We consider a state-dependent full-duplex relay channel with the channel states available non-causally at only the source, i.e., neither at the relay nor at the destination. For the discrete memoryless (DM) case, we establish lower and upper bounds on the channel capacity. The lower bound is obtained by a coding scheme at the source that uses a Gel’fand-Pinsker like binning scheme at the source...

The problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. &#10 Production systems like JIT are one of the many applications of the problem. This problem is studied in special cases and their optimal solutions are introduced with simple orders. In general, some effective conditions for ne...

Given are tight upper and lower bounds for the minimum rank among all matrices with a prescribed zero-nonzero pattern. The upper bound is based upon solving for a matrix with a given null space and, with optimal choices, produces the correct minimum rank. It leads to simple, but often accurate, bounds based upon overt statistics of the pattern. The lower bound is also conceptually simple. Often...

We study upper and lower bounds on the sample-complexity of learning near-optimal behaviour in finite-state discounted Markov Decision Processes (MDPs). We prove a new bound for a modified version of Upper Confidence Reinforcement Learning (UCRL) with only cubic dependence on the horizon. The bound is unimprovable in all parameters except the size of the state/action space, where it depends lin...

POMDP algorithms have made significant progress in recent years by allowing practitioners to find good solutions to increasingly large problems. Most approaches (including point-based and policy iteration techniques) operate by refining a lower bound of the optimal value function. Several approaches (e.g., HSVI2, SARSOP, grid-based approaches and online forward search) also refine an upper boun...

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

We prove that no algorithm for balanced binary search trees performing insertions and deletions in amortized time O(f(n)) can guarantee a height smaller than dlog(n + 1) + 1=f(n)e for all n. We improve the existing upper bound to dlog(n + 1) + log 2 (f(n))=f(n)e, thus almost matching our lower bound. We also improve the existing upper bound for worst case algorithms, and give a lower bound for ...

The problem of determining the sequence of a set of jobs with the objective function of minimizing the maximum earliness and tardiness in one machine is studied. Production systems like JIT are one of the many applications of the problem. This problem is studied in special cases and their optimal solutions are introduced with simple orders. In general, some effective conditions for neig...

In rigid plastic analysis one of the most widely applicable methods that is based on the minimum principle, is the combination of elementary mechanisms which uses the upper bound theorem. In this method a mechanism is searched which corresponds to the smallest load factor. Mathematical programming can be used to optimize this search process for simple fra...