Characterization of potential smoothness and Riesz basis property of Hill-Scr\"odinger operators with singular periodic potentials in terms of periodic, antiperiodic and Neumann spectra

The Hill operators Ly=-y''+v(x)y, considered with singular complex valued \pi-periodic potentials v of the form v=Q' with Q in L^2([0,\pi]), and subject to periodic, antiperiodic or Neumann boundary conditions have discrete spectra. For sufficiently large n, the disc {z: |z-n^2|<n} contains two periodic (if n is even) or antiperiodic (if n is odd) eigenvalues \lambda_n^-, \lambda_n^+ and one Neumann eigenvalue \nu_n. We show that rate of decay of the sequence |\lambda_n^+-\lambda_n^-|+|\lambda_n^+ - \nu_n| determines the potential smoothness, and there is a basis consisting of periodic (or antiperiodic) root functions if and only if for even (respectively, odd) n, \sup_{\lambda_n^+\neq \lambda_n^-}{|\lambda_n^+-\nu_n|/|\lambda_n^+-\lambda_n^-|} < \infty.Comment: arXiv admin note: substantial text overlap with arXiv:1207.094

Multivariate time series classification with temporal abstractions

The increase in the number of complex temporal datasets collected today has prompted the development of methods that extend classical machine learning and data mining methods to time-series data. This work focuses on methods for multivariate time-series classification. Time series classification is a challenging problem mostly because the number of temporal features that describe the data and are potentially useful for classification is enormous. We study and develop a temporal abstraction framework for generating multivariate time series features suitable for classification tasks. We propose the STF-Mine algorithm that automatically mines discriminative temporal abstraction patterns from the time series data and uses them to learn a classification model. Our experimental evaluations, carried out on both synthetic and real world medical data, demonstrate the benefit of our approach in learning accurate classifiers for time-series datasets. Copyright © 2009, Assocation for the Advancement of ArtdicaI Intelligence (www.aaai.org). All rights reserved

Shifting Priorities? Civic Identity in the Jewish State and the Changing Landscape of Israeli Constitutionalism

This thesis begins with an explanation of Israel’s foundational constitutional tension—namely, that its identity as a Jewish State often conflicts with liberal-democratic principles to which it is also committed. From here, I attempt to sketch the evolution of the state’s constitutional principles, pointing to Chief Justice Barak’s “constitutional revolution” as a critical juncture where the aforementioned theoretical tension manifested in practice, resulting in what I call illiberal or undemocratic “moments.” More profoundly, by introducing Israel’s constitutional tension into the public sphere, the Barak Court’s jurisprudence forced all of the Israeli polity to confront it. My next chapter utilizes the framework of a bill currently making its way through the Knesset—Basic Law: Israel as the Nation-State of the Jewish People—in order to draw out the past and future of Israeli civic identity. From a positivist perspective, much of my thesis points to why and how Israel often falls short of liberal-democratic principles. My final chapters demonstrate that neither the Supreme Court nor any other part of the Israeli polity appears particularly well-suited to stopping what I see as the beginning of a transformational shift in theory and in practice. In my view, this shift is making, and will continue to make, the state’s ethno-religious character the preeminent factor in Israeli Constitutionalism and civic identity

Mining Predictive Patterns and Extension to Multivariate Temporal Data

An important goal of knowledge discovery is the search for patterns in the data that can help explaining its underlying structure. To be practically useful, the discovered patterns should be novel (unexpected) and easy to understand by humans. In this thesis, we study the problem of mining patterns (defining subpopulations of data instances) that are important for predicting and explaining a specific outcome variable. An example is the task of identifying groups of patients that respond better to a certain treatment than the rest of the patients. We propose and present efficient methods for mining predictive patterns for both atemporal and temporal (time series) data. Our first method relies on frequent pattern mining to explore the search space. It applies a novel evaluation technique for extracting a small set of frequent patterns that are highly predictive and have low redundancy. We show the benefits of this method on several synthetic and public datasets. Our temporal pattern mining method works on complex multivariate temporal data, such as electronic health records, for the event detection task. It first converts time series into time-interval sequences of temporal abstractions and then mines temporal patterns backwards in time, starting from patterns related to the most recent observations. We show the benefits of our temporal pattern mining method on two real-world clinical tasks