Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is suppressed. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions within the above subclass.

Design of surface forces apparatus for tribology studies combined with nonlinear optical spectroscopy

We describe the design, calibration, and performance of surface forces apparatus with the capability of illumination of the contact interface for spectroscopic investigation using optical techniques. The apparatus can be placed in the path of a Nd-YAG laser for studies of the linear response or the second harmonic and sum-frequency generation from a material confined between the two surfaces. In addition to the standard fringes of equal chromatic order technique, which we have digitized for accurate and fast analysis, the distance of separation can be measured with a fiber-optic interferometer during spectroscopic measurements (2 Å resolution and 10 ms response time). The sample approach is accomplished through application of a motor drive, piezoelectric actuator, or electromagnetic lever deflection for variable degrees of range, sensitivity, and response time. To demonstrate the operation of the instrument, the stepwise expulsion of discrete layers of octamethylcyclotetrasiloxane from the contact is shown. Lateral forces may also be studied by using piezoelectric bimorphs to induce and direct the motion of one surface.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ·β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Land use changes, landscape ecology and their socioeconomic driving forces in the Spanish Mediterranean coast (the Maresme County, 1850-2005)

[cat] Utilitzem un conjunt de mètriques del paisatge per estudiar l'evolució a llarg termini seguida en una típica zona costanera del Mediterrani des de 1850 fins a 2005, que mostren una greu deterioració del medi ambient entre 1950 i 2005. Les principals forces motores d'aquesta degradació del paisatge han estat el creixement urbà experimentat a les antigues zones agrícoles situades a les planes litorals, juntament amb l'abandonament i la reforestació dels vessants dels pujols interceptats per àrees residencials de baixa densitat, carreteres i altres infraestructures lineals. Duem a terme una anàlisi estadística de redundància (RDA) amb la finalitat d'identificar els que considerem com alguns agents rectors socioeconòmics i polítics d'última instància d'aquests impactes ambientals. Els resultats confirmen les nostres hipòtesis interpretatives, que són que: 1) els canvis en les cobertes i usos del sòl determinen canvis en les propietats dels paisatge, tant estructurals com funcionals; 2) aquests canvis no es produeixen per atzar, sinó que estan relacionats amb factors geogràfics i forces socioeconòmiques i polítiques.

Land use changes, landscape ecology and their socioeconomic driving forces in the Spanish Mediterranean coast (the Maresme County, 1850-2005)

[cat] Utilitzem un conjunt de mètriques del paisatge per estudiar l'evolució a llarg termini seguida en una típica zona costanera del Mediterrani des de 1850 fins a 2005, que mostren una greu deterioració del medi ambient entre 1950 i 2005. Les principals forces motores d'aquesta degradació del paisatge han estat el creixement urbà experimentat a les antigues zones agrícoles situades a les planes litorals, juntament amb l'abandonament i la reforestació dels vessants dels pujols interceptats per àrees residencials de baixa densitat, carreteres i altres infraestructures lineals. Duem a terme una anàlisi estadística de redundància (RDA) amb la finalitat d'identificar els que considerem com alguns agents rectors socioeconòmics i polítics d'última instància d'aquests impactes ambientals. Els resultats confirmen les nostres hipòtesis interpretatives, que són que: 1) els canvis en les cobertes i usos del sòl determinen canvis en les propietats dels paisatge, tant estructurals com funcionals; 2) aquests canvis no es produeixen per atzar, sinó que estan relacionats amb factors geogràfics i forces socioeconòmiques i polítiques.