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An Optimal Randomised Cell Probe Lower Bound for Approximate Nearest Neighbour Searching

A. Chakrabarti, O. Regev
45th Annual IEEE Symposium on Foundations of Computer Science  
In this paper, for the first time, we obtain a randomised lower bound for ANN, thus addressing this shortcoming. Moreover, we show that our lower bound is optimal.  ...  We consider the approximate nearest neighbour search problem on the Hamming Cube {0, 1} d .  ...  Acknowledgments We would like to thank Paul Beame, Hartmut Klauck, Pranab Sen, and Xiaodong Sun for many helpful discussions about various aspects of this paper.  ... 
doi:10.1109/focs.2004.12 dblp:conf/focs/ChakrabartiR04 fatcat:idxmkpz7pzf3xmyhs7aamwkj3e

Lower bounds for predecessor searching in the cell probe model

Pranab Sen, S. Venkatesh
2008 Journal of computer and system sciences (Print)  
Our lower bound proof has the following advantages: it works for randomised query schemes too, while Beame and Fich's proof works for deterministic query schemes only.  ...  Fich, Optimal bounds for the predecessor problem and related problems, J. Comput.  ...  Subsequent work After the paper [35] was published, Chakrabarti and Regev [6] proved an optimal lower bound for randomised cell probe schemes for the approximate nearest neighbour searching problem  ... 
doi:10.1016/j.jcss.2007.06.016 fatcat:yqz6ikd5h5cv7frnwesey7s4de

Lower bounds for predecessor searching in the cell probe model [article]

Pranab Sen, S. Venkatesh
2003 arXiv   pre-print
Our lower bound proof has the following advantages: it works for randomised query schemes too, while Beame and Fich's proof works for deterministic query schemes only.  ...  Recently, Beame and Fich obtained optimal bounds on the number of probes needed by any deterministic query scheme if the associated storage scheme uses only n^O(1) cells of word size ( m)^O(1) bits.  ...  We also thank Ashwin Nayak for helpful discussions and for pointing out the reference [Man01] , and Jaikumar Radhakrishnan for reading an early draft of [SV01] and for enlightening discussions.  ... 
arXiv:cs/0309033v1 fatcat:26ooz6c7orb4hjsifamcdktxpm

Improved Similarity Search for Large Data in Machine Learning and Robotics

Josiah Walker
2019 Figshare  
to consider total memory usage, scalability, and sometimes construction costs for the search structures.This thesis presents a locality-sensitive hash (LSH) code generation method which has a lower computational  ...  This thesis presents techniques for accelerating similarity search methods on large datasets.  ...  Figure 5 . 2 : 52 Approximate cover tree search for 1-nearest-neighbour: predicted lower bound for recall compared to actual recall for values of s.  ... 
doi:10.6084/m9.figshare.9942509 fatcat:ajvkwfnmyff6hjw7kh2njeuosm

Quantum walks and quantum search on graphene lattices

Iain Foulger, Sven Gnutzmann, Gregor Tanner
2015 Physical Review A. Atomic, Molecular, and Optical Physics  
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms.  ...  Here, we demonstrate that continuous-time quantum walk search is possible in two-dimensions by changing the search topology to a graphene lattice, utilising the Dirac point in the energy spectrum.  ...  This means that for a search of a cell, at least for a 12 × 12 cell lattice, there is almost 50% probability of localising on the cell or its nearest-neighbour, that is, the additional vertex.  ... 
doi:10.1103/physreva.91.062323 fatcat:ukgylcp2bfhmfbz2j4so7s2ki4

A Review of Feature Selection and Feature Extraction Methods Applied on Microarray Data

Zena M. Hira, Duncan F. Gillies
2015 Advances in Bioinformatics  
We present some of the most popular methods for selecting significant features and provide a comparison between them.  ...  Their advantages and disadvantages are outlined in order to provide a clearer idea of when to use each one of them for saving computational time and resources.  ...  For classification, support vector machines (SVMs), -nearest neighbours, and probabilistic neural networks were used in an attempt to classify between cancerous and noncancerous breast tumours [24] .  ... 
doi:10.1155/2015/198363 pmid:26170834 pmcid:PMC4480804 fatcat:mnlyfcwcarhqjix63e46x63nka

Variational-State Quantum Metrology [article]

Bálint Koczor, Suguru Endo, Tyson Jones, Yuichiro Matsuzaki, Simon C. Benjamin
2020 arXiv   pre-print
We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the classically intractable high-dimensional  ...  We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.  ...  Fig. 4 b) (left) shows the optimal sensing times for the various probe states.  ... 
arXiv:1908.08904v3 fatcat:yavb7a7qdbddxb32qqpp3qnqi4

Variational-State Quantum Metrology

Bálint Koczor, Suguru Endo, Tyson Jones, Yuichiro Matsuzaki, Simon C Benjamin
2020 New Journal of Physics  
We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the high-dimensional space of quantum  ...  We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.  ...  TJ thanks the Clarendon Fund for their continued support.  ... 
doi:10.1088/1367-2630/ab965e fatcat:chwj3ws5ibcsxg75775tamx4ty

A dynamic and spatially periodic micro-pattern of HES5 expression underlies the probability of neuronal differentiation in the mouse spinal cord [article]

Veronica Biga, Joshua J Hawley, Emma Johns, Daniel Han, Jochen Kursawe, Paul Glendinning, Cerys S Manning, Nancy Papalopulu
2020 biorxiv/medrxiv   pre-print
Such dynamic expression is key for enabling cell state transitions in a tissue environment.  ...  We find that the HES5 microclusters are less dynamic in the presence of a Notch inhibitor showing that Notch mediated cell-cell communication is required for temporal characteristics.  ...  The multicellular approach extends the single-cell model by introducing an inhibitory Hill function to couple nearest-neighbour cells (in a fixed, no cell movement, hexagonal geometry) whereby high Hes5  ... 
doi:10.1101/2020.08.03.234369 fatcat:dflyuf2pgbegnn5sy4lm5ogdpe

A dynamic, spatially periodic, micro‐pattern of HES5 underlies neurogenesis in the mouse spinal cord

Veronica Biga, Joshua Hawley, Ximena Soto, Emma Johns, Daniel Han, Hayley Bennett, Antony D Adamson, Jochen Kursawe, Paul Glendinning, Cerys S Manning, Nancy Papalopulu
2021 Molecular Systems Biology  
We show that Notch signalling is required for temporal dynamics but not the spatial periodicity of HES5.  ...  Ultradian oscillations of HES Transcription Factors (TFs) at the single-cell level enable cell state transitions. However, the tissue-level organisation of HES5 dynamics in neurogenesis is unknown.  ...  The multicellular approach extends the single-cell model by introducing an inhibitory Hill function to couple nearest-neighbour cells (in a fixed, no cell movement, hexagonal geometry) whereby high Hes5  ... 
doi:10.15252/msb.20209902 pmid:34031978 pmcid:PMC8144840 fatcat:n22au4mvlfbphdm4ql2avcqqnu

Lower bounds for text indexing with mismatches and differences [chapter]

Vincent Cohen-Addad, Laurent Feuilloley, Tatiana Starikovskaya
2019 Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms  
Our lower bounds also apply to the dictionary look-up problem, where instead of a text one is given a set of strings. ACM Subject Classification Pattern matching, Cell-probe models and lower bounds  ...  This bound also extends to the setting where we only ask for (1 + ε)-approximate solutions for text indexing.  ...  Since the cell-probe model is stronger than the RAM model, this lower bound implies Ω(d/ log n) query time lower bound for the classic RAM data structures.  ... 
doi:10.1137/1.9781611975482.70 dblp:conf/soda/Cohen-AddadFS19 fatcat:apda62vinfgrhddtuo6geeszne

Lower bounds for text indexing with mismatches and differences [article]

Vincent Cohen-Addad, Tatiana Starikovskaya
2018 arXiv   pre-print
This bound also extends to the setting where we only ask for (1+ε)-approximate solutions for text indexing.  ...  We provide conditional and pointer-machine lower bounds that make a step toward explaining this phenomenon. We start by demonstrating lower bounds for k = Θ( n).  ...  Since the cell-probe model is stronger than the RAM model, this lower bound implies Ω(d/ log n) query time lower bound for the classic RAM data structures.  ... 
arXiv:1812.09120v1 fatcat:h6jov5yyfrh3vct77gcefjm6dm

Learning Robust Real-Time Cultural Transmission without Human Data [article]

Cultural General Intelligence Team, Avishkar Bhoopchand, Bethanie Brownfield, Adrian Collister, Agustin Dal Lago, Ashley Edwards, Richard Everett, Alexandre Frechette, Yanko Gitahy Oliveira, Edward Hughes, Kory W. Mathewson, Piermaria Mendolicchio (+7 others)
2022 arXiv   pre-print
This paves the way for cultural evolution as an algorithm for developing artificial general intelligence.  ...  We identify a surprisingly simple set of ingredients sufficient for generating cultural transmission and develop an evaluation methodology for rigorously assessing it.  ...  Acknowledgements We would like to thank many, both at DeepMind and in the wider community, for the conversations that have helped to shape this manuscript.  ... 
arXiv:2203.00715v1 fatcat:vlf5er6b4nhytn7lubbe42vbaa

TMVA - Toolkit for Multivariate Data Analysis [article]

A. Hoecker, P. Speckmayer, J. Stelzer, J. Therhaag, E. von Toerne, H. Voss, M. Backes, T. Carli, O. Cohen, A. Christov, D. Dannheim, K. Danielowski (+14 others)
2009 arXiv   pre-print
In high-energy physics, with the search for ever smaller signals in ever larger data sets, it has become essential to extract a maximum of the available information from the data.  ...  Sec. 8.3), the k-nearest neighbour method compares an observed (test) event to reference events from a training data set [2] .  ...  The k-NN algorithm searches for 20 nearest points in the nearest neighborhood (circle) of the query event, shown as a star.  ... 
arXiv:physics/0703039v5 fatcat:xec4mqsl5rgsrnljp2z2n6brj4

Systematic Biases In Weak Lensing Cosmology With The Dark Energy Survey

Simon Samuroff, Sarah Bridle
2019 Zenodo  
Chapter 4 describes an extension of the analysis on the hoopoe simulations into a detailed investigation of the impact of galaxy neighbours on shape measurement and shear cosmology.  ...  We use the cosmological inference pipeline of DES Y1 to explore the cosmological implications of neighbour bias and show that omitting blending from the calibration simulation for DES Y1 would bias the  ...  Using a similar nearest neighbour search as described above, we estimate mean distance to the nearest "bad" COSMOS profile to be ∼ 90 pixels.  ... 
doi:10.5281/zenodo.1162395 fatcat:nhm747tbx5buzdxqgx66reyoxq
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