Bounds on Slow Roll and the de Sitter Swampland

The recently introduced swampland criterion for de Sitter (arXiv:1806.08362) can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter $\epsilon_V$. This leads us to consider the other slow roll parameter $\eta_V$ more closely, and we are lead to conjecture that the bound is not necessarily on $\epsilon_V$, but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at ${\cal O}(1)$ in Planck units in any UV complete theory. A corollary is that $\epsilon_V$ need not necessarily be ${\cal O}(1)$, if $\eta_V \lesssim -{\cal O}(1)$ holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate arXiv:1806.08362, and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in $N$-flation.Comment: v2: many refs added, clarifications and comments added, improved wording regarding single/multi-field and potential/Hubble slow roll, typos fixe

Approximate Linear Time ML Decoding on Tail-Biting Trellises in Two Rounds

A linear time approximate maximum likelihood decoding algorithm on tail-biting trellises is prsented, that requires exactly two rounds on the trellis. This is an adaptation of an algorithm proposed earlier with the advantage that it reduces the time complexity from O(mlogm) to O(m) where m is the number of nodes in the tail-biting trellis. A necessary condition for the output of the algorithm to differ from the output of the ideal ML decoder is reduced and simulation results on an AWGN channel using tail-biting rrellises for two rate 1/2 convoluational codes with memory 4 and 6 respectively are reporte

A Distributed Scheduling Algorithm to Provide Quality-of-Service in Multihop Wireless Networks

Control of multihop Wireless networks in a distributed manner while providing end-to-end delay requirements for different flows, is a challenging problem. Using the notions of Draining Time and Discrete Review from the theory of fluid limits of queues, an algorithm that meets delay requirements to various flows in a network is constructed. The algorithm involves an optimization which is implemented in a cyclic distributed manner across nodes by using the technique of iterative gradient ascent, with minimal information exchange between nodes. The algorithm uses time varying weights to give priority to flows. The performance of the algorithm is studied in a network with interference modelled by independent sets

Towards a Finite-NN Hologram

We suggest that holographic tensor models related to SYK are viable candidates for exactly (ie., non-perturbatively in $N$) 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 $O(n)^3$ tensor model with arbitrary even $n$, 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

Strategic Human Resource Management: Three-Stage Process and Influencing Organisational Factors

A three-stage model for the process of strategic human resource management is developed in this paper. The three stages cover strategy formulation, implementation and evaluation. The inter-linkages in this dynamic model have been explored. The organisational factors that have enabling or deterring influence on the success of each of these three stages have been discussed. The paper highlights the key role played by HR professionals in these three stages.