is an open-source framework for parallel, grid-adaptive simulations of hydrodynamic and magnetohydrodynamic (MHD) astrophysical applications. The framework now supports radial grid stretching in combination with adaptive mesh refinement (AMR). The advantages of this combined approach are demonstrated with one-dimensional, two-dimensional and three-dimensional examples of spherically symmetric Bondi accretion, steady planar Bondi-Hoyle-Lyttleton flows, and wind accretion in Supergiant X-ray binaries. Another improvement is support for the generic splitting of any background magnetic field. We present several tests relevant for solar physics applications to demonstrate the advantages of field splitting on accuracy and robustness in extremely low plasma $\beta$ environments: a static magnetic flux rope, a magnetic null-point, and magnetic reconnection in a current sheet with either uniform or anomalous resistivity. Our implementation for treating anisotropic thermal conduction in multi-dimensional MHD applications is also described, which generalizes the original slope limited symmetric scheme from 2D to 3D. We perform ring diffusion tests that demonstrate its accuracy and robustness, and show that it prevents the unphysical thermal flux present in traditional schemes. The improved parallel scaling of the code is demonstrated with 3D AMR simulations of solar coronal rain, which show satisfactory strong scaling up to 2000 cores. Other framework improvements are also reported: the modernization and reorganization into a library, the handling of automatic regression tests, the use of inline/online Doxygen documentation, and a new future-proof data format for input/output
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    Geodesics (by definition) have intrinsic 4-acceleration zero. However, when expressed in terms of coordinates, the coordinate acceleration d^2x^i/dt^2 can very easily be non-zero, and the coordinate velocity dx^i/dt can behave unexpectedly. The situation becomes extremely delicate in the near-horizon limit --- where an inappropriate choice of coordinates can quite easily lead to significant confusion. We shall carefully explore the relative merits of horizon penetrating versus horizon-non-penetrating coordinates; arguing that in the near-horizon limit the coordinate acceleration d^2x^i/dt^2 is best interpreted in terms of horizon-penetrating coordinates.
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    We propose a covariant holographic entanglement negativity conjecture for time dependent mixed states of adjacent subsystems in conformal field theories dual to non-static bulk AdS configurations. Application of our conjecture to holographic $\mathrm{CFT_{1+1}}$s dual to non-extremal and extremal rotating BTZ black holes exactly reproduces the universal part of the entanglement negativity obtained through the replica technique, in the large central charge limit. This example provides compelling evidence for the universality of our conjecture.
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    We prove that the Fraïssé limit of a Fraïssé class $\mathcal C$ is the (unique) countable structure whose isomorphism type is comeager (with respect to a certain logic topology) in the Baire space of all structures whose age is contained in $\mathcal C$ and which are defined on a fixed countable universe. In particular, the set of groups isomorphic to Hall's universal group is comeager in the space of all countable locally finite groups and the set of fields isomorphic to the algebraic closure of $\mathbb F_p$ is comeager in the space of countable fields of characteristic $p$.
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    Mechanical or electromechanical amplifiers can exploit the high-Q and low noise features of mechanical resonance, in particular when parametric excitation is employed. Multi-frequency parametric excitation introduces tunability and is able to project weak input signals on a selected resonance. The present paper addresses multi degree of freedom mechanical amplifiers or resonators whose analysis and features require treatment of the spatial as well as temporal behavior. In some cases, virtual electronic coupling can alter the given topology of the resonator to better amplify specific inputs. An analytical development is followed by a numerical and experimental sensitivity and performance verifications, illustrating the advantages and disadvantages of such topologies.
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    In this paper, we construct some maps related to the motivic Galois action on depth-graded motivic multiple zeta values. And from these maps we give some short exact sequences about depth-graded motivic multiple zeta values in depth two and three. In higher depth we conjecture that there are exact sequences of the same type. And we will show from three conjectures about depth-graded motivic Lie algebra we can nearly deduce the exact sequences conjectures in higher depth. At last we give a new proof of the result that the modulo zeta(2)$ version motivic double zeta values is generated by the totally odd part. And we reduce the well-known conjecture that the modulo zeta (2) version motivic triple zeta values is generated by the totally odd part to an isomorphism conjecture in linear algebra.
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    Forecasting thermal load is a key component for the majority of optimization solutions for controlling district heating and cooling systems. Recent studies have analysed the results of a number of data-driven methods applied to thermal load forecasting, this paper presents the results of combining a collection of these individual methods in an expert system. The expert system will combine multiple thermal load forecasts in a way that it always tracks the best expert in the system. This solution is tested and validated using a thermal load dataset of 27 months obtained from 10 residential buildings located in Rottne, Sweden together with outdoor temperature information received from a weather forecast service. The expert system is composed of the following data-driven methods: linear regression, extremely randomized trees regression, feed-forward neural network and support vector machine. The results of the proposed solution are compared with the results of the individual methods.
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    We say that a positively homogeneous function admits a saddle representation by linear functions iff it admits both an inf-sup-representation and a sup-inf-representation with the same two-index family of linear functions. In the paper we show that each continuous positively homogeneous function can be associated with a two-index family of linear functions which provides its saddle representation. We also establish characteristic properties of those two-index families of linear functions which provides saddle representations of functions belonging to the subspace of Lipschitz continuous positively homogeneous functions as well as the subspaces of difference sublinear and piecewise linear functions.
  • Oct 18 2017 q-fin.EC arXiv:1710.06132v1
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    This study proposes the concept of disruptive firms: they are firms with market leadership that deliberate introduce new and improved generations of durable goods that destroy, directly or indirectly, similar products present in markets in order to support their competitive advantage and/or market leadership. These disruptive firms support technological and industrial change and induce consumers to buy new products to adapt to new socioeconomic environment. In particular, disruptive firms generate and spread path-breaking innovations in order to achieve and sustain the goal of a (temporary) profit monopoly. This organizational behaviour and strategy of disruptive firms support technological change. This study can be useful for bringing a new perspective to explain and generalize one of the determinants that generates technological and industrial change. Overall, then this study suggests that one of the general sources of technological change is due to disruptive firms (subjects), rather than disruptive technologies (objects), that generate market shifts in a Schumpeterian world of innovation-based competition.
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    An element $\alpha \in \mathbb F_{q^n}$ is \emphnormal if $\mathcal{B} = \{\alpha, \alpha^q, \ldots, \alpha^{q^{n-1}}\}$ forms a basis of $\mathbb F_{q^n}$ as a vector space over $\mathbb F_{q}$; in this case, $\mathcal{B}$ is a normal basis of $\mathbb F_{q^n}$ over $\mathbb F_{q}$. The notion of $k$-normal elements was introduced in Huczynska et al (2013). Using the same notation as before, $\alpha$ is $k$-normal if $\mathcal{B}$ spans a co-dimension $k$ subspace of $\mathbb F_{q^n}$. It can be shown that $1$-normal elements always exist in $\mathbb F_{q^n}$, and Huczynska et al (2013) show that elements that are simultaneously primitive and $1$-normal exist for $q \geq 3$ and for large enough $n$ when $\gcd(n,q) = 1$ (we note that primitive $1$-normals cannot exist when $n=2$). In this paper, we complete this theorem and show that primitive, $1$-normal elements of $\mathbb F_{q^n}$ over $\mathbb F_{q}$ exist for all prime powers $q$ and all integers $n \geq 3$, thus solving Problem 6.3 from Huczynska, et al (2013).
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    We investigate generalized notions of the nerve complex for a collection of subsets of a topological space. For a simplicial complex $\Delta$, we show that the homologies of these higher nerve complexes determine the depth of the Stanley-Reisner ring $k[\Delta]$ as well as the $f$-vector and $h$-vector of $\Delta$. We develop a strengthened version of the higher nerve complexes, called the nervous system of $\Delta$, that allows one to reconstruct $\Delta$. We present, as an application, a formula for computing regularity of monomial ideals and a new definition of "combinatorial depth" for local schemes.
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    Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection of models of $\Sigma$ with underlying set $\mathbb{N}$. Restricting to $\mathcal{L}_{\omega, \omega}(L)$, this answers an open question of Gaifman from 1964, via a translation between $S_\infty$-invariant measures and Gaifman's symmetric measure-models with strict equality. It also extends the known characterization in the case where $\Sigma$ implies a Scott sentence. To establish our result, we introduce machinery for building invariant measures from a directed system of countable structures with measures.
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    It is well known that the umbilic points of minimal surfaces in spaces of constant sectional curvature consist only of isolated points unless the surface is totally umbilic on some connected component, as for example the Hopf form is holomorphic. In this note, we prove that on Willmore surfaces in codimension one the umbilic set is locally a one dimensional real-analytic manifold without boundary or an isolated point.
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    I give a simple example of a local realistic problem with free will of observers and no detection loophole, but where the Bell inequality cannot be proved. The trick is based on random variables modeled by functions whose sum does not exist due to incompatibility of their domains.
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    Low-level programming languages such as C and C++ are vulnerable to errors related to the misuse of memory. Such errors include bounds overflows, sub-object bounds overflows, use-after-free, "reuse"-after-free and type confusion. These errors account for many of the exploits in programs implemented in such unsafe languages. Most bug detection tools (sanitizers) tend to focus only on detecting specific classes of errors, e.g. bounds overflow or type confusion only. In this paper, we present a new type confusion and memory error sanitizer based on dynamically checking the "effective type" (a.k.a. the dynamic type) of C/C++ objects at runtime. We show that this "effective type sanitizer" (EffectiveSan) can detect the memory misuse errors mentioned above, all while using the same underlying methodology (dynamic typing). Our approach uses a combination of low-fat pointers, type meta data and type check instrumentation. We also have a novel approach to preventing sub-object bound overflow errors leveraging on the C/C++ types. We show EffectiveSan finds type confusion, (sub-)object bounds overflow, and use-after-free bugs in the SPEC2006 benchmark suite.
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    We generalize the Bialynicki-Birula decomposition to singular schemes and apply it to the Hilbert scheme of points on an affine space. We find an infinite family of small, elementary and generically smooth components of the Hilbert scheme of points of the affine four-space. Our method gives easily verifiable sufficient conditions for proving that a point of the Hilbert scheme is smooth and lies on an elementary component. We also present a necessary condition for smoothability of a finite subscheme given by a homogeneous ideal.
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    Helgason showed that a given measure $f\in M(G)$ on a compact group $G$ should be in $L^2(G)$ automatically if all random Fourier series of $f$ are in $M(G)$. We explore a natural analogue of the theorem in the framework of compact quantum groups and apply the obtained results to study complete representability problem for convolution algebras of compact quantum groups as an operator algebra.
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    We study the quantity $$ \tau_n,k:=\frac|T_n^(k)(\omega_n,k)|T_n^(k)(1)\,, $$ where $T_n$ is the Chebyshev polynomial of degree $n$, and $\omega_{n,k}$ is the rightmost zero of $T_n^{(k+1)}$. Since the absolute values of the local maxima of $T_n^{(k)}$ increase monotonically towards the end-points of $[-1,1]$, the value $\tau_{n,k}$ shows how small is the largest critical value of $\,T_n^{(k)}\,$ relative to its global maximum $\,T_n^{(k)}(1)$. In this paper, we improve and extend earlier estimates by Erdős--Szegő, Eriksson and Nikolov in several directions. Firstly, we show that the sequence $\,\{\tau_{n,k}\}_{n=k+2}^{\infty}$ is monotonically decreasing in $n$, hence derive several sharp estimates, in particular $$ \tau_n,k \le \begincases \tau_k+4,k = \frac12k+1\,\frac3k+3\,, & n \ge k+4\u2009\tau_k+6,k = \frac12k+1\u2009(\frac5k+5)^2 \beta_k\,, & n \ge k+6\,, \endcases $$ where $\beta_k < \frac{2+\sqrt{10}}{5} \approx 1.032$. We also obtain an upper bound which is uniform in $n$ and $k$, and that implies in particular $$ \tau_n,k ≈\big(\frac2e\big)^k, \quad n \ge k^3/2; \qquad \tau_n,n-m ≈\big(\fracem2\big)^m/2 n^-m/2; \qquad \tau_n,n/2 ≈\big(\frac4\sqrt27\big)^n/2. $$ Finally, we derive the exact asymptotic formulae for the quantities $$ \tau_k^* := \lim_n\to∞\tau_n,k \quad \mbox and \quad \tau_m^** := \lim_n\to∞ n^m/2 \tau_n,n-m\,, $$ which show that our upper bounds for $\tau_{n,k}$ and $\tau_{n,n-m}$ are asymptotically correct with respect to the exponential terms given above.
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    There is the widespread belief that Agile neglects the product quality. This lack of understanding how Agile processes assure the quality of the product prevents especially companies from regulated domains from an adoption of Agile. This work aims to identify which Agile Practices contribute towards product quality. Hence, data from a survey study is analyzed to identify Ag-ile Practices which are beneficial or harmful for the quality of the product. From 49 practices that were used in the survey so far, 36 were perceived to have a positive impact on product quality, while four practices were rated as being harmful. The results enrich understanding of how product quality can be achieved in Agile, and support selection of practices to improve quality.
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    To model a realistic situation for the beginning we consider massive real scalar $\phi^4$ theory in a (1+1)-dimensional asymptotically static Minkowski spacetime with an intermediate stage of expansion. To have an analytic headway we assume that scalars have a big mass. At past and future infinities of the background we have flat Minkowski regions which are joint by the inflationary expansion region. We use the tree-level Keldysh propagator in the theory in question to calculate the expectation value of the stress-energy tensor which is, thus, due to the excitations of the zero-point fluctuations. Then we show that even for large mass, if the de Sitter expansion stage is long enough, the quantum loop corrections to the expectation value of the stress-energy tensor are not negligible in comparison with the tree-level contribution. That is revealed itself via the excitation of the higher-point fluctuations of the exact modes: During the expansion stage a non-zero particle number density for the exact modes is generated. This density is not Plankian and serves as a quench which leads to a thermalization in the out Minkowski stage.
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    We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical simulations in one and two spatial dimensions that suggest that oscillations are detrimental to invasion behaviour of the species.
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    It is well known that many geometric properties of Schubert varieties of type $A$ can be interpreted combinatorially. Given two permutations $w,x\in S_n$ we give a combinatorial consequence of the property that the smooth locus of the Schubert variety $X_w$ contains the Schubert cell $Y_x$. This is a necessary ingredient for the interpretation of recent representation-theoretic results of the author with Mínguez in terms of identities of Kazhdan--Lusztig polynomials.
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    Due to competing long range ferromagnetic order, the transition metals Fe, Co and Ni are not superconductors at ambient pressure. While superconductivity was observed in a non-magnetic phase of Fe, stabilized under pressure, it is yet to be discovered in Co and Ni under any experimental conditions. Here, we report emergence of superconductivity in the recently discovered high-density nonmagnetic face centered cubic phase in Co thin films below a transition temperature (Tc) of ~5.4 K, as revealed in experiments based on point-contact spectroscopy and resistance, and four-probe measurements of resistance at ambient pressure. We confirm the non-magnetic nature of the dense fcc phase of Co within first-principles density functional theory, and show that its superconductivity below 5 K originates from anomalous softening of zone-boundary phonons and their enhanced coupling with electrons upon biaxial strain.
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    The peculiar velocity field can be used to study the large-scale distribution of matter in the local universe and test cosmological models. However, present measurements of peculiar velocities are based on empirical distance indicators, which introduce large uncertainties. In this paper, we propose a method to derive the peculiar velocities, which bases on the distances measured from gravitational waves and the redshifts inferred from the host galaxies. Using the first gravitational wave event GW170817 from binary neutron star merger, we find that the peculiar velocity of the host galaxy NGC 4993 is $-275~\rm km~s^{-1}$, if the Hubble constant from Planck Collaboration is used. In future, with the uncertainty of the distance of GW events reducing to $0.1 \%$, the uncertainty of the peculiar velocity can be reduced to $\sim 10$ km/s at 100 Mpc. With accumulated GW events being observed, we can reconstruct the peculiar velocity field, which can be used to test the gravitational-instability paradigm and the $\Lambda$CDM model.
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    For a new class of algebras, called $EMV$-algebras, every idempotent element $a$ determines an $MV$-algebra which is important for the structure of the $EMV$-algebra. Therefore, instead of standard homomorphisms of $EMV$-algebras, we introduce $EMV$-morphisms as a family of $MV$-homomorphisms from $MV$-algebras $[0,a]$ into other ones. $EMV$-morphisms enable us to study categories of $EMV$-algebras where objects are $EMV$-algebras and morphisms are special classes of $EMV$-morphisms. The category is closed under product. In addition, we define free $EMV$-algebras on a set $X$ with respect to $EMV$-morphisms. If $X$ is finite, then the free $MV$-algebra on $X$ is a free $EMV$-algebras. For an infinite set $X$, the same is true introducing a so-called weakly free $EMV$-algebra.
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    In their paper, Li et al. [Nat. Commun. 8, 704 (2017)], analyse the Fermi surface of the trilayer nickelate La$_4$Ni$_3$O$_{10}$ using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) band structure calculations. The study describes the similarities and differences between the low-energy electronic structure of layered cuprates and nickelates; nonetheless, we find critical inconsistencies between the ARPES and DFT calculations based on a correctly simulated orthorhombic $Bmab$ phase of La$_4$Ni$_3$O$_{10}$, which refute the main claim that "La$_4$Ni$_3$O$_{10}$ has no pseudogap in the $d_{x^2-y^2}$ band, while it has an extra band of principally $d_{3z^2-r^2}$ orbital character, which presents a low temperature energy gap." We show that orthorhombic La$_4$Ni$_3$O$_{10}$ exhibits no pseudogap and that reconciliation between the ARPES data reported by Li et al. and the DFT band structure requires that La$_4$Ni$_3$O$_{10}$ is monoclinic at low-temperature, indicating it likely undergoes a displacive transition. Only the monoclinic phase exhibits the observed pseudogap.
  • PDF
    We will extend a recent result of B.~Choi and P.~Daskalopoulos (\citeCD). For any $n\ge 3$, $0<m<\frac{n-2}{n}$, $m\ne\frac{n-2}{n+2}$, $\beta>0$ and $\lambda>0$, we prove the higher order expansion of the radially symmetric solution $v_{\lambda,\beta}(r)$ of $\frac{n-1}{m}\Delta v^m+\frac{2\beta}{1-m} v+\beta x\cdot\nabla v=0$ in $\mathbb{R}^n$, $v(0)=\lambda$, as $r\to\infty$. As a consequence for any $n\ge 3$ and $0<m<\frac{n-2}{n}$ if $u$ is the solution of the equation $u_t=\frac{n-1}{m}\Delta u^m$ in $\mathbb{R}^n\times (0,\infty)$ with initial value $0\le u_0\in L^{\infty}(\mathbb{R}^n)$ satisfying $u_0(x)^{1-m}= \frac{2(n-1)(n-2-nm)}{(1-m)\beta |x|^2}\left(\log |x|-\frac{n-2-(n+2)m}{2(n-2-nm)}\log (\log |x|)+K_1+o(1))\right)$ as $|x|\to\infty$ for some constants $\beta>0$ and $K_1\in\mathbb{R}$, then as $t\to\infty$ the rescaled function $\widetilde{u}(x,t)=e^{\frac{2\beta}{1-m}t}u(e^{\beta t}x,t)$ converges uniformly on every compact subsets of $\mathbb{R}^n$ to $v_{\lambda_1,\beta}$ for some constant $\lambda_1>0$.
  • PDF
    We study the chiral magnetic effect for fermions with a small mass, which could be realized in slightly distorted Dirac semimetals. We give a formula for the intra-cone transition and find that the small mass allows for the helicity flipping in intra-cone transition. We also find that under the weaker magnetic field intra-cone transition through the excited states in Landau levels provides a new mechanism of helicity flipping, which exists even in massless limit.
  • PDF
    We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a decomposition space which is induced by a chaotic map of symbolic dynamics. In particular, the chaotic character of the tent map and the baker map on [0,1] are reconsidered based on decomposition dynamics involving symbolic dynamics with different two chaotic maps. As an example of compact metric space we exhibit a chaotic map existing on any given finite graph.
  • PDF
    We propose a new approach to introduce messenger-matter interactions in deflected anomaly mediated SUSY breaking mechanism with typical holomorphic terms in the Kahler potential. This approach is a unique feature of AMSB and has no analog in GMSB-type scenarios. New coupling strengths from the scaling of the (already known) Yukawa couplings always appear in this approach. With messenger-matter interactions in deflected AMSB, we can generate a realistic soft SUSY breaking spectrum for next-to-minimal supersymmetric standard model. Successful electroweak symmetry breaking conditions, which is not easy to satisfy in next-to-minimal supersymmetric standard model for ordinary AMSB-type scenario, can be satisfied in a large portion of parameter space in our scenarios. We study the relevant phenomenology for scenarios with (Bino-like) neutralino and axino LSP, respectively. In the case of axino LSP, the SUSY contributions to $\Delta a_\mu$ can possibly account for the muon g-2 discrepancy. The corresponding gluino masses, which are found to below 2.2 TeV, could be tested soon at LHC.

Recent comments

Siddhartha Das Oct 06 2017 03:18 UTC

Here is a work in related direction: "Unification of Bell, Leggett-Garg and Kochen-Specker inequalities: Hybrid spatio-temporal inequalities", Europhysics Letters 104, 60006 (2013), which may be relevant to the discussions in your paper. [https://arxiv.org/abs/1308.0270]

Bin Shi Oct 05 2017 00:07 UTC

Welcome to give the comments for this paper!

Bassam Helou Sep 22 2017 17:21 UTC

The initial version of the article does not adequately and clearly explain how certain equations demonstrate whether a particular interpretation of QM violates the no-signaling condition.
A revised and improved version is scheduled to appear on September 25.

James Wootton Sep 21 2017 05:41 UTC

What does this imply for https://scirate.com/arxiv/1608.00263? I'm guessing they still regard it as valid (it is ref [14]), but just too hard to implement for now.

Ben Criger Sep 08 2017 08:09 UTC

Oh look, there's another technique for decoding surface codes subject to X/Z correlated errors: https://scirate.com/arxiv/1709.02154

Aram Harrow Sep 06 2017 07:54 UTC

The paper only applies to conformal field theories, and such a result cannot hold for more general 1-D systems by 0705.4077 and other papers (assuming standard complexity theory conjectures).

Felix Leditzky Sep 05 2017 21:27 UTC

Thanks for the clarification, Philippe!

Philippe Faist Sep 05 2017 21:09 UTC

Hi Felix, thanks for the good question.

We've found it more convenient to consider trace-nonincreasing and $\Gamma$-sub-preserving maps (and this is justified by the fact that they can be dilated to fully trace-preserving and $\Gamma$-preserving maps on a larger system). The issue arises because

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