9,666 research outputs found
Random patterns in fish schooling enhance alertness: a hydrodynamic perspective
One of the most highly debated questions in the field of animal swarming and
social behaviour, is the collective random patterns and chaotic behaviour
formed by some animal species, in particular if there is a danger. Is such a
behaviour beneficial or unfavourable for survival? Here we report on one of the
most remarkable forms of animal swarming and social behaviour - fish schooling
- from a hydrodynamic point of view. We found that some fish species do not
have preferred orientation and they swarm in a random pattern mode, despite the
excess of energy consumed. Our analyses, which includes calculations of the
hydrodynamic forces between slender bodies, show that such a behaviour enhances
the transfer of hydrodynamic information, and thus enhances the survivability
of the school. These findings support the general hypothesis that a disordered
and non-trivial collective behaviour of individuals within a nonlinear
dynamical system is essential for optimising transfer of information - an
optimisation that might be crucial for survival.Comment: 12 pages, 5 figures, 1 tabl
A Note on Derived Geometric Interpretation of Classical Field Theories
In this note, we would like to provide a conceptional introduction to the
interaction between derived geometry and physics based on the formalism that
has been heavily studied by Kevin Costello. Main motivations of our current
attempt are as follows: (i) to provide a brief introduction to derived
algebraic geometry, which can be, roughly speaking, thought of as a higher
categorical refinement of an ordinary algebraic geometry, (ii) to understand
how certain derived objects naturally appear in a theory describing a
particular physical phenomenon and give rise to a formal mathematical
treatment, such as redefining a perturbative classical field theory (or its
quantum counterpart) by using the language of derived algebraic geometry, and
(iii) how the notion of factorization algebra together with certain higher
categorical structures come into play to encode the structure of so-called
observables in those theories by employing certain cohomological/homotopical
methods. Adopting such a heavy and relatively enriched language allows us to
formalize the notion of quantization and observables in quantum field theory as
well.Comment: 14 pages. This note serves as an introductory survey on certain
mathematical structures encoding the essence of Costello's approach to
derived-geometric formulation of field theories and the structure of
observables in an expository manne
M-Power Regularized Least Squares Regression
Regularization is used to find a solution that both fits the data and is
sufficiently smooth, and thereby is very effective for designing and refining
learning algorithms. But the influence of its exponent remains poorly
understood. In particular, it is unclear how the exponent of the reproducing
kernel Hilbert space~(RKHS) regularization term affects the accuracy and the
efficiency of kernel-based learning algorithms. Here we consider regularized
least squares regression (RLSR) with an RKHS regularization raised to the power
of m, where m is a variable real exponent. We design an efficient algorithm for
solving the associated minimization problem, we provide a theoretical analysis
of its stability, and we compare its advantage with respect to computational
complexity, speed of convergence and prediction accuracy to the classical
kernel ridge regression algorithm where the regularization exponent m is fixed
at 2. Our results show that the m-power RLSR problem can be solved efficiently,
and support the suggestion that one can use a regularization term that grows
significantly slower than the standard quadratic growth in the RKHS norm
Surfaces given with the Monge patch in E^4
A depth surface of E^3 is a range image observed from a single view can be
represented by a digital graph (Monge patch) surface . That is, a depth or
range value at a point (u,v) is given by a single valued function z=f(u,v). In
the present study we consider the surfaces in Euclidean 4-space E^4 given with
a Monge patch z=f(u,v),w=g(u,v). We investigated the curvature properties of
these surfaces. We also give some special examples of these surfaces which are
first defined by Yu. Aminov. Finally, we proved that every Aminov surface is a
non-trivial Chen surface.Comment: 1
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