Search results for "Mathematica"
showing 10 items of 7971 documents
Thresholding projection estimators in functional linear models
2008
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.
Isotonic regression for metallic microstructure data: estimation and testing under order restrictions
2021
Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physical inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ra…
Centrality measures for networks with community structure
2016
Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order to find the influential nodes, while on the other end, random strategies are completely agnostic ab…
A New Nonparametric Estimate of the Risk-Neutral Density with Applications to Variance Swaps
2021
We develop a new nonparametric approach for estimating the risk-neutral density of asset prices and reformulate its estimation into a double-constrained optimization problem. We evaluate our approach using the S\&P 500 market option prices from 1996 to 2015. A comprehensive cross-validation study shows that our approach outperforms the existing nonparametric quartic B-spline and cubic spline methods, as well as the parametric method based on the Normal Inverse Gaussian distribution. As an application, we use the proposed density estimator to price long-term variance swaps, and the model-implied prices match reasonably well with those of the variance future downloaded from the CBOE websi…
Reliability analysis of processes with moving cracked material
2015
Abstract The reliability of processes with moving elastic and isotropic material containing initial cracks is considered in terms of fracture. The material is modelled as a moving plate which is simply supported from two of its sides and subjected to homogeneous tension acting in the travelling direction. For tension, two models are studied: (i) tension is constant with respect to time, and (ii) tension varies temporally according to an Ornstein–Uhlenbeck process. Cracks of random length are assumed to occur in the material according to a stochastic counting process. For a general counting process, a representation of the nonfracture probability of the system is obtained that exploits condi…
Exact affine counter automata
2017
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las Vegas affine finite automata. Lastly, we show that how a counter helps for affine finite automata by showing that the language MANYTWINS, which is conjectured not to be recognized by affin…
Finite automata with advice tapes
2013
We define a model of advised computation by finite automata where the advice is provided on a separate tape. We consider several variants of the model where the advice is deterministic or randomized, the input tape head is allowed real-time, one-way, or two-way access, and the automaton is classical or quantum. We prove several separation results among these variants, demonstrate an infinite hierarchy of language classes recognized by automata with increasing advice lengths, and establish the relationships between this and the previously studied ways of providing advice to finite automata.
Time and space efficient quantum algorithms for detecting cycles and testing bipartiteness
2016
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms for deciding both properties in $\tilde{O}(n^{3/2})$ time and using $O(\log n)$ classical and quantum bits of storage in the adjacency matrix model. We then present quantum algorithms for deciding the two properties in the adjacency array model, which run in time $\tilde{O}(n\sqrt{d_m})$ and also require $O(\log n)$ space, where $d_m$ is the maximum degree of any vertex in the input graph.
Dirac equation as a quantum walk over the honeycomb and triangular lattices
2018
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to well-known physics partial differential equations, such as the Dirac equation. We show that these simulation results need not rely on the grid: the Dirac equation in $(2+1)$--dimensions can also be simulated, through local unitaries, on the honeycomb or the triangular lattice. The former is of interest in the study of graphene-like materials. The latter, we argue, opens the door for a generalization of the Dirac equation to arbitrary discrete surfaces.
On the origin of power law tails in price fluctuations
2003
In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the response of prices to transactions. They argue that the average market impact function follows a square root law, which gives power law tails for prices with exponent roughly -3. We demonstrate that the long-memory nature of order flow invalidates their statistical analysis of market impact, and present a more careful analysis that properly takes this into account. This makes i…