Off-diagonal impedance in amorphous wires and application to linear magnetic sensors

The magnetic-field behaviour of the off-diagonal impedance in Co-based amorphous wires is investigated under the condition of sinusoidal (50 MHz) and pulsed (5 ns rising time) current excitations. For comparison, the field characteristics of the diagonal impedance are measured as well. In general, when an alternating current is applied to a magnetic wire the voltage signal is generated not only across the wire but also in the coil mounted on it. These voltages are related with the diagonal and off-diagonal impedances, respectively. It is demonstrated that these impedances have a different behaviour as a function of axial magnetic field: the former is symmetrical and the latter is antisymmetrical with a near linear portion within a certain field interval. In the case of the off-diagonal response, the dc bias current eliminating circular domains is necessary. The pulsed excitation that combines both high and low frequency harmonics produces the off-diagonal voltage response without additional bias current or field. This suits ideal for a practical sensor circuit design. The principles of operation of a linear magnetic sensor based on C-MOS transistor circuit are discussed.Comment: Accepted to IEEE Trans. Magn. (2004

Residues and Topological Yang-Mills Theory in Two Dimensions

A residue formula which evaluates any correlation function of topological $SU_n$ Yang-Mills theory with arbitrary magnetic flux insertion in two dimensions are obtained. Deformations of the system by two form operators are investigated in some detail. The method of the diagonalization of a matrix valued field turns out to be useful to compute various physical quantities. As an application we find the operator that contracts a handle of a Riemann surface and a genus recursion relation.Comment: 23 pages, some references added, to appear in Rev.Math.Phy

Hybrid expansions for local structural relaxations

A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the ideal crystal positions, and the effect of ordering is described by interatomic-distance dependent pair potentials, while more subtle configurational aspects associated with correlations of three- and more sites are described purely within the cluster expansion formalism. Implementation of such a hybrid expansion in the context of the cluster variation method or Monte Carlo method gives improved ability to model phase stability in alloys from first-principles.Comment: 8 pages, 1 figur

Finite Automata for the Sub- and Superword Closure of CFLs: Descriptional and Computational Complexity

We answer two open questions by (Gruber, Holzer, Kutrib, 2009) on the state-complexity of representing sub- or superword closures of context-free grammars (CFGs): (1) We prove a (tight) upper bound of $2^{\mathcal{O}(n)}$ on the size of nondeterministic finite automata (NFAs) representing the subword closure of a CFG of size $n$. (2) We present a family of CFGs for which the minimal deterministic finite automata representing their subword closure matches the upper-bound of $2^{2^{\mathcal{O}(n)}}$ following from (1). Furthermore, we prove that the inequivalence problem for NFAs representing sub- or superword-closed languages is only NP-complete as opposed to PSPACE-complete for general NFAs. Finally, we extend our results into an approximation method to attack inequivalence problems for CFGs

Learning with Biased Complementary Labels

In this paper, we study the classification problem in which we have access to easily obtainable surrogate for true labels, namely complementary labels, which specify classes that observations do \textbf{not} belong to. Let $Y$ and $\bar{Y}$ be the true and complementary labels, respectively. We first model the annotation of complementary labels via transition probabilities $P(\bar{Y}=i|Y=j), i\neq j\in\{1,\cdots,c\}$, where $c$ is the number of classes. Previous methods implicitly assume that $P(\bar{Y}=i|Y=j), \forall i\neq j$, are identical, which is not true in practice because humans are biased toward their own experience. For example, as shown in Figure 1, if an annotator is more familiar with monkeys than prairie dogs when providing complementary labels for meerkats, she is more likely to employ "monkey" as a complementary label. We therefore reason that the transition probabilities will be different. In this paper, we propose a framework that contributes three main innovations to learning with \textbf{biased} complementary labels: (1) It estimates transition probabilities with no bias. (2) It provides a general method to modify traditional loss functions and extends standard deep neural network classifiers to learn with biased complementary labels. (3) It theoretically ensures that the classifier learned with complementary labels converges to the optimal one learned with true labels. Comprehensive experiments on several benchmark datasets validate the superiority of our method to current state-of-the-art methods.Comment: ECCV 2018 Ora

Reachability problems for products of matrices in semirings

We consider the following matrix reachability problem: given $r$ square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multiplied at left and right by prescribed row and column vectors, gives a prescribed scalar). We show that over any semiring, scalar reachability reduces to vector reachability which is equivalent to matrix reachability, and that for any of these problems, the specialization to any $r\geq 2$ is equivalent to the specialization to $r=2$. As an application of this result and of a theorem of Krob, we show that when $r=2$, the vector and matrix reachability problems are undecidable over the max-plus semiring $(Z\cup\{-\infty\},\max,+)$. We also show that the matrix, vector, and scalar reachability problems are decidable over semirings whose elements are ``positive'', like the tropical semiring $(N\cup\{+\infty\},\min,+)$.Comment: 21 page

A new path to measure antimatter free fall

We propose an experiment to measure the free fall acceleration of neutral antihydrogen atoms. The originality of this path is to first produce the Hbar+ ion