25,355 research outputs found

### Acceleration and Deceleration in Curvature Induced Phantom Model of the Late and Future Universe, Cosmic Collapse as Well as its Quantum Escape

Here, cosmology of the late and future universe is obtained from
$f(R)$-gravity with non-linear curvature terms $R^2$ and $R^3$ ($R$ being the
Ricci scalar curvature). It is different from $f(R)$-dark enrgy models, where
non-linear curvature terms are taken as gravitational alternative of dark
energy. In the present model, neither linear nor no-linear curvature terms are
taken as dark energy. Rather, dark energy terms are induced by curvature terms
in the Friedmann equation derived from $f(R)$-gravitational equations. It has
advantage over $f(R)$- dark energy models in the sense that the present model
satisfies WMAP results and expands as $\sim t^{2/3}$ during matter-dominance.
So, it does not have problems due to which $f(R)$-dark energy models are
criticized. Curvature-induced dark energy, obtained here, mimics phantom.
Different phases of this model, including acceleration and deceleration during
phantom phase, are investigated here.It is found that expansion of the universe
will stop at the age $(3.87 t_0 + 694.4 {\rm kyr})$ ($t_0$ being the present
age of the universe) and after this epoch, it will contract and collapse by the
time $(336.87 t_0 + 694.4 {\rm kyr})$. Further,it is shown that universe will
escape predicted collapse (obtained using classical mechanics) on making
quantum gravity corrections relevant near collapse time due to extremely high
energy density and large curvature analogous to the state of very early
universe. Interestingly, cosmological constant is also induced here, which is
very small in classical domain, but very high in quantum domain.Comment: 33 page

### Online codes for analog signals

This paper revisits a classical scenario in communication theory: a waveform
sampled at regular intervals is to be encoded so as to minimize distortion in
its reconstruction, despite noise. This transformation must be online (causal),
to enable real-time signaling; and should use no more power than the original
signal. The noise model we consider is an "atomic norm" convex relaxation of
the standard (discrete alphabet) Hamming-weight-bounded model: namely,
adversarial $\ell_1$-bounded. In the "block coding" (noncausal) setting, such
encoding is possible due to the existence of large almost-Euclidean sections in
$\ell_1$ spaces, a notion first studied in the work of Dvoretzky in 1961. Our
main result is that an analogous result is achievable even causally.
Equivalently, our work may be seen as a "lower triangular" version of $\ell_1$
Dvoretzky theorems. In terms of communication, the guarantees are expressed in
terms of certain time-weighted norms: the time-weighted $\ell_2$ norm imposed
on the decoder forces increasingly accurate reconstruction of the distant past
signal, while the time-weighted $\ell_1$ norm on the noise ensures vanishing
interference from distant past noise. Encoding is linear (hence easy to
implement in analog hardware). Decoding is performed by an LP analogous to
those used in compressed sensing

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