An in-between "implicit" and "explicit" complexity: Automata

Implicit Computational Complexity makes two aspects implicit, by manipulating programming languages rather than models of com-putation, and by internalizing the bounds rather than using external measure. We survey how automata theory contributed to complexity with a machine-dependant with implicit bounds model

Generalized Simulated Annealing

We propose a new stochastic algorithm (generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm recovers, as particular cases, the so called classical ("Boltzmann machine") and fast ("Cauchy machine") simulated annealings, and can be quicker than both. Key-words: simulated annealing; nonconvex optimization; gradient descent; generalized statistical mechanics.Comment: 13 pages, latex, 4 figures available upon request with the authors

Nonstandard entropy production in the standard map

We investigate the time evolution of the entropy for a paradigmatic conservative dynamical system, the standard map, for different values of its controlling parameter $a$. When the phase space is sufficiently ``chaotic'' (i.e., for large $|a|$), we reproduce previous results. For small values of $|a|$, when the phase space becomes an intricate structure with the coexistence of chaotic and regular regions, an anomalous regime emerges. We characterize this anomalous regime with the generalized nonextensive entropy, and we observe that for values of $a$ approaching zero, it lasts for an increasingly large time. This scenario displays a striking analogy with recent observations made in isolated classical long-range $N$-body Hamiltonians, where, for a large class of initial conditions, a metastable state (whose duration diverges with $1/N\to 0$) is observed before it crosses over to the usual, Boltzmann-Gibbs regime.Comment: Latex, 6 figure

Bundle-based pruning in the max-plus curse of dimensionality free method

Recently a new class of techniques termed the max-plus curse of dimensionality-free methods have been developed to solve nonlinear optimal control problems. In these methods the discretization in state space is avoided by using a max-plus basis expansion of the value function. This requires storing only the coefficients of the basis functions used for representation. However, the number of basis functions grows exponentially with respect to the number of time steps of propagation to the time horizon of the control problem. This so called "curse of complexity" can be managed by applying a pruning procedure which selects the subset of basis functions that contribute most to the approximation of the value function. The pruning procedures described thus far in the literature rely on the solution of a sequence of high dimensional optimization problems which can become computationally expensive. In this paper we show that if the max-plus basis functions are linear and the region of interest in state space is convex, the pruning problem can be efficiently solved by the bundle method. This approach combining the bundle method and semidefinite formulations is applied to the quantum gate synthesis problem, in which the state space is the special unitary group (which is non-convex). This is based on the observation that the convexification of the unitary group leads to an exact relaxation. The results are studied and validated via examples

Negatively Correlated Search

Evolutionary Algorithms (EAs) have been shown to be powerful tools for complex optimization problems, which are ubiquitous in both communication and big data analytics. This paper presents a new EA, namely Negatively Correlated Search (NCS), which maintains multiple individual search processes in parallel and models the search behaviors of individual search processes as probability distributions. NCS explicitly promotes negatively correlated search behaviors by encouraging differences among the probability distributions (search behaviors). By this means, individual search processes share information and cooperate with each other to search diverse regions of a search space, which makes NCS a promising method for non-convex optimization. The cooperation scheme of NCS could also be regarded as a novel diversity preservation scheme that, different from other existing schemes, directly promotes diversity at the level of search behaviors rather than merely trying to maintain diversity among candidate solutions. Empirical studies showed that NCS is competitive to well-established search methods in the sense that NCS achieved the best overall performance on 20 multimodal (non-convex) continuous optimization problems. The advantages of NCS over state-of-the-art approaches are also demonstrated with a case study on the synthesis of unequally spaced linear antenna arrays

Can local single-pass methods solve any stationary Hamilton-Jacobi-Bellman equation?

The use of local single-pass methods (like, e.g., the Fast Marching method) has become popular in the solution of some Hamilton-Jacobi equations. The prototype of these equations is the eikonal equation, for which the methods can be applied saving CPU time and possibly memory allocation. Then, some natural questions arise: can local single-pass methods solve any Hamilton-Jacobi equation? If not, where the limit should be set? This paper tries to answer these questions. In order to give a complete picture, we present an overview of some fast methods available in literature and we briefly analyze their main features. We also introduce some numerical tools and provide several numerical tests which are intended to exhibit the limitations of the methods. We show that the construction of a local single-pass method for general Hamilton-Jacobi equations is very hard, if not impossible. Nevertheless, some special classes of problems can be actually solved, making local single-pass methods very useful from the practical point of view.Comment: 19 page

For whom the gate tolls? How and why to free the refereed research literature online through author/ institution self-archiving, now

"All refereed journals will soon be available online; most of them already are. This means that anyone will be able to access them from any networked desk-top. The literature will all be interconnected by citation, author, and keyword/ subject links, allowing for unheard-of power and ease of access and navigability. Successive drafts of pre-refereeing preprints will be linked to the official refereed draft, as well as to any subsequent corrections, revisions, updates, comments, responses, and underlying empirical databases, all enhancing the self-correctiveness, interactivity and productivity of scholarly and scientific research and communication in remarkable new ways. New scientometric indicators of digital impact are also emerging (http://opcit.eprints.org) to chart the online course of knowledge. But there is still one last frontier to cross before science reaches the optimal and the inevitable: Just as there is no longer any need for research or researchers to be constrained by the access-blocking restrictions of paper distribution, there is no longer any need to be constrained by the impact-blocking financial fire-walls of Subscription/Site-License/Pay-Per-View (S/L/P) tolls for this give-away literature. Its authors/researchers have always donated their research reports for free (and its referees/ researchers have refereed for free), with the sole goal of maximizing their impact on subsequent research (by accessing the eyes and minds of fellow-researchers, present and future) and hence on society. Generic (OAi-compliant) software is now available free so that institutions can immediately create Eprint Archives in which their authors can self-archive all their refereed (published) papers for free for all forever (http://www.eprints.org/). These interoperable Open Archives (http://www.openarchives.org) will then be harvested into global, jointly searchable 'virtual archives' (e.g., http://arc.cs.odu.edu/). 'Scholarly Skywriting' in this Post Gutenberg Galaxy will be dramatically (and measurably) more interactive and productive, spawning its own new digital metrics of productivity and impact, allowing for an online 'embryology of knowledge'." (author's abstract)"Alle referierten Fachzeitschriften (refereed journals) werden bald online verfügbar sein; die meisten sind es schon. Das bedeutet, dass jeder von jedem vernetzten Arbeitsplatz in der Lage sein wird, Zugang zu diesen Zeitschriften zu haben. Die Literatur wird durch Zitierung, Autor und Schlagwort-/ Gegenstand-Links vollständig untereinander verbunden sein, wobei einmalige Leistung und Nutzungsfreundlichkeit in Zugang und Navigation gewährleistet werden. Fortlaufende Entwürfe von vorreferierten Vordrucken werden mit den offiziell begutachteten Entwürfen verlinkt, genauso wie mit allen anschließenden Korrekturen, Revisionen, Aktualisierungen, Kommentaren, Antworten und zu Grunde liegenden empirischen Datenbanken. All das verbessert die Fehlerbehebung, Interaktivität und Produktivität von wissenschaftlicher Forschung und Kommunikation auf bemerkenswerten, neuen Wegen. Neue wissenschaftsmetrische Indikatoren digitaler Auswirkungen kommen gerade auf (http://opcit.eprints.org), um den Online-Verlauf des Fachwissens auszuwerten. Jedoch gibt es eine letzte Barriere zu überwinden, bevor Wissenschaft das Optimum und das Notwendige erreicht: Gerade weil Forschung und Forscher nicht mehr an den Zugang blockierende Beschränkungen der Papierverteilung gebunden sind, gibt es auch keinen Bedarf mehr, abhängig von den wirkungsgehemmten finanziellen Fire-Walls von Gebühren für Subscription/Site-License/Pay-Per-View (S/L/P) für give-away Literatur zu sein. Deren Autoren/Forscher haben ihre Forschungsberichte immer umsonst gestiftet (und deren Gutachter/Forscher haben umsonst beurteilt) mit dem alleinigen Ziel, die Auswirkungen auf ihre nachfolgende Forschung (indem sie auf die Sicht und Meinung von Forschungskollegen aus Gegenwart und Vergangenheit zurückgriffen) und somit auch auf die Gesellschaft zu maximieren. Generische (OAi-konforme) Software ist nun frei zugänglich, so dass Institutionen sofort Eprint-Archive erstellen können, in denen ihre Autoren die Möglichkeit haben, alle ihre begutachteten (veröffentlichten) Dokumente kostenfrei für immer selbst zu archivieren (http://www.eprints.org/). Diese vollständig kompatiblen Offenen Archive (http://www.openarchives.org) werden dann in globalen, untereinander durchsuchbaren 'virtuellen Archiven' gesammelt (http://arc.cs.odu.edu/). 'Wissenschaftliche Himmelsschrift' (Scholarly Skywriting) in dieser PostGutenberg Galaxie wird grundlegend (und messbar) interaktiver und produktiver, indem sie ihre eigenen, neuen digitalen Maße der Produktivität und Auswirkung erzeugt, wobei eine online 'Embryologie des Fachwissens' berücksichtigt wird." (Autorenreferat