36,861 research outputs found
Testability of linear-invariant properties
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 75-80).Property Testing is the study of super-efficient algorithms that solve "approximate decision problems" with high probability. More precisely, given a property P, a testing algorithm for P is a randomized algorithm that makes a small number of queries into its input and distinguishes between whether the input satisfies P or whether the input is "far" from satisfying P, where "farness" of an object from P is measured by the minimum fraction of places in its representation that needs to be modified in order for it to satisfy P. Property testing and ideas arising from it have had significant impact on complexity theory, pseudorandomness, coding theory, computational learning theory, and extremal combinatorics. In the history of the area, a particularly important role has been played by linearinvariant properties, i.e., properties of Boolean functions on the hypercube which are closed under linear transformations of the domain. Examples of such properties include linearity, homogeneousness, Reed-Muller codes, and Fourier sparsity. In this thesis, we describe a framework that can lead to a unified analysis of the testability of all linear-invariant properties, drawing on techniques from additive combinatorics and from graph theory. We also show the first nontrivial lowerbound for the query complexity of a natural testable linear-invariant property.by Arnab Bhattacharyya.Ph.D
The Dimensions of Field Theory : From Particles to Strings
This is an editorial summary of the contents of a Book comprising a set of
Articles by acknowledged experts dealing with the impact of Field Theory on
major areas of physics (from elementary particles through condensed matter to
strings), arranged subjectwise under six broad heads. The Book which emphasizes
the conceptual, logical and formal aspects of the state of the art in these
respective fields, carries a Foreword by Freeman Dyson, and is to be published
by the Indian National Science Academy on the occasion of the International
Mathematical Year 2000. The authors and full titles of all the Articles (33)
are listed sequentially (in the order of their first appearance in the
narration) under the bibliography at the end of this Summary, while a few of
the individual articles to appear in the Book are already available on the LANL
internet.Comment: LaTex file, 24 page
BeSpaceD: Towards a Tool Framework and Methodology for the Specification and Verification of Spatial Behavior of Distributed Software Component Systems
In this report, we present work towards a framework for modeling and checking
behavior of spatially distributed component systems. Design goals of our
framework are the ability to model spatial behavior in a component oriented,
simple and intuitive way, the possibility to automatically analyse and verify
systems and integration possibilities with other modeling and verification
tools. We present examples and the verification steps necessary to prove
properties such as range coverage or the absence of collisions between
components and technical details
Improved Lower Bounds for Testing Triangle-freeness in Boolean Functions via Fast Matrix Multiplication
Understanding the query complexity for testing linear-invariant properties
has been a central open problem in the study of algebraic property testing.
Triangle-freeness in Boolean functions is a simple property whose testing
complexity is unknown. Three Boolean functions , and are said to be triangle free if there is no such that . This property
is known to be strongly testable (Green 2005), but the number of queries needed
is upper-bounded only by a tower of twos whose height is polynomial in 1 /
\epsislon, where \epsislon is the distance between the tested function
triple and triangle-freeness, i.e., the minimum fraction of function values
that need to be modified to make the triple triangle free. A lower bound of for any one-sided tester was given by Bhattacharyya and
Xie (2010). In this work we improve this bound to .
Interestingly, we prove this by way of a combinatorial construction called
\emph{uniquely solvable puzzles} that was at the heart of Coppersmith and
Winograd's renowned matrix multiplication algorithm
An Introduction to Nuclear Supersymmetry: a Unification Scheme for Nuclei
The main ideas behind nuclear supersymmetry are presented, starting from the
basic concepts of symmetry and the methods of group theory in physics. We
propose new, more stringent experimental tests that probe the supersymmetry
classification in nuclei and point out that specific correlations should exist
for particle transfer intensities among supersymmetric partners. We also
discuss possible ways to generalize these ideas to cases where no dynamical
symmetries are present. The combination of these theoretical and experimental
studies may play a unifying role in nuclear phenomena.Comment: 40 pages, 11 figures, lecture notes `VIII Hispalensis International
Summer School: Exotic Nuclear Physics', Oromana, Sevilla, Spain, June 9-21,
200
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Identifying Catch-Up Trajectories in Child Growth: New Methods with Evidence from Young Lives
Definitions of catch-up growth in anthropometric outcomes among young children vary across studies. This paper distinguishes between catch-up in the mean of a group toward that of a healthy reference population versus catch-up within the group, associated with a narrowing of the outcome distribution. In contrast to conventional empirical approaches based on dynamic panel models, the paper shows how catch-up can be tested via a latent growth framework. Combined with a flexible estimator incorporating individual-specific intercepts and slopes, this enables between- and within-group forms of catch-up to be tested in a unified setting. The application of the proposed approach reveals significant differences in the nature, extent, and drivers of catch-up growth across the four Young Lives countries (Ethiopia, India, Peru, and Vietnam). In addition, the paper shows how conclusions about catch-up are sensitive to the way in which anthropometric outcomes are expressed
Loops and Knots as Topoi of Substance. Spinoza Revisited
The relationship between modern philosophy and physics is discussed. It is
shown that the latter develops some need for a modernized metaphysics which
shows up as an ultima philosophia of considerable heuristic value, rather than
as the prima philosophia in the Aristotelian sense as it had been intended, in
the first place. It is shown then, that it is the philosophy of Spinoza in
fact, that can still serve as a paradigm for such an approach. In particular,
Spinoza's concept of infinite substance is compared with the philosophical
implications of the foundational aspects of modern physical theory. Various
connotations of sub-stance are discussed within pre-geometric theories,
especially with a view to the role of spin networks within quantum gravity. It
is found to be useful to intro-duce a separation into physics then, so as to
differ between foundational and empirical theories, respectively. This leads to
a straightforward connection bet-ween foundational theories and speculative
philosophy on the one hand, and between empirical theories and sceptical
philosophy on the other. This might help in the end, to clarify some recent
problems, such as the absence of time and causality at a fundamental level. It
is implied that recent results relating to topos theory might open the way
towards eventually deriving logic from physics, and also towards a possible
transition from logic to hermeneutic.Comment: 42 page
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