亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

An inner-product Hilbert space formulation of the Kemeny distance is defined over the domain of all permutations with ties upon the extended real line, and results in an unbiased minimum variance (Gauss-Markov) correlation estimator upon a homogeneous i.i.d. sample. In this work, we construct and prove the necessary requirements to extend this linear topology for both Spearman's \(\rho\) and Kendall's \(\tau_{b}\), showing both spaces to be both biased and inefficient upon practical data domains. A probability distribution is defined for the Kemeny \(\tau_{\kappa}\) estimator, and a Studentisation adjustment for finite samples is provided as well. This work allows for a general purpose linear model duality to be identified as a unique consistent solution to many biased and unbiased estimation scenarios.

We show that solution to the Hermite-Pad\'{e} type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev-Petviashvili) system and of its adjoint linear problem. Our result explains the appearence of various ingredients of the integrable systems theory in application to multiple orthogonal polynomials, numerical algorthms, random matrices, and in other branches of mathematical physics and applied mathematics where the Hermite-Pad\'{e} approximation problem is relevant. We present also the geometric algorithm, based on the notion of Desargues maps, of construction of solutions of the problem in the projective space over the field of rational functions. As a byproduct we obtain the corresponding generalization of the Wynn recurrence. We isolate the boundary data of the Hirota system which provide solutions to Hermite-Pad\'{e} problem showing that the corresponding reduction lowers dimensionality of the system. In particular, we obtain certain equations which, in addition to the known ones given by Paszkowski, can be considered as direct analogs of the Frobenius identities. We study the place of the reduced system within the integrability theory, which results in finding multidimensional (in the sense of number of variables) extension of the discrete-time Toda chain equations.

We develop two unfitted finite element methods for the Stokes equations based on $\mathbf{H}^{\text{div}}$-conforming finite elements. The first method is a cut finite element discretization of the Stokes equations based on the Brezzi-Douglas-Marini elements and involves interior penalty terms to enforce tangential continuity of the velocity at interior edges in the mesh. The second method is a cut finite element discretization of a three-field formulation of the Stokes problem involving the vorticity, velocity, and pressure and uses the Raviart-Thomas space for the velocity. We present mixed ghost penalty stabilization terms for both methods so that the resulting discrete problems are stable and the divergence-free property of the $\mathbf{H}^{\text{div}}$-conforming elements is preserved also for unfitted meshes. We compare the two methods numerically. Both methods exhibit robust discrete problems, optimal convergence order for the velocity, and pointwise divergence-free velocity fields, independently of the position of the boundary relative to the computational mesh.

We consider a mixed finite element method for a biharmonic equation with clamped boundary conditions based on biorthogonal systems with weakly imposed Dirichlet boundary condition. We show that the weak imposition of the boundary condition arising from a natural minimisation formulation allows to get an optimal a priori error estimate for the finite element scheme improving the existing error estimate for such a formulation without weakly imposed Dirichlet boundary condition. We also briefly outline the algebraic formulation arising from the finite element method.

Rueppel's conjecture on the linear complexity of the first $n$ terms of the sequence $(1,1,0,1,0^3,1,0^7,1,0^{15},\ldots)$ was first proved by Dai using the Euclidean algorithm. We have previously shown that we can attach a homogeneous (annihilator) ideal of $F[x,z]$ to the first $n$ terms of a sequence over a field $F$ and construct a pair of generating forms for it. This approach gives another proof of Rueppel's conjecture. We also prove additional properties of these forms and deduce the outputs of the LFSR synthesis algorithm applied to the first $n$ terms. Further, dehomogenising the leading generators yields the minimal polynomials of Dai.

The important Kemeny problem, which consists of computing median consensus rankings of an election with respect to the Kemeny voting rule, admits important applications in biology and computational social choice and was generalized recently via an interesting setwise approach by Gilbert et. al. Our first results establish optimal quantitative extensions of the Unanimity property and the well-known $3/4$-majority rule of Betzler et al. for the classical Kemeny median problem. Moreover, by elaborating an exhaustive list of quantified axiomatic properties (such as the Condorcet and Smith criteria, the $5/6$-majority rule, etc.) of the $3$-wise Kemeny rule where not only pairwise comparisons but also the discordance between the winners of subsets of three candidates are also taken into account, we come to the conclusion that the $3$-wise Kemeny voting scheme induced by the $3$-wise Kendall-tau distance presents interesting advantages in comparison with the classical Kemeny rule. For example, it satisfies several improved manipulation-proof properties. Since the $3$-wise Kemeny problem is NP-hard, our results also provide some of the first useful space reduction techniques by determining the relative orders of pairs of alternatives. Our works suggest similar interesting properties of higher setwise Kemeny voting schemes which justify and compensate for the more expensive computational cost than the classical Kemeny scheme.

In this paper we obtain complexity bounds for computational problems on algebraic power series over several commuting variables. The power series are specified by systems of polynomial equations: a formalism closely related to weighted context-free grammars. We focus on three problems -- decide whether a given algebraic series is identically zero, determine whether all but finitely many coefficients are zero, and compute the coefficient of a specific monomial. We relate these questions to well-known computational problems on arithmetic circuits and thereby show that all three problems lie in the counting hierarchy. Our main result improves the best known complexity bound on deciding zeroness of an algebraic series. This problem is known to lie in PSPACE by reduction to the decision problem for the existential fragment of the theory of real closed fields. Here we show that the problem lies in the counting hierarchy by reduction to the problem of computing the degree of a polynomial given by an arithmetic circuit. As a corollary we obtain new complexity bounds on multiplicity equivalence of context-free grammars restricted to a bounded language, language inclusion of a nondeterministic finite automaton in an unambiguous context-free grammar, and language inclusion of a non-deterministic context-free grammar in an unambiguous finite automaton.

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method {in two space dimensions} to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the $L^2$-norm and in a discrete energy norm. Finally, we present numerical examples to substantiate the theoretical findings.

In temporal extensions of Answer Set Programming (ASP) based on linear-time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in Metric Equilibrium Logic and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of some of its partial derivatives in $u$. DDEs occur frequently in combinatorics, especially in map enumeration. If a DDE is of fixed-point type then its solution $F(t,u)$ is unique, and a general result by Popescu (1986) implies that $F(t,u)$ is an algebraic power series. Constructive proofs of algebraicity for solutions of fixed-point type DDEs were proposed by Bousquet-M\'elou and Jehanne (2006). Bostan et. al (2022) initiated a systematic algorithmic study of such DDEs of order 1. We generalize this study to DDEs of arbitrary order. First, we propose nontrivial extensions of algorithms based on polynomial elimination and on the guess-and-prove paradigm. Second, we design two brand-new algorithms that exploit the special structure of the underlying polynomial systems. Last, but not least, we report on implementations that are able to solve highly challenging DDEs with a combinatorial origin.