1,210 research outputs found
Sub-millimeter Tests of the Gravitational Inverse-square Law
Motivated by a variety of theories that predict new effects, we tested the
gravitational 1/r^2 law at separations between 10.77 mm and 137 microns using
two different 10-fold azimuthally symmetric torsion pendulums and rotating
10-fold symmetric attractors. Our work improves upon other experiments by up to
a factor of about 100. We found no deviation from Newtonian physics at the 95%
confidence level and interpret these results as constraints on extensions of
the Standard Model that predict Yukawa or power-law forces. We set a constraint
on the largest single extra dimension (assuming toroidal compactification and
that one extra dimension is significantly larger than all the others) of R <=
160 microns, and on two equal-sized large extra dimensions of R <= 130 microns.
Yukawa interactions with |alpha| >= 1 are ruled out at 95% confidence for
lambda >= 197 microns. Extra-dimensions scenarios stabilized by radions are
restricted to unification masses M >= 3.0 TeV/c^2, regardless of the number of
large extra dimensions. We also provide new constraints on power-law potentials
V(r)\propto r^{-k} with k between 2 and 5 and on the gamma_5 couplings of
pseudoscalars with m <= 10 meV/c^2.Comment: 34 pages, 38 figure
Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems
Recent advances in molecular biology such as gene editing [1], bioelectric recording and manipulation [2] and live cell microscopy using fluorescent reporters [3], [4] – especially with the advent of light-controlled protein activation through optogenetics [5] – have provided the tools to measure and manipulate molecular signaling pathways with unprecedented spatiotemporal precision. This has produced ever increasing detail about the molecular mechanisms underlying development and regeneration in biological organisms. However, an overarching concept – that can predict the emergence of form and the robust maintenance of complex anatomy – is largely missing in the field. Classic (i.e., dynamic systems and analytical mechanics) approaches such as least action principles are difficult to use when characterizing open, far-from equilibrium systems that predominate in Biology. Similar issues arise in neuroscience when trying to understand neuronal dynamics from first principles. In this (neurobiology) setting, a variational free energy principle has emerged based upon a formulation of self-organization in terms of (active) Bayesian inference. The free energy principle has recently been applied to biological self-organization beyond the neurosciences [6], [7]. For biological processes that underwrite development or regeneration, the Bayesian inference framework treats cells as information processing agents, where the driving force behind morphogenesis is the maximization of a cell's model evidence. This is realized by the appropriate expression of receptors and other signals that correspond to the cell's internal (i.e., generative) model of what type of receptors and other signals it should express. The emerging field of the free energy principle in pattern formation provides an essential quantitative formalism for understanding cellular decision-making in the context of embryogenesis, regeneration, and cancer suppression. In this paper, we derive the mathematics behind Bayesian inference – as understood in this framework – and use simulations to show that the formalism can reproduce experimental, top-down manipulations of complex morphogenesis. First, we illustrate this ‘first principle’ approach to morphogenesis through simulated alterations of anterior-posterior axial polarity (i.e., the induction of two heads or two tails) as in planarian regeneration. Then, we consider aberrant signaling and functional behavior of a single cell within a cellular ensemble – as a first step in carcinogenesis as false ‘beliefs’ about what a cell should ‘sense’ and ‘do’. We further show that simple modifications of the inference process can cause – and rescue – mis-patterning of developmental and regenerative events without changing the implicit generative model of a cell as specified, for example, by its DNA. This formalism offers a new road map for understanding developmental change in evolution and for designing new interventions in regenerative medicine settings
Data Assimilation: A Mathematical Introduction
These notes provide a systematic mathematical treatment of the subject of
data assimilation
Reconstructing cosmological initial conditions from galaxy peculiar velocities. I. Reverse Zeldovich Approximation
We propose a new method to recover the cosmological initial conditions of the
presently observed galaxy distribution, which can serve to run constrained
simulations of the Local Universe. Our method, the Reverse Zeldovich
Approximation (RZA), can be applied to radial galaxy peculiar velocity data and
extends the previously used Constrained Realizations (CR) method by adding a
Lagrangian reconstruction step. The RZA method consists of applying the
Zeldovich approximation in reverse to galaxy peculiar velocities to estimate
the cosmic displacement field and the initial linear matter distribution from
which the present-day Local Universe evolved.We test our method with a mock
survey taken from a cosmological simulation. We show that the halo peculiar
velocities at z = 0 are close to the linear prediction of the Zeldovich
approximation, if a grouping is applied to the data to remove virial motions.
We find that the addition of RZA to the CR method significantly improves the
reconstruction of the initial conditions. The RZA is able to recover the
correct initial positions of the velocity tracers with a median error of only
1.36 Mpc/h in our test simulation. For realistic sparse and noisy data, this
median increases to 5 Mpc/h. This is a significant improvement over the
previous approach of neglecting the displacement field, which introduces errors
on a scale of 10 Mpc/h or even higher. Applying the RZA method to the upcoming
high-quality observational peculiar velocity catalogues will generate much more
precise constrained simulations of the Local Universe.Comment: Accepted for MNRAS 2012 December 1
A framework for the local information dynamics of distributed computation in complex systems
The nature of distributed computation has often been described in terms of
the component operations of universal computation: information storage,
transfer and modification. We review the first complete framework that
quantifies each of these individual information dynamics on a local scale
within a system, and describes the manner in which they interact to create
non-trivial computation where "the whole is greater than the sum of the parts".
We describe the application of the framework to cellular automata, a simple yet
powerful model of distributed computation. This is an important application,
because the framework is the first to provide quantitative evidence for several
important conjectures about distributed computation in cellular automata: that
blinkers embody information storage, particles are information transfer agents,
and particle collisions are information modification events. The framework is
also shown to contrast the computations conducted by several well-known
cellular automata, highlighting the importance of information coherence in
complex computation. The results reviewed here provide important quantitative
insights into the fundamental nature of distributed computation and the
dynamics of complex systems, as well as impetus for the framework to be applied
to the analysis and design of other systems.Comment: 44 pages, 8 figure
Stochastic resonance in chua's circuit driven by alpha-stable noise
Thesis (Master)--Izmir Institute of Technology, Electronics and Communication Engineering, Izmir, 2012Includes bibliographical references (leaves: 75-80)Text in English; Abstract: Turkish and Englishx, 80 leavesThe main aim of this thesis is to investigate the stochastic resonance (SR) in Chua's circuit driven by alpha-stable noise which has better approximation to a real-world signal than Gaussian distribution. SR is a phenomenon in which the response of a nonlinear system to a sub-threshold (weak) input signal is enhanced with the addition of an optimal amount of noise. There have been an increasing amount of applications based on SR in various fields. Almost all studies related to SR in chaotic systems assume that the noise is Gaussian, which leads researchers to investigate the cases in which the noise is non-Gaussian hence has infinite variance. In this thesis, the spectral power amplification which is used to quantify the SR has been evaluated through fractional lower order Wigner Ville distribution of the response of a system and analyzed for various parameters of alpha-stable noise. The results provide a visible SR effect in Chua’s circuit driven by symmetric and skewed-symmetric alpha-stable noise distributions. Furthermore, a series of simulations reveal that the mean residence time that is the average time spent by the trajectory in an attractor can vary depending on different alpha-stable noise parameters
Field-control, phase-transitions, and life's emergence
Instances of critical-like characteristics in living systems at each
organizational level as well as the spontaneous emergence of computation
(Langton), indicate the relevance of self-organized criticality (SOC). But
extrapolating complex bio-systems to life's origins, brings up a paradox: how
could simple organics--lacking the 'soft matter' response properties of today's
bio-molecules--have dissipated energy from primordial reactions in a controlled
manner for their 'ordering'? Nevertheless, a causal link of life's macroscopic
irreversible dynamics to the microscopic reversible laws of statistical
mechanics is indicated via the 'functional-takeover' of a soft magnetic
scaffold by organics (c.f. Cairns-Smith's 'crystal-scaffold'). A
field-controlled structure offers a mechanism for bootstrapping--bottom-up
assembly with top-down control: its super-paramagnetic components obey
reversible dynamics, but its dissipation of H-field energy for aggregation
breaks time-reversal symmetry. The responsive adjustments of the controlled
(host) mineral system to environmental changes would bring about mutual
coupling between random organic sets supported by it; here the generation of
long-range correlations within organic (guest) networks could include SOC-like
mechanisms. And, such cooperative adjustments enable the selection of the
functional configuration by altering the inorganic network's capacity to assist
a spontaneous process. A non-equilibrium dynamics could now drive the
kinetically-oriented system towards a series of phase-transitions with
appropriate organic replacements 'taking-over' its functions.Comment: 54 pages, pdf fil
Accuracy and stability of filters for dissipative PDEs
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation algorithms designed to update the estimation of the state in an on-line fashion, as data is acquired sequentially. For linear problems subject to Gaussian noise, filtering can be performed exactly using the Kalman filter. For nonlinear systems filtering can be approximated in a systematic way by particle filters. However in high dimensions these particle filtering methods can break down. Hence, for the large nonlinear systems arising in applications such as oceanography and weather forecasting, various ad hoc filters are used, mostly based on making Gaussian approximations. The purpose of this work is to study the accuracy and stability properties of these ad hoc filters. We work in the context of the 2D incompressible Navier-Stokes equation, although the ideas readily generalize to a range of dissipative partial differential equations (PDEs). By working in this infinite dimensional setting we provide an analysis which is useful for the understanding of high dimensional filtering, and is robust to mesh-refinement. We describe theoretical results showing that, in the small observational noise limit, the filters can be tuned to perform accurately in tracking the signal itself (filter accuracy), provided the system is observed in a sufficiently large low dimensional space; roughly speaking this space should be large enough to contain the unstable modes of the linearized dynamics. The tuning corresponds to what is known as variance inflation in the applied literature. Numerical results are given which illustrate the theory. The positive results herein concerning filter stability complement recent numerical studies which demonstrate that the ad hoc filters can perform poorly in reproducing statistical variation about the true signal
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