1,150 research outputs found

### Universal Lossless Compression with Unknown Alphabets - The Average Case

Universal compression of patterns of sequences generated by independently
identically distributed (i.i.d.) sources with unknown, possibly large,
alphabets is investigated. A pattern is a sequence of indices that contains all
consecutive indices in increasing order of first occurrence. If the alphabet of
a source that generated a sequence is unknown, the inevitable cost of coding
the unknown alphabet symbols can be exploited to create the pattern of the
sequence. This pattern can in turn be compressed by itself. It is shown that if
the alphabet size $k$ is essentially small, then the average minimax and
maximin redundancies as well as the redundancy of every code for almost every
source, when compressing a pattern, consist of at least 0.5 log(n/k^3) bits per
each unknown probability parameter, and if all alphabet letters are likely to
occur, there exist codes whose redundancy is at most 0.5 log(n/k^2) bits per
each unknown probability parameter, where n is the length of the data
sequences. Otherwise, if the alphabet is large, these redundancies are
essentially at least O(n^{-2/3}) bits per symbol, and there exist codes that
achieve redundancy of essentially O(n^{-1/2}) bits per symbol. Two sub-optimal
low-complexity sequential algorithms for compression of patterns are presented
and their description lengths analyzed, also pointing out that the pattern
average universal description length can decrease below the underlying i.i.d.\
entropy for large enough alphabets.Comment: Revised for IEEE Transactions on Information Theor

### Wormhole Structures in Logarithmic-Corrected $R^2$ Gravity

This paper is devoted to find the feasible shape functions for the
construction of static wormhole geometry in the frame work of
logarithmic-corrected $R^2$ gravity model. We discuss the asymptotically flat
wormhole solutions sustained by the matter sources with anisotropic pressure,
isotropic pressure and barotropic pressure. For anisotropic case, we consider
three shape functions and evaluate the null energy conditions and weak energy
conditions graphically along with their regions. Moreover, for barotropic and
isotropic pressures, we find shape function analytically and discuss its
properties. For the formation of traversable wormhole geometries, we cautiously
choose the values of parameters involved in $f(R)$ gravity model. We show
explicitly that our wormhole solutions violates the non-existence theorem even
with logarithmic corrections. We discuss all physical properties via graphical
analysis and it is concluded that the wormhole solutions with relativistic
formalism can be well justified with logarithmic corrections.Comment: 12 pages, 8 figure

### Defect multiplets of N=1 supersymmetry in 4d

Any 4d theory possessing $\mathcal{N}=1$ supersymmetry admits a so called
$\mathcal{S}$-multiplet, containing the conserved energy-momentum tensor and
supercurrent. When a defect is introduced into such a theory, the
$\mathcal{S}$-multiplet receives contributions localised on the defect, which
indicate the breaking of some translation symmetry and consequently also some
supersymmetries. We call this the defect multiplet. We classify such terms
corresponding to half-BPS defects which can be either three-dimensional,
preserving 3d $\mathcal{N}=1$, or two-dimensional, preserving
$\mathcal{N}=(0,2)$. The new terms localised on the defect furnish multiplets
of the reduced symmetry and give rise to the displacement operator

### Running couplings in equivariantly gauge-fixed SU(N) Yang--Mills theories

In equivariantly gauge-fixed SU(N) Yang--Mills theories, the gauge symmetry
is only partially fixed, leaving a subgroup $H\subset SU(N)$ unfixed. Such
theories avoid Neuberger's nogo theorem if the subgroup $H$ contains at least
the Cartan subgroup $U(1)^{N-1}$, and they are thus non-perturbatively well
defined if regulated on a finite lattice. We calculate the one-loop beta
function for the coupling $\tilde{g}^2=\xi g^2$, where $g$ is the gauge
coupling and $\xi$ is the gauge parameter, for a class of subgroups including
the cases that $H=U(1)^{N-1}$ or $H=SU(M)\times SU(N-M)\times U(1)$. The
coupling $\tilde{g}$ represents the strength of the interaction of the gauge
degrees of freedom associated with the coset $SU(N)/H$. We find that
$\tilde{g}$, like $g$, is asymptotically free. We solve the
renormalization-group equations for the running of the couplings $g$ and
$\tilde{g}$, and find that dimensional transmutation takes place also for the
coupling $\tilde{g}$, generating a scale $\tilde{\Lambda}$ which can be larger
than or equal to the scale $\Lambda$ associated with the gauge coupling $g$,
but not smaller. We speculate on the possible implications of these results.Comment: 14 pages, late

### Length-based cryptanalysis: The case of Thompson's Group

The length-based approach is a heuristic for solving randomly generated
equations in groups which possess a reasonably behaved length function. We
describe several improvements of the previously suggested length-based
algorithms, that make them applicable to Thompson's group with significant
success rates. In particular, this shows that the Shpilrain-Ushakov public key
cryptosystem based on Thompson's group is insecure, and suggests that no
practical public key cryptosystem based on this group can be secure.Comment: Final version, to appear in JM

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