Seiberg-Witten Curve for the E-String Theory

We construct the Seiberg-Witten curve for the E-string theory in six-dimensions. The curve is expressed in terms of affine E_8 characters up to level 6 and is determined by using the mirror-type transformation so that it reproduces the number of holomorphic curves in the Calabi-Yau manifold and the amplitudes of N=4 U(n) Yang-Mills theory on 1/2 K3. We also show that our curve flows to known five- and four-dimensional Seiberg-Witten curves in suitable limits.Comment: 18 pages, 1 figure; appendix C adde

Exceptional String: Instanton Expansions and Seiberg-Witten Curve

We investigate instanton expansions of partition functions of several toric E-string models using local mirror symmetry and elliptic modular forms. We also develop a method to obtain the Seiberg--Witten curve of E-string with arbitrary Wilson lines with the help of elliptic functions.Comment: 71 pages, three Wilson line

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

Containment and equivalence of weighted automata: Probabilistic and max-plus cases

This paper surveys some results regarding decision problems for probabilistic and max-plus automata, such as containment and equivalence. Probabilistic and max-plus automata are part of the general family of weighted automata, whose semantics are maps from words to real values. Given two weighted automata, the equivalence problem asks whether their semantics are the same, and the containment problem whether one is point-wise smaller than the other one. These problems have been studied intensively and this paper will review some techniques used to show (un)decidability and state a list of open questions that still remain

Feature weighting techniques for CBR in software effort estimation studies: A review and empirical evaluation

Context : Software effort estimation is one of the most important activities in the software development process. Unfortunately, estimates are often substantially wrong. Numerous estimation methods have been proposed including Case-based Reasoning (CBR). In order to improve CBR estimation accuracy, many researchers have proposed feature weighting techniques (FWT). Objective: Our purpose is to systematically review the empirical evidence to determine whether FWT leads to improved predictions. In addition we evaluate these techniques from the perspectives of (i) approach (ii) strengths and weaknesses (iii) performance and (iv) experimental evaluation approach including the data sets used. Method: We conducted a systematic literature review of published, refereed primary studies on FWT (2000-2014). Results: We identified 19 relevant primary studies. These reported a range of different techniques. 17 out of 19 make benchmark comparisons with standard CBR and 16 out of 17 studies report improved accuracy. Using a one-sample sign test this positive impact is significant (p = 0:0003). Conclusion: The actionable conclusion from this study is that our review of all relevant empirical evidence supports the use of FWTs and we recommend that researchers and practitioners give serious consideration to their adoption