
Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensedmatter physics, as well as in mathematical physics. This is specifically true for finitely correlated states or matrixproduct operators, designed to capture mixed states of onedimensional quantum systems. It is a wellknown open problem to find an efficient algorithm that decides whether a given matrixproduct operator actually represents a physical state that in particular has no negative eigenvalues. This question will be settled here, by showing that the problem is provably undecidable in the thermodynamic limit and that the finite version of the problem is shown to be NPhard in the system size. Furthermore, we discuss numerous connections between tensor network methods and (seemingly) different concepts treated before in the literature, such as hidden Markov models and tensor trains.

We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)dimensional discrete spacetime. The theory admits a diagrammatic representation in terms of a few local, circuit equivalence rules. Within this framework, we show the firstorderonly covariance of the Dirac QW. We then introduce the Clock QW and the Clock QCA, and prove that they are exactly discrete Lorentz covariant. The theory also allows for nonhomogeneous Lorentz transforms, between noninertial frames.

This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about using category theory in representing quantum computing and teleportation. We analyze very carefully the diagrammatic meaning of the usual representation of the MachZehnder interferometer, and we show how it can be generalized to associate to each composition of unitary transformations a "laboratory quantum diagram" such that particles moving though the many alternate paths in this diagram will mimic the quantum process represented by the composition of unitary transformations. This is a finite dimensional way to think about the Feynman Path Integral. We call our representation result the Path Theorem. Then we go back to the basics of networks and matrices and show how elements of quantum measurement can be represented with network diagrams.

Wolfgang Pfaff,
Bas Hensen,
Hannes Bernien,
Suzanne B. van Dam,
Machiel S. Blok,
Tim H. Taminiau,
Marijn J. Tiggelman,
Raymond N. Schouten,
Matthew Markham,
Daniel J. Twitchen,
Ronald Hanson
Apr 18 2014
quantph
condmat.meshall
Realizing robust quantum information transfer between longlived qubit registers is a key challenge for quantum information science and technology. Here we demonstrate unconditional teleportation of arbitrary quantum states between diamond spin qubits separated by 3 meters. We prepare the teleporter through photonmediated heralded entanglement between two distant electron spins and subsequently encode the source qubit in a single nuclear spin. By realizing a fully deterministic Bellstate measurement combined with realtime feedforward we achieve teleportation in each at tempt while obtaining an average state fidelity exceeding the classical limit. These results establish diamond spin qubits as a prime candidate for the realization of quantum networks for quantum communication and networkbased quantum computing.

Randomly breaking connections in a graph alters its transport properties, a model used to describe percolation. In the case of quantum walks, dynamic percolation graphs represent a special type of imperfections, where the connections appear and disappear randomly in each step during the time evolution. The resulting open system dynamics is hard to treat numerically in general. We shortly review the literature on this problem. We then present our method to solve the evolution on finite percolation graphs in the long time limit, applying the asymptotic methods concerning random unitary maps. We work out the case of one dimensional chains in detail and provide a concrete, step by step numerical example in order to give more insight into the possible asymptotic behavior. The results about the case of the twodimensional integer lattice are summarized, focusing on the Grover type coin operator.

Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground state wave functions. For systems with gapped boundaries, these quantities are representations of the mapping class group $MCG(\mathcal M)$ of the space manifold $\mathcal M$ on which the systems lives. We will here consider simple examples in three dimensions and give physical interpretation of these quantities, related to fusion algebra and statistics of particle and string excitations. In particular, we will consider dimensional reduction from 3+1D to 2+1D, and show how the induced 2+1D topological data contains information on the fusion and the braiding of nonAbelian string excitations in 3D. These universal quantities generalize the wellknown modular $S$ and $T$ matrices to any dimension.

In this article, we have introduced the first parallel corpus of Persian with more than 10 other European languages. This article describes primary steps toward preparing a Basic Language Resources Kit (BLARK) for Persian. Up to now, we have proposed morphosyntactic specification of Persian based on EAGLE/MULTEXT guidelines and specific resources of MULTEXTEast. The article introduces Persian Language, with emphasis on its orthography and morphosyntactic features, then a new PartofSpeech categorization and orthography for Persian in digital environments is proposed. Finally, the corpus and related statistic will be analyzed.

Let $n_0(N,k)$ be the number of initial Fourier coefficients necessary to distinguish newforms of level $N$ and even weight $k$. We produce extensive data to support our conjecture that if $N$ is a fixed squarefree positive integer and $k$ is large then $n_0(N,k)$ is the least prime that does not divide $N$.

We present a detailed study of the effects of Lévy $\alpha$stable disorder distributions on the optical and localization properties of excitonic systems. These distributions are a generalization of commonly studied Gaussian randomness ($\alpha = 2$). However, the more general case ($\alpha < 2$) includes also heavytailed behavior with a divergent second moment. These types of distributions give rise to novel effects, such as exchange broadening of the absorption spectra and anomalous localization of the excitonic states, which has been found in various excitonic systems. We provide a thorough examination of the localization behavior and the absorption spectra of excitons in chains with Lévy $\alpha$stable diagonal disorder. Several regimes are considered in detail: (i) weak disorder and small systems, where finite size effects become significant; (ii) intermediate disorder and/or larger systems for which exciton states around the exciton band edge spread over a number of monomers, and (iii) strong disorder where the exciton wave functions resemble the individual molecular states. We propose analytical approaches to describe the disorder scaling of relevant quantities for these three regimes of localization, which match excellently with numerical results. We also show the appearance of short localization segments caused by outliers (monomers having transition energies larger than the exciton band width). Such states give rise to an additional structure in the absorption spectrum, density of states, and in the nontrivial disorder scaling of the absorption band width.

We develop the data structure PReaCH (for Pruned Reachability Contraction Hierarchies) which supports reachability queries in a directed graph, i.e., it supports queries that ask whether two nodes in the graph are connected by a directed path. PReaCH adapts the contraction hierarchy speedup techniques for shortest path queries to the reachability setting. The resulting approach is surprisingly simple and guarantees linear space and near linear preprocessing time. Orthogonally to that, we improve existing pruning techniques for the search by gathering more information from a single DFStraversal of the graph. PReaCHindices significantly outperform previous data structures with comparable preprocessing cost. Methods with faster queries need significantly more preprocessing time in particular for the most difficult instances.

We describe a general method for verifying inequalities between realvalued expressions, especially the kinds of straightforward inferences that arise in interactive theorem proving. In contrast to approaches that aim to be complete with respect to a particular language or class of formulas, our method establishes claims that require heterogeneous forms of reasoning, relying on a NelsonOppenstyle architecture in which specialpurpose modules collaborate and share information. The framework is thus modular and extensible. A prototype implementation shows that the method is promising, complementing techniques that are used by contemporary interactive provers.

Recent years have witnessed a phenomenal growth in the computational capabilities and applications of GPUs. However, this trend has also led to dramatic increase in their power consumption. This paper surveys research works on analyzing and improving energy efficiency of GPUs. It also provides a classification of these techniques on the basis of their main research idea. Further, it attempts to synthesize research works which compare energy efficiency of GPUs with other computing systems, e.g. FPGAs and CPUs. The aim of this survey is to provide researchers with knowledge of stateoftheart in GPU power management and motivate them to architect highly energyefficient GPUs of tomorrow.

In this paper we study mildly singular del Pezzo foliations on complex projective manifolds with Picard number one

We study gravitational interactions of Higgs boson through the unique dimension4 operator $\xi H^\dag H R$, with $H$ the Higgs doublet and $R$ the Ricci scalar curvature. We analyze the effect of this dimensionless nonminimal coupling $\xi$ on weak gauge boson scattering in both Jordan and Einstein frames. We demonstrate that the weak boson scattering amplitudes computed in both frames are equal in flat background. We explicitly establish the longitudinalGoldstone equivalence theorem with nonzero $\xi$ coupling in both frames, and analyze the unitarity constraints. We further extend our study to Higgs inflation, and quantitatively derive the perturbative unitarity bounds via coupled channel analysis, under the large field background at the inflation scale. We analyze the unitarity constraints on the parameter space in both the conventional Higgs inflation and the improved models in light of the recent BICEP2 data.

We give a short proof of a theorem of Handel and Mosher stating that any finitely generated subgroup of $\text{Out}(F_N)$ either contains a fully irreducible automorphism, or virtually fixes the conjugacy class of a proper free factor of $F_N$, and we extend their result to non finitely generated subgroups of $\text{Out}(F_N)$.

The MHD slow mode wave has application to coronal seismology, MHD turbulence, and the solar wind where it can be produced by parametric instabilities. We consider analytically how a drifting ion species (e.g. He$^{++}$) affects the linear slow mode wave in a mainly electronproton plasma, with potential consequences for the aforementioned applications. Our main conclusions are: 1. For wavevectors highly oblique to the magnetic field, we find solutions that are characterized by very small perturbations of total pressure. Thus, our results may help to distinguish the MHD slow mode from kinetic Alfvén waves and nonpropagating pressurebalanced structures, which can also have very small total pressure perturbations. 2. For small ion concentrations, there are solutions that are similar to the usual slow mode in an electronproton plasma, and solutions that are dominated by the drifting ions, but for small drifts the wave modes cannot be simply characterized. 3. Even with zero ion drift, the standard dispersion relation for the highly oblique slow mode cannot be used with the Alfvén speed computed using the summed proton and ion densities, and with the sound speed computed from the summed pressures and densities of all species. 4. The ions can drive a nonresonant instability under certain circumstances. For low plasma beta, the threshold drift can be less than that required to destabilize electromagnetic modes, but damping from the Landau resonance can eliminate this instability altogether, unless $T_{\mathrm e}/T_{\mathrm p}\gg1$.

Calculations are reported for low energy, proton capture by 14N with the recoil corrected continuum shell model. An interaction from a fit to Cohen and Kurath (616) pshell matrix elements and Reid soft core gmatrix elements is employed. The prediction for 14N(p,\gamma)15O, based on this model and available data, is that S(0) equals 1.632 and S(30) is 1.625 keV b. Good agreement with available cross section data support this result. No evidence is found for significant contributions from the subthreshold resonance.

We extend Ng's characterisation of torsion pairs in the 2CalabiYau triangulated category generated by a 2spherical object to the characterisation of torsion pairs in the wCalabiYau triangulated category, $T_w$, generated by a wspherical object for any integer w. Inspired by the combinatorics of $T_w$ for w < 0, we also characterise the torsion pairs in a certain wCalabiYau orbit category of the bounded derived category of the path algebra of Dynkin type A.

A $\left(n,\ell,\gamma\right)$sharing set family of size $m$ is a family of sets $S_1,\ldots,S_m\subseteq [n]$ s.t. each set has size $\ell$ and each pair of sets shares at most $\gamma$ elements. We let $m\left(n,\ell,\gamma\right)$ denote the maximum size of any such set family and we consider the following question: How large can $m\left(n,\ell,\gamma\right)$ be? $\left(n,\ell,\gamma\right)$sharing set families have a rich set of applications including the construction of pseudorandom number generators and usable and secure password management schemes. We analyze the explicit construction of Blocki et al using recent bounds on the value of the $t$'th Ramanujan prime. We show that this explicit construction produces a $\left(4\ell^2\ln 4\ell,\ell,\gamma\right)$sharing set family of size $\left(2 \ell \ln 2\ell\right)^{\gamma+1}$ for any $\ell\geq \gamma$. We also show that the construction of Blocki et al can be used to obtain a weak $\left(n,\ell,\gamma\right)$sharing set family of size $m$ for any $m >0$. These results are competitive with the inexplicit construction of Raz et al for weak $\left(n,\ell,\gamma\right)$sharing families. We show that our explicit construction of weak $\left(n,\ell,\gamma\right)$sharing set families can be used to obtain a parallelizable pseudorandom number generator with a low memory footprint by using the pseudorandom number generator of Nisan and Wigderson. We also prove that $m\left(n,n/c_1,c_2n\right)$ must be a constant whenever $c_2 \leq \frac{2}{c_1^3+c_1^2}$. We show that this bound is nearly tight as $m\left(n,n/c_1,c_2n\right)$ grows exponentially fast whenever $c_2 > c_1^{2}$.

The Dirac oscillators are shown to be an excellent expansion basis for solutions of the Dirac equation by $R$matrix techniques. The combination of the Dirac oscillator and the $R$matrix approach provides a convenient formalism for reactions as well as bound state problems. The utility of the $R$matrix approach is demonstrated in relativistic impulse approximation calculations where exchange terms can be calculated exactly, and scattering waves made orthogonal to bound state wave functions.

The BICEP2 observation of a large tensortoscalar ratio, $r = 0.20^{+0.07}_{0.05}$, implies that the inflaton $\phi$ in singlefield inflation models must satisfy $\phi \sim 10M_{Pl}$ in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound $\phi \; ^{<}_{\sim} \; M_{Pl}$. Here we consider whether it is possible to have successful subPlanckian inflation in the case of twofield inflation. The trajectory in field space cannot be radial if the effective singlefield inflaton is to satisfy the Lyth bound. By considering a complex field $\Phi$, we show that a near circular but aperiodic modulation of a $\Phi^{4}$ potential can reproduce the results of $\phi^2$ chaotic inflation for $n_{s}$ and $r$ while satisfying $\Phi \; ^{<}_{\sim} \; 0.01 M_{Pl}$ throughout.

A search for WV gamma triple vector boson production is presented based on events containing a W boson decaying to a muon or an electron and a neutrino, a second V (W or Z) boson, and a photon. The data correspond to an integrated luminosity of 19.3 inverse femtobarns collected in 2012 with the CMS detector at the LHC in pp collisions at sqrt(s) = 8 TeV. An upper limit of 311 fb on the fiducial cross section for the WV gamma production process is obtained at 95% confidence level for photons with a transverse energy above 30 GeV and with an absolute value of pseudorapidity of less than 1.44. This limit is approximately a factor of 3.4 larger than the standard model predictions that are based on nexttoleading order QCD calculations. Since no evidence of anomalous WW gamma gamma or WWZ gamma quartic gauge boson couplings is found, this paper presents the first experimental limits on the dimension8 parameter f[T,0] and the CPconserving WWZ gamma parameters kappa[0,W] and kappa[C,W]. Limits are also obtained for the WW gamma gamma parameters a[0,W] and a[C,W].

In 2008, Haglund, Morse and Zabrocki formulated a Compositional form of the Shuffle Conjecture of Haglund et al. In very recent work, Gorsky and Negut by combining their discoveries with the work of SchiffmannVasserot on the symmetric function side and the work of Hikita on the combinatorial side, were led to formulate an infinite family of conjectures that extend the original Shuffle Conjecture of Haglund et al. In fact, they formulated one conjecture for each pair (m,n) of coprime integers. This work of GorskyNegut leads naturally to the question as to where the Compositional Shuffle Conjecture of HaglundMorseZabrocki fits into these recent developments. Our discovery here is that there is a compositional extension of the GorskyNegut Shuffle Conjecture for each pair (km,kn), with (m,n) coprime and k > 1.

Current data from the Planck satellite and the BICEP2 telescope favor, at around the $2 \sigma$ level, negative running of the spectral index of curvature perturbations from inflation. We show that for negative running $\alpha < 0$, the curvature perturbation amplitude has a maximum on scales larger than our current horizon size. A condition for the absence of eternal inflation is that the curvature perturbation amplitude always remain below unity on superhorizon scales. For current bounds on $n_{\rm S}$ from Planck, this corresponds to an upper bound of the running $\alpha <  4 \times 10^{5}$, so that even tiny running of the scalar spectral index is sufficient to prevent eternal inflation from occurring, as long as the running remains negative on scales outside the horizon. In singlefield inflation models, negative running is associated with a finite duration of inflation: we show that eternal inflation may not occur even in cases where inflation lasts as long as $10^4$ efolds.

In this paper, we point out a connection between large deviations and the problem of reliable stabilization for multichannel systems. Specifically, for a given class of (reliable) stabilizing statefeedbacks for a multichannel system with small random perturbations, we provide asymptotic estimates for the exit probability distributions on the position of statetrajectories at the first time of their exit from a given portion (or section) of a boundary of a given bounded open domain. Under certain conditions, these exit probability distributions satisfy large deviations with rate functions on the boundary of the domain (i.e., a family of exponential forms, with small exponential orders that depend on asymptotically small random perturbations in the system); and, moreover, they can be characterized by a set of solutions to certain boundary value problems. Finally, we comment on the implication of our result on a codesign technique, using a multiobjective optimization framework, for evaluating the performance of the (reliable) stabilizing statefeedbacks in the system (when there is a single failure in any of the control input channels) and the asymptotic estimates for the mean exit time of the statetrajectories from the given bounded open domain (which is linked with the performance of the whole system).

The exact dynamics of the entanglement between two harmonic modes generated by an angular momentum coupling is examined. Such system arises when considering a particle in a rotating anisotropic harmonic trap or a charged particle in a fixed harmonic potential in a magnetic field, and exhibits a rich dynamical structure, with stable, unstable and critical regimes according to the values of the rotational frequency or field and trap parameters. Consequently, it is shown that the entanglement generated from an initially separable gaussian state can exhibit quite distinct evolutions, ranging from quasiperiodic behavior in stable sectors to different types of unbounded increase in critical and unstable regions. The latter lead respectively to a logarithmic and linear growth of the entanglement entropy with time. It is also shown that entanglement can be controlled by tuning the frequency, such that it can be increased, kept constant or returned to a vanishing value just with stepwise frequency variations. Exact asymptotic expressions for the entanglement entropy in the different dynamical regimes are provided.

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a characterization theorem providing necessary and sufficient semantic conditions for a theory to be of presheaf type. This theorem subsumes all the previous partial results obtained on the subject and has several corollaries which can be used in practice for testing whether a given theory is of presheaf type as well as for generating new examples of theories belonging to this class. Along the way, we establish a number of other results of independent interest, including developments about colimits in the context of indexed categories, expansions of geometric theories and methods for constructing theories classified by a given presheaf topos.

The photodissociation crosssection of SrCl$^+$ is measured in the spectral range of 36000  46000 cm$^{1}$ using a modular timeofflight mass spectrometer (TOFMS). By irradiating a sample of trapped SrCl$^+$ molecular ions with a pulsed dye laser, X$^1\Sigma^+$ state molecular ions are electronically excited to the repulsive wall of the A$^1\Pi$ state, resulting in dissociation. Using the TOFMS, the fragments are detected and the photodissociation crosssection is determined for a broad range of photon energies. Detailed $\textit{ab initio}$ calculations of the molecular potentials and spectroscopic constants are also performed and are found to be in good agreement with experiment. The spectroscopic constants for SrCl$^+$ are also compared to those of another alkaline earth chalcogen, BaCl$^+$, in order to highlight structural differences between the two molecular ions. This work represents the first spectroscopy and $\textit{ab initio}$ calculations of SrCl$^+$.

We present a theory for the cloaking of arbitrarilyshaped objects and demonstrate electromagnetic scatteringcancellation through designed homogeneous coatings. First, in the smallparticle limit, we expand the dipole moment of a coated object in terms of its resonant modes. By zeroing the numerator of the resulting rational function, we accurately predict the permittivity values of the coating layer that abates the total scattered power. Then, we extend the applicability of the method beyond the smallparticle limit, deriving the radiation corrections of the scatteringcancellation permittivity within a perturbation approach. Our method permits the design of invisibility cloaks for irregularlyshaped devices such as complex sensors and detectors.

Classical spectral methods are subject to two fundamental limitations: they only can ac count for covariancerelated serial dependencies, and they require secondorder stationarity. Much attention has been devoted recently to quantilebased spectral methods that go beyond covariancebased serial dependence features. At the same time, methods relaxing stationarity into much weaker local stationarity conditions have been developed for a variety of timeseries models. Here, we are combining those two approaches by proposing quantilebased spectral methods for locally stationary processes. We therefore introduce timevarying versions of the copula spectra and periodograms that have been recently proposed in the literature, along with a new definition of strict local stationarity that allows us to handle completely general nonlinear processes without any moment assumptions, thus accommodating our quantilebased concepts and methods. We establish the consistency of our methods, and illustrate their power by means of simulations and an empirical study of the Standard & Poor's 500 series. This empirical study brings evidence of important variations in serial dependence structures both across time (crises and quiet periods exhibit quite different dependence structures) and across quantiles (dependencies between extreme quantiles are not the same as in the "median" range of the se ries). Such variations remain completely undetected, and are actually undetectable, via classical covariancebased spectral methods.

This paper presents relevant modern mathematical formulations for (classical) gauge field theories, namely, ordinary differential geometry, noncommutative geometry, and transitive Lie algebroids. They provide rigorous frameworks to describe YangMillsHiggs theories or gravitation theories, and each of them improves the paradigm of gauge field theories. A brief comparison between them is carried out, essentially due to the various notions of connection. However they reveal a compelling common mathematical pattern on which the paper concludes.

We discuss the necessity of using nonstandard boson operators for diagonalizing quadratic bosonic forms which are not positive definite and its convenience for describing the temporal evolution of the system. Such operators correspond to nonhermitian coordinates and momenta and are associated with complex frequencies. As application, we examine a bosonic version of a BCSlike pairing Hamiltonian, which, in contrast with the fermionic case, is stable just for limited values of the gap parameter and requires the use of the present extended treatment for a general diagonal representation. The dynamical stability of such forms and the occurrence of nondiagonalizable cases are also discussed.

We present a technique based on extended Lax Pairs to derive variablecoefficient generalizations of various Laxintegrable NLPDE hierarchies. As illustrative examples, we consider generalizations of KdV equations, three variants of generalized MKdV equations, and a recentlyconsidered nonlocal PTsymmetric NLS equation. It is demonstrated that the technique yields Lax or Sintegrable NLPDEs with both time AND spacedependent coefficients which are thus more general than almost all cases considered earlier via other methods such as the Painleve Test, Bell Polynomials, and various similarity methods. Employing the Painleve singular manifold method, some solutions are also presented for the generalized variablecoefficient integrable KdV and MKdV equations derived here. Current and future work is centered on generalizing other integrable hierarchies of NLPDEs similarly, and deriving various integrability properties such as solutions, Backlund Transformations, and hierarchies of conservation laws for these new integrable systems with variable coefficients.

We introduce a statistical method for predicting the types of human activity at the subsecond resolution using the triaxial accelerometry data. The major innovation is that we use labeled activity data from some subjects to predict the activity labels of other subjects. To achieve this, data are normalized at the subject level to match the standing up and lying down patterns of accelerometry data. This is necessary to account for differences between the variability in the position of the device relative to gravity, which are induced by the different body geometry and body placement. Data are also normalized at the device level to ensure that the magnitude of the signal at rest is similar across devices. After normalization we use movelets (a segment of continuous time series) extracted from some of the subjects to predict the movement type of the other subjects. The problem was motivated by and is applied to a laboratory study of 20 older participants who performed different activities while wearing accelerometers at the hip. Prediction results based on other people's labeled dictionaries of activity performed almost as well as those obtained using their own labeled dictionaries. These findings indicate that prediction of activity types in the wild may actually be possible, though more work remains to be done.

We study the optimal stopping problem for a monotonous dynamic risk measure induced by a BSDE with jumps in the Markovian case. We show that the value function is a viscosity solution of an obstacle problem for a partial integrodifferential variational inequality, and we provide an uniqueness result for this obstacle problem.

We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual sense, but with respect to a discounted distance measure that contracts arbitrarily long sequences of edges within the same subgroupoid (coset) and only counts transitions between cosets. Reduced products with such groupoids are sufficiently generic to be applicable to various constructions that are specified in terms of local glueing operations and require global finite closure. We here examine hypergraph coverings and extension tasks that lift local symmetries to global automorphisms.

The cutoff phenomenon for an ergodic Markov chain describes a sharp transition in the convergence to its stationary distribution, over a negligible period of time, known as cutoff window. We study the cutoff phenomenon for simple random walks on Kneser graphs, which is a family of ergodic Markov chains. Given two integers $n$ and $k$, the Kneser graph $K(2n+k,n)$ is defined as the graph with vertex set being all subsets of $\{1,\ldots,2n+k\}$ of size $n$ and two vertices $A$ and $B$ being connected by an edge if $A\cap B =\emptyset$. We show that for any $k=O(n)$, the random walk on $K(2n+k,n)$ exhibits a cutoff at $\frac{1}{2}\log_{1+k/n}{(2n+k)}$ with a window of size $O(\frac{n}{k})$.

A method for fabrication of polarization degenerate oxide apertured micropillar cavities is demon strated. Micropillars are etched such that the size and shape of the oxide front is controlled. The polarization splitting in the circular micropillar cavities due to the native and strain induced bire fringence can be compensated by elongating the oxide front in the [110] direction, thereby reducing stress in this direction. By using this technique we fabricate a polarization degenerate cavity with a quality factor of 1.7*?10^4 and a mode volume of 2.7 u?m3, enabling a calculated maximum Purcell factor of 11.

Let $S_k(\Gamma^{\mathrm{para}}(N))$ be the space of Siegel paramodular forms of level $N$ and weight $k$. Let $p\nmid N$ and let $\chi$ be a nontrivial quadratic Dirichlet character mod $p$. Based on our previous work, we define a linear twisting map $\mathcal{T}_\chi:S_k(\Gamma^{\mathrm{para}}(N))\rightarrow S_k(\Gamma^{\mathrm{para}}(Np^4))$. We calculate an explicit expression for this twist and give the commutation relations of this map with the Hecke operators and AtkinLehner involution for primes $\ell\neq p$.

From the solution of the heat and mass diffusion equations that describe the exothermic physical absorption of a gas into a liquid, compact formulae for the sums of two infinite series are derived. The method is general and should be applicable to other systems of linear, parabolic partial differential equations.

A unified model is constructed, based on flipped $SU(5)$ in which the proton is absolutely stable. The model requires the existence of new leptons with masses of order the weak scale. The possibility that the unification scale could be extremely low is discussed.

We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions possed interesting properties. The density of current and the nonrelativistic limit are analyzed where different conclusions are obtained.

In contextaware trust evaluation, using ontology tree is a popular approach to represent the relation between contexts. Usually, similarity between two contexts is computed using these trees. Therefore, the performance of trust evaluation highly depends on the quality of ontology trees. Fairness or granularity consistency is one of the major limitations affecting the quality of ontology tree. This limitation refers to inequality of semantic similarity in the most ontology trees. In other words, semantic similarity of every two adjacent nodes is unequal in these trees. It deteriorates the performance of contexts similarity computation. We overcome this limitation by weighting tree edges based on their semantic similarity. Weight of each edge is computed using Normalized Similarity Score (NSS) method. This method is based on frequencies of concepts (words) cooccurrences in the pages indexed by search engines. Our experiments represent the better performance of the proposed approach in comparison with established trust evaluation approaches. The suggested approach can enhance efficiency of any solution which models semantic relations by ontology tree.

We construct self similar finite energy solutions to the slightly supercritical generalized KdV equation. These self similar solutions bifurcate as a function of the exponent $p$ from the soliton at the $L^2$ critical exponent.

We establish a characterization of extreme amenability of any Polish group in Fraïssétheoretic terms in the setting of continuous logic, mirroring a theorem due to Kechris, Pestov and Todorcevic for closed subgroups of the permutation group of an infinite countable set.

De Sitter Quantum Gravity is a YangMills theory based on the de Sitter or SO(4,1) group and a promising candidate for a quantum theory of gravity. In this paper, an exact, static, spherically symmetric solution of the classical equations is derived. I show that when the Schwarzchild radius to distance ratio is at postNewtonian order the theory agrees with general relativity for all parameters but that, once the ratio becomes closer to unity, they differ. At the Schwarzchild radius from a black hole singularity, general relativity predicts an event horizon, which has become a controversial topic in quantum gravity because of information preservation issues. In the De Sitter theory I show, however, that timelike escape paths exist for any mass black hole until the singularity itself is reached. Since an event horizon has never been directly observed and there is currently no observation on which the two theories disagree, this provides a powerful test of the De Sitter theory.

We propose a general modelfree strategy for feedback control design of turbulent flows. This strategy called 'machine learning control' (MLC) is capable of exploiting nonlinear mechanisms in a systematic unsupervised manner. It relies on an evolutionary algorithm that is used to evolve an ensemble of feedback control laws until minimization of a targeted cost function. This methodology can be applied to any nonlinear multipleinput multipleoutput (MIMO) system to derive an optimal closedloop control law. MLC is successfully applied to the stabilization of nonlinearly coupled oscillators exhibiting frequency crosstalk, to the maximization of the largest Lyapunov exponent of a forced Lorenz system, and to the mixing enhancement in an experimental mixing layer flow. We foresee numerous potential applications to most nonlinear MIMO control problems, particularly in experiments.

For the onedimensional linear kinetic equation analytical solutions of problems about temperature jump and weak evaporation (condensation) over flat surface are received. The equation has integral of collisions BGK (Bhatnagar, Gross and Krook) and constant frequency of collisions of molecules. Distribution of concentration, mass speed and temperature is received.

Using all recent data on the differential cross sections and spin observables for the reaction $\gamma p \to K^+ \Lambda$, an energyindependent partialwave analysis is performed. The analysis requires multipoles up to $L = 2$; there is no evidence that the fit requires multipoles with $L=3$. At present the available data allow us to extract the dominant multipoles only. These are compatible with the multipoles obtained in the energydependent fit. This result supports the reliability of the BonnGatchina energydependent results.

The nonlinear affine Goldstone model of the emergent gravity, built on the nonlinearly realized/hidden affine symmetry, is concisely revisited. Beyond General Relativity, the explicit violation of general invariance/relativity, under preserving general covariance, is exposed. Dependent on a nondynamical affine connection, a generally covariant secondorder effective Lagrangian for metric gravity is worked out, with the general relativity violation and the gravitational dark matter serving as the signatures of emergence.

Viscous flow past a finite flat plate moving in direction normal to itself is studied numerically.The plate moves with velocity $at^p$, where $p=0,0.5,1,2$. We present the evolution of vorticity profiles, streaklines and streamlines, and study the dependence on the acceleration parameter $p$. Four stages in the vortex evolution, as proposed by Luchini & Tognaccini (2002), are clearly identified. The initial stage, in which the vorticity consists solely of a Rayleigh boundary layer, is shown to last for a timeinterval whose length shrinks to zero like $p^3$, as $p \to 0$. In the second stage, a center of rotation develops near the tip of the plate, well before a vorticity maximum within the vortex core develops. Once the vorticity maximum develops, its position oscillates and differs from the center of rotation. The difference between the two increases with increasing $p$, and decreases in time. In the third stage, the center of rotation and the shed circulation closely satisfy selfsimilar scaling laws for inviscid flow. Finally, in the fourth stage, the finite plate length becomes relevant and the flow begins to depart from the selfsimilar behaviour. While the core trajectory and circulation closely satisfy inviscid scaling laws, the vorticity maximum and the boundary layer thickness follow viscous scaling laws. The results are compared with experimental results of Pullin & Perry (1980), and Taneda & Honji (1971), where available.

The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between elasticity and disorder and test the asymptotic validity of the Weibull distribution through numerical simulations of the twodimensional random fuse model. Even when the local fracture strength follows the Weibull distribution, the global failure distribution is dictated by stress enhancement at the tip of the cracks and sometimes deviates from the Weibull law. Only in the case of a preexisting power law distribution of crack widths do we find that the failure strength is Weibull distributed. Contrary to conventional assumptions, even in this case, the Weibull exponent can not be simply inferred from the exponent of the initial crack width distribution. Our results thus raise some concerns on the applicability of the Weibull distribution in most practical cases.

We consider products of independent random matrices taken from the induced Ginibre ensemble with complex or quaternion elements. The joint densities for the complex eigenvalues of the product matrix can be written down exactly for a product of any fixed number of matrices and any finite matrix size. We show that the squared absolute values of the eigenvalues form a permanental process, generalising the results of Kostlan and Rider for single matrices to products of complex and quaternionic matrices. Based on these findings, we can first write down exact results and asymptotic expansions for the socalled hole probabilities, that a disc centered at the origin is void of eigenvalues. Second, we compute the asymptotic expansion for the opposite problem, that a large fraction of complex eigenvalues occupies a disc of fixed radius centered at the origin; this is known as the overcrowding problem. While the expressions for finite matrix size depend on the parameters of the induced ensembles, the asymptotic results agree to leading order with previous results for products of square Ginibre matrices.

In the context of convex optimization problems in Hilbert spaces, we induce inertial effects into the classical ADMM numerical scheme and obtain in this way socalled inertial ADMM algorithms, the convergence properties of which we investigate into detail. To this aim we make use of the inertial version of the DouglasRachford splitting method for monotone inclusion problems recently introduced in [12], in the context of concomitantly solving a convex minimization problem and its Fenchel dual. The convergence of both sequences of the generated iterates and of the objective function values is addressed. We also show how the obtained results can be extended to the treating of convex minimization problems having as objective a finite sum of convex functions.

O. Meshcheriakova,
S. Chadov,
A. K. Nayak,
U. K. Rößler,
J. Kübler,
G. André,
A. A. Tsirlin,
J. Kiss,
S. Hausdorf,
A. Kalache,
W. Schnelle,
M. Nicklas,
C. Felser
Apr 18 2014
condmat.mtrlsci
Noncollinear magnets provide essential ingredients for the next generation memory technology. It is a new prospect for the Heusler materials, already wellknown due to the diverse range of other fundamental characteristics. Here we present combined experimental/theoretical study of novel noncollinear tetragonal Mn2RhSn Heusler material exhibiting unusally strong canting of its magnetic sublattices. It undergoes a spinreorientation transition, induced by a temperature change and suppressed by the external magnetic field. In addition, because of the noncentrosymmetric structure, DzyaloshinskiiMoriya exchange and magnetic anisotropy, Mn2RhSn is supposed to be a promising candidate for realizing the skyrmion state in the Heusler family.

We present a MATLAB toolbox for five different classes of exponential integrators for solving (mildly) stiff ordinary differential equations or timedependent partial differential equations. For the efficiency of such exponential integrators it is essential to approximate the products of the matrix functions arising in these integrators with vectors in a stable, reliable and efficient way. The toolbox contains options for computing the matrix functions directly by diagonalization or by Pade approximation. For large scale problems, Krylov subspace methods are implemented as well. The main motivation for this toolbox was to provide general tools which on one hand allows one to easily run experiments with different exponential integrators and on the other hand to make it easily extensible by making it simple to include other methods or other options to compute the matrix functions. Thus we implemented the toolbox to be compatible with the ode solvers included in MATLAB. Most of the methods can be used with adaptive stepping.

The structural and magnetic properties of a new series of iridiumbased honeycomb lattices with the formula Na3delta(Na1xMgx)Ir2O6 (x = 0 to 1) are reported. As x and delta are increased, the honeycomb lattice contracts and the strength of the antiferromagnetic interactions decreases systematically due to a reduction in IrOIr bond angles. Samples with imperfect stoichiometry exhibit disordered magnetic freezing at temperatures Tf between 3.4 K and 5 K. This glassy magnetism likely arises due to the presence of nonmagnetic Ir3+, which are distributed randomly throughout the lattice, with a possible additional contribution from stacking faults. Together, these results demonstrate that chemical defects and nonstoichiometry have a significant effect on the magnetism of compounds in the A2IrO3 materials family.

We study the indecomposable summands of the permutation module obtained by inducing the trivial $\mathbb{F}(S_a\wr S_n)$module to the full symmetric group $S_{an}$ for any field $\mathbb{F}$ of odd prime characteristic $p$ such that $a<p\leq n$. In particular we characterize the vertices of such indecomposable summands. As a corollary we will disprove a modular version of Foulkes' Conjecture. In the second part of the article we will use this information to give a new description of some columns of the decomposition matrices of symmetric groups in terms of the ordinary character of the Foulkes module $\phi^{(a^n)}$.

Several trends have been identified in the prompt gammaray burst (GRB) emission: e.g. hardtosoft evolution, pulse width evolution with energy, time lags, hardnessintensity/fluence correlations. Recently Fermi has significantly extended the spectral coverage of GRB observations and improved the characterization of this spectral evolution. We study how internal shocks can reproduce these observations. In this model the emission comes from the synchrotron radiation of shock accelerated electrons, and the spectral evolution is governed by the evolution of the physical conditions in the shocked regions. We present a comprehensive set of simulations of a single pulse and investigate the impact of the model parameters, related to the shock microphysics and to the initial conditions in the ejecta. We find a general qualitative agreement between the model and the various observations used for the comparison. All these properties or relations are governed by the evolution of the peak energy and photon indices of the spectrum. In addition, we identify the conditions for a quantitative agreement. We find that the best agreement is obtained for (i) steep electron slopes (p>~2.7), (ii) microphysics parameters varying with shock conditions so that more electrons are accelerated in stronger shocks, (iii) steep variations of the initial Lorentz factor in the ejecta. When simulating short GRBs by contracting all timescales, all other parameters being unchanged, we show that the hardnessduration correlation is reproduced, as well as the evolution with duration of the pulse properties. Finally, we investigate the signature at high energy of these different scenarios and find distinct properties  delayed onset, longer emission, and flat spectrum in some cases  suggesting that internal shocks could have a significant contribution to the prompt LAT emission. [abridged]

Thermopower and electrical resistivity measurements transverse to the conducting chains of the quasionedimensional metal Li(0.9)Mo(6)O(17) are reported in the temperature range 5 K <= T <= 500 K. For T>= 400 K the interchain transport is determined by thermal excitation of charge carriers from a valence band ~ 0.14 eV below the Fermi level, giving rise to a large, ptype thermopower that coincides with a small, ntype thermopower along the chains. This dichotomy  semiconductorlike in one direction and metallic in a mutually perpendicular direction  gives rise to substantial transverse thermoelectric (TE) effects and a transverse TE figure of merit among the largest known for a single compound.

The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut. We study the Hypergraph Small Set Expansion problem, which, for a parameter $\delta \in (0,1/2]$, asks to compute the cut having the least expansion while having at most $\delta$ fraction of the vertices on the smaller side of the cut. We present two algorithms. Our first algorithm gives an $\tilde O(\delta^{1} \sqrt{\log n})$ approximation. The second algorithm finds a set with expansion $\tilde O(\delta^{1}(\sqrt{d_{\text{max}}r^{1}\log r\, \phi^*} + \phi^*))$ in a $r$uniform hypergraph with maximum degree $d_{\text{max}}$ (where $\phi^*$ is the expansion of the optimal solution). Using these results, we also obtain algorithms for the Small Set Vertex Expansion problem: we get an $\tilde O(\delta^{1} \sqrt{\log n})$ approximation algorithm and an algorithm that finds a set with vertex expansion $O\left(\delta^{1}\sqrt{\phi^V \log d_{\text{max}} } + \delta^{1} \phi^V\right)$ (where $\phi^V$ is the vertex expansion of the optimal solution). For $\delta=1/2$, Hypergraph Small Set Expansion is equivalent to the hypergraph expansion problem. In this case, our approximation factor of $O(\sqrt{\log n})$ for expansion in hypergraphs matches the corresponding approximation factor for expansion in graphs due to ARV.

We consider diffusion in arbitrary spatial dimension d with the addition of a resetting process wherein the diffusive particle stochastically resets to a fixed position at a constant rate $r$. We compute the nonequilibrium stationary state which exhibits nonGaussian behaviour. We then consider the presence of an absorbing target centred at the origin and compute the survival probability and mean time to absorption of the diffusive particle by the target. The mean absorption time is finite and has a minimum value at an optimal resetting rate $r^*$ which depends on dimension. Finally we consider the problem of a finite density of diffusive particles, each resetting to its own initial position. While the typical survival probability of the target at the origin decays exponentially with time regardless of spatial dimension, the average survival probability decays asymptotically as $\exp A (\log t)^d$ where $A$ is a constant. We explain these findings using an interpretation as a renewal process and arguments invoking extreme value statistics.

Cooperation is ubiquitous ranging from multicellular organisms to human societies. Population structures indicating individuals' limited interaction ranges are crucial to understand this issue. But it is still at large to what extend multiple interactions involving nonlinearity in payoff play a role on cooperation in structured populations. Here we show a rule, which determines the emergence and stabilization of cooperation, under multiple discounted, linear, and synergistic interactions. The rule is validated by simulations in homogenous and heterogenous structured populations. We find that the more neighbors there are the harder for cooperation to evolve for multiple interactions with linearity and discounting. For synergistic scenario, however, distinct from its pairwise counterpart, moderate number of neighbors can be the worst, indicating that synergistic interactions work with strangers but not with neighbors. Our results suggest that the combination of different factors which promotes cooperation alone can be worse than that with every single factor.

We investigate analytically the thermodynamical stability of vortices in the ground state of rotating 2dimensional BoseEinstein condensates confined in asymptotically homogeneous trapping potentials in the ThomasFermi regime. Our starting point is the GrossPitaevskii energy functional in the rotating frame. By estimating lower and upper bounds for this energy, we show that the leading order in energy and density can be described by the corresponding ThomasFermi quantities and we derive the next order contributions due to vortices. As an application, we consider a general potential of the form V(x,y) = (x^2+lambda^2 y^2)^s/2 with slope s ∈[2,infinity) and anisotropy lambda ∈(0,1] which includes the harmonic (s=2) and 'flat' (s > infinity) trap, respectively. For this potential, we derive the critical angular velocities for the existence of vortices and show that all vortices are singlyquantized. Moreover, we derive relations which determine the distribution of the vortices in the condensate i.e. the vortex pattern.

The observation data for artificial celestial body 43096, which had been obtained during 20062012 within the framework of international project "The Scientific Network of Optical Instruments for Astrometric and Photometric Observations"  International Scientific Optical Network (ISON), were processed. The Keplerian elements and state vector as of 24 November 2006 01:55:50.76 UTC were determined. The numerical integration of the motion equations was performed accounting for the perturbations due to the polar flattening of the Earth, Moon and Sun, as well as the solar radiation pressure. Based on the numerical model of a motion in the nearEarth space that accounts for only the most powerful perturbations, a new method for deorbiting artificial celestial bodies from high altitudes is suggested. For the first time such a considerable amount of data over long time intervals was gathered for the objects with high areatomass ratio that enabled to determine their specific characteristics.

In light of recent successes in measuring baryon acoustic oscillations in quasar absorption using the Lymanalpha (Lyalpha) transition, I explore the possibility of using the 1548 Ang transition of triplyionized carbon (C IV) as a tracer. While the Lyalpha forest is a more sensitive tracer of intergalactic gas, it is limited by the fact that it can only be measured in the optical window at redshifts z > 2. Quasars are challenging to identify and observe at these highredshifts, but the C IV forest can be probed down to redshifts z = 1.3, taking full advantage of the peak in the redshift distribution of quasars that can be targeted with high efficiency. I explore the strength of the C IV absorption signal and show that the absorbing population on the red side of the Lyalpha emission line is dominated by C IV. As a consequence, I argue that forthcoming surveys will have a sufficient increase in quasar number density to offset the lower sensitivity of the C IV forest and provide competitive precision using both the C IV autocorrelation and the C IVquasar cross correlation at <z> = 1.6.

In experiments, BoseEinstein condensates are prepared by cooling a dilute Bose gas in a trap. After the phase transition has been reached, the trap is switched off and the evolution of the condensate observed. The evolution is macroscopically described by the GrossPitaevskii equation. On the microscopic level, the dynamics of Bose gases are described by the $N$body Schrödinger equation. We review our article [BdS12] in which we construct a class of initial data in Fock space which are energetically close to the ground state and prove that their evolution approximately follows the GrossPitaevskii equation. The key idea is to model twoparticle correlations with a Bogoliubov transformation.

The $n$index Rényi mutual information and transfer entropy for the twodimensional kinetic Ising model with arbitrary singlespin dynamics in the thermodynamic limit are derived as functions of thermodynamic quantities. By means of Monte Carlo simulations with the Wolff algorithm, we calculate the information flows in the Ising model with the Metropolis dynamics and the Glauber dynamics. We find that, not only the global Rényi transfer entropy, but also the pairwise Rényi transfer entropy peaks in the disorder phase. Therefore, the Rényi information flows may be used as better tools than the Shannon counterparts in the study of phase transitions in complex dynamical systems.

We describe a new physical picture for the fragmentation of an energetic jet propagating through a dense QCD medium, which emerges from perturbative QCD and has the potential to explain the dijet asymmetry observed in PbPb collisions at the LHC. The central ingredient in this picture is the phenomenon of wave turbulence, which provides a very efficient mechanism for the transport of energy towards the medium, via many soft particles which propagate at large angles with respect to the jet axis.

This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A spreadingvanishing dichotomy is derived, namely the species either successfully spreads to the righthalfspace as time $t\to\infty$ and survives (persists) in the new environment, or it fails to establish and will extinct in the long run. The sharp criteria for spreading and vanishing is also obtained. When spreading happens, we estimate the asymptotic spreading speed of the free boundary.