Evaluating Variable-Length Multiple-Option Lists in Chatbots and Mobile Search

In recent years, the proliferation of smart mobile devices has lead to the gradual integration of search functionality within mobile platforms. This has created an incentive to move away from the "ten blue links'' metaphor, as mobile users are less likely to click on them, expecting to get the answer directly from the snippets. In turn, this has revived the interest in Question Answering. Then, along came chatbots, conversational systems, and messaging platforms, where the user needs could be better served with the system asking follow-up questions in order to better understand the user's intent. While typically a user would expect a single response at any utterance, a system could also return multiple options for the user to select from, based on different system understandings of the user's intent. However, this possibility should not be overused, as this practice could confuse and/or annoy the user. How to produce good variable-length lists, given the conflicting objectives of staying short while maximizing the likelihood of having a correct answer included in the list, is an underexplored problem. It is also unclear how to evaluate a system that tries to do that. Here we aim to bridge this gap. In particular, we define some necessary and some optional properties that an evaluation measure fit for this purpose should have. We further show that existing evaluation measures from the IR tradition are not entirely suitable for this setup, and we propose novel evaluation measures that address it satisfactorily.Comment: 4 pages, in Proceeding of SIGIR 201

On a Schwarzian PDE associated with the KdV Hierarchy

We present a novel integrable non-autonomous partial differential equation of the Schwarzian type, i.e. invariant under M\"obius transformations, that is related to the Korteweg-de Vries hierarchy. In fact, this PDE can be considered as the generating equation for the entire hierarchy of Schwarzian KdV equations. We present its Lax pair, establish its connection with the SKdV hierarchy, its Miura relations to similar generating PDEs for the modified and regular KdV hierarchies and its Lagrangian structure. Finally we demonstrate that its similarity reductions lead to the {\it full} Painlev\'e VI equation, i.e. with four arbitary parameters.Comment: 11 page

Nonisospectral integrable nonlinear equations with external potentials and their GBDT solutions

Auxiliary systems for matrix nonisospectral equations, including coupled NLS with external potential and KdV with variable coefficients, were introduced. Explicit solutions of nonisospectral equations were constructed using the GBDT version of the B\"acklund-Darboux transformation

Maxwell-Bloch equation and Correlation function for penetrable Bose gas

We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation value of a boson-valued solution for Maxwell-Bloch differential equation. We evaluate long-distance asymptotics of correlation functions in the small mass limit.Comment: LaTEX file, 20 pages, to appear J. Phys. A (1997

INVERSE SCATTERING TRANSFORM ANALYSIS OF STOKES-ANTI-STOKES STIMULATED RAMAN SCATTERING

Zakharov-Shabat--Ablowitz-Kaup-Newel-Segur representation for Stokes-anti-Stokes stimulated Raman scattering is proposed. Periodical waves, solitons and self-similarity solutions are derived. Transient and bright threshold solitons are discussed.Comment: 16 pages, LaTeX, no figure

Investigation of oxidation process of mechanically activated ultrafine iron powders

The oxidation of mechanically activated ultrafine iron powders was studied using X-ray powder diffraction and thermogravimetric analyzes. The powders with average particles size of 100 nm were made by the electric explosion of wire, and were subjected to mechanical activation in planetary ball mill for 15 and 40 minutes. It was shown that a certain amount of FeO phase is formed during mechanical activation of ultrafine iron powders. According to thermogravimetric analysis, the oxidation process of non-milled ultrafine iron powders is a complex process and occurs in three stages. The preliminary mechanical activation of powders considerably changes the nature of the iron powders oxidation, leads to increasing in the temperature of oxidation onset and shifts the reaction to higher temperatures. For the milled powders, the oxidation is more simple process and occurs in a single step

Explicit solutions of the four-wave mixing model

The dynamical degenerate four-wave mixing is studied analytically in detail. By removing the unessential freedom, we first characterize this system by a lower-dimensional closed subsystem of a deformed Maxwell-Bloch type, involving only three physical variables: the intensity pattern, the dynamical grating amplitude, the relative net gain. We then classify by the Painleve' test all the cases when singlevalued solutions may exist, according to the two essential parameters of the system: the real relaxation time tau, the complex response constant gamma. In addition to the stationary case, the only two integrable cases occur for a purely nonlocal response (Real(gamma)=0), these are the complex unpumped Maxwell-Bloch system and another one, which is explicitly integrated with elliptic functions. For a generic response (Re(gamma) not=0), we display strong similarities with the cubic complex Ginzburg-Landau equation.Comment: 16 pages, J Phys A Fast track communication, to appear 200

Existence and stability of hole solutions to complex Ginzburg-Landau equations

We consider the existence and stability of the hole, or dark soliton, solution to a Ginzburg-Landau perturbation of the defocusing nonlinear Schroedinger equation (NLS), and to the nearly real complex Ginzburg-Landau equation (CGL). By using dynamical systems techniques, it is shown that the dark soliton can persist as either a regular perturbation or a singular perturbation of that which exists for the NLS. When considering the stability of the soliton, a major difficulty which must be overcome is that eigenvalues may bifurcate out of the continuous spectrum, i.e., an edge bifurcation may occur. Since the continuous spectrum for the NLS covers the imaginary axis, and since for the CGL it touches the origin, such a bifurcation may lead to an unstable wave. An additional important consideration is that an edge bifurcation can happen even if there are no eigenvalues embedded in the continuous spectrum. Building on and refining ideas first presented in Kapitula and Sandstede (Physica D, 1998) and Kapitula (SIAM J. Math. Anal., 1999), we show that when the wave persists as a regular perturbation, at most three eigenvalues will bifurcate out of the continuous spectrum. Furthermore, we precisely track these bifurcating eigenvalues, and thus are able to give conditions for which the perturbed wave will be stable. For the NLS the results are an improvement and refinement of previous work, while the results for the CGL are new. The techniques presented are very general and are therefore applicable to a much larger class of problems than those considered here.Comment: 41 pages, 4 figures, submitte

EXPERIMENTAL RESEARCH ON CHROMATICITY FORMATION ON METALS SURFACE BY LASER RADIATION

The paper presents experimental studies and the way of chromaticity formation on stainless steel surface at the exposure of pulse laser radiation. Methods of reflection coefficient calculation of oxide iron films on iron are described. We perform calculation of reflection coefficient dependence on wavelength in the visible range and thickness of an oxidic film on the marked surface. The effect is shown that an oxidic film thickness has on the formed surface color owing to interference on the system of films of iron oxide and iron. It is shown how reflection function is displaced to the left and its amplitude decreases with the hade increase. By results of raster electronic microscopy significant oxygen increase in the places of exposure is recorded that points to formation of oxidic films. The profile analysis of oxidic films obtained on the metals surface is carried out and the dependence of chromaticity of the modified surface on laser radiation parameters is shown