Decision trees constructed by ID3-like algorithms suffer from an inability of detecting instances of categories not present in the set of training examples, i.e., they are discriminative representations. Instead, such instances are assigned to one of the classes actually present in the training set, resulting in undesired misclassifications. Two methods of reducing this problem by learning char...

Let Ω be a set and Ω1, . . . ,Ωm−1 subsets of Ω, being m an integer greater than one. For a given function f = (f1, . . . fm) : Ω → R, we prove the existence of a unique function α = (α1, . . . , αm) : Ω → R m such that

We prove Poincar e Duality for L p cohomology, 1 p 1 We study the pairings between L p and L 1 and construct characteristic classes.

1. a) Compute the Stiefel-Whitney classes of the tangent bundle of RP . (Use the method from class for the tangent Chern classes of complex projectives spaces.) b) Conclude that if the tangent bundle is trivial, then n = 2 − 1 for some m. (In fact n must be 0, 1, 3, 7, but this is much harder to prove; one proof uses the Bott periodicity theorem.) c) Deduce (very easily!) a complete characteriz...

We use homotopy theory to define certain rational coefficients characteristic numbers with integral values, depending on a given prime number q and positive integer t . We prove the first nontrivial degree formula and use it to show that existence of morphisms between algebraic varieties for which these numbers are not divisible by q give information on the degree of such morphisms or on zero c...

Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. Software implementations being rather slow, the study of hardware architectures became an active research area. In this paper, we discuss several algorithms to compute the ηT pairing in characteristic three and suggest further impr...

In this paper chemical amount rate to the exposed organism was examined. Dose characterizs the total amount of material to which an organism is exposed. The aim of this paper dynamic cumulative toxic effect was investigated. Single dosing and n-times dosing changes are expressed. This paper different routes of exposure and frequency of exposure were involved. Toxic effects also depend of the se...

We establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we ...

We explore relations between various variational problems for graphs: among the functionals considered are Euler characteristic χ(G), characteristic length μ(G), mean clustering ν(G), inductive dimension ι(G), edge density (G), scale measure σ(G), Hilbert action η(G) and spectral complexity ξ(G). A new insight in this note is that the local cluster coefficient C(x) in a finite simple graph can ...

This work treats a linear convection-diiusion problem. Diiusion and convection may be equally important or convection may dominate the problem. The method of characteristics is combined with an overlapping domain decomposition technique so that domain decomposition is naturally combined with the time stepping. In each time step, the algorithm rst determines the characteristic solution. Then a d...