The information divergence of a probability measure P from an exponential family E over a nite set is de ned as in mum of the divergences of P from Q subject to Q ∈ E . All directional derivatives of the divergence from E are explicitly found. To this end, behaviour of the conjugate of a log-Laplace transform on the boundary of its domain is analysed. The rst order conditions for P to be a maxi...

where [g]j,l=1 defines a C ∞-smooth Riemannian metric and b = (b1, ..., bm) and q are, correspondingly, C∞-smooth complex-valued 1-form and function on M . σ is a C∞-smooth complex-valued function on ∂M and ∂ν stands for the normal derivative. Let Rλ be the resolvent of (1), (2) which is meromorphic for λ ∈ C (see Sect. 3 and [1]) and let Rλ(x, y) be its Schwartz kernel. A natural analog of the...

In this paper we determine the number of the meaningful compositions of higher order of the differential operations and Gateaux directional derivative.

The characteristics of goal-directed actions tend to resemble those of previously executed actions, but it is unclear whether such effects depend strictly on action history, or also reflect context-dependent processes related to predictive motor planning. Here we manipulated the time available to initiate movements after a target was specified, and studied the effects of predictable movement se...

We consider spherical data Xi noised by a random rotation εi ∈ SO(3) so that only the sample Zi = εiXi, i = 1, . . . , N is observed. We define a nonparametric test procedure to distinguish H0 : ”the density f of Xi is the uniform density f0 on the sphere” and H1 : ”‖f − f0‖2 ≥ CψN and f is in a Sobolev space with smoothness s”. For a noise density fε with smoothness index ν, we show that an ad...

Horizontal directional drilling (HDD) is widely used in soil and rock engineering. In a variety of conditions, it is necessary to estimate the torque required for performing the reaming operation. Nevertheless, there is not presently a convenient method to accomplish this task. In this paper, to overcome this difficulty based on the basic concepts of rock engineering systems (RES), a model for ...

The improvement in speech recognition in noise obtained with directional microphones compared to omnidirectional microphones is referred to as the directional advantage. Laboratory studies have revealed substantial differences in the magnitude of the directional advantage across hearing-impaired listeners. This investigation examined whether persons who were successful users of directional micr...

Video analysis of crowded scenes is challenging due to the complex motion of individual people in the scene. The collective motion of pedestrians form a crowd flow, but individuals often largely deviate from it as they anticipate and react to each other. Deviations from the crowd decreases the pedestrian’s efficiency: a sociological concept that measures the difference of actual motion from the...

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of G~teaux, Fr6chet, and Hadamard are singled out from the general framework of cr-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equ...