2,727 research outputs found
The structure of the consecutive pattern poset
The consecutive pattern poset is the infinite partially ordered set of all
permutations where if has a subsequence of adjacent
entries in the same relative order as the entries of . We study the
structure of the intervals in this poset from topological, poset-theoretic, and
enumerative perspectives. In particular, we prove that all intervals are
rank-unimodal and strongly Sperner, and we characterize disconnected and
shellable intervals. We also show that most intervals are not shellable and
have M\"obius function equal to zero.Comment: 29 pages, 7 figures. To appear in IMR
Deterministic constant-temperature dynamics for dissipative quantum systems
A novel method is introduced in order to treat the dissipative dynamics of
quantum systems interacting with a bath of classical degrees of freedom. The
method is based upon an extension of the Nos\`e-Hoover chain (constant
temperature) dynamics to quantum-classical systems. Both adiabatic and
nonadiabatic numerical calculations on the relaxation dynamics of the
spin-boson model show that the quantum-classical Nos\`e-Hoover chain dynamics
represents the thermal noise of the bath in an accurate and simple way.
Numerical comparisons, both with the constant energy calculation and with the
quantum-classical Brownian motion treatment of the bath, show that the
quantum-classical Nos\`e-Hoover Chain dynamics can be used to introduce
dissipation in the evolution of a quantum subsystem even with just one degree
of freedom for the bath. The algorithm can be computationally advantageous in
modeling, within computer simulation, the dynamics of a quantum subsystem
interacting with complex molecular environments.Comment: Revised versio
Random graph model with power-law distributed triangle subgraphs
Clustering is well-known to play a prominent role in the description and
understanding of complex networks, and a large spectrum of tools and ideas have
been introduced to this end. In particular, it has been recognized that the
abundance of small subgraphs is important. Here, we study the arrangement of
triangles in a model for scale-free random graphs and determine the asymptotic
behavior of the clustering coefficient, the average number of triangles, as
well as the number of triangles attached to the vertex of maximum degree. We
prove that triangles are power-law distributed among vertices and characterized
by both vertex and edge coagulation when the degree exponent satisfies
; furthermore, a finite density of triangles appears as
.Comment: 4 pages, 2 figure; v2: major conceptual change
On intervals of the consecutive pattern poset
International audienceThe consecutive pattern poset is the infinite partially ordered set of all permutations where σ ≤ τ if τ has a subsequence of adjacent entries in the same relative order as the entries of σ. We study the structure of the intervals in this poset from topological, poset-theoretic, and enumerative perspectives. In particular, we prove that all intervals are rank-unimodal and strongly Sperner, and we characterize disconnected and shellable intervals. We also show that most intervals are not shellable and have Mo ̈bius function equal to zero
Statistical Mechanics of Quantum-Classical Systems with Holonomic Constraints
The statistical mechanics of quantum-classical systems with holonomic
constraints is formulated rigorously by unifying the classical Dirac bracket
and the quantum-classical bracket in matrix form.
The resulting Dirac quantum-classical theory, which conserves the holonomic
constraints exactly, is then used to formulate time evolution and statistical
mechanics. The correct momentum-jump approximation for constrained system
arises naturally from this formalism. Finally, in analogy with what was found
in the classical case, it is shown that the rigorous linear response function
of constrained quantum-classical systems contains non-trivial additional terms
which are absent in the response of unconstrained systems.Comment: Submitted to Journal of Chemical Physic
On Phase Transitions to Cooperation in the Prisoner's Dilemma
Game theory formalizes certain interactions between physical particles or
between living beings in biology, sociology, and economics, and quantifies the
outcomes by payoffs. The prisoner's dilemma (PD) describes situations in which
it is profitable if everybody cooperates rather than defects (free-rides or
cheats), but as cooperation is risky and defection is tempting, the expected
outcome is defection. Nevertheless, some biological and social mechanisms can
support cooperation by effectively transforming the payoffs. Here, we study the
related phase transitions, which can be of first order (discontinous) or of
second order (continuous), implying a variety of different routes to
cooperation. After classifying the transitions into cases of equilibrium
displacement, equilibrium selection, and equilibrium creation, we show that a
transition to cooperation may take place even if the stationary states and the
eigenvalues of the replicator equation for the PD stay unchanged. Our example
is based on adaptive group pressure, which makes the payoffs dependent on the
endogeneous dynamics in the population. The resulting bistability can invert
the expected outcome in favor of cooperation.Comment: For related work see http://www.soms.ethz.ch
On the Geometry and Entropy of Non-Hamiltonian Phase Space
We analyze the equilibrium statistical mechanics of canonical, non-canonical
and non-Hamiltonian equations of motion by throwing light into the peculiar
geometric structure of phase space. Some fundamental issues regarding time
translation and phase space measure are clarified. In particular, we emphasize
that a phase space measure should be defined by means of the Jacobian of the
transformation between different types of coordinates since such a determinant
is different from zero in the non-canonical case even if the phase space
compressibility is null. Instead, the Jacobian determinant associated with
phase space flows is unity whenever non-canonical coordinates lead to a
vanishing compressibility, so that its use in order to define a measure may not
be always correct. To better illustrate this point, we derive a mathematical
condition for defining non-Hamiltonian phase space flows with zero
compressibility. The Jacobian determinant associated with time evolution in
phase space is altogether useful for analyzing time translation invariance. The
proper definition of a phase space measure is particularly important when
defining the entropy functional in the canonical, non-canonical, and
non-Hamiltonian cases. We show how the use of relative entropies can circumvent
some subtle problems that are encountered when dealing with continuous
probability distributions and phase space measures. Finally, a maximum
(relative) entropy principle is formulated for non-canonical and
non-Hamiltonian phase space flows.Comment: revised introductio
Phase-Space Metric for Non-Hamiltonian Systems
We consider an invariant skew-symmetric phase-space metric for
non-Hamiltonian systems. We say that the metric is an invariant if the metric
tensor field is an integral of motion. We derive the time-dependent
skew-symmetric phase-space metric that satisfies the Jacobi identity. The
example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page
New ADS Functionality for the Curator
In this paper we provide an update concerning the operations of the NASA
Astrophysics Data System (ADS), its services and user interface, and the
content currently indexed in its database. As the primary information system
used by researchers in Astronomy, the ADS aims to provide a comprehensive index
of all scholarly resources appearing in the literature. With the current effort
in our community to support data and software citations, we discuss what steps
the ADS is taking to provide the needed infrastructure in collaboration with
publishers and data providers. A new API provides access to the ADS search
interface, metrics, and libraries allowing users to programmatically automate
discovery and curation tasks. The new ADS interface supports a greater
integration of content and services with a variety of partners, including ORCID
claiming, indexing of SIMBAD objects, and article graphics from a variety of
publishers. Finally, we highlight how librarians can facilitate the ingest of
gray literature that they curate into our system.Comment: Submitted to the Proceedings of Library and Information Services in
Astronomy VIII, Strasbourg, Franc
Vestibulo-Ocular Reflex Modification after Virtual Environment Exposure
Immersion in an illusory world is possible by means of virtual reality (VR), where environmental perception is modi
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c1c ed by artificial sensorial stimulation. The application of VR for the assessment and rehabilitation of pathologies affecting the vestibular system, in terms of both diagnosis and care, could represent an interesting new line of research. Our perception of reality is in fact based on static and dynamic spatial information perceived by our senses. During head movements in a virtual environment the images on the display and the labyrinthine information relative to the head angular accelerations differ and therefore a visuo-vestibular conflict is present. It is known that mismatches between visual and labyrinthine information may modify the vestibulo-oculomotor reflex (VOR) gain. We studied the post-immersion modifications in 20 healthy subjects (mean age 25 years) exposed to a virtual environment for 20 min by wearing a head-mounted display. VOR gain and phase were measured by means of harmonic sinusoidal stimulation in the dark before, at the end of and 30 min after VR exposure. A VOR gain reduction was observed in all subjects at the end of VR exposure which disappeared after 30 min. Our data show that exposure to a virtual environment can induce a temporary modi
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c1c cation of the VOR gain. This
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c1c nding can be employed to enable an artificial, instrumental modification of the VOR gain and therefore opens up new perspectives in the assessment and rehabilitation of vestibular diseases
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