Abstract:
A graph is inductive $k$-independent if there exists and ordering of its vertices $v_{1},...,v_{n}$ such that $\alpha(G[N(v_{i})\cap V_{i}])\leq k $ where $N(v_{i})$ is the neighborhood of $v_{i}$, $V_{i}=\{v_{i},...,v_{n}\}$ and $\alpha$ is the independence number. In this article, by answering to a question of [Y.Ye, A.Borodin, Elimination graphs, ACM Trans. Algorithms 8 (2) (2012) 14:1-14:23], we design a polynomial time approximation algorithm with ratio {$\overline{\Delta} \slash log(log(\overline{ \Delta}) \slash k)$ for the maximum clique and also show that the decision version of this problem is fixed parameter tractable for this particular family of graphs with complexity $O(1.2127^{(p+k-1)^{k}}n)$. Then we study a subclass of inductive $k$-independent graphs, namely $k$-degenerate graphs. A graph is $k$-degenerate if there exists an ordering of its vertices $v_{1},...,v_{n}$ such that $|N(v_{i})\cap V_{i}|\leq k $. Our contribution is an algorithm computing a maximum clique for this class of graphs in time $O(1.2127^{k}(n-k+1))$, thus improving previous best results. We also prove some structural properties for inductive $k$-independent graphs.

Abstract:
In this paper, we are interested in short homologically and homotopically independent loops based at the same point on Riemannian surfaces and metric graphs. First, we show that for every closed Riemannian surface of genus $g \geq 2$ and area normalized to $g$, there are at least $\ceil{\log(2g)+1}$ homotopically independent loops based at the same point of length at most $C\log(g)$, where $C$ is a universal constant. On the one hand, this result substantially improves Theorem $5.4.A$ of M. Gromov in \cite{G1}. On the other hand, it recaptures the result of S. Sabourau on the separating systole in \cite{SS} and refines his proof. Second, we show that for any two integers $b\geq 2$ with $1\leq n\leq b$, every connected metric graph $\Gamma$ of first Betti number $b$ and of length $b$ contains at least $n$ homologically independent loops based at the same point and of length at most $24(\log(b)+n)$. In particular, this result extends Bollob\`as-Szemer\'edi-Thomason's $\log(b)$ bound on the homological systole to at least $\log(b)$ homologically independent loops based at the same point. Moreover, we give examples of graphs where this result is optimal.

Abstract:
We present a new calculation method for solving inductive electric fields in the ionosphere. The time series of the potential part of the ionospheric electric field, together with the Hall and Pedersen conductances serves as the input to this method. The output is the time series of the induced rotational part of the ionospheric electric field. The calculation method works in the time-domain and can be used with non-uniform, time-dependent conductances. In addition, no particular symmetry requirements are imposed on the input potential electric field. The presented method makes use of special non-local vector basis functions called the Cartesian Elementary Current Systems (CECS). This vector basis offers a convenient way of representing curl-free and divergence-free parts of 2-dimensional vector fields and makes it possible to solve the induction problem using simple linear algebra. The new calculation method is validated by comparing it with previously published results for Alfvén wave reflection from a uniformly conducting ionosphere.

Abstract:
Machine learning(ML)is a major subfield of artificial intelligence(AI).It has been seen as a feasi- ble way of avoiding the knowledge bottleneck problem in knowledge-based systems development.Re- search on ML has concentrated in the main on inductive learning,a paradigm for inducing rules from unordered sets of exmaples.AQ11 and ID3,the two most widespread algorithms in ML,are both induc- tive.This paper first summarizes AQ11,ID3 and the newly-developed extension matrix approach based HCV algorithm;and then reviews the recent development of inductive learing and automatic knowledge acquisition from data bases.

Abstract:
In this paper, the sticker based DNA computing was used for solving the independent set problem. At first, solution space was constructed by using appropriate DNA memory complexes. We defined a new operation called “divide” and applied it in construction of solution space. Then, by application of a sticker based parallel algorithm using biological operations, independent set problem was resolved in polynomial time.

Abstract:
We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys. 11, 105052 (2009)] we solve a longstanding problem of convergence of the vN method. This opens the door to tailoring quantum calculations to the underlying classical phase space structure while retaining the accuracy of the Fourier grid basis. The method has the potential to provide enormous numerical savings as the dimensionality increases. In the classical limit the method reaches the remarkable efficiency of 1 basis function per 1 eigenstate. We illustrate the method for a challenging two-dimensional potential where the FGH method breaks down.

Abstract:
This paper presents a propagation model and inductive link budget based on link equations for chains of inductive loops as the basis for determining the link budget of an inductive communication and wireless power transfer systems. The link between the transmitter and receiver is modeled in similar format as in radio frequency systems. The transmitter antenna gain, path loss model and receiver antenna gain are also modeled for the inductive case. This allows the magnetic path loss to be estimated accurately. Also the induced receiver current due to a transmitter voltage can be computed apriori enabling efficient design of inductive links and transceivers.

Abstract:
A circuit of an inductive bridge negasensor on a L-negatron device with negative differential inductance is developed. Theoretical and experimental researches which were conduc-ted have shown that introduction of negatron to the circuit of inductive bridge sensor gives three times sensitivity advantage. A model of inductive sensor and negasensor on a L-negatron is developed. Possibility of simultane-ous research for sensor and negasensor is realized in this model.

Abstract:
A research of inductive conductometric cell is presented. An equivalent circuit and a mathematical model of inductive cell are given in the article. The model takes into account sample-coil capacity (i.e. capacity formed by the coil and the sample under study) and eddy currents. It is sample-coil capacity that makes inductive cell applicable for measurement of electrical conductivity of low conductive samples (specific conductance is less than 1S/m). The model can be used to calculate impedance of inductive cell for different characteristics of sample, materials and dimensions of cell without numerical solving of partial differential equations. Results of numerical simulation were verified by experiment for several devices with inductive cell. Some features that an engineer has to hold in mind while designing a conductometer based on inductive cell are discussed. Presented model can be useful for those who study inductively coupled plasma.

Abstract:
We construct the loop transform in the case of Abelian gauge theories as unitary operator given by the inductive limit of Fourier transforms on tori. We also show that its range, i.e.the space of kinematical states of the quantum loop representation, is the Hilbert space of square integrable complex valued functions on the group of loops.