Suppose X is a theorem of S4, and a realization for X has been constructed. If X ′ is a substitution instance of X, it is also a theorem of S4, and so is realizable, but the only available algorithm for producing a realization of X ′, so far, has been to apply a general realization algorithm to a cut-free proof of X ′. In effect we start over and the realization of X plays no role. It is the pu...

A generalization of forming derived and residual designs from tdesigns to subspace designs is proposed. A q-analog of a Theorem by van Tran, van Leijenhorst and Driessen is proven, stating that if for some (not necessarily realizable) parameter set the derived and residual parameter set are realizable, the same is true for the reduced parameter set. As a result, we get the existence of several ...

We show that for every integer k ≥ 2 and every k graphs G1, G2, . . . , Gk, there exists a hull graph with k hull vertices v1, v2, . . . , vk such that link L(vi) = Gi for 1 ≤ i ≤ k. Moreover, every pair a, b of integers with 2 ≤ a ≤ b is realizable as the hull number and geodetic number (or upper geodetic number) of a hull graph. We also show that every pair a, b of integers with a ≥ 2 and b ≥...

It has been established that local lattice spin Hamiltonians can be used for universal adiabatic quantum computation. However, the 2-local model Hamiltonians used in these proofs are general and hence do not limit the types of interactions required between spins. To address this concern, the present paper provides two simple model Hamiltonians that are of practical interest to experimentalists ...

Most of the existing active learning algorithms are based on the realizability assumption: The learner’s hypothesis class is assumed to contain a target function that perfectly classifies all training and test examples. This assumption can hardly ever be justified in practice. In this paper, we study how relaxing the realizability assumption affects the sample complexity of active learning. Fir...

The Wiener-Khintchine theorem dictates that the correlation function of any stationary, stochastic signal y(t) has as its Fourier transform a function that is necessarily both real and non-negative. In this paper, I explore the real-space, geometric consequences of this reciprocal-space non-negativity constraint. I review prior results addressing this issue, and I also introduce a family of new...

It is common clinical experience that individual patients vary in their response to different types of anti-hypertensive drugs. The best recognized example of this is the much poorer response of black subjects to angiotensin-converting enzyme (ACE) inhibitors compared with that of Caucasians. However, even within a relatively homogeneous group, individual responses vary greatly. This was shown ...

In this paper we examine a perceptron learning task. The task is realizable since it is provided by another perceptron with identical architecture. Both perceptrons have nonlinear sigmoid output functions. The gain of the output function determines the level of nonlinearity of the learning task. It is observed that a high level of nonlinearity leads to overfitting. We give an explanation for th...