598 research outputs found
A Low-Complexity Approach to Distributed Cooperative Caching with Geographic Constraints
We consider caching in cellular networks in which each base station is
equipped with a cache that can store a limited number of files. The popularity
of the files is known and the goal is to place files in the caches such that
the probability that a user at an arbitrary location in the plane will find the
file that she requires in one of the covering caches is maximized.
We develop distributed asynchronous algorithms for deciding which contents to
store in which cache. Such cooperative algorithms require communication only
between caches with overlapping coverage areas and can operate in asynchronous
manner. The development of the algorithms is principally based on an
observation that the problem can be viewed as a potential game. Our basic
algorithm is derived from the best response dynamics. We demonstrate that the
complexity of each best response step is independent of the number of files,
linear in the cache capacity and linear in the maximum number of base stations
that cover a certain area. Then, we show that the overall algorithm complexity
for a discrete cache placement is polynomial in both network size and catalog
size. In practical examples, the algorithm converges in just a few iterations.
Also, in most cases of interest, the basic algorithm finds the best Nash
equilibrium corresponding to the global optimum. We provide two extensions of
our basic algorithm based on stochastic and deterministic simulated annealing
which find the global optimum.
Finally, we demonstrate the hit probability evolution on real and synthetic
networks numerically and show that our distributed caching algorithm performs
significantly better than storing the most popular content, probabilistic
content placement policy and Multi-LRU caching policies.Comment: 24 pages, 9 figures, presented at SIGMETRICS'1
Computational Geometric and Algebraic Topology
Computational topology is a young, emerging field of mathematics that seeks out practical algorithmic methods for solving complex and fundamental problems in geometry and topology. It draws on a wide variety of techniques from across pure mathematics (including topology, differential geometry, combinatorics, algebra, and discrete geometry), as well as applied mathematics and theoretical computer science. In turn, solutions to these problems have a wide-ranging impact: already they have enabled significant progress in the core area of geometric topology, introduced new methods in applied mathematics, and yielded new insights into the role that topology has to play in fundamental problems surrounding computational complexity.
At least three significant branches have emerged in computational topology: algorithmic 3-manifold and knot theory, persistent homology and surfaces and graph embeddings. These branches have emerged largely independently. However, it is clear that they have much to offer each other. The goal of this workshop was to be the first significant step to bring these three areas together, to share ideas in depth, and to pool our expertise in approaching some of the major open problems in the field
The Quantum Monadology
The modern theory of functional programming languages uses monads for
encoding computational side-effects and side-contexts, beyond bare-bone program
logic. Even though quantum computing is intrinsically side-effectful (as in
quantum measurement) and context-dependent (as on mixed ancillary states),
little of this monadic paradigm has previously been brought to bear on quantum
programming languages.
Here we systematically analyze the (co)monads on categories of parameterized
module spectra which are induced by Grothendieck's "motivic yoga of operations"
-- for the present purpose specialized to HC-modules and further to set-indexed
complex vector spaces. Interpreting an indexed vector space as a collection of
alternative possible quantum state spaces parameterized by quantum measurement
results, as familiar from Proto-Quipper-semantics, we find that these
(co)monads provide a comprehensive natural language for functional quantum
programming with classical control and with "dynamic lifting" of quantum
measurement results back into classical contexts.
We close by indicating a domain-specific quantum programming language (QS)
expressing these monadic quantum effects in transparent do-notation, embeddable
into the recently constructed Linear Homotopy Type Theory (LHoTT) which
interprets into parameterized module spectra. Once embedded into LHoTT, this
should make for formally verifiable universal quantum programming with linear
quantum types, classical control, dynamic lifting, and notably also with
topological effects.Comment: 120 pages, various figure
What is Robotics: Why Do We Need It and How Can We Get It?
Robotics is an emerging synthetic science concerned with programming work. Robot technologies are quickly advancing beyond the insights of the existing science. More secure intellectual foundations will be required to achieve better, more reliable and safer capabilities as their penetration into society deepens. Presently missing foundations include the identification of fundamental physical limits, the development of new dynamical systems theory and the invention of physically grounded programming languages. The new discipline needs a departmental home in the universities which it can justify both intellectually and by its capacity to attract new diverse populations inspired by the age old human fascination with robots.
For more information: Kod*la
Sheaf semantics of termination-insensitive noninterference
We propose a new sheaf semantics for secure information flow over a space of
abstract behaviors, based on synthetic domain theory: security classes are
open/closed partitions, types are sheaves, and redaction of sensitive
information corresponds to restricting a sheaf to a closed subspace. Our
security-aware computational model satisfies termination-insensitive
noninterference automatically, and therefore constitutes an intrinsic
alternative to state of the art extrinsic/relational models of noninterference.
Our semantics is the latest application of Sterling and Harper's recent
re-interpretation of phase distinctions and noninterference in programming
languages in terms of Artin gluing and topos-theoretic open/closed modalities.
Prior applications include parametricity for ML modules, the proof of
normalization for cubical type theory by Sterling and Angiuli, and the
cost-aware logical framework of Niu et al. In this paper we employ the phase
distinction perspective twice: first to reconstruct the syntax and semantics of
secure information flow as a lattice of phase distinctions between "higher" and
"lower" security, and second to verify the computational adequacy of our sheaf
semantics vis-\`a-vis an extension of Abadi et al.'s dependency core calculus
with a construct for declassifying termination channels.Comment: Extended version of FSCD '22 paper with full technical appendice
Data Analysis Methods using Persistence Diagrams
In recent years, persistent homology techniques have been used to study data and dynamical systems. Using these techniques, information about the shape and geometry of the data and systems leads to important information regarding the periodicity, bistability, and chaos of the underlying systems. In this thesis, we study all aspects of the application of persistent homology to data analysis. In particular, we introduce a new distance on the space of persistence diagrams, and show that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Moreover, we introduce a clustering framework directly on the space of persistence diagrams, leveraging the notion of Fréchet means. Finally, we engage persistent homology with stochastic filtering techniques. In doing so, we prove that there is a notion of stability between the topologies of the optimal particle filter path and the expected particle filter path, which demonstrates that this approach is well posed. In addition to these theoretical contributions, we provide benchmarks and simulations of the proposed techniques, demonstrating their usefulness to the field of data analysis
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