7,276 research outputs found
On paths-based criteria for polynomial time complexity in proof-nets
Girard's Light linear logic (LLL) characterized polynomial time in the
proof-as-program paradigm with a bound on cut elimination. This logic relied on
a stratification principle and a "one-door" principle which were generalized
later respectively in the systems L^4 and L^3a. Each system was brought with
its own complex proof of Ptime soundness.
In this paper we propose a broad sufficient criterion for Ptime soundness for
linear logic subsystems, based on the study of paths inside the proof-nets,
which factorizes proofs of soundness of existing systems and may be used for
future systems. As an additional gain, our bound stands for any reduction
strategy whereas most bounds in the literature only stand for a particular
strategy.Comment: Long version of a conference pape
Cutoff for the East process
The East process is a 1D kinetically constrained interacting particle system,
introduced in the physics literature in the early 90's to model liquid-glass
transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that
its mixing time on sites has order . We complement that result and show
cutoff with an -window.
The main ingredient is an analysis of the front of the process (its rightmost
zero in the setup where zeros facilitate updates to their right). One expects
the front to advance as a biased random walk, whose normal fluctuations would
imply cutoff with an -window. The law of the process behind the
front plays a crucial role: Blondel showed that it converges to an invariant
measure , on which very little is known. Here we obtain quantitative
bounds on the speed of convergence to , finding that it is exponentially
fast. We then derive that the increments of the front behave as a stationary
mixing sequence of random variables, and a Stein-method based argument of
Bolthausen ('82) implies a CLT for the location of the front, yielding the
cutoff result.
Finally, we supplement these results by a study of analogous kinetically
constrained models on trees, again establishing cutoff, yet this time with an
-window.Comment: 33 pages, 2 figure
Scalable Image Retrieval by Sparse Product Quantization
Fast Approximate Nearest Neighbor (ANN) search technique for high-dimensional
feature indexing and retrieval is the crux of large-scale image retrieval. A
recent promising technique is Product Quantization, which attempts to index
high-dimensional image features by decomposing the feature space into a
Cartesian product of low dimensional subspaces and quantizing each of them
separately. Despite the promising results reported, their quantization approach
follows the typical hard assignment of traditional quantization methods, which
may result in large quantization errors and thus inferior search performance.
Unlike the existing approaches, in this paper, we propose a novel approach
called Sparse Product Quantization (SPQ) to encoding the high-dimensional
feature vectors into sparse representation. We optimize the sparse
representations of the feature vectors by minimizing their quantization errors,
making the resulting representation is essentially close to the original data
in practice. Experiments show that the proposed SPQ technique is not only able
to compress data, but also an effective encoding technique. We obtain
state-of-the-art results for ANN search on four public image datasets and the
promising results of content-based image retrieval further validate the
efficacy of our proposed method.Comment: 12 page
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Submodular relaxation for inference in Markov random fields
In this paper we address the problem of finding the most probable state of a
discrete Markov random field (MRF), also known as the MRF energy minimization
problem. The task is known to be NP-hard in general and its practical
importance motivates numerous approximate algorithms. We propose a submodular
relaxation approach (SMR) based on a Lagrangian relaxation of the initial
problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR
does not decompose the graph structure of the initial problem but constructs a
submodular energy that is minimized within the Lagrangian relaxation. Our
approach is applicable to both pairwise and high-order MRFs and allows to take
into account global potentials of certain types. We study theoretical
properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on
Pattern Analysis and Machine Intelligenc
Extended Connectors: Structuring Glue Operators in BIP
Based on a variation of the BIP operational semantics using the offer
predicate introduced in our previous work, we extend the algebras used to model
glue operators in BIP to encompass priorities. This extension uses the Algebra
of Causal Interaction Trees, T(P), as a pivot: existing transformations
automatically provide the extensions for the Algebra of Connectors. We then
extend the axiomatisation of T(P), since the equivalence induced by the new
operational semantics is weaker than that induced by the interaction semantics.
This extension leads to canonical normal forms for all structures and to a
simplification of the algorithm for the synthesis of connectors from Boolean
coordination constraints.Comment: In Proceedings ICE 2013, arXiv:1310.401
Affine and Projective Tree Metric Theorems
The tree metric theorem provides a combinatorial four-point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A related weaker four point condition characterizes dissimilarity maps derived from circular split systems known as Kalmanson metrics. The tree metric theorem was first discovered in the context of phylogenetics and forms the basis of many tree reconstruction algorithms, whereas Kalmanson metrics were first considered by computer scientists, and are notable in that they are a non-trivial class of metrics for which the traveling salesman problem is tractable. We present a unifying framework for these theorems based on combinatorial structures that are used for graph planarity testing. These are (projective) PC-trees, and their affine analogs, PQ-trees. In the projective case, we generalize a number of concepts from clustering theory, including hierarchies, pyramids, ultrametrics, and Robinsonian matrices, and the theorems that relate them. As with tree metrics and ultrametrics, the link between PC-trees and PQ-trees is established via the Gromov product
On duality and fractionality of multicommodity flows in directed networks
In this paper we address a topological approach to multiflow (multicommodity
flow) problems in directed networks. Given a terminal weight , we define a
metrized polyhedral complex, called the directed tight span , and
prove that the dual of -weighted maximum multiflow problem reduces to a
facility location problem on . Also, in case where the network is
Eulerian, it further reduces to a facility location problem on the tropical
polytope spanned by . By utilizing this duality, we establish the
classifications of terminal weights admitting combinatorial min-max relation
(i) for every network and (ii) for every Eulerian network. Our result includes
Lomonosov-Frank theorem for directed free multiflows and
Ibaraki-Karzanov-Nagamochi's directed multiflow locking theorem as special
cases.Comment: 27 pages. Fixed minor mistakes and typos. To appear in Discrete
Optimizatio
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