Activities in Combinatorial Pattern Matching

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Activities in Combinatorial Pattern Matching

• FDK SAB Meeting
• March 22 2004

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Algorithms on strings

• members J Kärkkäinen, V Mäkinen, K Fredriksson
  (-12/2002), K Lemström, H Tamm, S Inenaga
  (9/2003-), S Burkhardt (2/2004-)
• direct linear time construction of suffix arrays
  (J Kärkkäinen ICALP 03) elegant algorithm based
  on a novel approach textbook material
• gapped q-gram filters for approximate string
  matching (Burkhardt/Kärkkäinen) generalized
  q-grams give better filters

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Algorithms on strings (cont.)

• string database query systems
• efficient implementations of finite multitape
  automata
• minimization of finite-state automata
• THM A bideterministic finite-state automaton is
  minimal
• PhD project of H Tamm

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Transposition invariance
Transposition by -2
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Algorithms on strings (cont.)

• transposition invariant string matching
• motivated by music information retrieval
• A a1...am translated by t At a1t,
  ... ,amt
• translation invariant distance dT(A,B) min
  t?S d(At,B)

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Algorithms on strings (cont.)

• exact case is simple
• interval ai1 ai
• intervals(At) intervals(A)
• use interval sequences a2-a1, a3-a2, ,
  am-am-1 instead of originals in exact
  matching
• transposition invariance for free

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Algorithms on strings (cont.)

• approximate case edit distance
• repeat dynamic programming for all O(mn) relevant
  transpositions O(m2n2)
• apply sparse dynamic programming O(mn log m)
• V Mäkinens PhD Thesis (2003)

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Matches cover all pairs in DP table
bj-ai
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C C D C F E C C D C G F C C C1 A F E D B B A F G F
piano-roll representation
time
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Algorithms on strings Piano-roll matching

• geometric pattern matching under translations
  (Brass 2002)

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Algorithms on strings Patterns with small tree
dimension
kT 2
-Type of a positive edge (a,b) b-a -Tree
dimension kT of P smallest number of edge types
in a positive spanning tree of P
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Algorithms on strings Geometric generalization
of the Knuth-Morris-Pratt algorithm

• THM Translated occurrences of P with
  tree-dimension kT can be found in O(2mmkTn)
  bitvector operations on m bits long vectors.
• THM Finding kT is NP-complete can be
  approximated within logarithmic factor by the
  greedy set cover algorithm

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Algorithms on strings plans

• software library of string algorithms (J
  Kärkkäinen et al)
• continue with basic research index structures,
• inversion problems on sequences given a set of
  sequences find a model for them
• combine combinatorial and probabilistic approach

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Music retrieval and analysis

• members K Lemström, V Mäkinen, A Pienimäki
• efficient computational methods for music
  comparison, retrieval and analysis monophonic vs
  polyphonic music
• content-based retrieval query-by-humming
• geometric (piano-roll) sweepline algorithms
• query engine prototype
• open indexing of polyphonic music
• open distance measures for music, computational
  characterization of musical styles

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http//www.cs.helsinki.fi/group/cbrahms/demoengin
e/
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Biological sequence analysis

• members T Kivioja, K Palin, P Rastas, J Vilo
  (EBI)
• bioinformatics component of a novel DNA
  expression measurement technique TRAC developed
  at VTTBiotechnology selection and pooling of
  hybridization probes for entire genomes
• computational methods for optimizing cDNA-AFLP
  experiments
• T Kiviojas PhD Thesis (expected in 2004)

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Biological sequence analysis (cont)

• SPEXS tool for finding regulatory patterns
  (common motifs) from a set of sequences, with
  several applications J Vilos PhD Thesis (2002)
• general method for finding correlations between
  observed and predicted effects of gene knockout
  experiments (ECCB2002) gene regulatory networks
• the effect of SNPs on the binding affinities of
  transcription factors comparative genomics
  approach - clustering of binding site motifs over
  multiple genomes (unpublished)

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Biological sequence analysis (cont)

• algorithms for finding haplotype blocks and
  haplotype mosaics
• inversion of recombinations
• new Hidden Markov Model (unpublished)
• Minimum Description Length Principle EM
  algorithm
• c.f. group Mannila / group Toivonen

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Haplotype data
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Hidden Markov Model
Cross-over probabilities
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Metabolic modeling

• members J Rousu (postdoc in London), A Rantanen,
  E Pitkänen
• data from isotopic-tracing experiments
• new closed-form method for estimation of
  metabolic fluxes in steady state
• underdetermined linear systems
• propagation of information through the metabolic
  network, guided by the carbon maps of individual
  reactions
• prototype software system

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Metabolic modeling plans

• www server based on current prototype software
  (Neobio/TEKES)
• utilizing gene expression data
• what if analysis hypothetical reactions
• better algorithms bi-directional reactions, cell
  compartments, higher-order balance equations,
  improved propagation of information, incremental
  versions

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Computational structural biology

• members J Ravantti, K Fredriksson (-12/2002), T
  Mielikäinen, T Ojamies

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Computational struct. biology (cont)

• constrain-based algorithm for tomographic
  reconstruction
• sinogram-based (sound) method for noise reduction
  
• finding consistent orientations is NP-hard and
  inapproximable
• J Ravanttis PhD project

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Computational struct. biology (cont)

• BLAST for 3D density models (arrays of voxels)
  lots of applications
• model comparison substructure search shared
  substructures (all-against-all)
• translation-rotation invariance 6D search
• differences in distance and density scales
• solution under development contour extraction
  geometric hashing

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Computational struct. biology (cont)
Contour extraction
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Computational struct. biology (cont)
Original model
Model assembled from substructures