TY - JOUR
AB - In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table Ω0 preserving the integrability near the boundary have to be tangent to a finite dimensional space passing through Ω0.
AU - Huang, Guan
AU - Kaloshin, Vadim
ID - 8416
IS - 2
JF - Moscow Mathematical Journal
SN - 1609-4514
TI - On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables
VL - 19
ER -
TY - JOUR
AB - For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set U in phase space of fixed measure, where the set of initial points which lead to collision is O(μ120) dense as μ→0.
AU - Guardia, Marcel
AU - Kaloshin, Vadim
AU - Zhang, Jianlu
ID - 8418
IS - 2
JF - Archive for Rational Mechanics and Analysis
KW - Mechanical Engineering
KW - Mathematics (miscellaneous)
KW - Analysis
SN - 0003-9527
TI - Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem
VL - 233
ER -
TY - CONF
AB - This report presents the results of a friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In its third edition, seven tools have been applied to solve six different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, CORA/SX, HyDRA, Hylaa, JuliaReach, SpaceEx, and XSpeed. This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for. Due to the diversity of problems, we are not ranking tools, yet the presented results provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.
AU - Althoff, Matthias
AU - Bak, Stanley
AU - Forets, Marcelo
AU - Frehse, Goran
AU - Kochdumper, Niklas
AU - Ray, Rajarshi
AU - Schilling, Christian
AU - Schupp, Stefan
ID - 8570
T2 - EPiC Series in Computing
TI - ARCH-COMP19 Category Report: Continuous and hybrid systems with linear continuous dynamics
VL - 61
ER -
TY - JOUR
AB - We review V. I. Arnold’s 1963 celebrated paper [1] Proof of A. N. Kolmogorov’s Theorem on the Conservation of Conditionally Periodic Motions with a Small Variation in the Hamiltonian, and prove that, optimising Arnold’s scheme, one can get “sharp” asymptotic quantitative conditions (as ε → 0, ε being the strength of the perturbation). All constants involved are explicitly computed.
AU - Chierchia, Luigi
AU - Koudjinan, Edmond
ID - 8693
JF - Regular and Chaotic Dynamics
TI - V. I. Arnold’s “pointwise” KAM theorem
VL - 24
ER -
TY - JOUR
AB - Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over ℚ that contains a conic defined over ℚ .
AU - Browning, Timothy D
AU - Sofos, Efthymios
ID - 170
IS - 3-4
JF - Mathematische Annalen
TI - Counting rational points on quartic del Pezzo surfaces with a rational conic
VL - 373
ER -
TY - JOUR
AB - An upper bound sieve for rational points on suitable varieties isdeveloped, together with applications tocounting rational points in thin sets,to local solubility in families, and to the notion of “friable” rational pointswith respect to divisors. In the special case of quadrics, sharper estimates areobtained by developing a version of the Selberg sieve for rational points.
AU - Browning, Timothy D
AU - Loughran, Daniel
ID - 175
IS - 8
JF - Transactions of the American Mathematical Society
SN - 00029947
TI - Sieving rational points on varieties
VL - 371
ER -
TY - JOUR
AB - The abelian sandpile serves as a model to study self-organized criticality, a phenomenon occurring in biological, physical and social processes. The identity of the abelian group is a fractal composed of self-similar patches, and its limit is subject of extensive collaborative research. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second and third order harmonics resemble smooth stretchings, respectively translations, of the identity, while the ones induced by fourth order harmonics resemble magnifications and rotations. Starting with order three, the dynamics pass through extended regions of seemingly random configurations which spontaneously reassemble into accentuated patterns. We show that the space of harmonic functions projects to the extended analogue of the sandpile group, thus providing a set of universal coordinates identifying configurations between different domains. Since the original sandpile group is a subgroup of the extended one, this directly implies that it admits a natural renormalization. Furthermore, we show that the harmonic fields can be induced by simple Markov processes, and that the corresponding stochastic dynamics show remarkable robustness over hundreds of periods. Finally, we encode information into seemingly random configurations, and decode this information with an algorithm requiring minimal prior knowledge. Our results suggest that harmonic fields might split the sandpile group into sub-sets showing different critical coefficients, and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain.
AU - Lang, Moritz
AU - Shkolnikov, Mikhail
ID - 196
IS - 8
JF - Proceedings of the National Academy of Sciences
TI - Harmonic dynamics of the Abelian sandpile
VL - 116
ER -
TY - JOUR
AB - Prevailing models of sex-chromosome evolution were largely inspired by the stable and highly differentiated XY pairs of model organisms, such as those of mammals and flies. Recent work has uncovered an incredible diversity of sex-determining systems, bringing some of the assumptions of these traditional models into question. One particular question that has arisen is what drives some sex chromosomes to be maintained over millions of years and differentiate fully, while others are replaced by new sex-determining chromosomes before differentiation has occurred. Here, I review recent data on the variability of sex-determining genes and sex chromosomes in different non-model vertebrates and invertebrates, and discuss some theoretical models that have been put forward to account for this diversity.
AU - Vicoso, Beatriz
ID - 7146
IS - 12
JF - Nature Ecology & Evolution
SN - 2397-334X
TI - Molecular and evolutionary dynamics of animal sex-chromosome turnover
VL - 3
ER -
TY - CONF
AB - The expression of a gene is characterised by its transcription factors and the function processing them. If the transcription factors are not affected by gene products, the regulating function is often represented as a combinational logic circuit, where the outputs (product) are determined by current input values (transcription factors) only, and are hence independent on their relative arrival times. However, the simultaneous arrival of transcription factors (TFs) in genetic circuits is a strong assumption, given that the processes of transcription and translation of a gene into a protein introduce intrinsic time delays and that there is no global synchronisation among the arrival times of different molecular species at molecular targets.
In this paper, we construct an experimentally implementable genetic circuit with two inputs and a single output, such that, in presence of small delays in input arrival, the circuit exhibits qualitatively distinct observable phenotypes. In particular, these phenotypes are long lived transients: they all converge to a single value, but so slowly, that they seem stable for an extended time period, longer than typical experiment duration. We used rule-based language to prototype our circuit, and we implemented a search for finding the parameter combinations raising the phenotypes of interest.
The behaviour of our prototype circuit has wide implications. First, it suggests that GRNs can exploit event timing to create phenotypes. Second, it opens the possibility that GRNs are using event timing to react to stimuli and memorise events, without explicit feedback in regulation. From the modelling perspective, our prototype circuit demonstrates the critical importance of analysing the transient dynamics at the promoter binding sites of the DNA, before applying rapid equilibrium assumptions.
AU - Guet, Calin C
AU - Henzinger, Thomas A
AU - Igler, Claudia
AU - Petrov, Tatjana
AU - Sezgin, Ali
ID - 7147
SN - 0302-9743
T2 - 17th International Conference on Computational Methods in Systems Biology
TI - Transient memory in gene regulation
VL - 11773
ER -
TY - JOUR
AB - In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an O(n1−2/ω) round matrix multiplication algorithm, where ω<2.3728639 is the exponent of matrix multiplication. In conjunction with known techniques from centralised algorithmics, this gives significant improvements over previous best upper bounds in the congested clique model. The highlight results include:
1. triangle and 4-cycle counting in O(n0.158) rounds, improving upon the O(n1/3) algorithm of Dolev et al. [DISC 2012],
2. a (1+o(1))-approximation of all-pairs shortest paths in O(n0.158) rounds, improving upon the O~(n1/2)-round (2+o(1))-approximation algorithm given by Nanongkai [STOC 2014], and
3. computing the girth in O(n0.158) rounds, which is the first non-trivial solution in this model.
In addition, we present a novel constant-round combinatorial algorithm for detecting 4-cycles.
AU - Censor-Hillel, Keren
AU - Kaski, Petteri
AU - Korhonen, Janne
AU - Lenzen, Christoph
AU - Paz, Ami
AU - Suomela, Jukka
ID - 7150
IS - 6
JF - Distributed Computing
SN - 0178-2770
TI - Algebraic methods in the congested clique
VL - 32
ER -