2,561 research outputs found

    On the complexity of posets

    Get PDF
    AbstractThe purpose of this paper is to discuss several invariants each of which provides a measure of the intuitive notion of complexity for a finite partially ordered set. For a poset X the invariants discussed include cardinality, width, length, breadth, dimension, weak dimension, interval dimension and semiorder dimension denoted respectively X, W(X), L(X), B(X), dim(X). Wdim(X), Idim(X) and Sdim(X). Among these invariants the following inequalities hold. B(X)⩽Idim(X)⩽Sdim(X)⩽Wdim(X)⩽dim(X)⩽W(X). We prove that every poset X with three of more points contains a partly with Idim(X) Idim(X) {x,v}). If M denotes the set of maximal elements and A an arbitrary anticham of X we show that Idim(X)⩽W(X-M) and Idim(X)⩽2W(X-A). We also show that there exist functions f(n,t) and (gt) such that I(X)⩽n and Idim(X)⩽tsimply dim(X)⩽f(n,t and Sdim(X)⩽t implies dim(X)⩽g(t)

    Structure and optical properties of high light output halide scintillators

    Full text link
    Structural and optical properties of several high light output halide scintillators and closely related materials are presented based on first principles calculations. The optical properties are based on the Engel-Vosko generalized gradient approximation and the recently developed density functional of Tran and Blaha. The materials investigated are BaBr2_2, BaIBr, BaCl2_2, BaF2_2, BaI2_2, BiI3_3, CaI2_2, Cs2LiYCl_2LiYCl_6,CsBa, CsBa_2BrBr_5,CsBa, CsBa_2II_5,K, K_2LaBrLaBr_5,K, K_2LaClLaCl_5,K,K_2LaILaI_5,LaBr, LaBr_3,LaCl, LaCl_3,SrBr, SrBr_2,andYI, and YI_3.ForcomparisonresultsarepresentedfortheoxideCdWO. For comparison results are presented for the oxide CdWO_4.WefindthattheTranBlahafunctionalgivesgreatlyimprovedbandgapsandopticalpropertiesinthisclassofmaterials.Furthermore,wefindthatunlikeCdWO. We find that the Tran Blaha functional gives greatly improved band gaps and optical properties in this class of materials. Furthermore, we find that unlike CdWO_4$, most of these halides are highly isotropic from an optical point of view even though in many cases the crystal structures and other properties are not. This general result is rationalized in terms of halide chemistry. Implications for the development of ceramic halide scintillators are discussed

    Exploring Variation Between Artificial Grammar Learning Experiments: Outlining a Meta-Analysis Approach

    Get PDF
    Artificial grammar learning (AGL) has become an important tool used to understand aspects of human language learning and whether the abilities underlying learning may be unique to humans or found in other species. Successful learning is typically assumed when human or animal participants are able to distinguish stimuli generated by the grammar from those that are not at a level better than chance. However, the question remains as to what subjects actually learn in these experiments. Previous studies of AGL have frequently introduced multiple potential contributors to performance in the training and testing stimuli, but meta‐analysis techniques now enable us to consider these multiple information sources for their contribution to learning—enabling intended and unintended structures to be assessed simultaneously. We present a blueprint for meta‐analysis approaches to appraise the effect of learning in human and other animal studies for a series of artificial grammar learning experiments, focusing on studies that examine auditory and visual modalities. We identify a series of variables that differ across these studies, focusing on both structural and surface properties of the grammar, and characteristics of training and test regimes, and provide a first step in assessing the relative contribution of these design features of artificial grammars as well as species‐specific effects for learning

    On the Sign Problem in the Hirsch-Fye Algorithm for Impurity Problems

    Full text link
    We show that there is no fermion sign problem in the Hirsch and Fye algorithm for the single-impurity Anderson model. Beyond the particle-hole symmetric case for which a simple proof exists, this has been known only empirically. Here we prove the nonexistence of a sign problem for the general case by showing that each spin trace for a given Ising configuration is separately positive. We further use this insight to analyze under what conditions orbitally degenerate Anderson models or the two-impurity Anderson model develop a sign.Comment: 2 pages, no figure; published versio

    A multipole-Taylor expansion for the potential of gravitational lens MG J0414+0534

    Get PDF
    We employ a multipole-Taylor expansion to investigate how tightly the gravitational potential of the quadruple-image lens MG J0414+0534 is constrained by recent VLBI observations. These observations revealed that each of the four images of the background radio source contains four distinct components, thereby providing more numerous and more precise constraints on the lens potential than were previously available. We expand the two-dimensional lens potential using multipoles for the angular coordinate and a modified Taylor series for the radial coordinate. After discussing the physical significance of each term, we compute models of MG J0414+0534 using only VLBI positions as constraints. The best-fit model has both interior and exterior quadrupole moments as well as exterior m=3 and m=4 multipole moments. The deflector centroid in the models matches the optical galaxy position, and the quadrupoles are aligned with the optical isophotes. The radial distribution of mass could not be well constrained. We discuss the implications of these models for the deflector mass distribution and for the predicted time delays between lensed components.Comment: 44 pages, 5 figures, 11 tables, accepted for publication in Ap

    On FO2 quantifier alternation over words

    Full text link
    We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of the rankers defined by Weis and Immerman, to produce a decidable hierarchy of varieties which is interwoven with the quantifier alternation hierarchy -- and conjecturally equal to it. It follows that the latter hierarchy is decidable within one unit: given a formula alpha in FO^2[<], one can effectively compute an integer m such that alpha is equivalent to a formula with at most m+1 alternating blocks of quantifiers, but not to a formula with only m-1 blocks. This is a much more precise result than what is known about the quantifier alternation hierarchy within FO[<], where no decidability result is known beyond the very first levels

    Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length

    Full text link
    Single-particle transport in disordered potentials is investigated on scales below the localization length. The dynamics on those scales is concretely analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder. This analysis particularly includes the dependence of characteristic transport quantities on the amount of disorder and the energy interval, e.g., the mean free path which separates ballistic and diffusive transport regimes. For these regimes mean velocities, respectively diffusion constants are quantitatively given. By the use of the Boltzmann equation in the limit of weak disorder we reveal the known energy-dependencies of transport quantities. By an application of the time-convolutionless (TCL) projection operator technique in the limit of strong disorder we find evidence for much less pronounced energy dependencies. All our results are partially confirmed by the numerically exact solution of the time-dependent Schroedinger equation or by approximative numerical integrators. A comparison with other findings in the literature is additionally provided.Comment: 23 pages, 10 figure

    Limitations of Quantum Simulation Examined by Simulating a Pairing Hamiltonian using Nuclear Magnetic Resonance

    Full text link
    Quantum simulation uses a well-known quantum system to predict the behavior of another quantum system. Certain limitations in this technique arise, however, when applied to specific problems, as we demonstrate with a theoretical and experimental study of an algorithm to find the low-lying spectrum of a Hamiltonian. While the number of elementary quantum gates does scale polynomially with the size of the system, it increases inversely to the desired error bound ϵ\epsilon. Making such simulations robust to decoherence using fault-tolerance constructs requires an additional factor of 1/ϵ1/ \epsilon gates. These constraints are illustrated by using a three qubit nuclear magnetic resonance system to simulate a pairing Hamiltonian, following the algorithm proposed by Wu, Byrd, and Lidar.Comment: 6 pages, 2 eps figure

    Robust Chauvenet Outlier Rejection

    Full text link
    Sigma clipping is commonly used in astronomy for outlier rejection, but the number of standard deviations beyond which one should clip data from a sample ultimately depends on the size of the sample. Chauvenet rejection is one of the oldest, and simplest, ways to account for this, but, like sigma clipping, depends on the sample's mean and standard deviation, neither of which are robust quantities: Both are easily contaminated by the very outliers they are being used to reject. Many, more robust measures of central tendency, and of sample deviation, exist, but each has a tradeoff with precision. Here, we demonstrate that outlier rejection can be both very robust and very precise if decreasingly robust but increasingly precise techniques are applied in sequence. To this end, we present a variation on Chauvenet rejection that we call "robust" Chauvenet rejection (RCR), which uses three decreasingly robust/increasingly precise measures of central tendency, and four decreasingly robust/increasingly precise measures of sample deviation. We show this sequential approach to be very effective for a wide variety of contaminant types, even when a significant -- even dominant -- fraction of the sample is contaminated, and especially when the contaminants are strong. Furthermore, we have developed a bulk-rejection variant, to significantly decrease computing times, and RCR can be applied both to weighted data, and when fitting parameterized models to data. We present aperture photometry in a contaminated, crowded field as an example. RCR may be used by anyone at https://skynet.unc.edu/rcr, and source code is available there as well.Comment: 62 pages, 48 figures, 7 tables, accepted for publication in ApJ
    corecore