The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error the computed have been available only as estimates. In this paper, Pollak--Martinazzo lower-bound theory, in conjunction correlated Gaussian basis sets, is elaborated implemented provide subparts-per-million convergence ground- excited-state...

We study an approximate version of q-query LDCs (Locally Decodable Codes) over the real numbers and prove lower bounds on the encoding length of such codes. A q-query (α, δ)approximate LDC is a set V of n points in R so that, for each i ∈ [d] there are Ω(δn) disjoint q-tuples (u1, . . . ,uq) in V so that span(u1, . . . ,uq) contains a unit vector whose i’th coordinate is at least α. We prove ex...

In this paper we study the sequence length requirements of distance-based evolutionary tree building algorithms in the Jukes-Cantor model of evolution. By deriving lower bounds on sequence lengths required to recover the evolutionary tree topology correctly , we show that two algorithms, the Short Quartet Method and the Harmonic Greedy Triplets algorithms have optimal sequence length requirements.

We give an exponential lower bound on number of proof-lines in the proof system K of modal logic, i.e., we give an example of K-tautologies ψ1, ψ2, . . . s.t. every K-proof of ψi must have a number of proof-lines exponential in terms of the size of ψi. The result extends, for the same sequence of K-tautologies, to the systems K4, Gödel-L”́ob’s logic, S and S4. We also determine some speed-up rel...

A notion of ”communication complexity” is used to formally measure the degree to which a Boolean function is ”global”. An explicit combinatorial lower bound for this complexity measure is presented. In particular, this leads to an exp(Ω( √ n)) lower bound on the complexity of depth-restricted contact schemes computing some natural Boolean functions in NP.

We present general techniques for proving inapproximability results for several paradigmatic truthful multidimensional mechanism design problems. In particular, we demonstrate the strength of our techniques by exhibiting a lower bound of 2 − 1 m for the scheduling problem with m unrelated machines (formulated as a mechanism design problem in the seminal paper of Nisan and Ronen on Algorithmic M...

Given a graph, suppose that intruders hide on vertices or along edges of the graph. The fast searching problem is to find the minimum number of searchers required to capture all intruders satisfying the constraint that every edge is traversed exactly once and searchers are not allowed to jump. In this paper, we prove lower bounds on the fast search number. We present a linear time algorithm to ...

In this paper we give lower bounds for the representation of real univariate polynomials as sums of powers of degree 1 polynomials. We present two families of polynomials of degree d such that the number of powers that are required in such a representation must be at least of order d. This is clearly optimal up to a constant factor. Previous lower bounds for this problem were only of order Ω( √...

Both questions ask about some form of optimality. The first one is about optimality of an estimator, whereas the second one is about optimality of a bound. The difficulty of these questions varies depending on whether we are looking for a positive or a negative answer. Indeed, a positive answer to these questions simply consists in finding a better proof for the estimator we have studied (quest...

Correction networks are comparator networks that sort inputs differing from sorted sequences of length N in a small number of positions. The main application of such networks is producing fault-tolerant sorting networks. We show the lower bound 1.44log2 N on the depth of correction networks settling an open problem from [7]. This bound is tight since the upper bound 1.44log2 N is known.