The existing upper and lower bounds between entropy and error probability are mostly derived from the inequality of the entropy relations, which could introduce approximations into the analysis. We derive analytical bounds based on the closed-form solutions of conditional entropy without involving any approximation. Two basic types of classification errors are investigated in the context of bin...

We study upper and lower bounds on the sample-complexity of learning nearoptimal 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 line...

We show that a near-diagonal lower bound of the heat kernel of a Dirichlet form on a metric measure space with a regular measure implies an on-diagonal upper bound. If in addition the Dirichlet form is local and regular, then we obtain a full off-diagonal upper bound of the heat kernel provided the Dirichlet heat kernel on any ball satisfies a near-diagonal lower estimate. This reveals a new ph...

  In this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness and tardiness with idle times (n/1/I/ETmax). Due to the time complexity function, this sequencing problem belongs to a class of NP-hard ones. Thus, a special design of a simulated annealing (SA) method is applied to solve such a hard problem. To co...

Proof. If b ∈ B, then b is a lower bound for A, meaning that b ≤ a for all a ∈ A. Therefore, every element of A is an upper bound for B, so B is bounded above and thus, by the Axiom of Completeness, has a least upper bound supB. We want to see that supB satisfies the two conditions for being the greatest lower bound of A. i. If supB is not a lower bound for A, then there exists a ∈ A such that ...

xxx Working notes. Three main things remain to do. (1) Either include Tamar’s argument [now in separate document] for Theorem 5, or replace by some better construction for worst-case upper bound. (2) Put in the average-case lower bound calculus calculations needed in section 6. (3) General version of the worst-case lower bound method in section 7.3. A fourth thing one might contemplate: (4) Is ...

The IEEE DCF 802.11 is currently used as WLAN standard. The standard specifies the contention-based MAC mechanism, Distributed Coordination Function (DCF), which allows to share the wireless channel. In the DCF each node picks a random contention slot from the uniform distribution over the [lower bound, upper bound] interval, where the lower bound always equals 0 and the upper bound equals an i...