11,856 research outputs found
A class of index coding problems with rate 1/3
An index coding problem with messages has symmetric rate if all
messages can be conveyed at rate . In a recent work, a class of index coding
problems for which symmetric rate is achievable was characterised
using special properties of the side-information available at the receivers. In
this paper, we show a larger class of index coding problems (which includes the
previous class of problems) for which symmetric rate is
achievable. In the process, we also obtain a stricter necessary condition for
rate feasibility than what is known in literature.Comment: Shorter version submitted to ISIT 201
On Distance Magic Harary Graphs
This paper establishes two techniques to construct larger distance magic and
(a, d)-distance antimagic graphs using Harary graphs and provides a solution to
the existence of distance magicness of legicographic product and direct product
of G with C4, for every non-regular distance magic graph G with maximum degree
|V(G)|-1.Comment: 12 pages, 1 figur
Towards a Finite- Hologram
We suggest that holographic tensor models related to SYK are viable
candidates for exactly (ie., non-perturbatively in ) solvable holographic
theories. The reason is that in these theories, the Hilbert space is a spinor
representation, and the Hamiltonian (at least in some classes) can be arranged
to commute with the Clifford level. This makes the theory solvable level by
level. We demonstrate this for the specific case of the uncolored
tensor model with arbitrary even , and reduce the question of determining
the spectrum and eigenstates to an algebraic equation relating Young tableaux.
Solving this reduced problem is conceptually trivial and amounts to matching
the representations on either side, as we demonstrate explicitly at low levels.
At high levels, representations become bigger, but should still be tractable.
None of our arguments require any supersymmetry.Comment: 16 page
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The Ensemble of Conformations of Antifreeze Glycoproteins (AFGP8): A Study Using Nuclear Magnetic Resonance Spectroscopy.
The primary sequence of antifreeze glycoproteins (AFGPs) is highly degenerate, consisting of multiple repeats of the same tripeptide, Ala-Ala-Thr*, in which Thr* is a glycosylated threonine with the disaccharide beta-d-galactosyl-(1,3)-alpha-N-acetyl-d-galactosamine. AFGPs seem to function as intrinsically disordered proteins, presenting challenges in determining their native structure. In this work, a different approach was used to elucidate the three-dimensional structure of AFGP8 from the Arctic cod Boreogadus saida and the Antarctic notothenioid Trematomus borchgrevinki. Dimethyl sulfoxide (DMSO), a non-native solvent, was used to make AFGP8 less dynamic in solution. Interestingly, DMSO induced a non-native structure, which could be determined via nuclear magnetic resonance (NMR) spectroscopy. The overall three-dimensional structures of the two AFGP8s from two different natural sources were different from a random coil ensemble, but their "compactness" was very similar, as deduced from NMR measurements. In addition to their similar compactness, the conserved motifs, Ala-Thr*-Pro-Ala and Ala-Thr*-Ala-Ala, present in both AFGP8s, seemed to have very similar three-dimensional structures, leading to a refined definition of local structural motifs. These local structural motifs allowed AFGPs to be considered functioning as effectors, making a transition from disordered to ordered upon binding to the ice surface. In addition, AFGPs could act as dynamic linkers, whereby a short segment folds into a structural motif, while the rest of the AFGPs could still be disordered, thus simultaneously interacting with bulk water molecules and the ice surface, preventing ice crystal growth
Massive Scattering Amplitudes in Six Dimensions
We show that a natural spinor-helicity formalism that can describe massive
scattering amplitudes exists in dimensions. This is arranged by having
helicity spinors carry an index in the Dirac spinor {\bf 4} of the massive
little group, . In the high energy limit, two separate kinds
of massless helicity spinors emerge as required for consistency with
arXiv:0902.0981, with indices in the two 's of the massless little group
. The tensors of lead to particles with arbitrary spin, and
using these and demanding consistent factorization, we can fix and
point tree amplitudes of arbitrary masses and spins: we provide examples.
We discuss the high energy limit of scattering amplitudes and the Higgs
mechanism in this language, and make some preliminary observations about
massive BCFW recursion.Comment: 37 pages; v2: minor improvements, JHEP versio
Coded Caching based on Combinatorial Designs
We consider the standard broadcast setup with a single server broadcasting
information to a number of clients, each of which contains local storage
(called \textit{cache}) of some size, which can store some parts of the
available files at the server. The centralized coded caching framework,
consists of a caching phase and a delivery phase, both of which are carefully
designed in order to use the cache and the channel together optimally. In prior
literature, various combinatorial structures have been used to construct coded
caching schemes. In this work, we propose a binary matrix model to construct
the coded caching scheme. The ones in such a \textit{caching matrix} indicate
uncached subfiles at the users. Identity submatrices of the caching matrix
represent transmissions in the delivery phase. Using this model, we then
propose several novel constructions for coded caching based on the various
types of combinatorial designs. While most of the schemes constructed in this
work (based on existing designs) have a high cache requirement (uncached
fraction being or , being
the number of users), they provide a rate that is either constant or decreasing
() with increasing , and moreover require competitively
small levels of subpacketization (being ), which is an
extremely important parameter in practical applications of coded caching. We
mark this work as another attempt to exploit the well-developed theory of
combinatorial designs for the problem of constructing caching schemes,
utilizing the binary caching model we develop.Comment: 10 pages, Appeared in Proceedings of IEEE ISIT 201
Contrasting SYK-like Models
We contrast some aspects of various SYK-like models with large- melonic
behavior. First, we note that ungauged tensor models can exhibit symmetry
breaking, even though these are 0+1 dimensional theories. Related to this, we
show that when gauged, some of them admit no singlets, and are anomalous. The
uncolored Majorana tensor model with even is a simple case where gauge
singlets can exist in the spectrum. We outline a strategy for solving for the
singlet spectrum, taking advantage of the results in arXiv:1706.05364, and
reproduce the singlet states expected in . In the second part of the
paper, we contrast the random matrix aspects of some ungauged tensor models,
the original SYK model, and a model due to Gross and Rosenhaus. The latter,
even though disorder averaged, shows parallels with the Gurau-Witten model. In
particular, the two models fall into identical Andreev ensembles as a function
of . In an appendix, we contrast the (expected) spectra of AdS quantum
gravity, SYK and SYK-like tensor models, and the zeros of the Riemann Zeta
function.Comment: 45 pages, 17 figures; v2: minor improvements and rearrangements, refs
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