We consider the VC-dimension of a set of the neural networks of depth s with w adjustable parameters that has h hidden units of activation functions of at most q segments of degree at most d polynomials. When d 2 and q 2, the VC-dimension is O(ws(s log d + log(qh=s))), O(ws((h=s) log q) + log d), and (ws log(dqh=s)). When d 2 and q = 1, it is (ws log d). When d = 1 and q 2, it is (ws log(qh=s))...

Two dimensional plots (2-D) in digital documents on the web are an important source of information that is largely under-utilized. In this paper, we outline how data and text can be extracted automatically from these 2-D plots, thus eliminating a time consuming manual process. Our information extraction algorithm identifies the axes of the figures, extracts text blocks like axes-labels and lege...

We study various statistics regarding the distribution of points \[\left\{\left(\frac{d}{q},\frac{\overline{d}}{q}\right) \in \mathbb{T}^2 : d (\mathbb{Z}/q\mathbb{Z})^{\times}\right\}\] as $q$ tends to infinity. Due nontrivial bounds for Kloosterman sums, it is known that these equidistribute on torus. prove refinements this result, including discrepancy, small scale equidistribution, covering...

We prove that | ∑ d≤x μ(d)/d| log x ≤ 1/69 when x ≥ 96 955 and deduce from that: ∣ ∣ ∣ ∣ ∑{ d≤x, (d,q)=1 μ(d)/d ∣ ∣ ∣ ∣ log(x/q) ≤ 4 5 q/φ(q) for every x > q ≥ 1. We also give better constants when x/q is larger. Furthermore we prove that |1 − ∑ d≤x μ(d) log(x/d)/d| ≤ 3 14 / log x and several similar bounds, from which we also prove corresponding bounds when summing the same quantity, but with ...

The performance of anisotropic electrical machines is strongly dependent on the current loop characteristics. problems for achieving robustness and fast response, without overshoot oscillations, are mainly related to different values behavior direct quadrature inductances (L d , L xmlns:xlink="h...

We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an [[n, k, r, d]]q subsystem code, we drive new subsystem codes with parameters [[n + 1, k, r,≥ d]]q, [[n − 1, k + 1, r,≥ d − 1]]q , [[n, k − 1, r + 1, d]]q . We present the short subsystem codes. The interested readers shall consult our companion papers for upper...

In this paper, we mainly discuss the nonuniform average sampling and reconstruction in multiply generated shift-invariant subspaces \[ V_{p,q}(\Phi_r) = \bigg\{ \sum_{k_{1} \in \mathbf{Z}} \sum_{k_{2} \mathbf{Z}^{d}} c^T(k_{1},k_{2}) \Phi_r(\,\cdot-k_{1},\,\cdot-k_{2}): (c(k_{1},k_{2}))_{(k_{1},k_{2}) \mathbf{Z} \times \big( \ell^{p,q}(\mathbf{Z} \mathbf{Z}^d) \big)^r \bigg\} \] of mixed Lebesg...

We point out an interplay between Fq-Frobenius non-classical plane curves and complete (k, d)-arcs in P2(Fq). A typical example that shows how this works is the one concerning an Hermitian curve. We present some other examples here which give rise to the existence of new complete (k, d)-arcs with parameters k = d(q − d + 2) and d = (q − 1)/(q − 1), q being a power of the characteristic. In addi...

Due to the advantages of a self-excited induction generator (SEIG), it plays main role in sources renewable energy, such as wind turbines (WT). The regulation terminal voltage and frequency is poor under variable rotor speed load conditions at stand-alone operation mode. depends on excitation capacitance which can be controlled by capacitor bank static compensator. dynamical model machine descr...

This paper presents a finite element method (FEM)-based model, which describes the magnetic circuit of BMW i3 traction machine. The model has been reconstructed based on data available in public domain. reader is provided with numerical regarding flux linkage surfaces d- and q-axes, as well all information needed to develop space-vector machine steady-state, taking into consideration non-linear...