(Abstract) In this article, we disprove the long-standing conjecture, proposed by R. E. Bryant in 1986, that any binary operation on two Boolean functions can be performed by his BDD algorithm in input-output linear time. We present Boolean functions for which his algorithm requires quadratic time in the input-output size for any non-trivial binary operation such as ∧, ∨, and ⊕. For the operati...

In this article, we disprove the long-standing conjecture, proposed by R. E. Bryant in 1986, that his binary decision diagram (BDD) algorithm computes any binary operation on two Boolean functions in linear time in the input-output sizes. We present Boolean functions for which the time required by Bryant’s algorithm is a quadratic of the input-output sizes for all nontrivial binary operations, ...

The highly increasing amount of multimedia data leads to extremely growing databases which support users in searching and exploring the database contents. Content-based searching for similar objects inside such vivid and voluminous multimedia databases is typically accompanied by an immense amount of costly similarity computations among the stored data objects. In order to process similarity co...

we prove that every r-quadratic metric of scalar flag curvature with a dimension greater than twois of constant flag curvature. then we show that generalized douglas-weyl metrics contain r-quadraticmetrics as a special case, but the class of r-quadratic metric is not closed under projective transformations

in this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. in particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.

Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex optimization. We show how an interior method can be used to efficiently compute the proximal operator of a quadratic-support function under different metrics. When th...

This paper deals with systems described by constant coefficient linear partial differential equations (nD-systems) from a behavioral point of view. In this context we treat the linear quadratic control problem where the performance functional is the integral of a quadratic differential form. We look for characterizations of the set of stationary trajectories and of the set of local minimal traj...

This letter aims at refined error analysis for binary classification using support vector machine (SVM) with gaussian kernel and convex loss. Our first result shows that for some loss functions, such as the truncated quadratic loss and quadratic loss, SVM with gaussian kernel can reach the almost optimal learning rate provided the regression function is smooth. Our second result shows that for ...

In heartbeat detection tasks based on the Method of Constant Stimuli (MCS), subjects judge the simultaneity between their heartbeats and stimuli presented at six intervals ranging from 0 to 500 ms after the R-waves on an electrocardiogram. Because research suggests that subjects do not perceive stimuli at 0 or 500 ms as simultaneous, individual performance was indexed with quadratic trend analy...