
We propose a noncommutative extension of the Pauli stabilizer formalism. The aim is to describe a class of manybody quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are tensor products of singlequbit operators drawn from the group $\langle \alpha I, X,S\rangle$, where $\alpha=e^{i\pi/4}$ and $S=\operatorname{diag}(1,i)$. We provide techniques to efficiently compute various properties related to bipartite entanglement, expectation values of local observables, preparation by means of quantum circuits, parent Hamiltonians etc. We also highlight significant differences compared to the Pauli stabilizer formalism. In particular, we give examples of states in our formalism which cannot arise in the Pauli stabilizer formalism, such as topological models that support nonAbelian anyons.

Conventional quantum error correcting codes require multiple rounds of measurements to detect errors with enough confidence in faulttolerant scenarios. Here I show that for suitable topological stabilizer codes, such as gauge color codes, a single round is indeed enough. This feature is generic and is related to selfcorrection in the corresponding quantum Hamiltonian model.

Recently, it was shown that RepeatUntilSuccess (RUS) circuits can achieve a $2.5$ times reduction in expected $T$count over ancillafree techniques for singlequbit unitary decomposition. However, the previously best known algorithm to synthesize RUS circuits requires exponential classical runtime. In this paper we present an algorithm to synthesize an RUS circuit to approximate any given singlequbit unitary within precision $\varepsilon$ in probabilistically polynomial classical runtime. Our synthesis approach uses the Clifford+$T$ basis, plus one ancilla qubit and measurement. We provide numerical evidence that our RUS circuits have an expected $T$count on average $2.5$ times lower than the theoretical lower bound of $3 \log_2 (1/\varepsilon)$ for ancillafree singlequbit circuit decomposition.

Scalable quantum computing and communication requires the protection of quantum information from the detrimental effects of decoherence and noise. Previous work tackling this problem has relied on the original circuit model for quantum computing. However, recently a family of entangled resources known as graph states has emerged as a versatile alternative for protecting quantum information. Depending on the graph's structure, errors can be detected and corrected in an efficient way using measurementbased techniques. In this article we report an experimental demonstration of error correction using a graph state code. We have used an alloptical setup to encode quantum information into photons representing a fourqubit graph state. We are able to reliably detect errors and correct against qubit loss. The graph we have realized is setup independent, thus it could be employed in other physical settings. Our results show that graph state codes are a promising approach for achieving scalable quantum information processing.

Quantum spin ice represents a paradigmatic example on how the physics of frustrated magnets is related to gauge theories. In the present work we address the problem of approximately realizing quantum spin ice in two dimensions with cold atoms in optical lattices. The relevant interactions are obtained by weakly admixing van der Waals interactions between laser admixed Rydberg states to the atomic ground state atoms, exploiting the strong angular dependence of interactions between Rydberg pstates together with the possibility of designing steplike potentials. This allows us to implement Abelian gauge theories in a series of geometries, which could be demonstrated within state of the art atomic Rydberg experiments. We numerically analyze the family of resulting microscopic Hamiltonians and find that they exhibit both classical and quantum order by disorder, the latter yielding a quantum plaquette valence bond solid. We also present strategies to implement Abelian gauge theories using both s and pRydberg states in exotic geometries, e.g. on a 48 lattice.

It has been known since long time that many NPhard optimization problems can be solved in polynomial time when restricted to structures of constant treewidth. In this work we provide the first extension of such results to the quantum setting. We show that given a quantum circuit $C$ with $n$ uninitialized inputs, $poly(n)$ gates and treewidth $t$, one can compute in time $(\frac{n}{\delta})^{\exp(O(t))}$ a classical witness $y\in \{0,1\}^n$ that maximizes the acceptance probability of $C$ up to a $\delta$ additive factor. In particular our algorithm runs in polynomial time if $t$ is constant and $1/poly(n) \leq \delta < 1$. For unrestricted values of $t$ this problem is known to be hard for the complexity class QCMA, a quantum generalization of NP. In contrast, we show that the same problem is already NPhard if $t=O(\log n)$ even when $\delta$ is constant. Finally, we show that for $t=O(\log n)$ and constant $\delta$, it is QMAhard to find a quantum witness $\ket{\varphi}$ that maximizes the acceptance probability of a quantum circuit of treewidth $t$ up to a $\delta$ additive factor.

We show how two distrustful parties, "Bob" and "Charlie", can share a secret key with the help of a mutually trusted "Alice", counterfactually  that is with no informationcarrying particles travelling between any of the three parties.

Unphysical particles are commonly ruled out from the solution of physical equations, as they fundamentally cannot exist in any real system and, hence, cannot be examined experimentally in a direct fashion. One of the most celebrated equations that allows unphysical solutions is the relativistic Majorana equation\citeMajorana which might describe neutrinos and other exotic particles beyond the Standard Model. The equation's physical solutions, the Majorana fermions, are predicted to be their own antiparticles and as a consequence they have to be neutrally charged; the charged version however (called Majoranon) is, due to charge nonconservation, unphysical and cannot exist. On the other hand, charge conservation violation has been contemplated in alternative theories associated with higher spacetime dimensions or a nonvanishing photon mass; theories whose exotic nature makes experimental testing with current technology an impossible task. In our work, we present an experimental scheme based on optics with which we simulate the dynamics of a Majoranon, involving the implementation of unphysical charge conjugation and complex conjugation. We show that the internal dynamics of the Majoranon is fundamentally different from that of its close cousin, the Dirac particle, to illustrate the nature of the unphysical operations. For this we exploit the fact that in quantum mechanics the wave function itself is not a measurable quantity. Therefore, wave functions of real physical particles, in our case Dirac particles with opposite masses, can be superposed to a wave function of an unphysical particle, the Majoranon. Our results open a new front in the field of quantum simulations of exotic phenomena, with possible applications in condensed matter physics, topological quantum computing, and testing theories within and beyond the Standard Model with existing technology.

We study holographic entanglement entropy of nonlocal field theories both at extremality and finite temperature. The gravity duals, constructed in arXiv:1208.3469 [hepth], are characterized by a parameter $w$. Both the zero temperature backgrounds and the finite temperature counterparts are exact solutions of EinsteinMaxwelldilaton theory. For the extremal case we consider the examples with the entangling regions being a strip and a sphere. We find that the leading order behavior of the entanglement entropy always exhibits a volume law when the size of the entangling region is sufficiently small. We also clarify the condition under which the nexttoleading order result is universal. For the finite temperature case we obtain the analytic expressions both in the high temperature limit and in the low temperature limit. In the former case the leading order result approaches the thermal entropy, while the finite contribution to the entanglement entropy at extremality can be extracted by taking the zero temperature limit in the latter case. Moreover, we observe some peculiar properties of the holographic entanglement entropy when $w=1$.

We present the calculation of all nonplanar master integrals that are needed to describe production of two offshell vector bosons in collisions of two massless partons through NNLO in perturbative QCD. The integrals are computed analytically using differential equations in external kinematic variables and expressed in terms of Goncharov polylogarithms. These results provide the last missing ingredient needed for the computation of twoloop amplitudes that describe the production of two gauge bosons with different invariant masses in hadron collisions.

The microscopic modeling of spinorbit entangled $j=1/2$ Mott insulators such as the layered hexagonal Iridates Na$_2$IrO$_3$ and Li$_2$IrO$_3$ has spurred an interest in the physics of HeisenbergKitaev models. Here we explore the effect of lattice distortions on the formation of the collective spinorbital states which include not only conventionally ordered phases but also gapped and gapless spinorbital liquids. In particular, we demonstrate that in the presence of spatial anisotropies of the exchange couplings conventionally ordered states are formed through an orderbydisorder selection which is not only sensitive to the type of exchange anisotropy but also to the relative strength of the Heisenberg and Kitaev couplings. The spinorbital liquid phases of the Kitaev limit  a gapless phase in the vicinity of spatially isotropic couplings and a gapped Z$_2$ phase for a dominant spatial anisotropy of the exchange couplings  show vastly different sensitivities to the inclusion of a Heisenberg exchange. While the gapless phase is remarkably stable, the gapped Z$_2$ phase quickly breaks down in what might be a rather unconventional phase transition driven by the simultaneous condensation of its elementary excitations.

Percolation is the paradigm for random connectivity and has been one of the most applied statistical models. With simple geometrical rules a transition is obtained which is related to magnetic models. This transition is, in all dimensions, one of the most robust continuous transitions known. We present a very brief overview of more than 60 years of work in this area and discuss several open questions for a variety of models, including classical, explosive, invasion, bootstrap, and correlated percolation.

We harness general relativistic effects to gain quantum control on a stationary qubit in an optical cavity by controlling the noninertial motion of a different probe atom. Furthermore, we show that by considering relativistic trajectories of the probe, we enhance the efficiency of the quantum control. We explore the possible use of these relativistic techniques to build universal quantum gates.

In many fields of science, we observe a response variable together with a large number of potential explanatory variables, and would like to be able to discover which variables are truly associated with the response. At the same time, we need to know that the false discovery rate (FDR)the expected fraction of false discoveries among all discoveriesis not too high, in order to assure the scientist that most of the discoveries are indeed true and replicable. This paper introduces the knockoff filter, a new variable selection procedure controlling the FDR in the statistical linear model whenever there are at least as many observations as variables. This method achieves exact FDR control in finite sample settings no matter the design or covariates, the number of variables in the model, and the amplitudes of the unknown regression coefficients, and does not require any knowledge of the noise level. As the name suggests, the method operates by manufacturing knockoff variables that are cheaptheir construction does not require any new dataand are designed to mimic the correlation structure found within the existing variables, in a way that allows for accurate FDR control, beyond what is possible with permutationbased methods. The method of knockoffs is very general and flexible, and can work with a broad class of test statistics. We test the method in combination with statistics from the Lasso for sparse regression, and obtain empirical results showing that the resulting method has far more power than existing selection rules when the proportion of null variables is high. We also apply the knockoff filter to HIV data with the goal of identifying those mutations associated with a form of resistance to treatment plans.

This paper is concerned with twodimensional, steady, periodic water waves propagating at the free surface of water in a flow of constant vorticity over an impermeable flat bed. The motion of these waves is assumed to be governed both by surface tension and gravitational forces. A new reformulation of this problem is given, which is valid without restriction on the geometry or amplitude of the wave profiles and possesses a structure amenable to global bifurcation. The existence of global curves and continua of solutions bifurcating at certain parameter values from flat, laminar flows is then established through the application of realanalytic global bifurcation in the spirit of Dancer and the degreetheoretic global bifurcation theorem of Rabinowitz, respectively.

A system of two operator equations is considered  one of pseudomonotone type and the other of strongly monotone type  both being strongly coupled. Conditions are given that allow to reduce the solvability of this system to a single operator equation for a pseudomonotone mapping. This result is applied to a coupled system consisting of a parabolic equation of forth order in space of CahnHilliard type and a nonlinear elliptic equation of second order to a quasisteady mechanical equilibrium. Using an appropriate notation of weak solutions and a framework for evolution equations developed by Gröger, the system is reduced to a single parabolic operator equation and the existence of solutions are shown under restrictions on the strength of the coupling.

Controlled methods proved to be very effective in the study of assembly maps in algebraic Ktheory. For the questions concerning surjectivity of these maps in the context of geometries that have no immanent nonpositive curvature, the setting needs to be enlarged to bounded Gtheory with fibred control. We set up the natural framework for this theory. As should be expected, the Gtheory has better excision properties. The main result illustrates a fact that has no analogue in bounded Ktheory. It is one of the major technical tools used in our work on the Borel Conjecture about topological rigidity of aspherical manifolds. The general framework we develop will be useful for other applications to coarse bundles and stacks.

Sparse code multiple access (SCMA) is a new frequency domain nonorthogonal multipleaccess technique which can improve spectral efficiency of wireless radio access. With SCMA, different incoming data streams are directly mapped to codewords of different multidimensional cookbooks, where each codeword represents a spread transmission layer. Multiple SCMA layers share the same timefrequency resources of OFDMA. The sparsity of codewords makes the nearoptimal detection feasible through iterative message passing algorithm (MPA). Such low complexity of multilayer detection allows excessive codeword overloading in which the dimension of multiplexed layers exceeds the dimension of codewords. Optimization of overloading factor along with modulationcoding levels of layers provides a more flexible and efficient linkadaptation mechanism. On the other hand, the signal spreading feature of SCMA can improve linkadaptation as a result of less colored interference. In this paper a technique is developed to enable multiuser SCMA (MUSCMA) for downlink wireless access. User pairing, power sharing, rate adjustment, and scheduling algorithms are designed to improve the downlink throughput of a heavily loaded network. The advantage of SCMA spreading for lightly loaded networks is also evaluated.

We investigate the effect of electronphonon interactions on the coherence properties of single photons emitted from a semiconductor cavity QED system, i.e. a quantum dot embedded in an optical cavity. The degree of indistinguishability, governing the quantum mechanical interference between two single photons, is calculated as a function of important parameters describing the cavity QED system and the phonon reservoir, e.g. cavity quality factor, lightmatter coupling strength, temperature and phonon lifetime. We show that nonMarkovian effects play an important role in determining the coherence properties for typical parameter values and establish the conditions under which a Markovian approximation may be applied. The calculations are performed using a recently developed second order perturbation theory, the limits of validity of which are established by comparing to an exact diagonalization approach. We find that for large cavity decay rates the perturbation theory may break down.

We review the theory of regenerative processes, which are processes that can be intuitively seen as comprising of i.i.d.\ cycles. Although we focus on the classical definition, we present a more general definition that allows for some form of dependence between two adjacent cycles, and mention two further extensions of the second definition. We mention the connection of regenerative processes to the singleserver queue, to multiserver queues and more generally to Harris ergodic Markov chains and processes. In the main theorem, we pay some attention to the conditions under which a limiting distribution exists and provide references that should serve as a starting point for the interested reader.

When atoms are exposed to intense laser or microwave pulses ~10% of the atoms are found in Rydberg states subsequent to the pulse, even if it is far more intense than required for static field ionization. The optical spectra of the surviving Li atoms in the presence of a 38 GHz microwave field suggest how atoms survive an intense pulse. The spectra exhibit a periodic train of peaks 38 GHz apart. One peak is just below the limit, and with a 90 V/cm field amplitude the train extends from 300 GHz above the limit to 3000 GHz below it. The spectra and quantum mechanical calculations imply that the atoms survive in quasi stable states in which the Rydberg electron is in a weakly bound orbit infrequently returning to the ionic core during the intense pulse.

We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the elementary renewal theorem and avoids the technicalities in the proof that is presented in most textbooks. Moreover, we mention briefly the extension of the theory to partial rewards, where it is assumed that rewards are not accrued only at renewal epochs but also during the renewal cycle. For this case, we present a counterexample which indicates that the standard conditions for the renewal reward theorem are not sufficient; additional regularity assumptions are necessary. We present a few examples to indicate the usefulness of this theory, where we prove the inspection paradox and Little's law through the renewal reward theorem.

In this appendix we present an expanded version of Section 4 of our paper arXiv:1404.4596, including the proofs of all of the technical lemmas.

The concept of positional information is central to our understanding of how cells in a multicellular structure determine their developmental fates. Nevertheless, positional information has neither been defined mathematically nor quantified in a principled way. Here we provide an informationtheoretic definition in the context of developmental gene expression patterns and examine which features of expression patterns increase or decrease positional information. We connect positional information with the concept of positional error and develop tools to directly measure information and error from experimental data. We illustrate our framework for the case of gap gene expression patterns in the early Drosophila embryo and show how information that is distributed among only four genes is sufficient to determine developmental fates with single cell resolution. Our approach can be generalized to a variety of different model systems; procedures and examples are discussed in detail.

We show with a few descriptive examples the limitations of Artificial Neural Networks when they are applied to the analysis of independent stochastic data.

Context: The role of magnetic fields in the star formation process is a contentious matter of debate. In particular, no clear observational proof exists of a general influence by magnetic fields during the initial collapse of molecular clouds. Aims: Our aim is to examine magnetic fields and their influence on a wide range of spatial scales in lowmass starforming regions. Method: We trace the largescale magnetic field structure on scales of 10^310^5 AU in the local environment of Bok globules through optical and nearinfrared polarimetry and combine these measurements with existing submillimeter measurements, thereby characterizing the smallscale magnetic field structure on scales of 10^210^3 AU. Results: For the first time, we present polarimetric observations in the optical and nearinfrared of the three Bok globules B335, CB68, and CB54, combined with archival observations in the submillimeter and the optical. We find a significant polarization signal (P>=2%, P/sigma(P)>3) in the optical and nearinfrared for all three globules. Additionally, we detect a connection between the structure on scales of 10^210^3 AU to 10^310^4 AU for both B335 and CB68. Furthermore, for CB54, we trace ordered polarization vectors on scales of ~10^5 AU. We determine a magnetic field orientation that is aligned with the CO outflow in the case of CB54, but nearly perpendicular to the CO outflow for CB68. For B335 we find a change in the magnetic field oriented toward the outflow direction, from the inner core to the outer regions. Conclusion: We find strongly aligned polarization vectors that indicate dominant magnetic fields on a wide range of spatial scales.

A class of modified Duffing oscillator differential equations, having nonlinear damping forces, are shown to have finite time dynamics, i.e., the solutions oscillate with only a finite number of cycles, and, thereafter, the motion is zero. The relevance of this feature is briefly discussed in relationship to the mathematical modeling, analysis, and estimation of parameters for the vibrations of carbon nanotubes and graphene sheets, and macroscopic beams and plates.

We investigate by firstprinciples simulations the resonant electrontransfer lifetime from the excited state of an organic adsorbate to a semiconductor surface, namely isonicotinic acid on rutile TiO$_2$(110). The moleculesubstrate interaction is described using density functional theory, while the effect of a truly semiinfinite substrate is taken into account by Green's function techniques. Excitonic effects due to the presence of coreexcited atoms in the molecule are shown to be instrumental to understand the electrontransfer times measured using the socalled coreholeclock technique. In particular, for the isonicotinic acid on TiO$_2$(110), we find that the charge injection from the LUMO is quenched since this state lies within the substrate band gap. We compute the resonant chargetransfer times from LUMO+1 and LUMO+2, and systematically investigate the dependence of the elastic lifetimes of these states on the alignment among adsorbate and substrate states.

In this paper we study the harmonic elements of (convolution) Markov maps associated to (ergodic) actions of locally compact quantum groups on ($\sigma$finite) von Neumann algebras. We give several equivalent conditions under which the harmonic elements are trivial.

In the first part of the paper a generalized theoretical approach towards beam coupling impedances and stretchedwire measurements is introduced. Applied to a circular symmetric setup, this approach allows to estimate the systematic measurement error due to the presence of the wire. Further, the interaction of the beam or the TEM wave, respectively, with dispersive material such as ferrite is discussed. The dependence of the obtained impedances on the relativistic velocity $\beta$ is investigated and found as material property dependent. The conversion formulas for the TEM scattering parameters from measurements to impedances are compared with each other and the analytical impedance solution. In the second part of the paper the measurements are compared to numerical simulations of wakefields and scattering parameters. In practice, the measurements have been performed for the circularly symmetric example setup. The optimization of the measurement process is discussed. The paper concludes with a summary of systematic and statistic error sources for impedance bench measurements and their diminishment strategy.

We have performed terahertz timedomain magnetospectroscopy by combining a rapid scanning terahertz timedomain spectrometer based on the electronically coupled optical sampling method with a tabletop minicoil pulsed magnet capable of producing magnetic fields up to 30 T. We demonstrate the capability of this system by measuring coherent cyclotron resonance oscillations in a highmobility twodimensional electron gas in GaAs and interferenceinduced terahertz transmittance modifications in a magnetoplasma in lightly doped nInSb.

This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousels, give an overview of related problems in this area, and present an extensive literature review. Emphasis has been given on future research directions in this area.

In this paper, we propose a novel image set representation and classification method by maximizing the margin of image sets. The margin of an image set is defined as the difference of the distance to its nearest image set from different classes and the distance to its nearest image set of the same class. By modeling the image sets by using both their image samples and their affine hull models, and maximizing the margins of the images sets, the image set representation parameter learning problem is formulated as an minimization problem, which is further optimized by an expectation maximization (EM) strategy with accelerated proximal gradient (APG) optimization in an iterative algorithm. To classify a given test image set, we assign it to the class which could provide the largest margin. Experiments on two applications of videosequencebased face recognition demonstrate that the proposed method significantly outperforms stateoftheart image set classification methods in terms of both effectiveness and efficiency.

We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindleytype equation. We are interested in the timedependent behaviour of this system and derive explicit expressions for its timedependent waitingtime distribution, the correlation between waiting times, and the distribution of the cycle length. Since our model is closely related to Lindley's recursion, we compare our results to those derived for Lindley's recursion.

In this paper, we prove the unique continuation property for the weak solution of the plate equation with nonsmooth coefficients. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping.

The IDSgrep structural query system for Han character dictionaries is presented. This system includes a data model and syntax for describing the spatial structure of Han characters using Extended Ideographic Description Sequences (EIDSes) based on the Unicode IDS syntax; a language for querying EIDS databases, designed to suit the needs of font developers and foreign language learners; a bit vector index inspired by Bloom filters for faster query operations; a freely available implementation; and format translation from popular thirdparty IDS and XML character databases. Experimental results are included, with a comparison to other software used for similar applications.

In the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorithms for highdimensional polyhedra given by inequalities. In this paper we apply the concept of branchdecomposition to the vertex enumeration problem of polyhedra $P = \{x : Sx = b, x \geq 0\}$. Therefore, we introduce the concept of $k$module and show how it relates to the separators of the linear matroid generated by the columns of $S$. This then translates structural properties of the matroidal branchdecomposition to the context of polyhedra. We then use this to present a total polynomial time algorithm for polytopes $P$ for which the branchwidth of the linear matroid generated by $S$ is bounded by a constant $k$.

We demonstrate the nondestructive imaging of a lattice gas of ultracold bosons. Atomic fluorescence is induced in the simultaneous presence of degenerate Raman sideband cooling. The combined influence of these processes controllably cycles an atom between a dark state and a fluorescing state while eliminating heating and loss. Through spatially resolved sideband spectroscopy following the imaging sequence, we demonstrate the efficacy of this imaging technique in various regimes of lattice depth and fluorescence acquisition rate. Our work provides an important extension of quantum gas imaging to the nondestructive detection, control and manipulation of atoms in optical lattices. In addition, our technique can also be extended to atomic species that are less amenable to molassesbased lattice imaging.

The generic nonextremal KerrNewman black holes are holographically dual to hidden conformal field theories in two different pictures. The two pictures can be merged together to the CFT duals in general picture that are generated by $SL(2,\mathbb{Z})$ modular group. We find some extensions of the conformal symmetry generators that yield an extended local family of $SL(2,\mathbb{R})_L \times SL(2,\mathbb{R})_R$ hidden conformal symmetries for the KerrNewman black holes parameterized by one deformation parameter. The family of deformed hidden conformal symmetry for KerrNewman black holes also provides a set of deformed hidden conformal generators for the charged ReissnerNordstrom black holes. The set of deformed hidden conformal generators reduce to the hidden $SL(2,\mathbb{R})$ conformal generators for the ReissnerNordstrom black hole for specific value of deformation parameter. We also find agreement between the macroscopic and microscopic entropy and absorption cross section of scalars for the KerrNewman black hole by considering the appropriate temperatures and central charges for the deformed CFTs.

The Strukov model was the phenomenological model that accompanied the announcement of the first recognised physical instantiation of the memristor and, as such, it has been widely used. This model described the motion of a boundary, $w$, between two types of interconverting material, $R_{\mathrm{off}}$ and $R_{\mathrm{on}}$, seemingly under a uniform field across the entire device. In fact, what was intended was a field with a discontinuity at $w$, that was uniform between $0<x<w$. In this paper we show that the discontinuity is required for the Strukov model derivation to be completed, and thus the derivation as given does not describe a situation with a uniform field across the entire device. The discontinuity can be described as a Heaviside function, $H$, located on $w$, for which there are three common singlevalued approximations for $H(w)$. The Strukov model as intended includes an approximation for the Heaviside function (the field is taken to be the same as that across the $R_{\mathrm{on}}$ part of the device). We compare approximations and give solutions. We then extend the description of the field to a morerealistic continuously varying sigmoidal transition between two uniform fields and demonstrate that the centrosymmetric approximation model (taking the field as being the average of the fields across $R_{\mathrm{on}}$ and $R_{\mathrm{off}}$) is a better singlepoint model of that situation: the other two approximations over or underestimate the field.

This paper is devoted to the study of the generalized impedance boundary conditions (GIBCs) for a strongly absorbing obstacle in the \bf time regime in two and three dimensions. The GIBCs in the time domain are heuristically derived from the corresponding conditions in the time harmonic regime. The latters are frequency dependent except the one of order 0; hence the formers are nonlocal in time in general. The error estimates in the time regime can be derived from the ones in the time harmonic regime when the frequency dependence is wellcontrolled. This idea is originally due to Nguyen and Vogelius in \citeNguyenVogelius2 for the cloaking context. In this paper, we present the analysis to the GIBCs of orders 0 and 1. To implement the ideas in \citeNguyenVogelius2, we revise and extend the work of Haddar, Joly, and Nguyen in \citeHJNg1, where the GIBCs were investigated for a fixed frequency in three dimensions. Even though we heavily follow the strategy in \citeNguyenVogelius2, our analysis on the stability contains new ingredients and ideas. First, instead of considering the difference between solutions of the exact model and the approximate model, we consider the difference between their derivatives in time. This simple idea helps us to avoid the machinery used in \citeNguyenVogelius2 concerning the integrability with respect to frequency in the low frequency regime. Second, in the high frequency regime, the Morawetz multiplier technique used in \citeNguyenVogelius2 does not fit directly in our setting. Our proof makes use of a result by Hörmander in \citeHor. Another important part of the analysis in this paper is the wellposedness in the time domain for the approximate problems imposed with GIBCs on the boundary of the obstacle, which are nonlocal in time.

We discuss Liouville field theory in the framework of SchwingerDyson approach and derive a functional equation for the threepoint structure constant. We argue the existence of a second SchwingerDyson equation on the basis of the duality between the screening charge operators and obtain a second functional equation for the structure constant. We discuss the utility of the two functional equations to fix the structure constant uniquely.

The GaiaESO Public Spectroscopic Survey (GES) is conducting a largescale study of multielement chemical abundances of some 100 000 stars in the Milky Way with the ultimate aim of quantifying the formation history and evolution of young, mature and ancient Galactic populations. However, in preparing for the analysis of GES spectra, it has been noted that atomic oscillator strengths of important Fe I lines required to correctly model stellar line intensities are missing from the atomic database. Here, we present new experimental oscillator strengths derived from branching fractions and level lifetimes, for 142 transitions of Fe I between 3526 Å and 10864 Å, of which at least 38 are urgently needed by GES. We also assess the impact of these new data on solar spectral synthesis and demonstrate that for 36 lines that appear unblended in the Sun, Fe abundance measurements yield a small linebyline scatter (0.08 dex) with a mean abundance of 7.44 dex in good agreement with recent publications.

The QCD phase diagram at zero chemical potential and finite temperature subject to an external magnetic field is studied within the three flavor NambuJonaLasinio (NJL) model and the NJL model with the Polyakov loop (PNJL). A scalar coupling parameter dependent on the magnetic field intensity is considered. The scalar coupling has been fitted so that the lattice QCD pseudocritical chiral transition temperatures are reproduced and in the limit of large magnetic field decreases with the inverse of the magnetic field intensity. This dependence of the coupling allows to reproduce the lattice QCD results with respect to the quark condensates and Polyakov loop: due to the magnetic field the quark condensates are enhanced at low and high temperatures and suppressed for temperatures close to the transition temperatures and the Polyakov loop increases with the magnetic field.

We theoretically investigate the Tunneling Anisotropic MagnetoSeebeck effect in a realisticallymodeled CoPtMgOPt tunnel junction using coherent transport calculations. For comparison we study the tunneling magnetoSeebeck effect in CoPtMgOCoPt as well. We find that the magnetoSeebeck ratio of CoPtMgOPt exceeds that of CoPtMgOCoPt for small barrier thicknesses, reaching 175% at room temperature. This result provides a sharp contrast to the magnetoresistance, which behaves oppositely for all barrier thicknesses and differs by one order of magnitude between devices. Here the magnetoresistance results from differences in transmission brought upon by changing the tunnel junction's magnetization configuration. The magnetoSeebeck effect results from variations in asymmetry of the energydependent transmission instead. We report that this difference in origin allows for CoPtMgOPt to possess strong thermal magnetictransport anisotropy.

Cavity optomechanical systems are approaching a strongcoupling regime where the coherent dynamics of nanomechanical resonators can be manipulated and controlled by optical fields at the single photon level. Here we propose an interferometric scheme able to detect optomechanical coherent interaction at the singlephoton level which is experimentally feasible with stateoftheart devices and apparatus.

We introduce the associated Lah numbers. Some recurrence relations and convolution identities are established. An extension of the associated Stirling and Lah numbers to the rStirling and rLah numbers are also given. For all these sequences we give combinatorial interpretation, generating functions, recurrence relations, convolution identities. In the sequel, we develop a section on nested sums related to binomial coe?cient.

We present a complete nexttoleading order study of topsquark pair production at the LHC, including QCD and EW corrections. The calculation is performed within the Minimal Supersymmetric Standard Model and numerical results are presented for parameter regions compatible with the observed Higgs boson. We employ the most recent parton distribution functions including QED corrections and we find corrections to the inclusive stoppair production cross section up to 2530 % compared to the leadingorder prediction.

Many supersymmetric models such as the CMSSM feature a strip in parameter space where the lightest neutralino \chi is identified as the lightest supersymmetric particle (LSP), the lighter stop squark \tilde t_1 is the nexttolightest supersymmetric particle (NLSP), and the relic \chi cold dark matter density is brought into the range allowed by astrophysics and cosmology by coannihilation with the lighter stop squark \tilde t_1 NLSP. We calculate the stop coannihilation strip in the CMSSM, incorporating Sommerfeld enhancement effects, and explore the relevant phenomenological constraints and phenomenological signatures. In particular, we show that the \tilde t_1 may weigh several TeV, and its lifetime may be in the nanosecond range, features that are more general than the specific CMSSM scenarios that we study in this paper.

Online Bin Stretching is a semionline variant of bin packing in which the algorithm has to use the same number of bins as the optimal packing, but is allowed to slightly overpack the bins. The goal is to minimize the amount of overpacking, i.e., the maximum size packed into any bin. We give an algorithm for Online Bin Stretching with a stretching factor of 1.5 for any number of bins. We also show a specialized algorithm for three bins with a stretching factor of 11/8 = 1.375.

We observe microwave induced nonlocal resistance in magnetotransport in single and bilayer electronic systems. The obtained results provide evidence for an edge state current stabilized by microwave irradiation due to nonlinear resonances. Our observation are closely related to microwave induced oscillations and zero resistance states in a twodimensional (2D) electron system.

Despite its importance in atmospheric science, much remains unknown about the microscopic mechanism of heterogeneous ice nucleation. In this work, we perform hybrid Monte Carlo simulations of the heterogeneous nucleation of ice on a range of generic surfaces, both flat and structured, in order to probe the underlying factors affecting the nucleation process. The structured surfaces we study comprise one basal plane bilayer of ice with varying lattice parameters and interaction strengths. We show that what determines the propensity for nucleation is not just the surface attraction, but also the orientational ordering imposed on liquid water near a surface. In particular, varying the ratio of the surface's attraction and orientational ordering can change the mechanism by which nucleation occurs: ice can nucleate on the structured surface even when the orientational ordering imposed by the surface is weak, as the water molecules that interact strongly with the surface are themselves a good template for further growth. We also show that lattice matching is important for heterogeneous nucleation on the structured surface we study. We rationalise these bruteforce simulation results by explicitly calculating the interfacial free energies of ice and liquid water in contact with the nucleating surface and their variation with surface interaction parameters.

We give a comprehensive study of strong uniform attractors of nonautonomous dissipative systems for the case where the external forces are not translation compact. We introduce several new classes of external forces which are not translation compact, but nevertheless allow to verify the attraction in a strong topology of the phase space and discuss in a more detailed way the class of socalled normal external forces introduced before. We also develop a unified approach to verify the asymptotic compactness for such systems based on the energy method and apply it to a number of equations of mathematical physics including the NavierStokes equations, damped wave equations and reactiondiffusing equations in unbounded domains.

Online social networks (OSNs) are changing the way information spreads throughout the Internet. A deep understanding of information spreading in OSNs leads to both social and commercial benefits. In this paper, dynamics of information spreading (e.g., how fast and widely the information spreads against time) in OSNs are characterized, and a general and accurate model based on Interactive Markov Chains (IMCs) and meanfield theory is established. This model shows tight relations between network topology and information spreading in OSNs, e.g., the information spreading ability is positively related to the heterogeneity of degree distributions whereas negatively related to the degreedegree correlations in general. Further, the model is extended to feature the timevarying user behavior and the everchanging information popularity. By leveraging the meanfield theory, the model is able to characterize the complicated information spreading process (e.g., the dynamic patterns of information spreading) with six parameters. Extensive evaluations based on Renren's data set illustrate the accuracy of the model, e.g., it can characterize dynamic patterns of video sharing in Renren precisely and predict future spreading dynamics successfully.

Forced desorption of a semiflexible polymer chain on a solid substrate is theoretically investigated. The pulling force versus displacement is studied for different adsorption energy and persistence length P. It is found that the relationships between pulling force and cantilever displacement show a series of characteristic force spikes at different persistence length P. These force spikes becomes more pronounced but the average magnitude of this force decrease as P grows. Our results are of relevance to forced desorption of DNA on an attractive wall in singlemolecule pulling experiments.

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Duran, C. Padra, Appl. Numer. Math., 2012, for the approximation of Laplace eigenvalue problem with CrouzeixRaviart nonconforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and discuss the convergence of an adaptive algorithm when dealing with multiple eigenvalues.

We prove that every rightangled Artin group embeds into the $C^{\infty}$ diffeomorphism group of the unit interval. As a corollary, we show every limit group, and more generally every countable residually RAAG group, embeds into the $C^{\infty}$ diffeomorphism groups of the unit interval, the unit circle, and the real line. We also show that a rightangled Artin subgroup of the analytic diffeomorphism group of the circle is a free product of free abelian groups, thus showing that $C^{\infty}$ is the highest level of regularity which accommodates all rightangled Artin groups.

We study the $W^{'}$ phenomenology in composite Higgs/ warped extra dimensional models focusing on the effect of fermionic resonances at $\sim$1 TeV. After deriving the existing bounds from the current LHC8 analyses, we highlight the most promising signatures for $W^{'}$ discovery at the 14 TeV LHC. We find in particular very promising the study of $W^{'}$ decay modes into vectorlike top partners, specifically the decay into a doublet of custodian heavy fermions, $T_{5/3} T_{2/3}$, and the decay into a heavy fermion plus a Standard Model quark. We perform a detailed parton level analysis of the channel $W^{'}\to T_{5/3} T_{2/3}$ in the samesign dilepton final state, finding that it is a very promising signature to test the region at high $W^{'}$ mass, $m_{W^{'}}\gtrsim 2$ TeV, and of the $W^{'}\to Tb$ mode, that is one of the best channels to test the intermediate $W^{'}$ mass region and that, already with the LHC8 data, could extend the present exclusion bounds.

In this paper, we are concerned with regularized regression problems where the prior penalty is a piecewise regular/partly smooth gauge whose active manifold is linear. This encompasses as special cases the Lasso ($\lun$ regularizer), the group Lasso ($\lun\ldeux$ regularizer) and the $\linf$norm regularizer penalties. This also includes socalled analysistype priors, i.e. composition of the previously mentioned functionals with linear operators, a typical example being the total variation prior. We study the sensitivity of \textitany regularized minimizer to perturbations of the observations and provide its precise local parameterization. Our main result shows that, when the observations are outside a set of zero Lebesgue measure, the predictor moves locally stably along the same linear space as the observations undergo small perturbations. This local stability is a consequence of the piecewise regularity of the gauge, which in turn plays a pivotal role to get a closed form expression for the variations of the predictor w.r.t. observations which holds almost everywhere. When the perturbation is random (with an appropriate continuous distribution), this allows us to derive an unbiased estimator of the degrees of freedom and of the risk of the estimator prediction. Our results hold true without placing any assumption on the design matrix, should it be full column rank or not. They generalize those already known in the literature such as the Lasso problem, the general Lasso problem (analysis $\lun$penalty), or the group Lasso where existing results for the latter assume that the design is full column rank.

We consider a polling system where a group of an infinite number of servers visits sequentially a set of queues. When visited, each queue is attended for a random time. Arrivals at each queue follow a Poisson process, and service time of each individual customer is drawn from a general probability distribution function. Thus, each of the queues comprising the system is, in isolation, an M/G/$\infty$type queue. A job that is not completed during a visit will have a new service time requirement sampled from the servicetime distribution of the corresponding queue. To the best of our knowledge, this paper is the first in which an M/G/$\infty$type polling system is analysed. For this polling model, we derive the probability generating function and expected value of the queue lengths, and the LaplaceStieltjes transform and expected value of the sojourn time of a customer. Moreover, we identify the policy that maximises the throughput of the system per cycle and conclude that under the Hamiltoniantour approach, the optimal visiting order is \emphindependent of the number of customers present at the various queues at the start of the cycle.

We study a discrete hostparasitoid system where the host population follows the classical Ricker functional form and is also subject to Allee effects. We determine basins of attraction of the local attractors of the single population model when the host intrinsic growth rate is not large. In this situation, existence and local stability of the interior steady states for the hostparasitoid interaction are completely analyzed. If the host's intrinsic growth rate is large, then the interaction may support multiple interior steady states. Linear stability of these steady states is provided.

We discuss a singleserver multistation alternating queue where the preparation times and the service times are auto and crosscorrelated. We examine two cases. In the first case, preparation and service times depend on a common discrete time Markov chain. In the second case, we assume that the service times depend on the previous preparation time through their joint Laplace transform. The waiting time process is directly analysed by solving a Lindleytype equation via transform methods. Numerical examples are included to demonstrate the effect of the autocorrelation of and the crosscorrelation between the preparation and service times.

We report the observation of planar and anomalous Nernst effects in thin films of halfmetal ferromagnet La2/3Sr1/3MnO3 (LSMO). These fielddependent thermoelectric effects are quantified at different temperatures, and we show them to be directly related to the planar and anomalous Hall effect (AHE) in a ferromagnet with biaxial anisotropy. The temperature dependence of the anomalous Nernst effect is discussed in relationship with the possible mechanisms for AHE in this system. Our results also put an upper limit to a possible observation of the anisotropic Spin Seebeck effect in LSMO.

We demonstrate algorithmbased fault tolerance for silent, transient data corruption in "blackbox" preconditioners. We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both implemented in the Trilinos library. We evaluate faults that corrupt preconditioner results in both single and multiple MPI ranks. We then analyze how our approach behaves when then application is scaled. Our technique is based on a Selective Reliability approach that performs most operations in an unreliable mode, with only a few operations performed reliably. We also investigate two responses to faults and discuss the performance overheads imposed by each. For a nonsymmetric problem solved using GMRES and ILU, we show that at scale our fault tolerance approach incurs only 22% overhead for the worst case. With detection techniques, we are able to reduce this overhead to 1.8% in the worst case.

In this short note I show that the soft limit for colourordered treelevel YangMills amplitudes contains a subleading divergent term analogous to terms found recently by Cachazo and Strominger for treelevel gravity amplitudes.

For many years, theorists have calculated formulas for useful quantities in general gaugeYukawa theories. However, these cookbooks are often very difficult to use since the general notation is far removed from practical model building. In this paper, we present the structure delta which allows us to use a surprisingly convenient notation that bridges the gap between general gaugeYukawa theories and specific models. This is particularly useful for the computation of beta functions, but can also be extended to handle spontaneous symmetry breaking, the effective potential and a variety of other quantities. We will introduce it using the standard model of particle physics and a toy model with an SU(N_c) gauge symmetry.

We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, BA+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=1]=1p$. For $p=1$ this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for $p=0$ it describes the waiting time of the server in an alternating service model. For all other values of $p$ this model describes a FCFS queue in which the service times and interarrival times depend linearly and randomly on the waiting times. We derive the distribution of $W$ when $A$ is generally distributed and $B$ follows a phasetype distribution, and when $A$ is exponentially distributed and $B$ deterministic.

In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5competitive algorithm which is optimal. In fact, the algorithm always uses at most $\lceil1.5\cdot OPT\rceil$ bins and we show a matching lower bound of $\lceil1.5\cdot OPT\rceil$ for any value of $OPT\geq 2$. In particular, the absolute ratio of our algorithm is $5/3$ and this is optimal. For items of unrestricted sizes we give an asymptotically $3.5$competitive algorithm. When the items have sizes at most $1/d$ for a real $d \geq 2$ the asymptotic competitive ratio is $1.5+d/(d1)$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colorsthe Black and White Bin Packing problemwe prove that all Any Fit algorithms have absolute competitive ratio $3$. When the items have sizes at most $1/d$ for a real $d \geq 2$ we show that the Worst Fit algorithm is absolutely $(1+d/(d1))$competitive.

We carry out a firstprinciples atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linearscaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical meanfield theory (DMFT). This combination of methods explicitly accounts for dynamical and multireference quantum physics, such as valence and spin fluctuations, of the 3d electrons, whilst treating a significant proportion of the protein (more than 1000 atoms) with density functional theory. The computed electronic structure of the myoglobin complexes and the nature of the FeO2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long standing problem related to the quantummechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of many bodyeffects induced by the Hund's coupling mechanism results in the correct prediction of similar binding energies for oxy and carbonmonoxymyoglobin.

Using quantum mechanical perturbation theory (PT) we analyze how the energy of perturbation of different orders is renormalized in solids. We test the validity of PT analysis by considering a specific case of spinorbit coupling as a perturbation. We further compare the relativistic energy and magnetic anisotropy from the PT approach with direct density functional calculations in FePt, CoPt, FePd, MnAl, MnGa, FeNi, and tetragonally strained FeCo. In addition using decomposition of anisotropy into contributions from individual sites and different spin components we explain the microscopic origin of high anisotropy in FePt and CoPt magnets.