Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Precision Tests of the Standard Model

30 páginas, 11 figuras, 11 tablas.-- Comunicación presentada al 25º Winter Meeting on Fundamental Physics celebrado del 3 al 8 de MArzo de 1997 en Formigal (España).Precision measurements of electroweak observables provide stringent tests of the Standard Model structure and an accurate determination of its parameters. An overview of the present experimental status is presented.This work has been supported in part by CICYT (Spain) under grant No. AEN-96-1718.Peer reviewe

Strategic Learning for Active, Adaptive, and Autonomous Cyber Defense

The increasing instances of advanced attacks call for a new defense paradigm that is active, autonomous, and adaptive, named as the \texttt{`3A'} defense paradigm. This chapter introduces three defense schemes that actively interact with attackers to increase the attack cost and gather threat information, i.e., defensive deception for detection and counter-deception, feedback-driven Moving Target Defense (MTD), and adaptive honeypot engagement. Due to the cyber deception, external noise, and the absent knowledge of the other players' behaviors and goals, these schemes possess three progressive levels of information restrictions, i.e., from the parameter uncertainty, the payoff uncertainty, to the environmental uncertainty. To estimate the unknown and reduce uncertainty, we adopt three different strategic learning schemes that fit the associated information restrictions. All three learning schemes share the same feedback structure of sensation, estimation, and actions so that the most rewarding policies get reinforced and converge to the optimal ones in autonomous and adaptive fashions. This work aims to shed lights on proactive defense strategies, lay a solid foundation for strategic learning under incomplete information, and quantify the tradeoff between the security and costs.Comment: arXiv admin note: text overlap with arXiv:1906.1218

The Existence and Uniqueness of Nash Equilibrium Point in an m-player Game “Shoot Later, Shoot First!”

Duel of m players, Nash equilibrium,

Ambush frequency should increase over time during optimal predator search for prey

We advance and apply the mathematical theory of search games to model the problem faced by a predator searching for prey. Two search modes are available: ambush and cruising search. Some species can adopt either mode, with their choice at a given time traditionally explained in terms of varying habitat and physiological conditions. We present an additional explanation of the observed predator alternation between these search modes, which is based on the dynamical nature of the search game they are playing: the possibility of ambush decreases the propensity of the prey to frequently change locations and thereby renders it more susceptible to the systematic cruising search portion of the strategy. This heuristic explanation is supported by showing that in a new idealized search game where the predator is allowed to ambush or search at any time, and the prey can change locations at intermittent times, optimal predator play requires an alternation (or mixture) over time of ambush and cruise search. Thus, our game is an extension of the well-studied 'Princess and Monster'search game. Search games are zero sum games, where the pay-off is the capture time and neither the Searcher nor the Hider knows the location of the other. We are able to determine the optimal mixture of the search modes when the predator uses a mixture which is constant over time, and also to determine how the mode mixture changes over time when dynamic strategies are allowed (the ambush probability increases over time). In particular, we establish the 'square root law of search predation': the optimal proportion of active search equals the square root of the fraction of the region that has not yet been explored. © 2011 The Royal Society