193,002 research outputs found
Group-theoretic models of the inversion process in bacterial genomes
The variation in genome arrangements among bacterial taxa is largely due to
the process of inversion. Recent studies indicate that not all inversions are
equally probable, suggesting, for instance, that shorter inversions are more
frequent than longer, and those that move the terminus of replication are less
probable than those that do not. Current methods for establishing the inversion
distance between two bacterial genomes are unable to incorporate such
information. In this paper we suggest a group-theoretic framework that in
principle can take these constraints into account. In particular, we show that
by lifting the problem from circular permutations to the affine symmetric
group, the inversion distance can be found in polynomial time for a model in
which inversions are restricted to acting on two regions. This requires the
proof of new results in group theory, and suggests a vein of new combinatorial
problems concerning permutation groups on which group theorists will be needed
to collaborate with biologists. We apply the new method to inferring distances
and phylogenies for published Yersinia pestis data.Comment: 19 pages, 7 figures, in Press, Journal of Mathematical Biolog
Combinatorics and geometry of finite and infinite squaregraphs
Squaregraphs were originally defined as finite plane graphs in which all
inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e.,
the vertices not incident with the outer face) have degrees larger than three.
The planar dual of a finite squaregraph is determined by a triangle-free chord
diagram of the unit disk, which could alternatively be viewed as a
triangle-free line arrangement in the hyperbolic plane. This representation
carries over to infinite plane graphs with finite vertex degrees in which the
balls are finite squaregraphs. Algebraically, finite squaregraphs are median
graphs for which the duals are finite circular split systems. Hence
squaregraphs are at the crosspoint of two dualities, an algebraic and a
geometric one, and thus lend themselves to several combinatorial
interpretations and structural characterizations. With these and the
5-colorability theorem for circle graphs at hand, we prove that every
squaregraph can be isometrically embedded into the Cartesian product of five
trees. This embedding result can also be extended to the infinite case without
reference to an embedding in the plane and without any cardinality restriction
when formulated for median graphs free of cubes and further finite
obstructions. Further, we exhibit a class of squaregraphs that can be embedded
into the product of three trees and we characterize those squaregraphs that are
embeddable into the product of just two trees. Finally, finite squaregraphs
enjoy a number of algorithmic features that do not extend to arbitrary median
graphs. For instance, we show that median-generating sets of finite
squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the
corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure
Active shielding of magnetic field with circular space-time characteristic
Aim. The synthesis of two degree of freedom robust two circuit system of active shielding of magnetic field with circular spacetime characteristic, generated by overhead power lines with "triangle" type of phase conductors arrangements for reducing the magnetic flux density to the sanitary standards level and to reducing the sensitivity of the system to plant parameters uncertainty. Methodology. The synthesis is based on the multi-criteria game decision, in which the payoff vector is calculated on the basis of the Maxwell equations quasi-stationary approximation solutions. The game decision is based on the stochastic particles multiswarm optimization algorithms. The initial parameters for the synthesis by system of active shielding are the location of the overhead power lines with respect to the shielding space, geometry and number of shielding coils, operating currents, as well as the size of the shielding space and magnetic flux density normative value, which should be achieved as a result of shielding. The objective of the synthesis is to determine their number, configuration, spatial arrangementand and shielding coils currents, setting algorithm of the control systems as well as the resulting of the magnetic flux density value at the shielding space. Results. Computer simulation and field experimental research results of two degree of freedom robust two circuit system of active shielding of magnetic field, generated by overhead power lines with Β«triangleΒ» type of phase conductors arrangements are given. The possibility of initial magnetic flux density level reducing and system sensitivity reducing to the plant parameters uncertainty is shown. Originality. For the first time the synthesis, theoretical and experimental research of two degree of freedom robust two -circuit t system of active shielding of magnetic field generated by single-circuit overhead power line with phase conductors triangular arrangements carried out. Practical value. Practical recommendations from the point of view of the practical implementation on reasonable choice of the spatial arrangement of two shielding coils of robust two -circuit system of active shielding of the magnetic field with circular space-time characteristic generated by single-circuit overhead power line with phase conductors triangular arrangements are given.Π¦Π΅Π»Ρ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Ρ ΠΊΡΡΠ³ΠΎΠ²ΠΎΠΉ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎ-Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΎΠΉ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ² Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π΄ΠΎ ΡΡΠΎΠ²Π½Ρ ΡΠ°Π½ΠΈΡΠ°ΡΠ½ΡΡ
Π½ΠΎΡΠΌ ΠΈ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΠ΅ΡΠΎΠ΄ΠΎΠ»ΠΎΠ³ΠΈΡ. Π‘ΠΈΠ½ΡΠ΅Π· ΠΎΡΠ½ΠΎΠ²Π°Π½ Π½Π° ΡΠ΅ΡΠ΅Π½ΠΈΠΈ ΠΌΠ½ΠΎΠ³ΠΎΠΊΡΠΈΡΠ΅ΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΈΠ³ΡΡ, Π² ΠΊΠΎΡΠΎΡΠΎΠΉ Π²Π΅ΠΊΡΠΎΡΠ½ΡΠΉ Π²ΡΠΈΠ³ΡΡΡ Π²ΡΡΠΈΡΠ»ΡΠ΅ΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π°Π½ΠΈΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΠΉ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠΉ ΠΠ°ΠΊΡΠ²Π΅Π»Π»Π° Π² ΠΊΠ²Π°Π·ΠΈΡΡΠ°ΡΠΈΠΎΠ½Π°ΡΠ½ΠΎΠΌ ΠΏΡΠΈΠ±Π»ΠΈΠΆΠ΅Π½ΠΈΠΈ. Π Π΅ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ³ΡΡ Π½Π°Ρ
ΠΎΠ΄ΠΈΡΡΡ Π½Π° ΠΎΡΠ½ΠΎΠ²Π΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΡΠΎΡ
Π°ΡΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΠΌΡΠ»ΡΡΠΈΠ°Π³Π΅Π½ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ ΠΌΡΠ»ΡΡΠΈΡΠΎΠ΅ΠΌ ΡΠ°ΡΡΠΈΡ. ΠΡΡ
ΠΎΠ΄Π½ΡΠΌΠΈ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠ°ΠΌΠΈ Π΄Π»Ρ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ²Π»ΡΡΡΡΡ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΠ΅ Π²ΡΡΠΎΠΊΠΎΠ²ΠΎΠ»ΡΡΠ½ΠΎΠΉ
Π»ΠΈΠ½ΠΈΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ ΠΏΠΎ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΡ ΠΊ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠΌΡ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Ρ, Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ, ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²ΠΎ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ² ΠΈ ΡΠ°Π±ΠΎΡΠΈΠ΅ ΡΠΎΠΊΠΈ Π»ΠΈΠ½ΠΈΠΈ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ°Π·ΠΌΠ΅ΡΡ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ Π½ΠΎΡΠΌΠ°ΡΠΈΠ²Π½ΠΎΠ΅ Π·Π½Π°ΡΠ΅Π½ΠΈΠ΅ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, ΠΊΠΎΡΠΎΡΠΎΠ΅ Π΄ΠΎΠ»ΠΆΠ½ΠΎ Π±ΡΡΡ Π΄ΠΎΡΡΠΈΠ³Π½ΡΡΠΎ Π² ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΠ΅ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ. ΠΠ°Π΄Π°ΡΠ΅ΠΉ ΡΠΈΠ½ΡΠ΅Π·Π° ΡΠ²Π»ΡΠ΅ΡΡΡ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠ΅ ΠΊΠΎΠ»ΠΈΡΠ΅ΡΡΠ²Π°, ΠΊΠΎΠ½ΡΠΈΠ³ΡΡΠ°ΡΠΈΠΈ, ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ ΠΈ ΡΠΎΠΊΠΎΠ² ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ, Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΡΠ°Π±ΠΎΡΡ ΡΠΈΡΡΠ΅ΠΌΡ ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ, Π° ΡΠ°ΠΊΠΆΠ΅ ΡΠ΅Π·ΡΠ»ΡΡΠΈΡΡΡΡΠ΅Π³ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π² ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠΌ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅. Π Π΅Π·ΡΠ»ΡΡΠ°ΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΡΠ΅Π·ΡΠ»ΡΡΠ°ΡΡ ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΈ ΠΏΠΎΠ»Π΅Π²ΡΡ
ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΡ
ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΠΉ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ². ΠΠΎΠΊΠ°Π·Π°Π½Π° Π²ΠΎΠ·ΠΌΠΎΠΆΠ½ΠΎΡΡΡ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠΎΠ²Π½Ρ ΠΈΠ½Π΄ΡΠΊΡΠΈΠΈ ΠΈΡΡ
ΠΎΠ΄Π½ΠΎΠ³ΠΎ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Π²Π½ΡΡΡΠΈ ΡΠΊΡΠ°Π½ΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π° ΠΈ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΡΠ²ΡΡΠ²ΠΈΡΠ΅Π»ΡΠ½ΠΎΡΡΠΈ ΡΠΈΡΡΠ΅ΠΌΡ ΠΊ Π½Π΅ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½Π½ΠΎΡΡΡΠΌ ΠΏΠ°ΡΠ°ΠΌΠ΅ΡΡΠΎΠ² ΠΎΠ±ΡΠ΅ΠΊΡΠ° ΡΠΏΡΠ°Π²Π»Π΅Π½ΠΈΡ. ΠΡΠΈΠ³ΠΈΠ½Π°Π»ΡΠ½ΠΎΡΡΡ. ΠΠΏΠ΅ΡΠ²ΡΠ΅ ΠΏΡΠΎΠ²Π΅Π΄Π΅Π½Ρ ΡΠΈΠ½ΡΠ΅Π·, ΡΠ΅ΠΎΡΠ΅ΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΠΈ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°Π»ΡΠ½ΡΠ΅ ΠΈΡΡΠ»Π΅Π΄ΠΎΠ²Π°Π½ΠΈΡ ΠΊΠΎΠΌΠ±ΠΈΠ½ΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ, Π³Π΅Π½Π΅ΡΠΈΡΡΠ΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ². ΠΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠ°Ρ ΡΠ΅Π½Π½ΠΎΡΡΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΈΠ΅ ΡΠ΅ΠΊΠΎΠΌΠ΅Π½Π΄Π°ΡΠΈΠΈ ΠΏΠΎ ΠΎΠ±ΠΎΡΠ½ΠΎΠ²Π°Π½Π½ΠΎΠΌΡ Π²ΡΠ±ΠΎΡΡ Ρ ΡΠΎΡΠΊΠΈ Π·ΡΠ΅Π½ΠΈΡ ΠΏΡΠ°ΠΊΡΠΈΡΠ΅ΡΠΊΠΎΠΉ ΡΠ΅Π°Π»ΠΈΠ·Π°ΡΠΈΠΈ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎΠ³ΠΎ ΡΠ°ΡΠΏΠΎΠ»ΠΎΠΆΠ΅Π½ΠΈΡ Π΄Π²ΡΡ
ΡΠΊΡΠ°Π½ΠΈΡΡΡΡΠΈΡ
ΠΎΠ±ΠΌΠΎΡΠΎΠΊ Π΄Π²ΡΡ
ΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ ΡΠΎΠ±Π°ΡΡΠ½ΠΎΠΉ ΡΠΈΡΡΠ΅ΠΌΡ Π°ΠΊΡΠΈΠ²Π½ΠΎΠ³ΠΎ ΡΠΊΡΠ°Π½ΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΌΠ°Π³Π½ΠΈΡΠ½ΠΎΠ³ΠΎ ΠΏΠΎΠ»Ρ Ρ ΠΊΡΡΠ³ΠΎΠ²ΠΎΠΉ ΠΏΡΠΎΡΡΡΠ°Π½ΡΡΠ²Π΅Π½Π½ΠΎ-Π²ΡΠ΅ΠΌΠ΅Π½Π½ΠΎΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΎΠΉ, ΡΠΎΠ·Π΄Π°Π²Π°Π΅ΠΌΠΎΠ³ΠΎ ΠΎΠ΄Π½ΠΎΠΊΠΎΠ½ΡΡΡΠ½ΠΎΠΉ Π²ΠΎΠ·Π΄ΡΡΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠ΅ΠΉ ΡΠ»Π΅ΠΊΡΡΠΎΠΏΠ΅ΡΠ΅Π΄Π°ΡΠΈ Ρ ΡΡΠ΅ΡΠ³ΠΎΠ»ΡΠ½ΡΠΌ ΠΏΠΎΠ΄Π²Π΅ΡΠΎΠΌ ΠΏΡΠΎΠ²ΠΎΠ΄ΠΎΠ²
Quasi-Parallel Segments and Characterization of Unique Bichromatic Matchings
Given n red and n blue points in general position in the plane, it is
well-known that there is a perfect matching formed by non-crossing line
segments. We characterize the bichromatic point sets which admit exactly one
non-crossing matching. We give several geometric descriptions of such sets, and
find an O(nlogn) algorithm that checks whether a given bichromatic set has this
property.Comment: 31 pages, 24 figure
- β¦