A polytope P ⊂ R is centrally symmetric (cs, for short) if P = −P . A cs polytope P is k-neighborly if every set of k of its vertices, no two of which are antipodes, is the vertex set of a face of P . In their recent paper [7], Linial and Novik give probabilistic constructions for highly neighborly cs polytopes. Namely, based on probabilistic techniques due to Garnaev and Gluskin [4], they cons...

Metrical task systems (MTS), introduced by Borodin, Linial, and Saks [5], is a cost minimization problem defined on a metric space (X, dX) and informally described as follows: A given system has a set of internal states X . The aim of the system is to perform a given sequence of tasks. The performance of each task has a certain cost that depends on the task and the state of the system. The syst...

Most of our applications of harmonic analysis to computer science will involve only Parseval’s identity. Theorem 4.1 (Parseval’s Identity). ‖f‖2 = ‖f̂‖2 Corollary 4.2. 〈f, g〉 = 〈f̂ , ĝ〉. Proof. Note that 〈f + g, f + g〉 = ‖f + g‖2 = ‖f̂ + g‖2 = ‖f̂ + ĝ‖2. Now as 〈f + g, f + g〉 = ‖f‖2 + ‖g‖2 + 2〈f, g〉, and similarly ‖f̂ + ĝ‖2 = ‖f̂‖2 + ‖ĝ‖2 + 2〈f̂ , ĝ〉, applying Parseval to ‖f‖2 and ‖g‖2 and equating fi...

Gli scritti di Leonardo Sciascia (1921-1989) ci accompagnano ancora oggi alla scoperta della storia e dell’arte Racalmuto, suo paese natale, ripercorrendone i luoghi più emblematici le significative opere d’arte, come numerose tele dipinte dal pittore Pietro D’Asaro, Il “Monocolo Racalmuto. Nel romanzo La Sicilia metafora (1979) lo scrittore dichiarava apertamente questo profondo legame annotan...

An Information Theoretic Approach to the Supervised Partitioning of the Hierarchical Protein Space Menachem Fromer*, Moriah Friedlich, Noam Kaplan, Nathan Linial and Michal Linial 1 School of Computer Science and Engineering, The Hebrew University of Jerusalem, Israel 2 Department of Biological Chemistry, Institute of Life Sciences, The Hebrew University of Jerusalem, Israel [email protected]...

In this paper we investigate the problem of searching monotone multi-dimensional arrays. We generalize Linial and Saks’ search algorithm [2] for monotone 3-dimensional arrays to d-dimensions with d ≥ 4. Our new search algorithm is asymptotically optimal for d = 4.