2,244 research outputs found
On the design of an implementation of kinetic minimum spanning trees
En aquest projecte dissenyem una possible implementació dels arbres cinètics d'expansió mínims proposats teòricament per Agarwal et al. a 'Parametric and kinetic minimum spanning trees'. El problema que es vol resoldre amb aquesta proposta és el de mantenir un arbre d'expansió mínim d'un graf amb pesos que canvia al llarg del temps. Els possibles canvis del graf són causats per canvis als pesos de les arestes -els quals són funció d'un paràmetre t que representa el temps- a més de permetre addicions i supressions d'arestes i actualitzacions de la funció de càlcul del pes de les arestes.In this project, we design a possible implementation of kinetic minimum spanning trees proposed theoretically by Agarwal et al. in 'Parametric and kinetic minimum spanning trees'. The problem we try to solve with this proposal is to maintain a minimum spanning tree of an edge-weighted graph that changes through time. The possible changes in the graph come from changes in the edge weights -which are functions of a parameter t which represents time- in addition to permitting additions and deletions of vertices and edges and updates to the edge weight calculation function
On the tradeoff between stability and fit
In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state.
We provide a precise formulation for this tradeoff and analyze the resulting stable extensions of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of Probability Proportional to Size (PPS) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-k, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions and discuss efficient incremental algorithms that can find new solutions as the input changes
Renormalization: an advanced overview
We present several approaches to renormalization in QFT: the multi-scale
analysis in perturbative renormalization, the functional methods \`a la
Wetterich equation, and the loop-vertex expansion in non-perturbative
renormalization. While each of these is quite well-established, they go beyond
standard QFT textbook material, and may be little-known to specialists of each
other approach. This review is aimed at bridging this gap.Comment: Review, 130 pages, 33 figures; v2: misprints corrected, refs. added,
minor improvements; v3: some changes to sect. 5, refs. adde
The Boltzmann-Grad Limit of a Hard Sphere System: Analysis of the Correlation Error
We present a quantitative analysis of the Boltzmann-Grad (low-density) limit
of a hard sphere system. We introduce and study a set of functions (correlation
errors) measuring the deviations in time from the statistical independence of
particles (propagation of chaos). In the context of the BBGKY hierarchy, a
correlation error of order measures the event where particles are
connected by a chain of interactions preventing the factorization. We show
that, provided , such an error flows to zero with
the average density , for short times, as , for some positive . This provides an information
on the size of chaos, namely, different particles behave as dictated by the
Boltzmann equation even when diverges as a negative power of .
The result requires a rearrangement of Lanford perturbative series into a
cumulant type expansion, and an analysis of many-recollision events.Comment: 98 pages, 12 figures. Subject of the Harold Grad Lecture at the 29th
International Symposium on Rarefied Gas Dynamics (Xi'an, China). This revised
version contains new results (a theorem on the convergence of high order
fluctuations; estimates of integrated correlation error) and several
improvements of presentation, inspired by comments of the anonymous refere
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