319 research outputs found
Geometry of mutation classes of rank 3 quivers
We present a geometric realization for all mutation classes of quivers of rank 3 with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by Ο-rotations for the cyclic ones. The geometric behavior of the model turns out to be controlled by the Markov constant p2 + q2 + r 2 β pqr, where p, q,r are the weights of arrows in a quiver. We also classify skew-symmetric mutation-finite real 3Γ3 matrices and explore the structure of acyclic representatives in finite and infinite mutation classes
Acyclic cluster algebras, reflection groups, and curves on a punctured disc
We establish a bijective correspondence between certain non-self-intersecting curves in an n-punctured disc and positive c-vectors of acyclic cluster algebras whose quivers have multiple arrows between every pair of vertices. As a corollary, we obtain a proof of LeeβLee conjecture [15] on the combinatorial description of real Schur roots for acyclic quivers with multiple arrows, and give a combinatorial characterization of seeds in terms of curves in an n-punctured disc
Coxeter groups, quiver mutations and geometric manifolds
We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh, and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every quiver or diagram of finite or affine type a CW-complex with a proper action of a finite (or affine) Coxeter group. These CW-complexes undergo mutations agreeing with mutations of quivers and diagrams. We also generalize the construction to quivers and diagrams originating from unpunctured surfaces and orbifolds
On hyperbolic Coxeter n-polytopes with n + 2 facets
A convex polytope admits a Coxeter decomposition if it is tiled by finitely many Coxeter polytopes such that any two tiles having a common facet are symmetric with respect to this facet. In this paper, we classify all Coxeter decompositions of compact hyperbolic Coxeter n-polytopes with n + 2 facets. Furthermore, going out from SchlΓ€fliβs reduction formula for simplices we construct in a purely combinatorial way a volume formula for arbitrary polytopes and compute the volumes of all compact Coxeter polytopes in β4 which are products of simplice
Cluster algebras from surfaces and extended affine Weyl groups
We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space V , and with every triangulation a basis in V , such that any mutation of a cluster (i.e., a flip of a triangulation) transforms the corresponding bases into each other by partial reflections. Furthermore, every triangulation gives rise to an extended affine Weyl group of type A, which is invariant under flips. The construction is also extended to exceptional skew-symmetric mutation-finite cluster algebras of types
ΠΠΎΠΌΠ΅Π½Π½ΡΠΉ ΡΠΏΠΈΡΠ°ΠΊΡΠΈΠ°Π»ΡΠ½ΡΠΉ ΡΠΎΡΡ ΡΠ΅Π³Π½Π΅ΡΠΎΡΠ»Π΅ΠΊΡΡΠΈΡΠ΅ΡΠΊΠΈΡ ΠΏΠ»Π΅Π½ΠΎΠΊ ΡΠΈΡΠ°Π½Π°ΡΠ° Π±Π°ΡΠΈΡ-ΡΡΡΠΎΠ½ΡΠΈΡ Π½Π° ΡΠ°ΠΏΡΠΈΡΠ΅
The model of the crystal epitaxial growth of multicomponent films on single crystal substrates with domain corresponds are presented to an example of a solid solution of barium strontium titanate on sapphire substrates (r-cut). Domain matched epitaxial growth involves the matching of the film and substrate lattice planes having a similar structure, by matching domains. Varying the component composition of the solid solution allows to change the domain size in the range sufficient to reduce the mismatch of the lattice of barium strontium titanate and sapphire. Thus, it is possible to design an epitaxial film growth of various solid solutions on single-crystal substrates.ΠΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Π° ΠΌΠΎΠ΄Π΅Π»Ρ ΡΠΏΠΈΡΠ°ΠΊΡΠΈΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΎΡΡΠ° ΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠ½ΠΎΠ³ΠΎΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΡΡ
ΠΏΠ»Π΅Π½ΠΎΠΊ Π½Π° ΠΌΠΎΠ½ΠΎΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠ΄Π»ΠΎΠΆΠΊΠ°Ρ
Ρ Π΄ΠΎΠΌΠ΅Π½Π½ΡΠΌ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠ΅ΠΌ Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ ΡΠ²Π΅ΡΠ΄ΠΎΠ³ΠΎ ΡΠ°ΡΡΠ²ΠΎΡΠ° ΡΠΈΡΠ°Π½Π°ΡΠ° Π±Π°ΡΠΈΡ-ΡΡΡΠΎΠ½ΡΠΈΡ Π½Π° ΠΏΠΎΠ΄Π»ΠΎΠΆΠΊΠ°Ρ
ΡΠ°ΠΏΡΠΈΡΠ° (r-ΡΡΠ΅Π·). ΠΠΎΠΌΠ΅Π½Π½ΡΠΉ ΡΠΏΠΈΡΠ°ΠΊΡΠΈΠ°Π»ΡΠ½ΡΠΉ ΡΠΎΡΡ ΠΏΡΠ΅Π΄ΠΏΠΎΠ»Π°Π³Π°Π΅Ρ ΡΠΎΠ³Π»Π°ΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΏΠ»ΠΎΡΠΊΠΎΡΡΠ΅ΠΉ ΡΠ΅ΡΠ΅ΡΠΊΠΈ ΠΏΠ»Π΅Π½ΠΊΠΈ ΠΈ ΠΏΠΎΠ΄Π»ΠΎΠΆΠΊΠΈ, ΠΈΠΌΠ΅ΡΡΠΈΡ
ΡΡ
ΠΎΠΆΡΡ ΡΡΡΡΠΊΡΡΡΡ, ΠΏΡΡΠ΅ΠΌ ΡΠΎΠΏΠΎΡΡΠ°Π²Π»Π΅Π½ΠΈΡ Π΄ΠΎΠΌΠ΅Π½ΠΎΠ², ΠΊΡΠ°ΡΠ½ΡΡ
ΡΠ΅Π»ΠΎΠΌΡ ΡΠΈΡΠ»Ρ ΠΌΠ΅ΠΆΠΏΠ»ΠΎΡΠΊΠΎΡΡΠ½ΡΡ
ΡΠ°ΡΡΡΠΎΡΠ½ΠΈΠΉ. ΠΠ°ΡΡΠΈΡΠΎΠ²Π°Π½ΠΈΠ΅ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½ΡΠ½ΠΎΠ³ΠΎ ΡΠΎΡΡΠ°Π²Π° ΡΠ²Π΅ΡΠ΄ΠΎΠ³ΠΎ ΡΠ°ΡΡΠ²ΠΎΡΠ° ΠΏΠΎΠ·Π²ΠΎΠ»ΡΠ΅Ρ ΠΈΠ·ΠΌΠ΅Π½ΡΡΡ ΡΠ°Π·ΠΌΠ΅Ρ Π΄ΠΎΠΌΠ΅Π½Π° Π² Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π΅, Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎΠΌ Π΄Π»Ρ ΡΠ½ΠΈΠΆΠ΅Π½ΠΈΡ ΡΠ°ΡΡΠΎΠ³Π»Π°ΡΠΎΠ²Π°Π½ΠΈΡ ΡΠ΅ΡΠ΅ΡΠΎΠΊ ΡΠΈΡΠ°Π½Π°ΡΠ° Π±Π°ΡΠΈΡ-ΡΡΡΠΎΠ½ΡΠΈΡ ΠΈ ΡΠ°ΠΏΡΠΈΡΠ° Π΄ΠΎ Π·Π½Π°ΡΠ΅Π½ΠΈΡ, Π΄ΠΎΡΡΠ°ΡΠΎΡΠ½ΠΎΠ³ΠΎ Π΄Π»Ρ ΡΠΏΠΈΡΠ°ΠΊΡΠΈΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΎΡΡΠ°. Π’Π°ΠΊΠΈΠΌ ΠΎΠ±ΡΠ°Π·ΠΎΠΌ, ΠΌΠΎΠΆΠ½ΠΎ ΡΠΏΡΠΎΠ΅ΠΊΡΠΈΡΠΎΠ²Π°ΡΡ ΡΠΏΠΈΡΠ°ΠΊΡΠΈΠ°Π»ΡΠ½ΡΠΉ ΡΠΎΡΡ ΠΏΠ»Π΅Π½ΠΎΠΊ ΡΠ°Π·Π»ΠΈΡΠ½ΡΡ
ΡΠ²Π΅ΡΠ΄ΡΡ
ΡΠ°ΡΡΠ²ΠΎΡΠΎΠ² Π½Π° ΠΌΠΎΠ½ΠΎΠΊΡΠΈΡΡΠ°Π»Π»ΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΏΠΎΠ΄Π»ΠΎΠΆΠΊΠ°Ρ
Tri-critical behavior in rupture induced by disorder
We discover a qualitatively new behavior for systems where the load transfer
has limiting stress amplification as in real fiber composites. We find that the
disorder is a relevant field leading to tri--criticality, separating a
first-order regime where rupture occurs without significant precursors from a
second-order regime where the macroscopic elastic coefficient exhibit power law
behavior. Our results are based on analytical analysis of fiber bundle models
and numerical simulations of a two-dimensional tensorial spring-block system in
which stick-slip motion and fracture compete.Comment: Revtex, 10 pages, 4 figures available upon reques
Electrocardiogram Monitoring Wearable Devices and Artificial-Intelligence-Enabled Diagnostic Capabilities: A Review
Worldwide, population aging and unhealthy lifestyles have increased the incidence of high-risk health conditions such as cardiovascular diseases, sleep apnea, and other conditions. Recently, to facilitate early identification and diagnosis, efforts have been made in the research and development of new wearable devices to make them smaller, more comfortable, more accurate, and increasingly compatible with artificial intelligence technologies. These efforts can pave the way to the longer and continuous health monitoring of different biosignals, including the real-time detection of diseases, thus providing more timely and accurate predictions of health events that can drastically improve the healthcare management of patients. Most recent reviews focus on a specific category of disease, the use of artificial intelligence in 12-lead electrocardiograms, or on wearable technology. However, we present recent advances in the use of electrocardiogram signals acquired with wearable devices or from publicly available databases and the analysis of such signals with artificial intelligence methods to detect and predict diseases. As expected, most of the available research focuses on heart diseases, sleep apnea, and other emerging areas, such as mental stress. From a methodological point of view, although traditional statistical methods and machine learning are still widely used, we observe an increasing use of more advanced deep learning methods, specifically architectures that can handle the complexity of biosignal data. These deep learning methods typically include convolutional and recurrent neural networks. Moreover, when proposing new artificial intelligence methods, we observe that the prevalent choice is to use publicly available databases rather than collecting new data
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