Showing papers on "Operator (computer programming) published in 2015"

Unfolding spinor wave functions and expectation values of general operators: Introducing the unfolding-density operator

Abstract: We show that the spectral weights W mK (k ) used for the unfolding of two-component spinor eigenstates ∣ ∣ ψ SC mK ⟩=|α⟩|ψ SC mK ,α⟩+|β⟩|ψ SC mK ,β⟩ can be decomposed as the sum of the pa ...

Model-independent precision constraints on dimension-6 operators

Abstract: We discuss electroweak precision constraints on dimension-6 operators in the effective theory beyond the standard model. We identify the combinations of these operators that are constrained by the pole observables (the W and Z masses and on-shell decays) and by the W boson pair production. To this end, we define a set of effective couplings of W and Z bosons to fermions and to itself, which capture the effects of new physics corrections. This formalism clarifies which operators are constrained by which observable, independently of the adopted basis of operators. We obtain numerical constraints on the coefficients of dimension-6 operator in a form that can be easily adapted to any particular basis of operators, or any particular model with new heavy particles.

Hidden symmetries and decay for the wave equation on the Kerr spacetime

Abstract: Energy and decay estimates for the wave equation on the exterior region of slowly rotating Kerr spacetimes are proved. The method used is a generalisation of the vector-field method that allows the use of higher-order symmetry operators. In particular, our method makes use of the second-order Carter operator, which is a hidden symmetry in the sense that it does not correspond to a Killing symmetry of the spacetime.

Worldline approach to semi-classical conformal blocks

Abstract: We extend recent results on semi-classical conformal blocks in 2d CFT and their relation to 3D gravity via the AdS/CFT correspondence. We consider four-point functions with two heavy and two light external operators, along with the exchange of a light operator. By explicit computation, we establish precise agreement between these CFT objects and a simple picture of particle worldlines joined by cubic vertices propagating in asymptotically AdS3 geometries (conical defects or BTZ black holes). We provide a simple argument that explains this agreement.

Crossover Operators in Genetic Algorithms:A Review

Abstract: The performance of Genetic Algorithm (GA) depends on various operators. Crossover operator is one of them. Crossover operators are mainly classified as application dependent crossover operators and application independent crossover operators. Effect of crossover operators in GA is application as well as encoding dependent. This paper will help researchers in selecting appropriate crossover operator for better results. The paper contains description about classical standard crossover operators, binary crossover operators, and application dependant crossover operators. Each crossover operator has its own advantages and disadvantages under various circumstances. This paper reviews the crossover operators proposed and experimented by various researchers.

On the numerical approximation of the Perron-Frobenius and Koopman operator

Abstract: Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - e.g. Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches. The results will be illustrated using simple stochastic differential equations and molecular dynamics examples.

Analytic bootstrap at large spin

Abstract: We use analytic conformal bootstrap methods to determine the anomalous dimensions and OPE coefficients for large spin operators in general conformal field theories in four dimensions containing a scalar operator of conformal dimension Δ ϕ . It is known that such theories will contain an infinite sequence of large spin operators with twists approaching 2Δ ϕ + 2n for each integer n. By considering the case where such operators are separated by a twist gap from other operators at large spin, we analytically determine the n, Δ ϕ dependence of the anomalous dimensions. We find that for all n, the anomalous dimensions are negative for Δ ϕ satisfying the unitarity bound. We further compute the first subleading correction at large spin and show that it becomes universal for large twist. In the limit when n is large, we find exact agreement with the AdS/CFT prediction corresponding to the Eikonal limit of a 2-2 scattering with dominant graviton exchange.

Nonrenormalization Theorems without Supersymmetry.

Abstract: We derive a new class of one-loop nonrenormalization theorems that strongly constrain the running of higher dimension operators in a general four-dimensional quantum field theory. Our logic follows from unitarity: cuts of one-loop amplitudes are products of tree amplitudes, so if the latter vanish then so too will the associated divergences. Finiteness is then ensured by simple selection rules that zero out tree amplitudes for certain helicity configurations. For each operator we define holomorphic and antiholomorphic weights, (w, w¯) = (n − h,n + h), where n and h are the number and sum over helicities of the particles created by that operator. We argue that an operator O_i can only be renormalized by an operator O_j if w_i ≥ w_j and w¯_i ≥ w¯_j, absent nonholomorphic Yukawa couplings. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model. Since our claims rely on unitarity and helicity rather than an explicit symmetry, they apply quite generally.

Ten equivalent definitions of the fractional Laplace operator

Abstract: This article reviews several definitions of the fractional Laplace operator (-Delta)^{alpha/2} (0 < alpha < 2) in R^d, also known as the Riesz fractional derivative operator, as an operator on Lebesgue spaces L^p, on the space C_0 of continuous functions vanishing at infinity and on the space C_{bu} of bounded uniformly continuous functions. Among these definitions are ones involving singular integrals, semigroups of operators, Bochner's subordination and harmonic extensions. We collect and extend known results in order to prove that all these definitions agree: on each of the function spaces considered, the corresponding operators have common domain and they coincide on that common domain.

An efficient matrix product operator representation of the quantum chemical Hamiltonian

Abstract: We describe how to efficiently construct the quantum chemical Hamiltonian operator in matrix product form. We present its implementation as a density matrix renormalization group (DMRG) algorithm for quantum chemical applications. Existing implementations of DMRG for quantum chemistry are based on the traditional formulation of the method, which was developed from the point of view of Hilbert space decimation and attained higher performance compared to straightforward implementations of matrix product based DMRG. The latter variationally optimizes a class of ansatz states known as matrix product states, where operators are correspondingly represented as matrix product operators (MPOs). The MPO construction scheme presented here eliminates the previous performance disadvantages while retaining the additional flexibility provided by a matrix product approach, for example, the specification of expectation values becomes an input parameter. In this way, MPOs for different symmetries — abelian and non-abelian — and different relativistic and non-relativistic models may be solved by an otherwise unmodified program.

Properties of the Katugampola fractional derivative with potential application in quantum mechanics

Abstract: Katugampola [e-print arXiv:1410.6535] recently introduced a limit based fractional derivative, Dα (referred to in this work as the Katugampola fractional derivative) that maintains many of the familiar properties of standard derivatives such as the product, quotient, and chain rules. Typically, fractional derivatives are handled using an integral representation and, as such, are non-local in character. The current work starts with a key property of the Katugampola fractional derivative, Dα[y]=t1−αdydt, and the associated differential operator, Dα = t1−αD1. These operators, their inverses, commutators, anti-commutators, and several important differential equations are studied. The anti-commutator serves as a basis for the development of a self-adjoint operator which could potentially be useful in quantum mechanics. A Hamiltonian is constructed from this operator and applied to the particle in a box model.

Accident response using autonomous vehicle monitoring

Abstract: Methods and systems are provided for monitoring use of a vehicle having one or more autonomous (and/or semi-autonomous) operation features to determine and respond to incidents, such as collisions, thefts, or breakdowns. According to certain aspects, operating data from sensors within or near the vehicle may be used to determine when an incident has occurred and determine an appropriate response. The responses may include contacting a third party to provide assistance, such as local emergency services. In some embodiments, occurrence of the incident may be verified by automated communication with the vehicle operator.

Abstract Volterra Integro-Differential Equations

Abstract: PREFACE NOTATION INTRODUCTION PRELIMINARIES Vector-valued functions, closed operators and integration in sequentially complete locally convex spaces Laplace transform in sequentially complete locally convex spaces Operators of fractional differentiation, Mittag-Leffler and Wright functions (a k)-REGULARIZED C-RESOLVENT FAMILIES IN LOCALLY CONVEX SPACES Definition and main structural properties of (a k)-regularized C-resolvent families Wellposedness of related abstract Cauchy problems Convoluted C-semigroups and convoluted C-cosine functions in locally convex spaces Differential and analytical properties of (a k)-regularized C-resolvent families Systems of abstract time-fractional equations q-Exponentially equicontinuous (a k)-regularized C-resolvent families Abstract differential operators generating fractional resolvent families Perturbation theory for abstract Volterra equations Bounded perturbation theorems Unbounded perturbation theorems Time-dependent perturbations of abstract Volterra equations Approximation and convergence of (a k)-regularized C-resolvent families (a k)-Regularized (C1 C2)-existence and uniqueness families Complex powers of (a b C)-nonnegative operators and fractional resolvent families generated by them Complex powers of a C-sectorial operator A satisfying 0 2 (C(A)) The Balakrishnan operators Complex powers of almost C-nonnegative operators The case m = 1 Semigroups generated by fractional powers of almost C-sectorial operators Fractional powers of (a b C)-nonnegative operators and semigroups generated by them The existence and growth of mild solutions of operators generating fractionally integrated C-semigroups and cosine functions in locally convex spaces Representation of powers Abstract multi-term fractional differential equations k-Regularized (C1 C2)-existence and uniqueness propagation families for (2) k-Regularized (C1 C2)-existence and uniqueness families for (2) Approximation and convergence of k-regularized C-resolvent propagation families further results, examples and applications (a k)-Regularized C-resolvent families and abstract multi-term fractional differential equations HYPERCYCLIC AND TOPOLOGICALLY MIXING PROPERTIES OF CERTAIN CLASSES OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS Hypercyclic and topologically mixing properties of abstract rst order equations Disjoint hypercyclic semigroups Hypercyclic and topologically mixing properties of abstract second order equations C-Distribution cosine functions, almost C-distribution cosine functions and integrated C-cosine functions Hypercyclicity and chaos for C-distribution cosine functions and integrated C-cosine functions Hypercyclic and chaotic properties of cosine functions Disjoint hypercyclicity of C-distribution cosine functions Hypercyclic and topologically mixing properties of abstract multi-term fractional differential equations Hypercyclic and topologically mixing properties of -times C-regularized resolvent families Hypercyclic and topologically mixing properties of solutions of (2) with Aj = cjI cj 2 C j 2 Nn1 Topological dynamics of certain classes of abstract time-fractional PDEs with unilateral backward shifts Index

Factorization of Mellin amplitudes

Abstract: We introduce Mellin amplitudes for correlation functions of k scalar operators and one operator with spin in conformal field theories (CFT) in general dimension. We show that Mellin amplitudes for scalar operators have simple poles with residues that factorize in terms of lower point Mellin amplitudes, similarly to what happens for scattering amplitudes in flat space. Finally, we study the flat space limit of Anti-de Sitter (AdS) space, in the context of the AdS/CFT correspondence, and generalize a formula relating CFT Mellin amplitudes to scattering amplitudes of the bulk theory, including particles with spin.

Bootstrapping $O(N)$ vector models in 4 $< d <$ 6

Abstract: We use the conformal bootstrap to study conformal field theories with O(N) global symmetry in d=5 and d=5.95 space-time dimensions that have a scalar operator ϕi transforming as an O(N) vector. The crossing symmetry of the four-point function of this O(N) vector operator, along with unitarity assumptions, determines constraints on the scaling dimensions of conformal primary operators in the ϕi×ϕj operator product expansionImposing a lower bound on the second smallest scaling dimension of such an O(N)-singlet conformal primary, and varying the scaling dimension of the lowest one, we obtain an allowed region that exhibits a kink located very close to the interacting O(N)-symmetric conformal field theory conjectured to exist recently by Fei, Giombi, and Klebanov. Under reasonable assumptions on the dimension of the second lowest O(N) singlet in the ϕi×ϕj operator product expansion, we observe that this kink disappears in d=5 for small enough N, suggesting that in this case an interacting O(N) conformal field theory may cease to exist for N below a certain critical value.

Rosetta: an operator basis translator for standard model effective field theory

Abstract: We introduce Rosetta, a program allowing for the translation between different bases of effective field theory operators. We present the main functions of the program and provide an example of usage. One of the Lagrangians which Rosetta can translate into has been implemented into FeynRules, which allows Rosetta to be interfaced into various high-energy physics programs such as Monte Carlo event generators. In addition to popular bases choices, such as the Warsaw and Strongly Interacting Light Higgs bases already implemented in the program, we also detail how to add new operator bases into the Rosetta package. In this way, phenomenological studies using an effective field theory framework can be straightforwardly performed.

Systematic classification of two-loop realizations of the Weinberg operator

Abstract: We systematically analyze the d = 5 Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop contributions, are guaranteed to be absent. And (ii) finite 2-loop diagrams, which correspond to the 1-loop generation of some particular vertex appearing in a given 1-loop neutrino mass model, thus being effectively 2-loop. From the large list of all possible 2-loop diagrams, the vast majority are infinite corrections to lower order neutrino mass models and only a moderately small number of diagrams fall into these two interesting classes. Moreover, all diagrams in class (i) are just variations of three basic diagrams, with examples discussed in the literature before. Similarly, we also show that class (ii) diagrams consists of only variations of these three plus two more basic diagrams. Finally, we show how our results can be consistently and readily used in order to construct two-loop neutrino mass models.

Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators

Abstract: We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of the method that finds a solution of a variational inequality that is also a fixed point of a quasi-nonexpansive operator. We establish the weak convergence of the methods without any Lipschitzian continuity assumption on operators.

Joint Assignment, Scheduling, and Routing Models to Home Care Optimization: A Pattern-Based Approach

Abstract: The design of efficient home care services is a quite recent and challenging field of study. We propose an integrated approach that jointly addresses: i the assignment of operators to patients so as to guarantee the compatibility between skills associated with operators and patient visits; ii the scheduling of the visits in a given planning horizon; and iii the determination of the operator tours in every day of the planning horizon. The main home care problem we investigate refers to providers dedicated to palliative care and terminal patients. In this context, balancing objective functions are particularly relevant. Therefore, two balancing functions are studied, i.e., maxmin, which maximizes the minimum operator utilization factor, and minmax, which minimizes the maximum operator utilization factor. In both cases, the concept of pattern is introduced as a key tool to jointly address assignment, scheduling, and routing decisions, where a pattern specifies a possible schedule for skilled visits. The approach we propose is, however, able to cope with peculiarities from other home care contexts. Model extensions to handle scenarios other than the palliative one are discussed in the paper. Extensive computational results are reported both on palliative home care instances based on real data, and on two real-world data sets from the literature, related to contexts very different from the palliative one. For both data sets the proposed approach is able to find solutions of good quality. In the palliative context, the results show that the selection of the pattern generation policy is crucial to solve large instances efficiently. Furthermore, the maxmin criterion is able to return more balanced solutions; i.e., the difference between the maximum and the minimum operator utilization factors is very small. On the other hand, the minmax criterion is more suitable for minimizing the operating costs, since it computes solutions with smaller total traveled time.

Matrix models from operators and topological strings, 2

Abstract: The quantization of mirror curves to toric Calabi--Yau threefolds leads to trace class operators, and it has been conjectured that the spectral properties of these operators provide a non-perturbative realization of topological string theory on these backgrounds. In this paper, we find an explicit form for the integral kernel of the trace class operator in the case of local P1xP1, in terms of Faddeev's quantum dilogarithm. The matrix model associated to this integral kernel is an O(2) model, which generalizes the ABJ(M) matrix model. We find its exact planar limit, and we provide detailed evidence that its 1/N expansion captures the all genus topological string free energy on local P1xP1.

Proximal Algorithms in Statistics and Machine Learning

Abstract: Proximal algorithms are useful for obtaining solutions to difficult optimization problems, especially those involving nonsmooth or composite objective functions. A proximal algorithm is one whose basic iterations involve the proximal operator of some function, whose evaluation requires solving a specific optimization problem that is typically easier than the original problem. Many familiar algorithms can be cast in this form, and this “proximal view” turns out to provide a set of broad organizing principles for many algorithms useful in statistics and machine learning. In this paper, we show how a number of recent advances in this area can inform modern statistical practice. We focus on several main themes: (1) variable splitting strategies and the augmented Lagrangian; (2) the broad utility of envelope (or variational) representations of objective functions; (3) proximal algorithms for composite objective functions; and (4) the surprisingly large number of functions for which there are closed-form solutions of proximal operators. We illustrate our methodology with regularized Logistic and Poisson regression incorporating a nonconvex bridge penalty and a fused lasso penalty. We also discuss several related issues, including the convergence of nondescent algorithms, acceleration and optimization for nonconvex functions. Finally, we provide directions for future research in this exciting area at the intersection of statistics and optimization.

Hilbert series and operator bases with derivatives in effective field theories

Abstract: We introduce a systematic framework for counting and finding independent operators in effective field theories, taking into account the redundancies associated with use of the classical equations of motion and integration by parts. By working in momentum space, we show that the enumeration problem can be mapped onto that of understanding a polynomial ring in the field momenta. All-order information about the number of independent operators in an effective field theory is encoded in a geometrical object of the ring known as the Hilbert series. We obtain the Hilbert series for the theory of N real scalar fields in (0+1) dimensions--an example, free of space-time and internal symmetries, where aspects of our framework are most transparent. Although this is as simple a theory involving derivatives as one could imagine, it provides fruitful lessons to be carried into studies of more complicated theories: we find surprising and rich structure from an interplay between integration by parts and equations of motion and a connection with SL(2,C) representation theory which controls the structure of the operator basis.

A discrete artificial bee colony algorithm incorporating differential evolution for the flow-shop scheduling problem with blocking

Abstract: A flow-shop scheduling problem with blocking has important applications in a variety of industrial systems but is underrepresented in the research literature. In this study, a novel discrete artificial bee colony (ABC) algorithm is presented to solve the above scheduling problem with a makespan criterion by incorporating the ABC with differential evolution (DE). The proposed algorithm (DE-ABC) contains three key operators. One is related to the employed bee operator (i.e. adopting mutation and crossover operators of discrete DE to generate solutions with good quality); the second is concerned with the onlooker bee operator, which modifies the selected solutions using insert or swap operators based on the self-adaptive strategy; and the last is for the local search, that is, the insert-neighbourhood-based local search with a small probability is adopted to improve the algorithm's capability in exploitation. The performance of the proposed DE-ABC algorithm is empirically evaluated by applying it to well-kno...

2, 84, 30, 993, 560, 15456, 11962, 261485, ...: Higher dimension operators in the SM EFT

Abstract: In a companion paper, we show that operator bases for general effective field theories are controlled by the conformal algebra. Equations of motion and integration by parts identities can be systematically treated by organizing operators into irreducible representations of the conformal group. In the present work, we use this result to study the standard model effective field theory (SM EFT), determining the content and number of higher dimension operators up to dimension 12, for an arbitrary number of fermion generations. We find additional operators to those that have appeared in the literature at dimension 7 (specifically in the case of more than one fermion generation) and at dimension 8. (The title sequence is the total number of independent operators in the SM EFT with one fermion generation, including hermitian conjugates, ordered in mass dimension, starting at dimension 5.)

Semantic Backpropagation for Designing Search Operators in Genetic Programming

Abstract: In genetic programming, a search algorithm is expected to produce a program that achieves the desired final computation state (desired output). To reach that state, an executing program needs to traverse certain intermediate computation states. An evolutionary search process is expected to autonomously discover such states. This can be difficult for nontrivial tasks that require long programs to be solved. The semantic backpropagation algorithm proposed in this paper heuristically inverts the execution of evolving programs to determine the desired intermediate computation states. Two search operators, random desired operator and approximately geometric semantic crossover, use the intermediate states determined by semantic backpropagation to define subtasks of the original programming task, which are then solved using an exhaustive search. The operators outperform the standard genetic search operators and other semantic-aware operators when compared on a suite of symbolic regression and Boolean benchmarks. This result and additional analysis conducted in this paper indicate that semantic backpropagation helps evolution to identify the desired intermediate computation states and makes the search process more efficient.